Recent zbMATH articles in MSC 70https://zbmath.org/atom/cc/702024-05-13T19:39:47.825584ZWerkzeugPeriodic and breather solutions for miscellaneous soliton in metamaterials model by computational schemeshttps://zbmath.org/1532.351122024-05-13T19:39:47.825584Z"Mohyaldeen, Sherin Youns"https://zbmath.org/authors/?q=ai:mohyaldeen.sherin-youns"Manafian, Jalil"https://zbmath.org/authors/?q=ai:manafian-heris.jalil"Ilhan, Onur Alp"https://zbmath.org/authors/?q=ai:ilhan.onur-alp"Abotaleb, Mostafa"https://zbmath.org/authors/?q=ai:abotaleb.mostafa"Hajar, Afandiyeva"https://zbmath.org/authors/?q=ai:hajar.afandiyevaSummary: In this paper, the novel exact solitary wave solutions for the generalized nonlinear Schrödinger equation with parabolic nonlinear (NL) law employing the improved \(\cosh(\Gamma(\varpi)) - \operatorname{sech}(\Gamma(\varpi))\) function scheme and the combined \(\cos(\Gamma(\varpi)) - \sec(\Gamma(\varpi))\) function scheme are found. Diverse collections of hyperbolic and trigonometric function solutions acquired rely on a map between the considered equation and an auxiliary ODE. Received solutions are recast in several hyperbolic, rational and trigonometric forms based on different restrictions between parameters involved in equations and integration constants that appear in the solution. A few significant ones among the reported solutions are pictured to perceive the physical utility and peculiarity of the considered model utilizing mathematical software. The main subject of this work is that one can visualize and update the knowledge to overcome the most common techniques and defeat to solve the ODEs and PDEs. We demonstrated that these solutions validated the program using Maple and found them correct. The proposed methodology for solving the metamaterials model has been designed to be effectual, unpretentious, expedient and manageable. Applications of the solutions by the mentioned techniques will be useful to investigate the signals properties of optical fibers, plasma physics phenomena, electromagnetic fields occurrences and various types of nonlinear metamaterials models.Dissipative solutions to Hamiltonian systemshttps://zbmath.org/1532.352882024-05-13T19:39:47.825584Z"Bianchini, Stefano"https://zbmath.org/authors/?q=ai:bianchini.stefano"Leccese, Giacomo Maria"https://zbmath.org/authors/?q=ai:leccese.giacomo-mariaSummary: We extend the notion of dissipative particle solutions [the first author and \textit{S. Daneri}, J. Differ. Equations 368, 173--202 (2023; Zbl 07700855)] to the case of Hamiltonian flow in the space of probability measures \(\mu \in \mathscr{P}(\mathbb{R}^d \times \mathbb{R}^d)\) in the sense of [\textit{L. Ambrosio} and \textit{W. Gangbo}, Commun. Pure Appl. Math. 61, No. 1, 18--53 (2008; Zbl 1132.37028)]. The Hamiltonian is of the form
\[
H(\mu) = \int V(q,p) \mu (dqdp) + \frac{1}{2} \int \int W(q,p,q',p') \mu (dqdp)\mu (dq'dp'),
\]
with at most quadratic growth, so that a conservative flow
\[
\dot{q} = \nabla_p V+\int \nabla_p W \mu, \quad \dot{p} = -\nabla_q V -\int\nabla_q W \mu
\]
is uniquely defined.
The dissipative solution is defined by requiring that the equation of \(p\) is replaced by
\[
p(t) = \mathbb{P}_t \bigg( p(0) + \int_0^t \bigg[ -\nabla_q V-\int \nabla_q W \mu\bigg] ds \bigg).
\]
where \(\mathbb{P}_t\) is the projection on the space of functions corresponding to the restriction map
\[
\mathbb{T}_t \gamma = \gamma 1\!\!\mathbf{I}_{s>t}.
\]
Equivalently the particles merge preserving the average momentum \(p\). We obtain several results on the structure of dissipative solutions; among them, regularity, dissipation of energy, approximations with finite particles solutions, density of conservative solutions. The proofs require additional technical difficulties, not present in the analysis of [the first author and Daneri, loc. cit.] where \(H(q,p)=p^2 /2\).Comparative analysis of obstacle approximation strategies for the steady incompressible Navier-Stokes equationshttps://zbmath.org/1532.353472024-05-13T19:39:47.825584Z"Krzyżanowski, Piotr"https://zbmath.org/authors/?q=ai:krzyzanowski.piotr"Malikova, Sadokat"https://zbmath.org/authors/?q=ai:malikova.sadokat"Mucha, Piotr Bogusław"https://zbmath.org/authors/?q=ai:mucha.piotr-boguslaw"Piasecki, Tomasz"https://zbmath.org/authors/?q=ai:piasecki.tomaszSummary: This paper aims to compare and evaluate various obstacle approximation techniques employed in the context of the steady incompressible Navier-Stokes equations. Specifically, we investigate the effectiveness of a standard volume penalization approximation and an approximation method utilizing high viscosity inside the obstacle region, as well as their composition. Analytical results concerning the convergence rate of these approaches are provided, and extensive numerical experiments are conducted to validate their performance.Stationary coupled KdV hierarchies and related Poisson structureshttps://zbmath.org/1532.354072024-05-13T19:39:47.825584Z"Fordy, Allan P."https://zbmath.org/authors/?q=ai:fordy.allan-p"Huang, Qing"https://zbmath.org/authors/?q=ai:huang.qingSummary: In this paper we continue our analysis of the stationary flows of \(M\) component, coupled KdV (cKdV) hierarchies and their modifications. We describe the general structure of the \(t_1\) and \(t_2\) flows, using the case \(M = 3\) as our main example. One of our stationary reductions gives \(N\) degrees of freedom, superintegrable systems. When \(N = 1\) (for \(t_1)\) and \(N = 2\) (for \(t_2)\), we have Poisson maps, which give multi-Hamiltonian representations of the flows. We discuss the general structure of these Poisson tensors and give explicit forms for the case \(M = 3\). In this case there are 3 modified hierarchies, each with 4 Poisson brackets.
The stationary \(t_2\) flow (for \(N = 2)\) is separable in parabolic coordinates. Each Poisson bracket has rank 4, with \(M + 1\) Casimirs. The \(4 \times 4\) ``core'' of the Poisson tensors are nonsingular and related by a ``recursion operator''. The remaining part of each tensor is built out of the two commuting Hamiltonian vector fields, depending upon the specific Casimirs. The Poisson brackets are generalised to include the entire class of potential, separable in parabolic coordinates. The Jacobi identity imposes specific dependence on some parameters, representing the Casimirs of the extended canonical bracket. This general case is no longer a stationary cKdV flow, with Lax representation. We give a recursive procedure for constructing the Lax representation of the stationary flow for all values of \(M\), \textit{without} having to go through the stationary reduction.Generalized Darboux transformation for nonlinear Schrödinger system on general Hermitian symmetric spaces and rogue wave solutionshttps://zbmath.org/1532.354142024-05-13T19:39:47.825584Z"Asadi, Esmaeel"https://zbmath.org/authors/?q=ai:asadi.esmaeel"Riaz, H. W. A."https://zbmath.org/authors/?q=ai:riaz.h-wajahat-ahmed.2"Ganjkhanloo, Mohammad Ali"https://zbmath.org/authors/?q=ai:ganjkhanloo.mohammad-aliSummary: In this paper, a generalized Darboux transformation is obtained for Fordy-Kulish NLS (nonlinear Schrödinger) systems on general Hermitian symmetric spaces in order to rigorously obtain rogue wave solutions for these systems. In particular, we express the generalized algebraic relations in a simple and elegant compact form. As an illustration, we derive multi-soliton, breather-type and mainly rogue wave solutions of triangular patterns for single- and multi-component NLS systems on \(CP^1\) and \(SP(2)/U(2),\) respectively. We also analyze the modulation instability of proper plane wave solutions. In order to get visual intuition for the dynamics of the result and solutions for the running examples, the associated simulations of profiles are furnished as well.The existence of multiple topologically distinct solutions to \(\sigma_{2, p}\)-energyhttps://zbmath.org/1532.354452024-05-13T19:39:47.825584Z"Taghavi, Mojgan"https://zbmath.org/authors/?q=ai:taghavi.mojgan"Shahrokhi-Dehkordi, Mohammad S."https://zbmath.org/authors/?q=ai:shahrokhi-dehkordi.m-sSummary: Let \(\mathbb{X} \subset \mathbb{R}^n\) be a bounded Lipschitz domain and consider the \(\sigma_{2, p}\)-energy functional
\[
\mathbb{F}_{\sigma_{2, p}} [u; \mathbb{X}] := \int_{\mathbb{X}} \big|{\wedge}^2 \nabla u\big|^p dx,
\]
with \(p \in \, ]1, \infty]\) over the space of measure preserving maps
\[
\mathcal{A}_p (\mathbb{X}) = \big\{u \in W^{1, 2p}\big(\mathbb{X}, \mathbb{R}^n\big) : u|_{\partial \mathbb{X}} = {x}, \; \det \nabla u =1 \text{ for } \mathcal{L}^n \text{-a.e. in } \mathbb{X}\big\}.
\]
In this article we address the question of multiplicity \textit{versus} uniqueness for \textit{extremals} and \textit{strong} local minimizers of the \(\sigma_{2, p}\)-energy funcional \(\mathbb{F}_{\sigma_{2, p}} [\cdot; \mathbb{X}]\) in \(\mathcal{A}_p (\mathbb{X})\). We use a topological class of maps referred to as \textit{generalised} twists and examine them in connection with the Euler-Lagrange equations associated with \(\sigma_{2, p}\)-energy functional over \(\mathcal{A}_p (\mathbb{X})\). Most notably, we prove the existence of a countably infinite of topologically distinct twisting solutions to the later system in all \textit{even} dimensions by linking the system to a set of nonlinear isotropic ODEs on the Lie group \(\mathrm{SO}(n)\). In sharp contrast in \textit{odd} dimensions the only solution is the map \(u \equiv x\). The result relies on a careful analysis of the \textit{full} versus the \textit{restricted} Euler-Lagrange equations. Indeed, an analysis of curl-free vector fields generated by symmetric matrix fields plays a pivotal role.Propagation of chaos for topological interactions by a coupling techniquehttps://zbmath.org/1532.354562024-05-13T19:39:47.825584Z"Degond, Pierre"https://zbmath.org/authors/?q=ai:degond.pierre"Pulvirenti, Mario"https://zbmath.org/authors/?q=ai:pulvirenti.mario"Rossi, Stefano"https://zbmath.org/authors/?q=ai:rossi.stefanoSummary: We consider a system of particles that interact through a jump process. The jump intensities are functions of the proximity rank of the particles, a type of interaction referred to as topological in the literature. Such interactions have been shown relevant for the modelling of bird flocks. We show that, in the large number of particles limit and under minimal smoothness assumptions on the data, the model converges to a kinetic equation which was derived in earlier works both formally and rigorously under more stringent regularity assumptions. The proof relies on the coupling method which assigns to the particle and limiting processes a joint process posed on the cartesian product of the two configuration spaces of the former processes. By appropriate estimates in a suitable Wasserstein metric, we show that the distance between the two processes tends to zero as the number of particles tends to infinity, with an error typical of the law of large numbers.The time-fractional generalized Z-K equation: analysis of Lie group, similarity reduction, conservation laws, and explicit solutionshttps://zbmath.org/1532.354742024-05-13T19:39:47.825584Z"AL-Denari, Rasha B."https://zbmath.org/authors/?q=ai:al-denari.rasha-b"Ahmed, Engy. A."https://zbmath.org/authors/?q=ai:ahmed.engy-a"Tharwat, Mohammed M."https://zbmath.org/authors/?q=ai:tharwat.mohammed-m(no abstract)Symplectic and inverse spectral geometry of integrable systems: a glimpse and open problemshttps://zbmath.org/1532.370022024-05-13T19:39:47.825584Z"Pelayo, Álvaro"https://zbmath.org/authors/?q=ai:pelayo.alvaroSummary: We first give a glimpse of finite dimensional classical integrable Hamiltonian systems from the point of view of symplectic geometry and briefly discuss their quantum counterparts, with an emphasis on recent progress on inverse spectral geometry. Then we propose several open problems about the geometry, topology and dynamics of these systems. The problems are largely motivated by the works of a number of authors, including Arnold, Atiyah, Colin de Verdière, Delzant, Duistermaat, Eliasson, Fomenko, Guillemin, Kolmogorov, Kostant, Moser and Sternberg.On Dirac structures admitting a variational approachhttps://zbmath.org/1532.370512024-05-13T19:39:47.825584Z"Cosserat, Oscar"https://zbmath.org/authors/?q=ai:cosserat.oscar"Kotov, Alexei"https://zbmath.org/authors/?q=ai:kotov.alexei"Laurent-Gengoux, Camille"https://zbmath.org/authors/?q=ai:laurent-gengoux.camille"Ryvkin, Leonid"https://zbmath.org/authors/?q=ai:ryvkin.leonid"Salnikov, Vladimir"https://zbmath.org/authors/?q=ai:salnikov.vladimirSummary: We discuss the notion of horizontal cohomology for Dirac structures and, more generally, Lie algebroids. We then use this notion {to describe the condition allowing} a variational formulation of Dirac dynamics.Linearity of minimally superintegrable systems in a static electromagnetic fieldhttps://zbmath.org/1532.370532024-05-13T19:39:47.825584Z"Bertrand, S."https://zbmath.org/authors/?q=ai:bertrand.sylvain|bertrand.sebastien"Nucci, M. C."https://zbmath.org/authors/?q=ai:nucci.maria-claraThe manuscript deals with superintegrable systems in a static electromagnetic field. The focus is exploring hidden symmetries leading to linearizable equations. Fifteen nonlinear minimally superintegrable systems are analyzed and linearized by means of their hidden symmetries.
The paper contains an extensive analysis, including a plethora of cases and subcases studied in detail. The results align with the conjecture that all three-dimensional minimally superintegrable systems are linearizable, employing hidden symmetries.
Reviewer: J. M. Hoff da Silva (Guaratinguetá)Koenigs theorem and superintegrable Liouville metricshttps://zbmath.org/1532.370542024-05-13T19:39:47.825584Z"Valent, Galliano"https://zbmath.org/authors/?q=ai:valent.gallianoThe author gives a complete classification of all two-dimensional strictly Riemannian metrics of Liouville type whose geodesic Hamiltonian admits three functionally independent first integrals all quadratic in the momenta, i.e., with geodesic flow quadratically superintegrable. The cases when one or two of the first integrals can be reduced to linear in the momenta ones are excluded. Liouville metrics are the two-dimensional metrics admitting complete integrals of the geodesic Hamilton-Jacobi equation additively separable in some coordinate system, hence admitting at least one first integral which is quadratic in the momentum and independent from the Hamiltonian: the Liouville first integral. First, the subcase of Koenigs metrics, the ones corresponding to surfaces of revolution, is considered and the Koenigs classification of quadratically superintegrable metrics is obtained by a direct proof. Then, the more general case of Liouville metrics is considered. All the possible solutions are obtained by searching for the most general quadratic first integral commuting with both the Hamiltonian and the Liouville quadratic first integral. The integration is performed by taking into account the fact that two of the components of the third first integral must be harmonically conjugate. Eight normal forms of the metric are determined, and the three-dimensional algebra of first integrals of each form is explicitly described. Coupling-constant metamorphosis, a transformation between Hamiltonian systems preserving integrability and superintegrability, is employed to recover some cases of quadratically superintegrable systems known in the literature.
Reviewer: Giovanni Rastelli (Vercelli)Response solutions of a class of degenerate quasi-periodic systems with a small parameterhttps://zbmath.org/1532.370562024-05-13T19:39:47.825584Z"Yang, Xiaomei"https://zbmath.org/authors/?q=ai:yang.xiaomei"Xu, Junxiang"https://zbmath.org/authors/?q=ai:xu.junxiangSummary: This paper considers a special class of quasi-periodic systems with a small parameter, whose unperturbed part has a degenerate equilibrium point. We prove the existence of response solutions for many sufficiently small parameters. The proof is based on some formal KAM techniques and the Leray-Schauder Continuation Theorem.Practical perspectives on symplectic accelerated optimizationhttps://zbmath.org/1532.370682024-05-13T19:39:47.825584Z"Duruisseaux, Valentin"https://zbmath.org/authors/?q=ai:duruisseaux.valentin"Leok, Melvin"https://zbmath.org/authors/?q=ai:leok.melvinSummary: Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Bregman Lagrangian and Hamiltonian systems from the variational framework introduced by \textit{A. Wibisono} et al. [Proc. Natl. Acad. Sci. USA 113, No. 47, E7351--E7358 (2016; Zbl 1404.90098)]. In this paper, we discuss practical considerations which can significantly boost the computational performance of these optimization algorithms and considerably simplify the tuning process. In particular, we investigate how momentum restarting schemes ameliorate computational efficiency and robustness by reducing the undesirable effect of oscillations and ease the tuning process by making time-adaptivity superfluous. We also discuss how temporal looping helps avoiding instability issues caused by numerical precision, without harming the computational efficiency of the algorithms. Finally, we compare the efficiency and robustness of different geometric integration techniques and study the effects of the different parameters in the algorithms to inform and simplify tuning in practice. From this paper emerge symplectic accelerated optimization algorithms whose computational efficiency, stability and robustness have been improved, and which are now much simpler to use and tune for practical applications.On the weighted inertia-energy approach to forced wave equationshttps://zbmath.org/1532.490202024-05-13T19:39:47.825584Z"Mainini, Edoardo"https://zbmath.org/authors/?q=ai:mainini.edoardo"Percivale, Danilo"https://zbmath.org/authors/?q=ai:percivale.daniloIn this paper, the authors study the weighted inertia-energy approach to forced wave equations. More precisely, they show the convergence of minimizers of weighted inertia-energy functionals to solutions of initial value problems for a class of nonlinear wave equations.
Reviewer: Savin Treanţă (Bucureşti)Pseudospectral methods for nonlinear pendulum equationshttps://zbmath.org/1532.650412024-05-13T19:39:47.825584Z"Le Anh Nhat"https://zbmath.org/authors/?q=ai:le-anh-nhat.Summary: The article searched on mathematics and numerical solutions for the nonlinear pendulum (Chaotic pendulum). The numerical solution that was used for our research suitably the pseudospectral methods. With these equations, we studied and calculated on the interval \([-1, 1]\), with boundary conditions already known. We used the software Mathematica 10.4 to calculate the results of the problems.The elliptic integral machine: a collision-based model of computationhttps://zbmath.org/1532.680192024-05-13T19:39:47.825584Z"Melnik, Igor A. C."https://zbmath.org/authors/?q=ai:melnik.igor-a-cSummary: In this work we will show how any elliptic integral can be computed by analyzing the asymptotic behavior of idealized mechanical models. Specifically, our results reveal how a set of circular billiard systems computes the canonical set of three elliptic integrals defined by Legendre. We will treat these Newtonian systems as a particular application of the billiard-ball model, a ballistic computer idealized by Eduard Fredkin and Tommaso Toffoli. Initially, we showed how to define the initial conditions in order to encode the computation of a set of integral functions. We then combined our first conclusions with results established in the 18th and 19th centuries mostly by Euler, Lagrange, Legendre and Gauss in developing the theory of integral functions. In this way, we derived collision-based methods to compute elementary functions, integrals functions and mathematical constants. In particular, from the Legendre identity for elliptic integrals, we were able to define a new collision-based method to compute the number \(\pi \), while an identity demonstrated by Gauss revealed a new method to compute the arithmeticgeometric mean. In order to explore the computational potential of the model, we admitted a hypothetical device that measures the total number of collisions between the balls and the boundary. There is even the possibility that the methods we are about to describe could one day be experimentally applied using optical phenomena, as recent studies indicate that it is possible to implement collision-based computation with solitons.Toward finiteness of central configurations for the planar six-body problem by symbolic computations. I: Determine diagrams and ordershttps://zbmath.org/1532.700012024-05-13T19:39:47.825584Z"Chang, Ke-Ming"https://zbmath.org/authors/?q=ai:chang.ke-ming"Chen, Kuo-Chang"https://zbmath.org/authors/?q=ai:chen.kuo-chang|chen.kuochangSummary: In a series of papers we develop symbolic computation algorithms to investigate finiteness of central configurations for the planar \(n\)-body problem. Our approach is based on \textit{A. Albouy} and \textit{V. Kaloshin}'s work on finiteness of central configurations for the 5-body problems [Ann. Math. (2) 176, No. 1, 535--588 (2012; Zbl 1362.70014)]. In their paper, bicolored graphs called \textit{zw}-diagrams were introduced for possible scenarios when the finiteness conjecture fails, and proving finiteness amounts to exclusions of central configurations associated to these diagrams. Following their method, the amount of computations becomes enormous when there are more than five bodies. In this paper we introduce matrix algebra for determination of possible diagrams and asymptotic orders, devise several criteria to reduce computational complexity, and determine possible \textit{zw}-diagrams by automated deductions. For the planar six-body problem, we show that there are at most 86 \textit{zw}-diagrams.Analytical models of mesh stiffness for cracked spur gears considering gear body deflection and dynamic simulationhttps://zbmath.org/1532.700022024-05-13T19:39:47.825584Z"Jiang, Hanjun"https://zbmath.org/authors/?q=ai:jiang.hanjun"Liu, Fuhao"https://zbmath.org/authors/?q=ai:liu.fuhaoSummary: Accurate mesh stiffness models for cracked spur gears are critical to obtain gearbox failure characteristics. However, the influence of crack on gear body deflection is often ignored by most researchers. In this study, analytical models of mesh stiffness for cracked spur gears considering gear body deflection are proposed. Both the cracked tooth and the adjacent tooth are included to simulate the mesh stiffness with tooth crack. Effects of crack length and inclination angle on mesh stiffness are investigated by these analytical models. Dynamic simulation is conducted by a six-degrees-of-freedom dynamic model incorporating the developed analytical mesh stiffness models. Frequency spectrum analysis and statistical indicators are adopted in order to evaluate the effects of tooth crack. The simulated results reveal that tooth crack produces mesh stiffness reduction in a complete rotation period for both the cracked tooth and the adjacent tooth. The total mesh stiffness is not only affected by the cracked tooth but also by the adjacent tooth due to tooth crack. The proposed analytical models can provide relatively accurate mesh stiffness for cracked spur gears by considering gear body deflection. The dynamic response obtained in this simulation by the proposed model has more obvious impulsive feature than the one without considering the effect of crack on the adjacent tooth and gear body, which are more convenient for tooth crack fault diagnosis.On the squares and cubes in the set of finite fieldshttps://zbmath.org/1532.700032024-05-13T19:39:47.825584Z"Kovalëv, Mikhail Dmitrievich"https://zbmath.org/authors/?q=ai:kovalev.mikhail-dmitrievichSummary: The paper provides a definition of the hinge mechanism, taking into account its kinematic nature. This definition differs significantly from that adopted by a number of mathematicians in recent works. If we use the definition accepted today, which does not take into account the kinematic background, then the classical result of \textit{A. B. Kempe} [Proc. Lond. Math. Soc. 7, 213--216 (1876; JFM 08.0544.04)] about the possibility of drawing by parts of an arbitrary plane algebraic curve with hinges of suitably chosen plane hinge mechanisms cannot be considered sufficiently substantiated by Kempe himself. This has been noted in the modern literature [\textit{M. Kapovich} and \textit{J. J. Millson}, Topology 41, No. 6, 1051--1107 (2002; Zbl 1056.14077)], and even led to accusations of Kempe in error. The development and modern substantiation of Kempe's result proposed in the works [Zbl 1056.14077; \textit{H. C. King}, Turk. J. Math. 23, No. 1, 33--56 (1999; Zbl 0962.55009)] is, in essence, a modification of Kempe's method for constructing the required mechanism from brick mechanisms performing algebraic actions. However, it is based on the use of a complex language of modern algebraic geometry, which leads to the replacement of Kemp's short and transparent reasoning by an order of magnitude longer and difficult to understand texts. In our definition of the hinge mechanism, we can give a rigorous formulation of Kempe's theorem, for the proof of which Kempe's arguments with minimal refinements are sufficient. This updated proof is provided in the paper. The paper discusses the modern development of Kempé's result, and the claims against Kempé's reasoning. It also gives general ideas about mathematics that the author has in connection with the Kempé theorem and its modern development.A loop-by-loop defect rectification procedure for optimal synthesis of Stephenson III path generatorshttps://zbmath.org/1532.700042024-05-13T19:39:47.825584Z"Singh, Ramanpreet"https://zbmath.org/authors/?q=ai:singh.ramanpreet"Chaudhary, Himanshu"https://zbmath.org/authors/?q=ai:chaudhary.himanshu"Singh, Amit K."https://zbmath.org/authors/?q=ai:singh.amit-kSummary: This paper presents a formulation of constraints for the synthesis of Stephenson III mechanism and a loop-by-loop defect-rectification procedure. The procedure divides the Stephenson III mechanism into two loops, namely, Loop I, i.e., four-bar, and Loop II, i.e., five-bar mechanisms. Then, the defects are identified using the established methodology to formulate the defect-specific constraints in the simplified form. Based on the constraints, an optimization problem is formulated to synthesize a Stephenson III mechanism for path generation. A well-established meta-heuristic algorithm is used to solve the constrained optimization problem. For demonstrating the effectiveness of the formulated constraints, two numerical examples are considered, in which Stephenson III path generator mechanisms are synthesized. It is found that the mechanisms synthesized using the proposed procedure are defect-free when constraints are imposed, which is verified using the stick-diagram.Maximum overhang of sticky stackshttps://zbmath.org/1532.700052024-05-13T19:39:47.825584Z"Lengvárszky, Zsolt"https://zbmath.org/authors/?q=ai:lengvarszky.zsolt"Shepherd, Debbie"https://zbmath.org/authors/?q=ai:shepherd.debbieSummary: We consider a variation of the ``overhang'' problem where blocks stick together.Nonlinear dynamics of the primary oscillation circuit of a MEMS gyroscope under the action of phase-locked loop and automatic gain control systemshttps://zbmath.org/1532.700062024-05-13T19:39:47.825584Z"Igumnova, Vasilisa Sergeevna"https://zbmath.org/authors/?q=ai:igumnova.vasilisa-sergeevna"Lukin, Alekseĭ Vyacheslavovich"https://zbmath.org/authors/?q=ai:lukin.aleksei-vyacheslavovich"Popov, Ivan Alekseevich"https://zbmath.org/authors/?q=ai:popov.ivan-alekseevich"Kuznetsov, Nikolaĭ Vladimirovich"https://zbmath.org/authors/?q=ai:kuznetsov.nikolay-v"Lobachev, Mikhail Yur'evich"https://zbmath.org/authors/?q=ai:lobachev.mikhail-yurevich"Belyaev, Yakov Valer'evich"https://zbmath.org/authors/?q=ai:belyaev.yakov-valerevichSummary: In this work, we study the dynamics of primary oscillations of a high-Q micromechanical resonator -- a sensitive element of an RR-type MEMS gyroscope -- under the action of various implementations of a phase-locked loop system operating in conjunction with an automatic gain control system for an electrostatic drive. The study of the dynamics of the object is carried out both numerically and analytically -- using the averaging method. Conditions for the stability of a stationary regime in a linear approximation are obtained. The questions of accuracy of various methods of numerical solution of differential equations of the circuit of primary oscillations are considered. The influence of the mechanical nonlinearity of the resonator on the dynamics of the resonator and the control system has been studied. An implementation of a low-order PLL circuit that does not contain a double-frequency spurious signal at the output of the phase detector is proposed. The output characteristics of control systems (speed, capture bandwidth, etc.) are analyzed and qualitative conclusions are drawn about the features of the interaction between the dynamics of a mechanical oscillatory link and the PLL-ARC circuit.Linear invariant relations for the equations of motion of a gyrostat with a variable gyrostatic momenthttps://zbmath.org/1532.700072024-05-13T19:39:47.825584Z"Shchetinina, O. K."https://zbmath.org/authors/?q=ai:shchetinina.o-k"Denysenko, V. I."https://zbmath.org/authors/?q=ai:denysenko.v-i"Didenko, Yu. F."https://zbmath.org/authors/?q=ai:didenko.yu-f"Bilousova, S. V."https://zbmath.org/authors/?q=ai:bilousova.s-vSummary: We consider the problem of motion of a gyrostat under the action of potential and gyroscopic forces in the case where its gyrostatic moment is variable. We analyze the conditions of existence of linear invariant relations for equations of the Kirchhoff-Poisson class. A new solution of these equations is obtained in terms of the elementary functions of time.Euler-Poisson equations of a dancing spinning top, integrability and examples of analytical solutionshttps://zbmath.org/1532.700082024-05-13T19:39:47.825584Z"Deriglazov, Alexei A."https://zbmath.org/authors/?q=ai:deriglazov.aleksei-aleksandrovichSummary: Equations of a rotating body with one point constrained to move freely on a plane (dancing top) are deduced from the Lagrangian variational problem. They formally look like the Euler-Poisson equations of a heavy body with fixed point, immersed in a fictitious gravity field. Using this analogy, we have found examples of analytical solutions for the case of a heavy symmetrical dancing top. They describe the motions with center of mass keeping its height fixed above the supporting plane. General solution to equations of a dancing top in terms of exponential of Hamiltonian field is given. An extra constraint, that take into account the reaction of supporting plane, leads to modification of the canonical Poisson structure and therefore the integrability according to Liouville is under the question.Stability and long-time behaviour of a rigid body containing a damperhttps://zbmath.org/1532.700092024-05-13T19:39:47.825584Z"Arsenault, Evan"https://zbmath.org/authors/?q=ai:arsenault.evan"Mazzone, Giusy"https://zbmath.org/authors/?q=ai:mazzone.giusyThe article investigates the stability and long-term behavior of a coupled system comprising two rigid bodies separated by a thin layer of lubricant. It establishes stability conditions, indicating that permanent rotations of the entire system, with solids at relative rest, are exponentially stable only when the axis of rotation aligns with the principal axis of inertia of the outer body. All other equilibria are normally hyperbolic, signifying instability.
In terms of convergence to equilibrium, the article demonstrates that all solutions to the governing equations converge to an equilibrium configuration irrespective of the initial conditions.
Concerning numerical evidence and attainability conditions, the article presents numerical evidence supporting the stability results and discusses conditions ensuring the attainability of the stable configurations.
Regarding the methodology, the article utilizes a linearization principle for the stability analysis of dynamical systems with a center manifold. It characterizes the long-term behavior through a careful analysis of the partially dissipative system of equations governing the motion of the coupled system.
Reviewer: Ioannis Dassios (Dublin)The orbital stability analysis of pendulum oscillations of a heavy rigid body with a fixed point under the Goryachev-Chaplygin conditionhttps://zbmath.org/1532.700102024-05-13T19:39:47.825584Z"Bardin, B. S."https://zbmath.org/authors/?q=ai:bardin.boris-sabirovich"Maksimov, B. A."https://zbmath.org/authors/?q=ai:maksimov.b-aSummary: We consider the motion of a heavy rigid body with a fixed point in a uniform gravitational field under the assumption that the principal moments of inertia satisfy the Goryachev-Chaplygin condition at the fixed point. We study the orbital stability problem for small pendulum oscillations of the body. We derive the equations of perturbed motion and reduce the problem to the study of the stability of the equilibrium position of a second order \(2 \pi \)-periodic Hamiltonian system. We find regions of parametric resonance and perform the nonlinear analysis of orbital stability outside these regions.Nonlinear vibration phenomena in hydrodynamically supported rotor systemshttps://zbmath.org/1532.700112024-05-13T19:39:47.825584Z"Nitzschke, Steffen"https://zbmath.org/authors/?q=ai:nitzschke.steffen"Woschke, Elmar"https://zbmath.org/authors/?q=ai:woschke.elmar"Strackeljan, Cornelius"https://zbmath.org/authors/?q=ai:strackeljan.corneliusSummary: It is a well-known fact, that hydrodynamically supported systems are prone to nonlinear vibrations. Their exact simulative prediction with respect to frequency and amplitude is complicated by the fact that different system properties interact. The paper at hand outlines an approach that takes all relevant influences like rigid body motions, elastic deformations, nonlinear relation between fluid film pressure and bearing kinematics as well as temperature increase due to power loss or adjacent heat sources into account as detailed as necessary. Both journal and thrust bearings are considered as they contribute to the system's stiffness and damping capabilities. The approach is applied to self-excited pad vibrations of tilting pad thrust bearings as well as the run-up simulation of a turbocharger rotor under different axial loads. Both models are validated against measurements.
{\copyright} 2023 The Authors. \textit{GAMM - Mitteilungen} published by Wiley-VCH GmbH.Multi-surface sliding mode control of continuum robots with mismatched uncertaintieshttps://zbmath.org/1532.700122024-05-13T19:39:47.825584Z"Alqumsan, Ahmad Abu"https://zbmath.org/authors/?q=ai:alqumsan.ahmad-abu"Khoo, Suiyang"https://zbmath.org/authors/?q=ai:khoo.suiyang"Norton, Michael"https://zbmath.org/authors/?q=ai:norton.michael-i|norton.michael-mSummary: In this paper, we tackle the control problem of continuum robots with mismatched uncertainties. Uncertainties that affect systems through any of their states and may not be directly accessed by their controllers. These uncertainties emerge in a system either due to unmodeled dynamics, practical limitations, or external disturbances. Continuum robots possess highly nonlinear dynamic behaviour due to their elastic nature and operate within undefined or congested environments, exposing them to such uncertainties. However, mismatched uncertainties in the continuum robots' field, are yet to be addressed. Here, we tackle this problem and propose the first robust control for continuum robots that assures its robustness property under mismatched uncertainties. To this end, we first derive the dynamic model for our continuum robot by considering it as an elastic rod and then applying Cosserat rod theory. This will result in a general dynamic model that does not require any design or operative assumption. Next, we design our robust controller utilizing multi-surface sliding mode control, a method capable of handling nonlinear systems under mismatched uncertainties. Finally, we include simulations to validate our controller's performance.Robotic grasp analysis using deformable solid mechanicshttps://zbmath.org/1532.700132024-05-13T19:39:47.825584Z"Dharbaneshwer, S. J."https://zbmath.org/authors/?q=ai:dharbaneshwer.s-j"Subramanian, Sankara J."https://zbmath.org/authors/?q=ai:subramanian.sankara-j"Kohlhoff, Kai"https://zbmath.org/authors/?q=ai:kohlhoff.kaiSummary: Given an object and a hand, identifying a robust grasp out of an infinite set of grasp candidates is a challenging problem, and several grasp synthesis approaches have been proposed in the robotics community to find the promising ones. Most of the approaches assume both the object and the hand to be rigid and evaluate the robustness of the grasp based on the wrenches acting at contact points. Since rigid body mechanics is used in these works, the actual distribution of the contact tractions is not considered, and contacts are represented by their resultant wrenches. However, the tractions acting at the contact interfaces play a critical role in the robustness of the grasp, and not accounting for these in detail is a serious limitation of the current approaches. In this paper, we replace the conventional wrench-based rigid-body approaches with a deformable-body mechanics formulation as is conventional in solid mechanics. We briefly review the wrench-based grasp synthesis approaches in the literature and address the drawbacks present in them from a solid mechanics standpoint. In our formulation, we account for deformation in both the grasper and the object and evaluate the robustness of grasp based on the distribution of normal and tangential tractions at the contact interface. We contrast how a given grasp situation is solved using conventional wrench space formulations and deformable solid mechanics and show how tractions on the contacting surfaces influence the grasp equilibrium. Recognizing that contact areas can be correlated to contact tractions, we propose a grasp performance index, \(\pi\), based on the contact areas. We also devise a grasp analysis strategy to identify robust grasps under random perturbations and implement it using Finite Element Method (FEM) to study a few grasps. One of the key aspects of our Finite Element (FE)-based approach is that it can be used to monitor the dynamic interaction between object and hand for judging grasp robustness. We then compare our measure, \(\pi \), with conventional grasp quality measures, \( \epsilon\) and \(v\) and show that it successfully accounts for the effect of the physical characteristics of the object and hand (such as the mass, Young's modulus and coefficient of friction) and identifies robust grasps that are in line with human intuition and experience.Robust multi-objective optimization of parallel manipulatorshttps://zbmath.org/1532.700142024-05-13T19:39:47.825584Z"Lara-Molina, Fabian A."https://zbmath.org/authors/?q=ai:lara-molina.fabian-a"Dumur, Didier"https://zbmath.org/authors/?q=ai:dumur.didierSummary: This paper presents a novel robust optimal design for parallel manipulators to optimize the performance indices subject to the unavoidable effect of the uncertainties. The robust optimization proposed in the present contribution consists of a multi-objective optimization problem that aims at maximizing the performance index and robustness criterion simultaneously. The design variables should be adjusted to minimize the effects of the uncertainties and maximize the performance index. The single-objective optimization problem is also carried out to evaluate the optimal design obtained by using the proposed robust optimization approach. Numerical results illustrate the benefits of the proposed robust optimization applied to the optimal kinematic design of a parallel Cartesian manipulator with clearances and the optimal dynamic design of a Stewart-Gough platform.Fully numerical computation of heteroclinic connection families in the spatial three-body problemhttps://zbmath.org/1532.700152024-05-13T19:39:47.825584Z"Henry, Damennick B."https://zbmath.org/authors/?q=ai:henry.damennick-b"Scheeres, Daniel J."https://zbmath.org/authors/?q=ai:scheeres.daniel-jSummary: Heteroclinic connections in the spatial circular restricted three-body problem play an important role in astrodynamics. This paper presents a fully numerical methodology for the computation of the two-parameter families of connections that exist between families of invariant tori in the three-body problem. The computation of connections is presented as a two-point boundary value problem in which the initial and final states belong to unstable and stable manifolds of two respective normally hyperbolic invariant manifolds. A flow map torus computation procedure is modified to compute particular trajectories within these spaces, and a robust two-parameter continuation scheme is paired with a shooting technique to compute the entire connection family. Results are provided in the Sun-Earth and Earth-Moon representations of the spatial three-body problem. The Sun-Earth connection family works to verify the methodology with previously developed semi-analytical connection computation techniques. The Earth-Moon example demonstrates the methodology in a setting where fully numerical techniques are required to study the connection family.Networks of periodic orbits in the circular restricted three-body problem with first order post-Newtonian termshttps://zbmath.org/1532.700162024-05-13T19:39:47.825584Z"Zotos, Euaggelos E."https://zbmath.org/authors/?q=ai:zotos.euaggelos-e"Papadakis, K. E."https://zbmath.org/authors/?q=ai:papadakis.konstantinos-e"Suraj, Md Sanam"https://zbmath.org/authors/?q=ai:suraj.md-sanam"Mittal, Amit"https://zbmath.org/authors/?q=ai:mittal.amit"Aggarwal, Rajiv"https://zbmath.org/authors/?q=ai:aggarwal.rajivSummary: The motivation of this article is to numerically investigate the orbital dynamics of the planar post-Newtonian circular restricted problem of three bodies. By numerically integrating several large sets of initial conditions of orbits we obtain the basins of escape. Additionally, we determine the influence of the transition parameter on the orbital structure of the system, as well as on the families of simple symmetric periodic orbits. The networks and the stability of the symmetric periodic orbits are revealed, while the corresponding critical periodic solutions are also identified. The parametric evolution of the horizontal and the vertical stability of the periodic orbits are also monitored, as a function of the transition parameter.Symmetric constellations of satellites moving around a central body of large masshttps://zbmath.org/1532.700172024-05-13T19:39:47.825584Z"Fenucci, Marco"https://zbmath.org/authors/?q=ai:fenucci.marco"Gronchi, Giovanni Federico"https://zbmath.org/authors/?q=ai:gronchi.giovanni-federicoThe use of variational methods to search for periodic solutions of the 3-body problem can be traced back to Poincaré. In the last two decades several new periodic solutions of the Newtonian \(N\)-body problem have been found by direct methods of calculus of variations. In this paper, the authors consider a \((1 + N)\)-body problem in which one particle has mass \(m_0 \gg 1\) and the remaining \(N\) have unitary mass. Imposing symmetry and topological constraints, the authors search for periodic orbits of this system by variational method and they also use \( \Gamma \)-convergence theory to study the asymptotic behaviour of these orbits, as the mass of the central body increases. Based on this theory, they can understand the motion of the satellites for large values of \(m_0\). In the end, they consider some examples with special symmetry.
Reviewer: Yuwei Ou (Jinan)Bounds on energy and angular momentum loss in the full \(n\)-body problemhttps://zbmath.org/1532.700182024-05-13T19:39:47.825584Z"Scheeres, D. J."https://zbmath.org/authors/?q=ai:scheeres.daniel-j"Brown, G. M."https://zbmath.org/authors/?q=ai:brown.gavin-mSummary: A new bound on the amended potential in an \(n\)-body system is derived and applied to the partitioning of energy and angular momentum in a disrupting gravitational aggregate. This result provides analytic insight into how energy and angular momentum can be lost or partitioned between different collections of bodies as they escape from each other. To better understand the possible outcomes in such a situation, some specific numerical tests are also performed for systems of \(N = 3, 4, 5, 6\). The results confirm that disrupting systems always lose energy, with a characteristic stochastic distribution of the lost energy. We also find that the system loses most of its angular momentum, although individual escaping components can retain significant nonzero angular momentum vectors that can be uniformly distributed in space as the number of bodies in the system increases.On the uniqueness of convex central configurations in the planar 4-body problemhttps://zbmath.org/1532.700192024-05-13T19:39:47.825584Z"Sun, Shanzhong"https://zbmath.org/authors/?q=ai:sun.shanzhong"Xie, Zhifu"https://zbmath.org/authors/?q=ai:xie.zhifu"You, Peng"https://zbmath.org/authors/?q=ai:you.pengThe paper uses numerical methods to establish the uniqueness of convex central configurations in the planar 4-body problem. The authors follow the work of \textit{J. M. Cors} and \textit{G. E. Roberts} [Nonlinearity 25, No. 2, 343--370 (2012; Zbl 1235.70033)], who established that the space of central configurations in the 4-body problem is three-dimensional. Specifically, for a given set of masses \((m_1, 1, m_3, m_4) \in [0.6, 1]^3\) with a particular ordering established, it is shown that there is a unique central configuration.
After establishing the equations for the configuration and factoring out symmetry and scaling, the equations to be solved are given. The equations are solved using interval arithmetic and the Krawczyk operator. Both are reviewed and explained with examples in the text. For a given set of masses, a suitable product of intervals is given where a solution may exist. These are divided into smaller sub-intervals. Intervals on which zeros of the target functions do not exist are ruled out. For the remaining candidate intervals, the Krawczyk operator is used as a second tool to eliminate intervals that do not contain a solution. If multiple intervals still possibly contain a solution, a bisection method is used, and this process continues until the subintervals are sufficiently small and only one subinterval contains a solution. This establishes the uniqueness for the given set of mass values.
The above process can only be carried out in a finite number of discrete mass choices. The implicit function theorem is used to establish the radius of a ``uniqueness mass ball'' in the space of masses \((m_1, m_3, m_4)\) about these points. For any set of masses within this ball, any central configuration is shown to be unique. After working through this process on an initial set of points, it is determined whether or not the space \([0.6, 1]^3\) has been fully covered or not. If not, new points are generated and the process is repeated until the entire space is covered. Thus the uniqueness is established for all masses in the space.
The authors point out that the method can be extended for a wider interval of masses, but the numerical method takes a greater amount of time as this is done. In particular, as the masses get smaller, the radii of the uniqueness mass balls become smaller, so the number of balls increases rapidly.
Overall, the paper is interesting, well organized, and very clear. Helpful concrete examples are given throughout, explaining the process. While the authors point out that more non-numerical work should be done to fully solve the problem, this is still a noteworthy result, and will be of interest to those working in central configurations.
Reviewer: Skyler C. Simmons (Orem)Horizontal transport in the bouncing ball system with a sawtooth-shaped tablehttps://zbmath.org/1532.700202024-05-13T19:39:47.825584Z"Okishio, Yudai"https://zbmath.org/authors/?q=ai:okishio.yudai"Ito, Hiroaki"https://zbmath.org/authors/?q=ai:ito.hiroaki"Kitahata, Hiroyuki"https://zbmath.org/authors/?q=ai:kitahata.hiroyukiSummary: The system that consists of a ball bouncing off a sawtooth-shaped table vibrating vertically is considered. The horizontal motion in this system is caused by the table shape, and we plotted the mean horizontal velocity as a function of the asymmetry of the table shape. The ball is transported in the direction which the gentler slopes face for the high-bounce parameter region. To give a description to the net asymmetric transport, we derive a simplified model using assumptions of high bounce and probabilistic collision to the left or right slopes. The simplified model exhibits a horizontal transport qualitatively similar to that observed in the original model.A dynamical interpretation of sequential decay in reactive scatteringhttps://zbmath.org/1532.700212024-05-13T19:39:47.825584Z"Gonzalez Montoya, Francisco"https://zbmath.org/authors/?q=ai:gonzalez-montoya.francisco"Jung, Christof"https://zbmath.org/authors/?q=ai:jung.christof"Seligman, Thomas H."https://zbmath.org/authors/?q=ai:seligman.thomas-hSummary: The topic of this article is a dynamical explanation of the sequential decay in rearrangement scattering. The essential observation is the behaviour of trajectories close to the basin boundary of the breakup channel. As a most simplistic example of demonstration, we use a version of the perturbed three particle Calogero-Moser system in a 1-dimensional position space.Computer-assisted proofs of existence of KAM tori in planetary dynamical models of \(\upsilon\)-And \(\mathbf{b}\)https://zbmath.org/1532.700222024-05-13T19:39:47.825584Z"Mastroianni, Rita"https://zbmath.org/authors/?q=ai:mastroianni.rita"Locatelli, Ugo"https://zbmath.org/authors/?q=ai:locatelli.ugoSummary: We reconsider the problem of the orbital dynamics of the innermost exoplanet of the \(\upsilon\)-Andromedæsystem (i.e., \(\upsilon\)-And \(\mathbf{b}\)) into the framework of a Secular Quasi-Periodic Restricted Hamiltonian model. This means that we preassign the orbits of the planets that are expected to be the biggest ones in that extrasolar system (namely, \(\upsilon\)-And \(\mathbf{c}\) and \(\upsilon\)-And \(\mathbf{d})\). The Fourier decompositions of their secular motions are injected in the equations describing the orbital dynamics of \(\upsilon\)-And \(\mathbf{b}\) under the gravitational effects exerted by those two exoplanets. By a computer-assisted procedure, we prove the existence of KAM tori corresponding to orbital motions that we consider to be very robust configurations, according to the analysis and the numerical explorations made in our previous article. The computer-assisted assisted proofs are successfully performed for two variants of the Secular Quasi-Periodic Restricted Hamiltonian model, which differs for what concerns the effects of the relativistic corrections on the orbital motion of \(\upsilon\)-And \(\mathbf{b}\), depending on whether they are considered or not.New adiabatic invariants for disturbed non-material volumeshttps://zbmath.org/1532.700232024-05-13T19:39:47.825584Z"Li, Lin"https://zbmath.org/authors/?q=ai:li.lin.12|li.lin.6|li.lin.9|li.lin.2|li.lin.3|li.lin.5|li.lin|li.lin.1The framework of the present paper is the field of non-material volumes, and specifically the dynamics induced by the so-called Mei symmetry for disturbed non-material volumes. After formulating the Lagrangian formalism of such a system and defining the Mei symmetrical perturbation in this context, new adiabatic invariants are obtained which, in particular cases, reproduce the expression of exact invariants previously obtained in the literature. The evolution of these adiabatic invariants is tested on a particular example of application, namely the motion of a rocket under an external force proportional to the displacement times the mass of the rocket.
Reviewer: Fernando Casas (Castellón de la Plana)On isochronicityhttps://zbmath.org/1532.700242024-05-13T19:39:47.825584Z"Treschev, D. V."https://zbmath.org/authors/?q=ai:treshchev.dmitrij-vSummary: We obtain a complete set of explicit necessary and sufficient conditions for the isochronicity of a Hamiltonian system with one degree of freedom. The conditions are presented in terms of the Taylor coefficients of the Hamiltonian function and have the form of an infinite collection of polynomial equations.Minimally driven Kapitza oscillator: a pedagogical perspective from Newtonian mechanics and geometryhttps://zbmath.org/1532.700252024-05-13T19:39:47.825584Z"Pal, Mainak"https://zbmath.org/authors/?q=ai:pal.mainak(no abstract)Nonlinear energy harvesting from rotating systemhttps://zbmath.org/1532.700262024-05-13T19:39:47.825584Z"Wang, Dan"https://zbmath.org/authors/?q=ai:wang.dan.3"Chen, Fangqi"https://zbmath.org/authors/?q=ai:chen.fangqi"Hao, Zhifeng"https://zbmath.org/authors/?q=ai:hao.zhifeng"Wiercigroch, Marian"https://zbmath.org/authors/?q=ai:wiercigroch.marianSummary: A simple electromagnetic energy harvester with a cubic nonlinear stiffness is proposed and dynamic responses as well as the potential power harvested are studied in this paper. The proposed nonlinear electromagnetic vibration energy harvester can be installed on a host base that is rotating at a constant speed and vibrating vertically. Considering the combination of the vertically vibrating and rotating frequency of the host base, the 1:1 primary resonance is investigated by the method of multiple scales. The dynamic characteristics of responses in terms of system parameters are studied and bifurcation curves are constructed. In addition to possessing the resonance characteristics, some saddle-node bifurcations occur for the steady-state solutions under certain conditions. Moreover, the effects of system parameters on the output average power are investigated as well. The results of analysis show that multiple frequency bands and parameter regions exist where a large power can be harvested due to the nonlinear resonances. Introducing the nonlinearity not only can increase the power output but also expand the frequency bands and parameter regions to harvest more power. A carefully selected system parameters can help to optimize the average power harvested in the design.Enhanced vehicle shimmy performance using inerter-based suppression mechanismhttps://zbmath.org/1532.700272024-05-13T19:39:47.825584Z"Wang, Yong"https://zbmath.org/authors/?q=ai:wang.yong.35|wang.yong.18|wang.yong.45|wang.yong.11|wang.yong.10|wang.yong.13|wang.yong.27|wang.yong.15|wang.yong.3|wang.yong.17|wang.yong.6|wang.yong.2|wang.yong.25|wang.yong.32|wang.yong.14|wang.yong.16"Xu, Bingbing"https://zbmath.org/authors/?q=ai:xu.bingbing"Meng, Haodong"https://zbmath.org/authors/?q=ai:meng.haodongSummary: Shimmy may occur in the vehicle normal driving process, which is a harmful motion and should be controlled in practical engineering. In order to improve the vehicle driving and handling stability, four kinds of passive inerter-based suppression mechanisms are proposed and applied in the vehicle suspension to improve its shimmy performance. The configurations S1 and S2 are composed of one inerter and one damper, which are in parallel-connected and series-connected, respectively, furthermore, an auxiliary spring is added to constitute configurations S3 and S4. Combined with the magic nonlinear tire model, the vehicle shimmy model with four inerter-based suppression mechanisms is established using Lagrange theory, its shimmy performance is studied using bifurcation analysis method, the stable area and limit cycle oscillation (LCO) magnitude of the system are obtained and compared with those of the original suspension system. The effect of the structural parameters of the inerter-based suppression mechanisms on the vehicle shimmy performance is analyzed, and the structural parameter optimization of the inerter-based suppression mechanism is investigated. The results show that the only parallel-connected and series-connected configurations S1 and S2 have little improvement effect on the vehicle shimmy performance. As the configurations S3 and S4 are used, the unstable area dominated by left and right steering shimmy reduces, the shimmy occurred vehicle velocity range becomes narrower and the maximum LCO magnitude of the front wheel swing motion becomes smaller, which suppresses the vehicle shimmy effectively and clarifies the benefits of the inerter and the necessity of adding the auxiliary spring. In addition, larger inertance of the inerter and smaller stiffness of the auxiliary spring is beneficial to improve the vehicle shimmy performance. The optimized structural parameters of the configurations S3 and S4 are obtained, which maintain the vehicle shimmy system stable, and further shorten the time for the vehicle shimmy system to reach stability. Therefore, the inerter-based suppression mechanism can effectively restrain the vehicle shimmy motion and give guiding significance for the design of vehicle shimmy suppression mechanism.Postflight recovery of the rotational motion of a small space vehicle from solar sensor informationhttps://zbmath.org/1532.700282024-05-13T19:39:47.825584Z"Belokonov, I. V."https://zbmath.org/authors/?q=ai:belokonov.i-v.1"Lomaka, I. A."https://zbmath.org/authors/?q=ai:lomaka.i-a(no abstract)Analysis of dynamics and control during the deployment of an annular tether group of spacecrafthttps://zbmath.org/1532.700292024-05-13T19:39:47.825584Z"Zabolotnov, Yu. M."https://zbmath.org/authors/?q=ai:zabolotnov.yu-m"Nazarova, A. A."https://zbmath.org/authors/?q=ai:nazarova.asiya-a"Wang, Changqing"https://zbmath.org/authors/?q=ai:wang.changqing(no abstract)Control of the rotation of a solid (spacecraft) with a combined optimality criterion based on quaternionshttps://zbmath.org/1532.700302024-05-13T19:39:47.825584Z"Levskii, M. V."https://zbmath.org/authors/?q=ai:levskii.m-v(no abstract)Nonholonomic dynamics and control of road vehicles: moving toward automationhttps://zbmath.org/1532.700312024-05-13T19:39:47.825584Z"Qin, Wubing B."https://zbmath.org/authors/?q=ai:qin.wubing-b"Zhang, Yiming"https://zbmath.org/authors/?q=ai:zhang.yiming"Takács, Dénes"https://zbmath.org/authors/?q=ai:takacs.denes"Stépán, Gábor"https://zbmath.org/authors/?q=ai:stepan.gabor"Orosz, Gábor"https://zbmath.org/authors/?q=ai:orosz.gabor.1(no abstract)On auxiliary fields and Lagrangians for relativistic wave equationshttps://zbmath.org/1532.700322024-05-13T19:39:47.825584Z"Sharapov, Alexey"https://zbmath.org/authors/?q=ai:sharapov.alexey-a"Shcherbatov, David"https://zbmath.org/authors/?q=ai:shcherbatov.davidA setup is presented to obtain a Lagrangian formulation for a set of partial differential equations. More specifically, the problem is investigated when the equations are linear partial differential equations with constant coefficients. The setup is used for the case of massive free fields of integer spins.
Reviewer: Mohammad Khorrami (Tehrān)A cohomological obstruction in higher-dimensional Chern-Simons gauge theorieshttps://zbmath.org/1532.700332024-05-13T19:39:47.825584Z"Palese, Marcella"https://zbmath.org/authors/?q=ai:palese.marcella"Winterroth, Ekkehart"https://zbmath.org/authors/?q=ai:winterroth.ekkehartSummary: We study a set of cohomology classes which emerge in the cohomological formulations of the calculus of variations as obstructions to the existence of (global) solutions of the Euler-Lagrange equations of Chern-Simons gauge theories in higher dimensions \(2p+1 > 3\).Free vibration and stability of an axially moving thin circular cylindrical shell using multiple scales methodhttps://zbmath.org/1532.740492024-05-13T19:39:47.825584Z"Mohamadi, Arash"https://zbmath.org/authors/?q=ai:mohamadi.arash"Shahgholi, Majid"https://zbmath.org/authors/?q=ai:shahgholi.majid"Ghasemi, Faramarz Ashenai"https://zbmath.org/authors/?q=ai:ghasemi.faramarz-ashenaiSummary: This paper investigates the linear free vibration of axially moving simply supported thin circular cylindrical shells with constant and time-dependent velocity considering the effect of viscous structure damping. Classical shell theory is employed to express strain-displacement relation. Linear elasticity theory is used to write stress-strain relation considering Hook's Law. Governing equations in cylindrical coordinates are derived using the Hamilton principle. Equilibrium equations are rewritten with the help of Donnell-Mushtari shell theory simplification assumptions. Motion equations for displacements in axial and circumferential directions are solved analytically concerning to displacement in the radial direction. As the displacement in the radial direction is the combination of driven and companion modes, the third motion equation is discretized using the Galerkin method. The set of ordinary differential equation obtained from the Galerkin method is solved using the steady-state method, which in practice leads to the prediction of the exact frequencies of vibration. By employing multiple scale method the critical speed values of a circular cylindrical shell and several types of instabilities are discussed. The numerical results show that by increasing the mean velocity, the system always loses stability by the divergence instability in different modes, and the critical speed values of lower modes are higher than those of higher modes. As well as the unstable regions for the resonances between velocity function fluctuation frequencies and the linear combination of natural frequencies is gained from the solvability condition of second order multiple scale method. The accuracy of the method is checked against the available data.Effects of rotary inertia on sub- and super-critical free vibration of an axially moving beamhttps://zbmath.org/1532.740732024-05-13T19:39:47.825584Z"Ding, Hu"https://zbmath.org/authors/?q=ai:ding.hu"Li, Yi"https://zbmath.org/authors/?q=ai:li.yi.11"Chen, Li-Qun"https://zbmath.org/authors/?q=ai:chen.liqunSummary: The most important issue in the vibration study of an engineering system is dynamics modeling. Axially moving continua is often discussed without the inertia produced by the rotation of the continua section. The main goal of this paper is to discover the effects of rotary inertia on the free vibration characteristics of an axially moving beam in the sub-critical and super-critical regime. Specifically, an integro-partial-differential nonlinear equation is modeled for the transverse vibration of the moving beam based on the generalized Hamilton principle. Then the effects of rotary inertia on the natural frequencies, the critical speed, post-buckling vibration frequencies are presented. Two kinds of boundary conditions are also compared. In super-critical speed range, the straight configuration of the axially moving beam loses its stability. The buckling configurations are derived from the corresponding nonlinear static equilibrium equation. Then the natural frequencies of the post-buckling vibration of the super-critical moving beam are calculated by using local linearization theory. By comparing the critical speed and the vibration frequencies in the sub-critical and super-critical regime, the effects of the inertia moment due to beam section rotation are investigated. Several interesting phenomena are disclosed. For examples, without rotary inertia, the study overestimates the stability of the axially moving beam. Moreover, the relative differences between the super-critical fundamental frequencies of the two theories may increase with an increasing beam length.Estimation and elimination of eigenvalue splitting and vibration instability of ring-shaped periodic structure subjected to three-axis angular velocity componentshttps://zbmath.org/1532.740762024-05-13T19:39:47.825584Z"Liu, Jinlong"https://zbmath.org/authors/?q=ai:liu.jinlong"Wang, Shiyu"https://zbmath.org/authors/?q=ai:wang.shiyu"Wang, Zheren"https://zbmath.org/authors/?q=ai:wang.zheren"Gao, Nan"https://zbmath.org/authors/?q=ai:gao.nan.2|gao.nan|gao.nan.3|gao.nan.1"Zhang, Dongsheng"https://zbmath.org/authors/?q=ai:zhang.dongshengSummary: Stable operation is one of the most crucial requirements for resonators in vibratory gyroscopes and ultrasonic motors, but eigenvalue splitting can deteriorate operation stability. This work aims at the estimation and elimination of eigenvalue splitting and vibration instability of resonators arranged in a fashion of ring-shaped periodic structures (RPS). An analytical model is developed by Hamilton's principle, where in-plane bending displacements, grouped supports and angular velocity components applied about three orthogonal directions are incorporated. Eigensolutions for the proposed rotational and mirror symmetric topologies are formulated by perturbation-superposition method, based on which eigenvalue splitting, vibration instability and their evolution with grouped supports and angular velocity are examined. The results verify the behaviors of splitting and instability share similar rules with those RPS having equally-spaced supports, but they change remarkably with grouping patterns. The dependences of grouping patterns and parameters on vibrations are demonstrated based on sample RPS. The splitting and instability are estimated by eigensolutions, and they can be suppressed or even eliminated by the proposed two types of topologies. Comparisons between the two topologies are made in terms of the requirements from engineering practice. Main results are also compared with those in the open literature.Elastic indentation of a rough surface by a conical punchhttps://zbmath.org/1532.740962024-05-13T19:39:47.825584Z"Borri-Brunetto, Mauro"https://zbmath.org/authors/?q=ai:borri-brunetto.mauro"Ciavarella, Michele"https://zbmath.org/authors/?q=ai:ciavarella.micheleSummary: In the contact of a cone with a rough plane the mean pressure in the contact area is constant. In particular, above a critical ratio of the opening angle of the cone with respect to the rms gradient of surface roughness, the mean pressure is the same of that for nominally flat contact, no matter how large is the normal load. We introduce a new variable, namely, the local density of contact area, whose integral over the smooth nominal contact domain gives the real contact area. The results given by the theoretical model agree with the numerical simulations of the same problem presented in the paper.A structure preserving stochastic perturbation of classical water wave theoryhttps://zbmath.org/1532.760262024-05-13T19:39:47.825584Z"Street, Oliver D."https://zbmath.org/authors/?q=ai:street.oliver-dSummary: The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. Here, we derive stochastic equations for the behaviour of surface gravity waves using an approach which is designed to preserve the geometric structure of the equations of fluid motion beneath the surface. In doing so, we find a stochastic equation for the evolution of a velocity potential and, more significantly, demonstrate that the stochastic equations for water wave dynamics have a Hamiltonian structure which mirrors that found by Zakharov for the deterministic theory. This involves a perturbation of the velocity field which, unlike the deterministic velocity, need not be irrotational for the problem to close.Spacetime geometry of spin, polarization, and wavefunction collapsehttps://zbmath.org/1532.810042024-05-13T19:39:47.825584Z"Beil, Charlie"https://zbmath.org/authors/?q=ai:beil.charlieSummary: To incorporate quantum nonlocality into general relativity, we propose that the preparation and measurement of a quantum system are simultaneous events. To make progress in realizing this proposal, we introduce a spacetime geometry that is endowed with particles which have no distinct points in their worldlines; we call these particles `pointons'. This new geometry recently arose in non-Noetherian algebraic geometry. We show that on such a spacetime, metrics are degenerate and tangent spaces have variable dimension. This variability then implies that pointons are spin-\(\frac{1}{2}\) fermions that satisfy the Born rule, where a projective measurement of spin corresponds to an actual projection of tangent spaces of different dimensions. Furthermore, the 4-velocities of pointons are necessarily replaced by their Hodge duals, and this transfer from vector to pseudo-tensor introduces a free choice of orientation that we identify with electric charge. Finally, a simple composite model of electrons and photons results from the metric degeneracy, and from this we obtain a new ontological model of photon polarization.Bell nonlocality in maximal-length quantum mechanicshttps://zbmath.org/1532.810102024-05-13T19:39:47.825584Z"Bosso, Pasquale"https://zbmath.org/authors/?q=ai:bosso.pasquale"Illuminati, Fabrizio"https://zbmath.org/authors/?q=ai:illuminati.fabrizio"Petruzziello, Luciano"https://zbmath.org/authors/?q=ai:petruzziello.luciano"Wagner, Fabian"https://zbmath.org/authors/?q=ai:wagner.fabian-jSummary: In this paper, we investigate the consequences of maximal length as well as minimal momentum scales on nonlocal correlations shared by two parties of a bipartite quantum system. To this aim, we rely on a general phenomenological scheme which is usually associated with the non-negligible spacetime curvature at cosmological scales, namely the extended uncertainty principle. In so doing, we find that quantum correlations are degraded if the deformed quantum mechanical model mimics a positive cosmological constant. This opens up the possibility to recover classicality at sufficiently large distances.A simple and fast approach for computing the fusion reactivities with arbitrary ion velocity distributionshttps://zbmath.org/1532.810192024-05-13T19:39:47.825584Z"Xie, Huasheng"https://zbmath.org/authors/?q=ai:xie.huashengSummary: Calculating fusion reactivity involves a complex six-dimensional integral of the fusion cross section and ion velocity distributions of two reactants. We demonstrate a simple Monte Carlo approach that efficiently computes this integral for arbitrary ion velocity distributions with a time complexity of \(O(N)\), where \(N\) is the number of samples. This approach generates random numbers that satisfy the reactant velocity distributions. In cases where these numbers are not readily available, we propose using Gaussian random numbers with weighted factors. For cases where only a small number of \(N\) samples are available, a \(O(N^2)\) method can be used. We benchmarked this approach against analytical results for drift bi-Maxwellian distributions and provided examples of drift ring beam and slowing down distributions. Our results show that the error can be less than 1\% with \(N \sim 10^4\) samples for our standard approach.Asymptotically optimal prepare-measure quantum key distribution protocolhttps://zbmath.org/1532.810202024-05-13T19:39:47.825584Z"Shu, Hao"https://zbmath.org/authors/?q=ai:shu.haoSummary: Quantum key distribution (QKD) could be the most significant application of quantum information theory. In nearly four decades, although substantial QKD protocols are developed, the BB84 protocol and its variants are still the most researched ones. It is well-known that the secure bound of qubit error rate (QBER) of BB84 protocol is about 11\% while it can be increased to 12.6\% by six-state protocol. It would not be surprising that employing more basis could increase the bound. However, what is the optimal protocol, and how to analyze it? In this paper, investigations of asymptotically optimal QKD protocols are proposed. Precisely, We present an abstraction of prepare-measure QKD protocols and investigate two special cases which are optimal among all protocols coding by the same states. Our analysis demonstrates that the asymptotically optimal QBER bounds coding by orthogonal qubits are about 27.28\% for both memory C-NOT attacks and memoryless C-NOT attacks while the bounds coding by non-orthogonal states in two mutually unbiased bases are about 22.73\% for memory and 28.69\% for memoryless C-NOT attacks. The protocols are idealized but might be asymptotically realized while their optimality indicates the ultimate potential of QKD protocols. Although the analysis only contains a special kind of attack, it provides a framework for investigating such protocols.A semi-quantum private comparison with high-level security third partyhttps://zbmath.org/1532.810212024-05-13T19:39:47.825584Z"Li, Jian"https://zbmath.org/authors/?q=ai:li.jian.20"Wang, Zhuo"https://zbmath.org/authors/?q=ai:wang.zhuo"Ye, Chongqiang"https://zbmath.org/authors/?q=ai:ye.chongqiang"Che, Fanting"https://zbmath.org/authors/?q=ai:che.fantingSummary: Based on three-particle pure states, a new anonymous semi-quantum privacy comparison is proposed to deal with the threat of quantum computing power faced by users without complete quantum capabilities in the post-quantum era. In this scheme, quantum entanglement and quantum uncertainty principles are used to ensure third party security, measurement attack security and entanglement attack security. Compared with most semi-quantum privacy comparison schemes, it reduces the risk of TP evil and improves communication efficiency. Therefore, the scheme has stronger safety and higher efficiency.Primary ionization density produced by charged fragments in the working volume of the fission chambershttps://zbmath.org/1532.810262024-05-13T19:39:47.825584Z"Khrushchinsky, A. A."https://zbmath.org/authors/?q=ai:khrushchinsky.a-a"Kuten, S. A."https://zbmath.org/authors/?q=ai:kuten.semen-a"Le, Thi Dieu Hien"https://zbmath.org/authors/?q=ai:le.thi-dieu-hien"Babichev, L. F."https://zbmath.org/authors/?q=ai:babichev.l-f.1(no abstract)Quasinormal modes and stability of higher dimensional rotating black holes under massive scalar perturbationshttps://zbmath.org/1532.810292024-05-13T19:39:47.825584Z"Lu, Kai-Peng"https://zbmath.org/authors/?q=ai:lu.kai-peng"Li, Wenbin"https://zbmath.org/authors/?q=ai:li.wenbin"Huang, Jia-Hui"https://zbmath.org/authors/?q=ai:huang.jiahuiSummary: We consider the stability of six-dimensional singly rotating Myers-Perry black holes under massive scalar perturbations. Using Leaver's continued fraction method, we compute the quasinormal modes of the massive scalar fields. All modes found are damped under the quasinormal boundary conditions. It is also found that long-living modes called quasiresonances exist for large scalar masses as in the four-dimensional Kerr black hole case. Our numerical results provide a direct and complement evidence for the stability of six-dimensional MP black holes under massive scalar perturbation.Magnetic operators in 2D compact scalar field theories on the latticehttps://zbmath.org/1532.810362024-05-13T19:39:47.825584Z"Abe, Motokazu"https://zbmath.org/authors/?q=ai:abe.motokazu"Morikawa, Okuto"https://zbmath.org/authors/?q=ai:morikawa.okuto"Onoda, Soma"https://zbmath.org/authors/?q=ai:onoda.soma"Suzuki, Hiroshi"https://zbmath.org/authors/?q=ai:suzuki.hiroshi.2"Tanizaki, Yuya"https://zbmath.org/authors/?q=ai:tanizaki.yuyaSummary: In lattice compact gauge theories, we must impose the admissibility condition to have well-defined topological sectors. The admissibility condition, however, usually forbids the presence of magnetic operators, and it is not so trivial if one can study the physics of magnetic objects that depends on the topological term, such as the Witten effect, on the lattice. In this paper, we address this question in the case of 2D compact scalars as it would be one of the simplest examples having analogues of the monopole and the topological term. To define the magnetic operator, we propose the ``excision method,'' which consists of excising lattice links (or bonds) in an appropriate region containing the magnetic operator and defining the dual lattice in a particular way. The size of the excised region is \(O(1)\) in lattice units so that the magnetic operator becomes point-like in the continuum limit. We give the lattice derivation of the 't Hooft anomalies between the electric and magnetic symmetries and also derive the higher-group-like structure related to the Witten effect.Green hyperbolic complexes on Lorentzian manifoldshttps://zbmath.org/1532.810372024-05-13T19:39:47.825584Z"Benini, Marco"https://zbmath.org/authors/?q=ai:benini.marco.1"Musante, Giorgio"https://zbmath.org/authors/?q=ai:musante.giorgio"Schenkel, Alexander"https://zbmath.org/authors/?q=ai:schenkel.alexanderSummary: We develop a homological generalization of Green hyperbolic operators, called Green hyperbolic complexes, which cover many examples of derived critical loci for gauge-theoretic quadratic action functionals in Lorentzian signature. We define Green hyperbolic complexes through a generalization of retarded and advanced Green's operators, called retarded and advanced Green's homotopies, which are shown to be unique up to a contractible space of choices. We prove homological generalizations of the most relevant features of Green hyperbolic operators, namely that (1) the retarded-minus-advanced cochain map is a quasi-isomorphism, (2) a differential pairing (generalizing the usual fiber-wise metric) on a Green hyperbolic complex leads to covariant and fixed-time Poisson structures and (3) the retarded-minus-advanced cochain map is compatible with these Poisson structures up to homotopy.Finite temperature properties of an integrable zigzag ladder chainhttps://zbmath.org/1532.810402024-05-13T19:39:47.825584Z"Tavares, T. S."https://zbmath.org/authors/?q=ai:tavares.t-sean"Ribeiro, G. A. P."https://zbmath.org/authors/?q=ai:ribeiro.g-a-pSummary: We consider the interaction-round-a-face version of the six-vertex model for arbitrary anisotropy parameter, which allow us to derive an integrable one-dimensional quantum Hamiltonian with three-spin interactions. We apply the quantum transfer matrix approach for the face model version of the six-vertex model. The integrable quantum Hamiltonian shares some thermodynamical properties with the Heisenberg XXZ chain, but has different ordering and critical exponents. Two gapped phases are the dimerized antiferromagnetic order and the usual antiferromagnetic (Néel) order for positive nearest neighbor Ising coupling. In between these, there is an extended critical region, which is a quantum spin-liquid with broken parity symmetry inducing an oscillatory behavior at the long distance \(<\sigma_1^z\sigma_{\ell + 1}^z>\) correlation. At finite temperatures, the numerical solution of the non-linear integral equations allows for the determination of the correlation length as well as for the momentum of the oscillation.Integrable degenerate \(\mathcal{E}\)-models from 4d Chern-Simons theoryhttps://zbmath.org/1532.810422024-05-13T19:39:47.825584Z"Liniado, Joaquin"https://zbmath.org/authors/?q=ai:liniado.joaquin"Vicedo, Benoît"https://zbmath.org/authors/?q=ai:vicedo.benoitSummary: We present a general construction of integrable degenerate \(\mathcal{E}\)-models on a 2d manifold \(\Sigma\) using the formalism of \textit{K. Costello} and \textit{M. Yamazaki} [``Gauge theory and integrability, III'', Preprint, \url{arXiv:1908.02289}] based on 4d Chern-Simons theory on \(\Sigma \times \mathbb{C}P^1\). We begin with a physically motivated review of the mathematical results of \textit{M. Benini} et al. [Commun. Math. Phys. 389, No. 3, 1417--1443 (2022; Zbl 1486.81145)] where a unifying 2d action was obtained from 4d Chern-Simons theory which depends on a pair of 2d fields \(h\) and \(\mathcal{L}\) on \(\Sigma\) subject to a constraint and with \(\mathcal{L}\) depending rationally on the complex coordinate on \(\mathbb{C}P^1\). When the meromorphic 1-form \(\omega\) entering the action of 4d Chern-Simons theory is required to have a double pole at infinity, the constraint between \(h\) and \(\mathcal{L}\) was solved in [\textit{S. Lacroix} and \textit{B. Vicedo}, SIGMA, Symmetry Integrability Geom. Methods Appl. 17, Paper 058, 45 p. (2021; Zbl 1510.17051)] to obtain integrable non-degenerate \(\mathcal{E}\)-models. We extend the latter approach to the most general setting of an arbitrary 1-form \(\omega\) and obtain integrable degenerate \(\mathcal{E}\)-models. To illustrate the procedure, we reproduce two well-known examples of integrable degenerate \(\mathcal{E}\)-models: the pseudo-dual of the principal chiral model and the bi-Yang-Baxter \(\sigma\)-model.Anisotropic spin generalization of elliptic Macdonald-Ruijsenaars operators and \(R\)-matrix identitieshttps://zbmath.org/1532.810432024-05-13T19:39:47.825584Z"Matushko, M."https://zbmath.org/authors/?q=ai:matushko.m-g"Zotov, Andrei"https://zbmath.org/authors/?q=ai:zotov.andrei-vSummary: We propose commuting set of matrix-valued difference operators in terms of the elliptic Baxter-Belavin \(R\)-matrix in the fundamental representation of \(\mathrm{GL}_M\). In the scalar case \(M=1\), these operators are the elliptic Macdonald-Ruijsenaars operators, while in the general case they can be viewed as anisotropic versions of the quantum spin Ruijsenaars Hamiltonians. We show that commutativity of the operators for any \(M\) is equivalent to a set of \(R\)-matrix identities. The proof of identities is based on the properties of elliptic \(R\)-matrix including the quantum and the associative Yang-Baxter equations. As an application of our results, we introduce elliptic version of q-deformed Haldane-Shastry model.Quantum vector fields via quantum doubles and their applicationshttps://zbmath.org/1532.810462024-05-13T19:39:47.825584Z"Gurevich, Dimitry"https://zbmath.org/authors/?q=ai:gurevich.dimitry"Saponov, Pavel"https://zbmath.org/authors/?q=ai:saponov.pavel-aSummary: By treating generators of the reflection equation algebra corresponding to a Hecke symmetry as quantum analogs of vector fields, we exhibit the corresponding Leibniz rule via the so-called quantum doubles. The role of the function algebra in such a double is attributed to another copy of the reflection equation algebra. We consider two types of quantum doubles: these giving rise to the quantum analogs of left vector fields acting on the function algebra and those giving rise to quantum analogs of the adjoint vector fields acting on the same algebra. Also, we introduce quantum partial derivatives in the generators of the reflection equation algebra and then at the limit \(q\rightarrow 1\) we get quantum partial derivatives on the enveloping algebra \(U(gl_N)\) as well as on a certain its extension.
For the entire collection see [Zbl 1519.35008].Non-abelian Carroll-Field-Jackiw term in a Rarita-Schwinger modelhttps://zbmath.org/1532.810472024-05-13T19:39:47.825584Z"Gomes, M."https://zbmath.org/authors/?q=ai:gomes.marcelo-o-c"Lima, J. G."https://zbmath.org/authors/?q=ai:lima.j-g"Mariz, T."https://zbmath.org/authors/?q=ai:mariz.tiago"Nascimento, J. R."https://zbmath.org/authors/?q=ai:nascimento.jose-roberto|nascimento.jose-r"Petrov, A. Yu."https://zbmath.org/authors/?q=ai:yu-petrov.a|petrov.albert-yuSummary: In this paper, we demonstrate the possibility of generating a non-Abelian Carroll-Field-Jackiw (CFJ) term in the theory of a non-Abelian gauge field coupled to a spin-3/2 field in the presence of the constant axial vector field. Applying two regularization schemes, we prove that this term is finite and ambiguous, particularly vanishing within the 't Hooft-Veltman scheme.Deformations of Yang-Baxter operators via \(n\)-Lie algebra cohomologyhttps://zbmath.org/1532.810602024-05-13T19:39:47.825584Z"Elhamdadi, Mohamed"https://zbmath.org/authors/?q=ai:elhamdadi.mohamed"Zappala, Emanuele"https://zbmath.org/authors/?q=ai:zappala.emanueleSummary: We introduce a cohomology theory of \(n\)-ary self-distributive objects in the tensor category of vector spaces that classifies their infinitesimal deformations. For \(n\)-ary self-distributive objects obtained from \(n\)-Lie algebras we show that (\(n\)-ary) Lie cohomology naturally injects in the self-distributive cohomology and we prove, under mild additional assumptions, that the map is an isomorphism of second cohomology groups. This shows that the self-distributive deformations are completely classified by the deformations of the Lie bracket. This theory has important applications in the study of Yang-Baxter operators as the self-distributive deformations determine nontrivial deformations of the Yang-Baxter operators derived from \(n\)-ary self-distributive structures. In particular, we show that there is a homomorphism from the second self-distributive cohomology to the second cohomology of the associated Yang-Baxter operator. Moreover, we prove that when the self-distributive structure is induced by a Lie algebra with trivial center, we get a monomorphism. We construct a deformation theory based on simultaneous deformations, where both the coalgebra and self-distributive structures are deformed simultaneously. We show that when the Lie algebra has trivial cohomology (e.g. for semi-simple Lie algebras) the simultaneous deformations might still be nontrivial, producing corresponding Yang-Baxter operator deformations. We provide examples and computations in low dimensions, and we completely characterize 2-cocycles for the self-distributive objects obtained from all the nontrivial real Lie algebras of dimension 3, i.e. the Bianchi I--IX, and all the nontrivial complex Lie algebras of dimension 3.Erratum to: ``\(\mathcal{N} = 4\) supersymmetric Yang-Mills thermodynamics to order \(\lambda^2\)''https://zbmath.org/1532.810622024-05-13T19:39:47.825584Z"Du, Qianqian"https://zbmath.org/authors/?q=ai:du.qianqian"Strickland, Michael"https://zbmath.org/authors/?q=ai:strickland.michael"Tantary, Ubaid"https://zbmath.org/authors/?q=ai:tantary.ubaidSummary: In this erratum we correct an error made in our paper [ibid. 2021, No. 8, Paper No. 64, 29 p. (2021; Zbl 1469.81069)]. The end result is that one of the terms contributing at \(O(\lambda^2)\) changes from \(-45/16\) to \(-21/8\). This represents a small numerical correction to the originally reported result and none of our conclusions are changed. Due to this correction we also update the generalized Padé approximant that interpolates between the weak- and strong-coupling limits and the final figure comparing various approximations to the scaled entropy density.Super Cartan geometry and the super Ashtekar connectionhttps://zbmath.org/1532.810632024-05-13T19:39:47.825584Z"Eder, Konstantin"https://zbmath.org/authors/?q=ai:eder.konstantinSummary: This work is devoted to the geometric approach to supergravity. More precisely, we interpret \(\mathcal{N}=1\), \(D=4\) supergravity as a super Cartan geometry which provides a link between supergravity and Yang-Mills theory. To this end, we first review important aspects of the theory of supermanifolds and we establish a link between various different approaches. We then introduce super Cartan geometries using the concept of so-called enriched categories. This, among other things, will enable us to implement anticommutative fermionic fields. We will then also show that non-extended \(D=4\) supergravity naturally arises in this framework. Finally, using this gauge-theoretic interpretation as well as the chiral structure of the underlying supersymmetry algebra, we will derive graded analoga of Ashtekar's self-dual variables and interpret them in terms of generalized super Cartan connections. This gives canonical chiral supergravity the structure of a Yang-Mills theory with gauge supergroup similar to the self-dual variables in ordinary first-order Einstein gravity. We then construct the parallel transport map corresponding to the super connection in mathematical rigorous way using again enriched categories. This provides the possibility of quantizing gravity and matter degrees of freedom in loop quantum gravity in a unified way. Kindly check and confirm inserted city and country name are correctly identified. City and country name are correct.Various mechanisms for double capture from helium targets by alpha particleshttps://zbmath.org/1532.810652024-05-13T19:39:47.825584Z"Belkić, Dževad"https://zbmath.org/authors/?q=ai:belkic.dzevadSummary: An analysis is presented using six quantum-mechanical four-body distorted wave (DW) theories for double capture (DC) in ion-atom collisions at intermediate and high energies. They all satisfy the correct boundary conditions in the entrance and exit channels. This implies the usage of short-range perturbation potentials in compliance with the exact behaviors of scattering wave functions at infinitely large separations of particles. Specifically, total cross sections \(Q\) are analyzed for collisions of alpha particles with helium targets. Regarding the relative quantitative performance of the studied DW theories at different impact energies \(E\), our main focus is on the sensitivity of \(Q\) to various collisional mechanisms. The usual mechanism in most DW theories assumes that both electrons undergo the same type of collisions with nuclei. These are either single or double collisions in one or two steps, respectively, per channel, but without their mixture in either channel. The signatures of double collisions in differential cross sections are the Thomas peaks. By definition, these cannot be produced by single collisions. There is another DC pathway, which is actually favored by the existing experimental data. It is a hybrid, two-center mechanism which, in each channel separately, combines a single collision for one electron with a double collision for the other electron. The ensuing DW theory is called the four-body single-double scattering (SDS-4B) method. It appears that this mechanism in the SDS-4B method is more probable than double collisions for each electron in both channels predicted by the four-body continuum distorted wave (CDW-4B) method. This is presently demonstrated for \(Q\) at energies \(E=[200,8000]\) keV in DC exemplified by alpha particles colliding with helium targets.Complex Langevin method on rotating matrix quantum mechanics at thermal equilibriumhttps://zbmath.org/1532.810712024-05-13T19:39:47.825584Z"Azuma, Takehiro"https://zbmath.org/authors/?q=ai:azuma.takehiro"Morita, Takeshi"https://zbmath.org/authors/?q=ai:morita.takeshi"Yoshida, Hiroki"https://zbmath.org/authors/?q=ai:yoshida.hirokiSummary: Rotating systems in thermal equilibrium are ubiquitous in our world. In the context of high-energy physics, rotations would affect the phase structure of quantum chromodynamics (QCD). However, the standard Monte Carlo methods in rotating systems are problematic because the chemical potentials for the angular momenta (angular velocities) cause sign problems even for bosonic variables. In this article, we demonstrate that the complex Langevin method (CLM) may overcome this issue. We apply the CLM to the Yang-Mills (YM)-type one-dimensional matrix model (matrix quantum mechanics) that is a large-\(N\) reduction (or dimensional reduction) of the \((D + 1)\)-dimensional \(U(N)\) pure YM theory [bosonic Banks-Fischler-Shenker-Susskind (BFSS) model]. This model shows a large-\(N\) phase transition at finite temperature, which is analogous to the confinement/deconfinement transition of the original YM theory, and our CLM predicts that the transition temperature decreases as the angular momentum chemical potential increases. In order to verify our results, we compute several quantities via the minimum sensitivity method and find good quantitative agreements. Hence, the CLM works properly in this rotating system. We also argue that our results are qualitatively consistent with a holography and the recent studies of the imaginary angular velocity in QCD. As a byproduct, we develop an analytic approximation to treat the so-called ``small black hole'' phase in the matrix model.Comparative study of the heavy-quark dynamics with the Fokker-Planck equation and the plastino-plastino equationhttps://zbmath.org/1532.810742024-05-13T19:39:47.825584Z"Megías, Eugenio"https://zbmath.org/authors/?q=ai:megias.eugenio"Deppman, Airton"https://zbmath.org/authors/?q=ai:deppman.airton"Pasechnik, Roman"https://zbmath.org/authors/?q=ai:pasechnik.roman"Tsallis, Constantino"https://zbmath.org/authors/?q=ai:tsallis.constantinoSummary: The Fokker-Planck Equation (FPE) is a fundamental tool for the investigation of kinematic aspects of a wide range of systems. The Plastino-Plastino Equation (PPE) is the correct generalization describing the kinematic evolution of complex systems consistent with \(q\)-statistics. In the present work, we use this particular problem to compare the results obtained with the FPE and the PPE, and discuss the different aspects of the dynamical evolution of the system according to the solutions for each equation. We observe clear differences in the solutions for all the cases studied here and discuss possible experimental investigations that can indicate which of those equations better describes the heavy-quark kinematics in the medium. The results obtained here have implications in the study of anomalous diffusion in porous and granular media, in Cosmology and Astrophysics. The obtained results reinforce the validity of the relation \((q - 1)^{-1} = (11/3)N_c - (4/3)(N_f/2)\), where \(N_c\) and \(N_f\) are, respectively, the number of colours and the effective number of flavours. This equation was recently established in the context of a fractal approach to QCD in the non-perturbative regime.QCD mesonic screening masses using Gribov quantizationhttps://zbmath.org/1532.810752024-05-13T19:39:47.825584Z"Sumit"https://zbmath.org/authors/?q=ai:sumit.s"Haque, Najmul"https://zbmath.org/authors/?q=ai:haque.najmul"Patra, Binoy Krishna"https://zbmath.org/authors/?q=ai:patra.binoy-krishnaSummary: The screening masses of mesons provide a gauge invariant and definite order parameter of chiral symmetry restoration. Different mesonic correlation lengths for flavor non-singlets, at least up to NLO, are well-defined gauge invariant physical quantities calculated earlier using the perturbative resummation techniques. The NLO perturbative results match the available non-perturbative lattice QCD results at the high-temperature regime. We have studied the spatial correlation lengths of various mesonic observables using the non-perturbative Gribov resummation, both for quenched QCD and \((2 + 1)\) flavor QCD. The study follows the analogies with the NRQCD effective theory, a well-known theory for studying heavy quarkonia at zero temperature.Scalar triplet leptogenesis with a CP violating phasehttps://zbmath.org/1532.810782024-05-13T19:39:47.825584Z"Chongdar, Sreerupa"https://zbmath.org/authors/?q=ai:chongdar.sreerupa"Mishra, Sasmita"https://zbmath.org/authors/?q=ai:mishra.sasmitaSummary: We study baryogenesis through leptogenesis via decay of triplet scalars embedded in the Standard Model. We consider two triplets scenario where the vacuum expectation value developed by one of the triplets is complex. The coupling of the triplet Higgs with the Standard Model leptons and Higgs scalar allows two decay channels, with branching ratios \(B_L\) and \(B_\phi\), respectively. It is known that the hierarchy between the two branching ratios (\(B_L \gg B_\phi\) or \(B_\phi \gg B_L\)), is sensitive to the generation of adequate CP violation and efficiency of leptogenesis. Working in a hierarchical limit of branching ratios and requiring adequate CP violation, we find the mass of the lightest triplet can be as low as \(1 \times 10^{10}\) GeV. In the temperature regime \([10^9, 10^{12}]\) GeV, flavor effects, especially two-flavor effects become important in the study of leptogenesis. In two-flavored regime we study flavor effects in leptogenesis. It is observed that adequate baryon asymmetry can not be obtained for purely flavored leptogenesis, which corresponds to the hierarchical branching ratios, \(B_L \gg B_\phi\). But the hierarchy in the other way \(B_\phi \gg B_L\) still allows successful baryogenesis through leptogenesis. The phase of the complex vacuum expectation value of the triplet scalar is constrained by requiring non-zero CP violation. Considering the mass scale of triplet scalars as TeV scale, we also study resonant leptogenesis in the light of TeV scale physics.Search for the signal of vector-like bottom quark at LHeC in the final state with \(3b\)-jetshttps://zbmath.org/1532.810822024-05-13T19:39:47.825584Z"Zeng, Qing-Guo"https://zbmath.org/authors/?q=ai:zeng.qingguo"Pan, Yu-Si"https://zbmath.org/authors/?q=ai:pan.yu-si"Zhang, Jian"https://zbmath.org/authors/?q=ai:zhang.jian.20|zhang.jian.23|zhang.jian.16|zhang.jian.1|zhang.jian.42|zhang.jian.8|zhang.jian.25|zhang.jian.14|zhang.jian.4|zhang.jian.7|zhang.jian.2Summary: Vector-like quarks arise in many new theories beyond the Standard Model, which is driven by several theoretical issues. In a framework of the Standard Model simply extended by an \(SU(2)\) singlet vector-like bottom quark, we present a study of single production of such vector-like bottom quark at the LHeC. The work is preformed with assuming the LHeC with center of mass energy \(\sqrt{ s} = 1.98\) TeV and an integrated luminosity \(\mathcal{L} = 1000\mathrm{fb}^{-1}\). We focus on the process \(e^- p \to \nu_e B\to \nu_e b H(\mathrm{orZ}) \to\nu_{\mathrm{e}} \mathrm{bb}\overline{\mathrm{b}}\). The signal is searched in events with three \(b\)-jets within final state. Exclusion (discover) capability of the LHeC for the signal of the vector-like bottom quark are obtained at \(2\sigma\) (\(5\sigma\)) confidence level. Our result demonstrates a significant improvement compared to previous relevant researches. We also discuss the capability of LHeC for the singlet \(B\) search with combined analysis from other experiments.Application of floating spherical Gaussian orbital approach in redefining the atomic periodic descriptorhttps://zbmath.org/1532.810862024-05-13T19:39:47.825584Z"Kumari, Dimple"https://zbmath.org/authors/?q=ai:kumari.dimple"Saloni, Saloni"https://zbmath.org/authors/?q=ai:saloni.saloni"Labarca, Martín"https://zbmath.org/authors/?q=ai:labarca.martin"Chakraborty, Tanmoy"https://zbmath.org/authors/?q=ai:chakraborty.tanmoySummary: Chemistry plays a vital role in the improvement of the narrative properties of atoms and molecules. Many attempts have been made in this field and a few quantities like electronegativity, electron affinity, electrophilicity, polarizability, ionization potential, etc. have been introduced. Electronegativity is an important chemical construct that plays an essential role to clarify several chemical, biochemical, and physicochemical interactions. We have thoroughly studied the different periodic descriptors which are involved to define various electronegativity scales based on either theoretical concepts or experimental findings. The Floating Spherical Gaussian Orbital Approach (FSGO), being one of the the most studied ab initio methods, has been utilized in this study to develop a scale of electronegativity in terms of compressibility factor. We have proposed a model to compute atomic electronegativity values of 51 elements of the periodic table. The computed electronegativity scale observes the periodic trend and justifies many chemical phenomena. Molecular electronegativity values have also been computed using the computed atomic electronegativity data and utilized to verify the Electronegativity Equalization Principle.Implementation of chiral two-nucleon forces to nuclear many-body methods with Gaussian-wave packetshttps://zbmath.org/1532.810902024-05-13T19:39:47.825584Z"Fukui, Tokuro"https://zbmath.org/authors/?q=ai:fukui.tokuroSummary: Many-body methods that use Gaussian-wave packets to describe nucleon spatial distribution have been widely employed for depicting various phenomena in nuclear systems, in particular clustering. So far, however, the chiral effective field theory, a state-of-the-art theory of nuclear force, has not been applied to such methods. In this paper, we give the formalism to calculate the two-body matrix elements of the chiral two-nucleon forces using the Gaussian-wave packets. We also visualize the matrix elements and investigate the contributions of the central and tensor forces. This work is a foothold towards an \textit{ab initio} description of various cluster phenomena in view of nucleons, pions, and many-nucleon forces.Hall motions in Carroll dynamicshttps://zbmath.org/1532.810912024-05-13T19:39:47.825584Z"Marsot, L."https://zbmath.org/authors/?q=ai:marsot.loic"Zhang, P.-M."https://zbmath.org/authors/?q=ai:zhang.pengming"Chernodub, M."https://zbmath.org/authors/?q=ai:chernodub.maxim-n"Horvathy, P. A."https://zbmath.org/authors/?q=ai:horvathy.peter-aSummary: ``Do Carroll particles move?'' The answer depends on the characteristics of the particle such as its mass, spin, electric charge, and magnetic moment. A massive Carroll particle (closely related to fractons) does not move; its immobility follows from Carroll boost symmetry which implies dipole conservation, but not conversely. A massless Carroll particle may propagate by following the Hall law, consistently with the partial breaking of the Carroll boost symmetry. The framework is extended to Carroll field theory. In \(d = 2\) space dimensions, the Carroll group has a two-fold central extension which allows us to generalize the dynamics to massive and massless particles, including anyons. The anyonic spin and magnetic moment combine with the doubly-extended structure parametrized by two Casimir invariants interpreted as intrinsic magnetization and non-commutativity parameter. The extended Carroll particle subjected to an electromagnetic background field moves following a generalized Hall law which includes a Zeeman force. This theory is illustrated by massless, uncharged anyons with doubly-centrally extended structure we call exotic photons, which move on the horizon of a Black Hole, giving rise to an anyonic spin-Hall Effect.Symmetric universal character, integrable hierarchy, and affine Yangian of \(\mathfrak{gl}(1)\)https://zbmath.org/1532.810922024-05-13T19:39:47.825584Z"Yang, Qianqian"https://zbmath.org/authors/?q=ai:yang.qianqian"Li, Chuanzhong"https://zbmath.org/authors/?q=ai:li.chuanzhongSummary: We define a symmetric universal character by using the affine Yangian of \(\mathfrak{gl}(1)\), which is related with a pair of 2D Young diagram which is considered as 3D Young diagrams with only one layer in \(z\)-axis direction. We also define the symmetric universal character hierarchy and prove that all symmetric universal characters are tau functions of this integrable hierarchy. Then, we construct the Boson-Fermion correspondence in the symmetric universal character hierarchy and symmetric universal character can be realized through them. Finally, the \((m, n)\)-soliton solution of the symmetric universal character hierarchy is given by vertex operators.Structure of the plane waves for a spin 3/2 particlehttps://zbmath.org/1532.810942024-05-13T19:39:47.825584Z"Ivashkevich, A. V."https://zbmath.org/authors/?q=ai:ivashkevich.alina-vSummary: The structure of the plane waves solutions for a relativistic spin 3/2 particle described by 16-component vector-bispinor is studied. In massless case, two representations are used: Rarita - Schwinger basis, and a special second basis in which the wave equation contains the Levi-Civita tensor. In the second representation it becomes evident the existence of gauge solutions in the form of 4-gradient of an arbitrary bispinor. General solution of the massless equation consists of six independent components, it is proved in an explicit form that four of them may be identified with the gauge solutions, and therefore may be removed. This procedure is performed in the Rarita - Schwinger basis as well. For the massive case, in Rarita - Schwinger basis four independent solutions are constructed explicitly.Bias reduced semidefinite relaxation method for 3-D rigid body localization using AOAhttps://zbmath.org/1532.901492024-05-13T19:39:47.825584Z"Wang, Gang"https://zbmath.org/authors/?q=ai:wang.gang.35"Ho, K. C."https://zbmath.org/authors/?q=ai:ho.kin-chu|ho.ken-chung|ho.kwok-chiang|ho.ka-chong|ho.kwang-chien"Chen, Xianjing"https://zbmath.org/authors/?q=ai:chen.xianjingEditorial remark: No review copy delivered.Anti-unwinding nonsingular terminal sliding mode control with attitude maneuver planning for flexible spacecrafthttps://zbmath.org/1532.930302024-05-13T19:39:47.825584Z"Dong, Rui-Qi"https://zbmath.org/authors/?q=ai:dong.ruiqi"Nagamune, Ryozo"https://zbmath.org/authors/?q=ai:nagamune.ryozo"Wu, Ai-Guo"https://zbmath.org/authors/?q=ai:wu.aiguoSummary: In this article, a novel control approach with a dynamic parameter and an attitude maneuver planning scheme is proposed for flexible spacecraft to achieve anti-unwinding attitude maneuver control and vibration suppression. In order to suppress the flexible modal vibration of the flexible spacecraft during the attitude maneuver, an attitude maneuver path is planned by the proposed attitude maneuver planning scheme with four input impulses satisfying some conditions. For tracking the planned reference attitude maneuver path without unwinding phenomenon, a robust attitude maneuver controller with a dynamic parameter is proposed based on a novel switching function which contains terminal and non-terminal sliding manifolds. Besides, the obtained sliding surface contains two equilibria. Finite-time convergence and unwinding-free performance of the closed-loop system are analyzed by Lyapunov theory. The simulation results demonstrate that the proposed attitude control scheme possesses robustness and anti-unwinding performance. Besides, the flexible vibration can be suppressed by tracking the planned attitude maneuver path.
{{\copyright} 2022 John Wiley \& Sons Ltd.}Dual-mode robust model predictive control for the tracking control of nonholonomic mobile robothttps://zbmath.org/1532.930762024-05-13T19:39:47.825584Z"Meng, Huan"https://zbmath.org/authors/?q=ai:meng.huan"Zhang, Jinhui"https://zbmath.org/authors/?q=ai:zhang.jinhui"Li, Sihang"https://zbmath.org/authors/?q=ai:li.sihangSummary: In this article, a novel dual-mode robust model predictive control (MPC) approach is proposed for solving the tracking control problem of nonholonomic mobile robot with additive bounded disturbance. To reduce the negative effects of disturbance, and drive the state of real system closer to the one of nominal system, a robust reference signal is introduced into the cost function of MPC. In order to reduce the computation burden caused by online optimization of MPC and further improve the tracking accuracy, a dual-mode control structure consisting of the robust MPC and the local nonlinear robust control is developed, in which the local nonlinear robust control law is applied within a specified terminal region. Finally, simulation results on the nonholonomic mobile robot are presented to show the validity of the proposed control approach.
{{\copyright} 2023 John Wiley \& Sons Ltd.}Discrete gain scheduling control approach to elliptical orbit rendezvous system with actuator saturationhttps://zbmath.org/1532.930982024-05-13T19:39:47.825584Z"Gao, Xiangyu"https://zbmath.org/authors/?q=ai:gao.xiangyu"He, Dongyan"https://zbmath.org/authors/?q=ai:he.dongyan"Teo, Kok Lay"https://zbmath.org/authors/?q=ai:teo.kok-lay"Wang, Jianqiao"https://zbmath.org/authors/?q=ai:wang.jianqiao"Yang, Hongfu"https://zbmath.org/authors/?q=ai:yang.hongfuSummary: This paper studies the discrete gain scheduling control design problem of elliptical orbit spacecraft rendezvous system with actuator saturation. Due to the presence of actuator saturation, the dynamic performance of the spacecraft rendezvous system degrades significantly. In order to improve the dynamic performance of the system, a discrete gain scheduling control approach is adopted to construct a group of time-invariant ellipsoidal invariant sets, which can be used to determine the switching points of the discrete gain scheduling control. By choosing some discrete parameter values, the discrete gain scheduling control is obtained from a solution of a periodic Riccati matrix differential equation. Under the control obtained, the dynamic performance of the system is much improved while accomplishing successfully the rendezvous mission of the spacecraft. Finally, a practical example is provided to show the effectiveness of the proposed control design approach.
{{\copyright} 2022 John Wiley \& Sons Ltd.}A unified methodology for the power efficiency analysis of physical systemshttps://zbmath.org/1532.931242024-05-13T19:39:47.825584Z"Tebaldi, Davide"https://zbmath.org/authors/?q=ai:tebaldi.davide"Zanasi, Roberto"https://zbmath.org/authors/?q=ai:zanasi.robertoSummary: In this paper, the problem of power efficiency evaluation for \(n\)-ports physical systems is investigated. The efficiency analysis that we perform highlights the necessary and sufficient conditions for the system to be passive, and outlines the guidelines for the efficiency maps computation. After addressing the problem from a formal point of view, the analysis is deepened for the case of two-ports linear and nonlinear physical systems, and for the cases of three and four-ports linear systems. The efficiency analysis and the computation of the efficiency maps are addressed as a function of the power variables characterizing all the energetic ports of the considered systems. Furthermore, the salient properties of the efficiency are highlighted and discussed. The theoretical analysis which is developed is then applied to some physical systems of interest for industries and engineers working in the electromechanical, hydraulic and automotive fields: a DC electric motor driving an hydraulic pump for the two-ports systems class, a single-stage planetary gear set for the three-ports systems class, and a Ravigneaux planetary gear set for the four-ports systems class.Passivity-based control of nonlinear active dynamic vibration absorberhttps://zbmath.org/1532.931272024-05-13T19:39:47.825584Z"Hao, Sheng"https://zbmath.org/authors/?q=ai:hao.sheng"Yamashita, Yuh"https://zbmath.org/authors/?q=ai:yamashita.yuh"Kobayashi, Koichi"https://zbmath.org/authors/?q=ai:kobayashi.koichiSummary: In this article, a nonlinear active dynamic vibration absorber based on passivity-based energy shaping control is proposed. Using the proposed method, the vibrations that are excited by force and velocity disturbances simultaneously can be controlled. The control law only uses the relative displacement and velocity of the vibration system, which can be easily measured by sensors. The numerical solutions to the partial differential equations are not required in our proposed method. The main idea of the controller's parameters design is to convert a plant system with a nonlinear dynamic vibration absorber into a desired system with multiple virtual skyhook dampers. We also derive the parameters' selection guidelines for the proposed controller. The global asymptotical stability is guaranteed through passivity-based control theory, although the parameter design is based on linearization. We verify the effectiveness of the proposed controller by some simulations on a cart-pendulum system.
{{\copyright} 2023 John Wiley \& Sons Ltd.}Tracking control of nonlinear systems actuated by saturated oscillatory force generatorhttps://zbmath.org/1532.931282024-05-13T19:39:47.825584Z"Homaeinezhad, Mohammad Reza"https://zbmath.org/authors/?q=ai:homaeinezhad.mohammad-reza"Gavari, Mohammad Abbasi"https://zbmath.org/authors/?q=ai:abbasi-gavari.mohammadSummary: This research has been devoted to the construction of a permanent-stable algorithm for tracking control of a nonlinear 1-degree of freedom (DOF) mechanical system affected by a second-order vibratory constrained actuator. The dynamics of the actuator is involved in governing equation of the mechanical system, and using the two-step Adams-Bashforth and Adams-Moulton methods, the resultant continuous-time model is formulated in the discrete-time domain. The discrete-time model of the whole system is then employed in a discrete-time power reaching law-based controller architecture. Using the reaching law strategy and considering the saturation boundaries of the actuation system, various available bounds of position and velocity control signals can be determined with respect to the reaching law coefficients. Then, special optimization algorithms are employed to determine the optimal value of position and velocity power reaching law coefficients as well as the optimally modified trajectory references. The position and velocity control commands resulting from the concept of optimal trajectory reference, along with the optimal reaching law coefficient, ensure the permanent-stable tracking control of both position and velocity modes regarding the actuation constraint. In the next step, another concept, namely the optimal combined position-velocity controller, is taken into account, which is a Gaussian-weighted average of the position and velocity control commands to form the main control command of the proposed controller. Consequently, the designed controller will be a permanent-stable control approach that never violates the actuation constraint. Finally, numerical simulations are conducted to evaluate the performance of the proposed method for two types of desired inputs, including piecewise-step and harmonic trajectories. The results suggest the proposed controller efficiency in satisfying pre-determined characteristics.Nonreversible motion of a system of interacting bodies along a rough horizontal straight linehttps://zbmath.org/1532.931352024-05-13T19:39:47.825584Z"Bolotnik, N. N."https://zbmath.org/authors/?q=ai:bolotnik.nikolay-n|bolotnik.nikolai-n"Figurina, T. Yu."https://zbmath.org/authors/?q=ai:figurina.tatiana-yuThis work considers the problem of controlling the position of a set of multiple interacting bodies, starting from an initial zero displacement (and velocity) position, to a final position, along a straight line, under the constraint that the bodies do not change the direction of their motion. The friction considered is Coulomb dry friction. So in essence this is an optimal control problem. The authors address the problem in a fluent manner, following knowledge of Newton's laws, and multibody interacting mechanical systems. So any reader with a background in mechanical engineering and modeling can follow the proof, not requiring a background on optimal control.
Reviewer: Lazaros Moysis (Larisa)Hybrid control of attitude maneuver and structural vibration for a large phased array antenna satellitehttps://zbmath.org/1532.931422024-05-13T19:39:47.825584Z"Lu, Guangyu"https://zbmath.org/authors/?q=ai:lu.guangyu"Liu, Xiang"https://zbmath.org/authors/?q=ai:liu.xiang"Cai, Guoping"https://zbmath.org/authors/?q=ai:cai.guoping"Sun, Jun"https://zbmath.org/authors/?q=ai:sun.jun.4"Zhu, Dongfang"https://zbmath.org/authors/?q=ai:zhu.dongfangSummary: This paper focuses on the study about hybrid control strategy of attitude maneuver and structural vibration for a large phased array antenna satellite. The satellite system is equipped with cable actuators in the antenna structure and control moment gyros on the central satellite. Firstly, the rigid-flexible coupling dynamic model of the entire satellite system is established based on the hybrid coordinate method. Then a control strategy is presented which could realize the ideal attitude maneuver of satellite while suppressing the structural vibration simultaneously. The proposed strategy is contained of two parts: the attitude controller is designed based on the computed torque method, and the vibration controller is achieved by using a piecewise cost function which could ensure the unidirectional and saturated constraints of cable actuators. Finally, numerical simulations of a large antenna satellite model demonstrate that the structural vibration during the attitude maneuver process can be suppressed effectively by applying the proposed control strategy.An adaptive time-varying barrier Lyapunov function-based attitude tracking control for spacecrafts without angular velocity measurementhttps://zbmath.org/1532.931642024-05-13T19:39:47.825584Z"Hu, Hui"https://zbmath.org/authors/?q=ai:hu.hui"Wang, Bo"https://zbmath.org/authors/?q=ai:wang.bo.3|wang.bo.12|wang.bo.4|wang.bo.9|wang.bo.5|wang.bo.2|wang.bo.24|wang.bo.6|wang.bo|wang.bo.1"Liu, Lei"https://zbmath.org/authors/?q=ai:liu.lei"Cheng, Zhongtao"https://zbmath.org/authors/?q=ai:cheng.zhongtaoSummary: In this paper, based on a novel adaptive time-varying barrier Lyapunov function (A-TBLF), we propose an output feedback tracking controller for spacecrafts with adaptive time-varying state constraints. The adaptive time-varying barrier is adapted with the real-time constrained state but not constant or a predefined function. It is guaranteed that the constrained state converges into the predefined domain whenever it starts. Moreover, a barrier update restart scheme is designed in the A-TBLF method to prevent potential barrier violations. Furthermore, we consider the input explosion of the BLF-based controller when the state is close to the barrier. A nonlinear margin function is introduced to avoid continuous input saturation, resulting in a smooth and cost-effective control input. On the other hand, as the accurate angular velocity measurement is assumed to be unavailable, it is proposed an adaptive observer chain with finite-time estimation to the angular velocity and the lumped disturbance. Therefore, only the attitude angle is used to design the controller and the attitude tracking error can be further eliminated. Simulation results verify the effectiveness of the proposed method, and comparative simulations show the superiorities than other control methods with time-varying state constraints.
{{\copyright} 2022 John Wiley \& Sons Ltd.}Event-driven fault-tolerant attitude control of spacecraft with finite-time disturbance observer under input saturationhttps://zbmath.org/1532.932232024-05-13T19:39:47.825584Z"Amrr, Syed Muhammad"https://zbmath.org/authors/?q=ai:amrr.syed-muhammad"Saidi, Abdelaziz Salah"https://zbmath.org/authors/?q=ai:saidi.abdelaziz-salah"Nabi, M."https://zbmath.org/authors/?q=ai:nabi.mahmudun|nabi.muneer|nabi.moinSummary: This paper investigates the attitude stabilization problem for a bandwidth-constrained spacecraft subjected to model uncertainty, external disturbances, actuator faults, and saturated input. The proposed attitude controller is developed by combining the disturbance observer with an event-trigger technique to provide disturbance attenuation meanwhile respecting the constraint on the wireless control network. The proposed disturbance observer estimates the lumped disturbance within a finite time, and its output is then fed to the composite control law. The presented control scheme relaxes the use of a priori upper bound knowledge of disturbance and resolves the unwinding problem in the quaternion-based attitude representation. The closed-loop stability analysis under the proposed algorithm shows the uniformly ultimately bounded convergence of state trajectories. Moreover, the designed event trigger approach avoids the behavior. The numerical simulation with comparative analysis illustrates the efficacy of the proposed controller in terms of convergence time, steady-state bound, rate of control update, and energy consumption.
{{\copyright} 2023 John Wiley \& Sons Ltd.}Robust adaptive control for spacecraft attitude synchronization subject to external disturbances: a performance adjustable event-triggered mechanismhttps://zbmath.org/1532.932282024-05-13T19:39:47.825584Z"Hu, Wenfeng"https://zbmath.org/authors/?q=ai:hu.wenfeng"Li, Zichuang"https://zbmath.org/authors/?q=ai:li.zichuang"Dai, Ming-Zhe"https://zbmath.org/authors/?q=ai:dai.ming-zhe"Huang, Tingwen"https://zbmath.org/authors/?q=ai:huang.tingwenSummary: This article addresses the leader-following synchronization problem of multiple rigid spacecraft systems affected by external disturbances with the directed topology. An event-triggered distributed observer is proposed to estimate the leader's state. By integrating a performance adjustable function (PAF) into the event-triggered mechanism, the sampling frequency and estimation speed can be adjusted. Based on the event-triggered distributed observer, an adaptive event-triggered control scheme is proposed to aganist the external disturbances. With the adaptive event-triggered control scheme, continuous communication between spacecraft is no longer required and Zeno-free property can be guaranteed. The effectiveness of the theoretical results is verified by a numerous example.
{{\copyright} 2022 John Wiley \& Sons Ltd.}Minimum-time optimal control of robotic manipulators based on Hamel's integratorshttps://zbmath.org/1532.932682024-05-13T19:39:47.825584Z"An, Zhipeng"https://zbmath.org/authors/?q=ai:an.zhipeng"Wu, Huibin"https://zbmath.org/authors/?q=ai:wu.huibin|wu.huibin.1"Shi, Donghua"https://zbmath.org/authors/?q=ai:shi.donghuaSummary: In this paper, we develop a framework of time optimization path planning for robotic manipulators surrounded by static obstacles. Our approach is based on the recursive dynamics method and Hamel's integrators. We adopt the linear programming techniques to solve the problem of the collision avoidance expressed as state constraints. The resulting algorithm is simple to implement and the performance of this approach is demonstrated through two examples. Numerical results are shown to validate the efficiency of the proposed algorithm.On input-to-state stability Lyapunov functions for mechanical systemshttps://zbmath.org/1532.933042024-05-13T19:39:47.825584Z"Aleksandrov, Alexander"https://zbmath.org/authors/?q=ai:aleksandrov.aleksandr-yurevich"Efimov, Denis"https://zbmath.org/authors/?q=ai:efimov.denis-v"Dashkovskiy, Sergey"https://zbmath.org/authors/?q=ai:dashkovskiy.sergey-nSummary: For two canonical models of mechanical systems with disturbances presented by Rayleigh- and Liénard-type equations, several designs of Lyapunov functions are investigated. Under given restrictions, the existence of these functions implies global or local input-to-state stability property for the systems. The proposed stability conditions are constructive, which is demonstrated in applications.
{{\copyright} 2022 John Wiley \& Sons Ltd.}Fast fixed-time attitude tracking control of spacecraft with prescribed performancehttps://zbmath.org/1532.933292024-05-13T19:39:47.825584Z"Zhang, Haichao"https://zbmath.org/authors/?q=ai:zhang.haichao"Chen, Zhaoyue"https://zbmath.org/authors/?q=ai:chen.zhaoyue"Xiao, Bing"https://zbmath.org/authors/?q=ai:xiao.bing"Li, Bo"https://zbmath.org/authors/?q=ai:li.bo.44Summary: The attitude tracking control problem of rigid spacecraft subjected to external disturbance and prescribed performance is studied. A fast fixed-time stability theorem is firstly developed. A continuous disturbance observer is then designed with its estimation error can be driven into a tiny neighborhood containing zero within fixed time. Moreover, the spacecraft attitude tracking error constrained by prescribed performance function is transformed into an unconstrained dynamics. A disturbance observer-based prescribed performance tracking controller is designed to stabilize the unconstrained dynamics within fixed time. It also means that the attitude tracking errors meet the prescribed performance as the stabilization of the unconstrained dynamics. Spacecraft simulation examples are finally given to validate the effectiveness of the proposed controller.
{{\copyright} 2023 John Wiley \& Sons Ltd.}Finite-time constrained attitude regulation for spacecraft formation with disturbances on \(SO(3)\)https://zbmath.org/1532.933322024-05-13T19:39:47.825584Z"Zhu, Shengjie"https://zbmath.org/authors/?q=ai:zhu.shengjie"Zhang, Yuanyuan"https://zbmath.org/authors/?q=ai:zhang.yuanyuan.1"Zong, Xiaofeng"https://zbmath.org/authors/?q=ai:zong.xiaofeng"Li, Renfu"https://zbmath.org/authors/?q=ai:li.renfuSummary: This paper addresses the finite-time constrained attitude regulation problem for spacecraft formation with disturbances on \(SO(3)\). An artificial potential function (APF) is constructed based on the rotation matrix to handle the attitude constraints. By combining the terminal sliding mode control technique with the APF, a robust control law is proposed to achieve the almost globally constrained attitude regulation for spacecraft formation with disturbances in finite time. Then a leader-following robust control law is developed using a modified finite-time distributed observer when some spacecraft cannot obtain the desired attitude directly. Based on the Lyapunov stability theory and Artstein's transformation, the sufficient conditions are strictly derived for spacecraft formation to guarantee the almost globally leader-following finite-time constrained attitude regulation with disturbances and communication delay. Numerical simulations are presented to demonstrate the effectiveness of the proposed control laws.
{{\copyright} 2023 John Wiley \& Sons Ltd.}Global consensus-based formation control of perturbed nonholonomic mobile robots with time varying delayshttps://zbmath.org/1532.933412024-05-13T19:39:47.825584Z"Romero, Jose Guadalupe"https://zbmath.org/authors/?q=ai:romero.jose-guadalupe"Nuño, Emmanuel"https://zbmath.org/authors/?q=ai:nuno.emmanuel"Aldana, Carlos I."https://zbmath.org/authors/?q=ai:aldana.carlos-iSummary: This paper proposes a smooth time-variant PID-like control scheme for networks composed of nonholonomic vehicles modeled as differential drive robots affected by \textit{unknown} input constant disturbances and transmission variable \textit{time-delays} in the communication channel. Using Barbalat's Lemma and under the fact that the interconnecting graph is undirected and connected, it is proved that all robots positions asymptotically converge to a position in a given desired formation and they all agree on the center of this formation, while the orientations asymptotically reach a consensus value. Besides, it is proved that given the structure of the proposed \textit{new integral} action, the external constant disturbances are rejected (exactly estimated) and that velocities converge to zero. Simulation results, with a robot network composed of eight nonholonomic vehicles and considering disturbances subjected to step changes, are presented to illustrate the robustness of the proposed control scheme.