Recent zbMATH articles in MSC 78https://zbmath.org/atom/cc/782022-09-13T20:28:31.338867ZWerkzeugEmbedded eigenvalues of the Neumann problem in a strip with a box-shaped perturbationhttps://zbmath.org/1491.351322022-09-13T20:28:31.338867Z"Cardone, Giuseppe"https://zbmath.org/authors/?q=ai:cardone.giuseppe"Durante, T."https://zbmath.org/authors/?q=ai:durante.tiziana"Nazarov, S. A."https://zbmath.org/authors/?q=ai:nazarov.sergei-aleksandrovichSummary: We consider the spectral Neumann problem for the Laplace operator in an acoustic waveguide \(\Pi_l^\varepsilon\) formed by the union of an infinite strip and a narrow box-shaped perturbation of size \(2l\times\varepsilon\), where \(\varepsilon>0\) is a small parameter. We prove the existence of the length parameter \(l_k^\varepsilon=\pi k+O(\varepsilon)\) with any \(k=1,2,3,\dots\) such that the waveguide \(\Pi_{l_k^\varepsilon}^\varepsilon\) supports a trapped mode with an eigenvalue \(\lambda_k^\varepsilon=\pi^2-4\pi^4 l^2\varepsilon^2+O(\varepsilon^3)\) embedded into the continuous spectrum. This eigenvalue is unique in the segment \([0,\pi^2]\), and it is absent in the case \(l\neq l_k^\varepsilon\). The detection of this embedded eigenvalue is based on a criterion for trapped modes involving an artificial object, the augmented scattering matrix. The main difficulty is caused by the rather specific shape of the perturbed wall \(\partial\Pi_l^\varepsilon\), namely a narrow rectangular bulge with corner points, and we discuss available generalizations for other piecewise smooth boundaries.Analysis and computation of the transmission eigenvalues with a conductive boundary conditionhttps://zbmath.org/1491.351392022-09-13T20:28:31.338867Z"Harris, I."https://zbmath.org/authors/?q=ai:harris.isaac"Kleefeld, A."https://zbmath.org/authors/?q=ai:kleefeld.andreasThe authors consider the transmission eigenvalue problem with conductive boundary conditions, where we look for \(k \in \mathbb{C}\) and non-trivial \((w,v) \in L^2(D) \times L^2(D)\) such that
\[\begin{split}& \Delta w +k^2 n w=0, \quad \Delta v + k^2 v=0 \quad\text{in}\quad D, \\
&w-v=0, \quad {\partial_{\nu} w}-{\partial_\nu v}= \eta v \quad \text{on} \quad \partial D,
\end{split}\]
with \(w-v \in H^2(D) \cap H^1_0(D)\) (endowed with \(\| \cdot \| = \|\Delta \cdot \|_{L^2(D)}\)), considering \(D \subset \mathbb{R}^d\) (\(d = 2, 3\)) to be a bounded simply connected open set, with \(\nu\) being the unit outward normal to the boundary \(\partial D\) which is smooth enough so that the well-posedness estimate for the Poisson problem and the \(H^2\) elliptic regularity estimate hold. Here, the refractive index \(n(x)\) is considered as a scalar bounded real-valued function defined in \(D\) and the conductivity parameter \(\eta (x)\) is a scalar bounded real-valued function defined on the boundary \(\partial D\).
This is studied both analytically and numerically. The authors use the variational method to deduce the theoretical results. In particular, it is exhibited that there is a lower bound on the real transmission eigenvalues provided \(\eta\) is strictly positive on \(\partial D\) and \(n-1\) is either uniformly positive or negative in \(D\). In addition, the convergence as \(\eta\) tends to infinity is analysed. Boundary integral equations for various interior transmission eigenvalue problems are derived and used in the included numerical experiments, being possible to compute multiple interior transmission eigenvalue problems with a constant refractive index. Moreover, taking profit from the limiting behavior, numerical estimates of the refractive index are presented.
Reviewer: Luis Filipe Pinheiro de Castro (Aveiro)Soliton resolution for the Wadati-Konno-Ichikawa equation with weighted Sobolev initial datahttps://zbmath.org/1491.353062022-09-13T20:28:31.338867Z"Li, Zhi-Qiang"https://zbmath.org/authors/?q=ai:li.zhiqiang.1"Tian, Shou-Fu"https://zbmath.org/authors/?q=ai:tian.shoufu"Yang, Jin-Jie"https://zbmath.org/authors/?q=ai:yang.jinjieSummary: In this work, we employ the \(\bar{\partial}\)-steepest descent method to investigate the Cauchy problem of the Wadati-Konno-Ichikawa (WKI) equation with initial conditions in weighted Sobolev space \(\mathcal{H}(\mathbb{R})\). The long time asymptotic behavior of the solution \(q(x, t)\) is derived in a fixed space-time cone \(S(y_1,y_2,v_1,v_2)=\{(y,t)\in\mathbb{R}^2: y=y_0+vt, ~y_0\in [y_1,y_2], v\in [v_1,v_2]\}\). Based on the resulting asymptotic behavior, we prove the soliton resolution conjecture of the WKI equation which includes the soliton term confirmed by \(N(\mathcal{I})\)-soliton on discrete spectrum and the \(t^{-\frac{1}{2}}\) order term on continuous spectrum with residual error up to \(O(t^{-\frac{3}{4}})\).On a higher integral invariant for closed magnetic lines, revisitedhttps://zbmath.org/1491.353292022-09-13T20:28:31.338867Z"Akhmet'ev, Peter M."https://zbmath.org/authors/?q=ai:akhmetev.petr-mSummary: We recall a definition of an asymptotic invariant of classical link, which is called \(M\)-invariant. \(M\)-invariant is a special Massey integral, this integral has an ergodic form and is generalized for magnetic fields with open magnetic lines in a bounded \(3D\)-domain. We present a proof that this integral is well defined. A combinatorial formula for \(M\)-invariant using the Conway polynomial is presented. The \(M\)-invariant is a higher invariant, it is not a function of pairwise linking numbers of closed magnetic lines. We discuss applications of \(M\)-invariant for MHD.Continued gravitational collapse for gaseous star and pressureless Euler-Poisson systemhttps://zbmath.org/1491.353372022-09-13T20:28:31.338867Z"Huang, Feimin"https://zbmath.org/authors/?q=ai:huang.feimin"Yao, Yue"https://zbmath.org/authors/?q=ai:yao.yueInexact GMRES iterations and relaxation strategies with fast-multipole boundary element methodhttps://zbmath.org/1491.353502022-09-13T20:28:31.338867Z"Wang, Tingyu"https://zbmath.org/authors/?q=ai:wang.tingyu"Layton, Simon K."https://zbmath.org/authors/?q=ai:layton.simon-k"Barba, Lorena A."https://zbmath.org/authors/?q=ai:barba.lorena-aSummary: Boundary element methods produce dense linear systems that can be accelerated via multipole expansions. Solved with Krylov methods, this implies computing the matrix-vector products within each iteration with some error, at an accuracy controlled by the order of the expansion, \(p\). We take advantage of a unique property of Krylov iterations that allows lower accuracy of the matrix-vector products as convergence proceeds, and propose a relaxation strategy based on progressively decreasing \(p\). In extensive numerical tests of the relaxed Krylov iterations, we obtained speed-ups of between \(1.5 \times\) and \(2.3 \times\) for Laplace problems and between \(2.7 \times\) and \(3.3 \times\) for Stokes problems. We include an application to Stokes flow around red blood cells, computing with up to 64 cells and problem size up to 131k boundary elements and nearly 400k unknowns. The study was done with an in-house multi-threaded C++ code, on a hexa-core CPU. The code is available on its version-control repository, \url{https://github.com/barbagroup/fmm-bem-relaxed}, and we share reproducibility packages for all results in \url{https://github.com/barbagroup/inexact-gmres/}.A canonical model of the one-dimensional dynamical Dirac system with boundary controlhttps://zbmath.org/1491.353682022-09-13T20:28:31.338867Z"Belishev, Mikhail I."https://zbmath.org/authors/?q=ai:belishev.mikhail-igorevitch"Simonov, Sergey A."https://zbmath.org/authors/?q=ai:simonov.sergey-aSummary: The one-dimensional Dirac dynamical system \(\Sigma\) is
\[
iu_t+i\sigma_3\, u_x+Vu = 0, \quad x, t>0; \quad u|_{t = 0} = 0, \quad x>0; \quad u_1|_{x = 0} = f, \quad t>0,
\] where \(\sigma_3 = \begin{pmatrix}1&0 \\ 0&-1\end{pmatrix}\) is the Pauli matrix; \(V = \begin{pmatrix}0&p\\ \bar{p}&0\end{pmatrix}\) with \(p = p(x)\) is a potential; \(u = \begin{pmatrix}u_1^f(x, t) \\ u_2^f(x, t)\end{pmatrix}\) is the trajectory in \(\mathscr{H} = L_2(\mathbb{R}_+;\mathbb{C}^2); \, f\in\mathscr{F} = L_2([0, \infty);\mathbb{C})\) is a boundary control. System \(\Sigma\) is not controllable: the total reachable set \(\mathscr{U} = \mathrm{span}_{t>0}\{u^f(\cdot, t)\, |\, \, f \in \mathscr{F} \}\) is not dense in \(\mathscr{H}\), but contains a controllable part \(\Sigma_u\). We construct a dynamical system \(\Sigma_a\), which is controllable in \(L_2(\mathbb{R}_+;\mathbb{C})\) and connected with \(\Sigma_u\) via a unitary transform. The construction is based on geometrical optics relations: trajectories of \(\Sigma_a\) are composed of jump amplitudes that arise as a result of projecting in \(\overline{\mathscr{U}}\) onto the reachable sets \(\mathscr{U}^t = \{u^f(\cdot, t)\, |\, \, f\in \mathscr{F}\}\). System \(\Sigma_a\), which we call the \textit{amplitude model} of the original \(\Sigma\), has the same input/output correspondence as system \(\Sigma\). As such, \(\Sigma_a\) provides a canonical completely reachable realization of the Dirac system.Integrability, modulational instability and mixed localized wave solutions for the generalized nonlinear Schrödinger equationhttps://zbmath.org/1491.353942022-09-13T20:28:31.338867Z"Li, Xinyue"https://zbmath.org/authors/?q=ai:li.xinyue"Han, Guangfu"https://zbmath.org/authors/?q=ai:han.guangfu"Zhao, Qiulan"https://zbmath.org/authors/?q=ai:zhao.qiulanSummary: Under investigation in this paper is the generalized nonlinear Schrödinger (g-NLS) equation which has extensive applications in various physical fields. Firstly, we prove Liouville integrability of this equation by deriving its bi-Hamiltonian structures applying the variational identity. Nextly, we calculate the modulational instability for the possible reason of the formation of the rogue wave. Moreover, based on the generalized \((2, N-2)\)-fold Darboux transformation (DT), we can derive several mixed localized wave solutions such as breathers, rogue waves and semi-rational solitons for this equation, and accurately analyze a lot of important physical quantities. Finally, we present these solutions graphically by choosing appropriate parameters and discuss their dynamic behavior. It is worth noting that all of these solutions can change from a strong interaction to a weak interaction by choosing the parameters. This may also be one of the reasons why relevant wave structures presenting diversity, and useful to explain some physical phenomena in nonlinear optics.Optical solitons in fiber Bragg gratings with quadratic-cubic law of nonlinear refractive index and cubic-quartic dispersive reflectivityhttps://zbmath.org/1491.353972022-09-13T20:28:31.338867Z"Zayed, Elsayed M. E."https://zbmath.org/authors/?q=ai:zayed.elsayed-m-e"Alngar, Mohamed E. M."https://zbmath.org/authors/?q=ai:alngar.mohamed-e-m"Biswas, Anjan"https://zbmath.org/authors/?q=ai:biswas.anjan"Ekici, Mehmet"https://zbmath.org/authors/?q=ai:ekici.mehmet"Khan, Salam"https://zbmath.org/authors/?q=ai:khan.salam"Alzahrani, Abdullah K."https://zbmath.org/authors/?q=ai:alzahrani.abdullah-khamis-hassan"Belic, Milivoj R."https://zbmath.org/authors/?q=ai:belic.milivoj-rSummary: This paper recovers cubic-quartic perturbed solitons in fiber Bragg gratings with quadratic-cubic law nonlinear refractive index. The unified Riccati equation expansion method and the modified Kudryashov's approach make this retrieval of soliton solutions possible. The parameter constraints, for the existence of such solitons, are also presented.Time-dependent electromagnetic scattering from thin layershttps://zbmath.org/1491.354082022-09-13T20:28:31.338867Z"Nick, Jörg"https://zbmath.org/authors/?q=ai:nick.jorg"Kovács, Balázs"https://zbmath.org/authors/?q=ai:kovacs.balazs"Lubich, Christian"https://zbmath.org/authors/?q=ai:lubich.christianSummary: The scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this includes a thin coating around a perfect conductor and the skin effect of a highly conducting material. The approach taken in this work is to derive, analyse and discretize a system of time-dependent boundary integral equations that determines the tangential traces of the scattered electric and magnetic fields. In a familiar second step, the fields are evaluated in the exterior domain by a representation formula, which uses the time-dependent potential operators of Maxwell's equations. The time-dependent boundary integral equation is discretized with Runge-Kutta based convolution quadrature in time and Raviart-Thomas boundary elements in space. Using the frequency-explicit bounds from the well-posedness analysis given here together with known approximation properties of the numerical methods, the full discretization is proved to be stable and convergent, with explicitly given rates in the case of sufficient regularity. Taking the same Runge-Kutta based convolution quadrature for discretizing the time-dependent representation formulas, the optimal order of convergence is obtained away from the scattering boundary, whereas an order reduction occurs close to the boundary. The theoretical results are illustrated by numerical experiments.Coupled domain-boundary variational formulations for Hodge-Helmholtz operatorshttps://zbmath.org/1491.354092022-09-13T20:28:31.338867Z"Schulz, Erick"https://zbmath.org/authors/?q=ai:schulz.erick"Hiptmair, Ralf"https://zbmath.org/authors/?q=ai:hiptmair.ralfSummary: We couple the mixed variational problem for the generalized Hodge-Helmholtz or Hodge-Laplace equation posed on a bounded 3D Lipschitz domain with the first-kind boundary integral equations arising from the latter when constant coefficients are assumed in the unbounded complement. Recently developed Calderón projectors for the relevant boundary integral operators are used to perform a symmetric coupling. We prove stability of the coupled problem away from resonant frequencies by establishing a generalized Gårding inequality (T-coercivity). The resulting system of equations describes the scattering of monochromatic electromagnetic waves at a bounded inhomogeneous isotropic body possibly having a ``rough'' surface. The low-frequency robustness of the potential formulation of Maxwell's equations makes this model a promising starting point for Galerkin discretization.Stability for quantitative photoacoustic tomography revisitedhttps://zbmath.org/1491.354492022-09-13T20:28:31.338867Z"Bonnetier, Eric"https://zbmath.org/authors/?q=ai:bonnetier.eric"Choulli, Mourad"https://zbmath.org/authors/?q=ai:choulli.mourad"Triki, Faouzi"https://zbmath.org/authors/?q=ai:triki.faouziSummary: This paper deals with the issue of stability in determining the absorption and the diffusion coefficients in quantitative photoacoustic imaging. We establish a global conditional Hölder stability inequality from the knowledge of two internal data obtained from optical waves, generated by two point sources in a region where the optical coefficients are known.The linear sampling method for penetrable cylinder with inclusions for obliquely incident polarized electromagnetic waveshttps://zbmath.org/1491.354512022-09-13T20:28:31.338867Z"Deng, Xia"https://zbmath.org/authors/?q=ai:deng.xia"Guo, Jun"https://zbmath.org/authors/?q=ai:guo.jun"Li, Jin"https://zbmath.org/authors/?q=ai:li.jin|li.jin.4|li.jin.1|li.jin.3|li.jin.5|li.jin.2"Yan, Guozheng"https://zbmath.org/authors/?q=ai:yan.guozhengSummary: Consider the scattering of electromagnetic waves by a penetrable homogeneous cylinder at oblique incident. The Maxwell equations are then reduced to a system of a pair of the two-dimensional Helmholtz equations for \(z\)-components of the electric and magnetic field through coupled oblique boundary conditions. This paper studies an inverse problem of recovering the penetrable obstacle from the far-field pattern of the electric field. The well-known linear sampling method is used to solve this problem. Compared with the usual inverse scattering problem, the coupled system and the oblique derivative boundary condition bring difficulties in theoretical analysis. Some numerical examples are presented to illustrate the validity and feasibility of the proposed method.Series reversion in Calderón's problemhttps://zbmath.org/1491.354562022-09-13T20:28:31.338867Z"Garde, Henrik"https://zbmath.org/authors/?q=ai:garde.henrik"Hyvönen, Nuutti"https://zbmath.org/authors/?q=ai:hyvonen.nuuttiSummary: This work derives explicit series reversions for the solution of Calderón's problem. The governing elliptic partial differential equation is \(\nabla \cdot (A\nabla u)=0\) in a bounded Lipschitz domain and with a matrix-valued coefficient. The corresponding forward map sends \(A\) to a projected version of a local Neumann-to-Dirichlet operator, allowing for the use of partial boundary data and finitely many measurements. It is first shown that the forward map is analytic, and subsequently reversions of its Taylor series up to specified orders lead to a family of numerical methods for solving the inverse problem with increasing accuracy. The convergence of these methods is shown under conditions that ensure the invertibility of the Fréchet derivative of the forward map. The introduced numerical methods are of the same computational complexity as solving the linearised inverse problem. The analogous results are also presented for the smoothened complete electrode model.Method of orthogonal polynomials for an approximate solution of singular integro-differential equations as applied to two-dimensional diffraction problemshttps://zbmath.org/1491.450162022-09-13T20:28:31.338867Z"Rasol'ko, G. A."https://zbmath.org/authors/?q=ai:rasolko.galina-alekseevna"Volkov, V. M."https://zbmath.org/authors/?q=ai:volkov.vasilii-mikhailovichSummary: We consider a mathematical model of scattering of \(H \)-polarized electromagnetic waves by a screen with a curvilinear boundary based on a singular integro-differential equation with a Cauchy kernel and a logarithmic singularity. The integrands contain both the unknown function and its first derivative. For the numerical analysis of this model, two computational schemes are constructed based on the representation of the unknown function in the form of a linear combination of orthogonal Chebyshev polynomials and spectral relations, which permit one to obtain simple analytical expressions for the singular component of the equation. The expansion coefficients of the solution in terms of the basis of Chebyshev polynomials are calculated as a solution of the corresponding system of linear algebraic equations. The results of numerical experiments show that the error in the approximate solution on a grid of 20--30 nodes does not exceed the roundoff error.Optimal shape of stellarators for magnetic confinement fusionhttps://zbmath.org/1491.490312022-09-13T20:28:31.338867Z"Privat, Yannick"https://zbmath.org/authors/?q=ai:privat.yannick"Robin, Rémi"https://zbmath.org/authors/?q=ai:robin.remi"Sigalotti, Mario"https://zbmath.org/authors/?q=ai:sigalotti.marioSummary: We are interested in the design of stellarators, devices for the production of controlled nuclear fusion reactions alternative to tokamaks. The confinement of the plasma is entirely achieved by a helical magnetic field created by the complex arrangement of coils fed by high currents around a toroidal domain. Such coils describe a surface called ``coil winding surface'' (CWS). In this paper, we model the design of the CWS as a shape optimization problem, so that the cost functional reflects both optimal plasma confinement properties, through a least square discrepancy, and also manufacturability, thanks to geometrical terms involving the lateral surface or the curvature of the CWS.
We completely analyze the resulting problem: on the one hand, we establish the existence of an optimal shape, prove the shape differentiability of the criterion, and provide the expression of the differential in a workable form. On the other hand, we propose a numerical method and perform simulations of optimal stellarator shapes. We discuss the efficiency of our approach with respect to the literature in this area.A space-time Trefftz discontinuous Galerkin method for the linear Schrödinger equationhttps://zbmath.org/1491.650932022-09-13T20:28:31.338867Z"Gómez, Sergio"https://zbmath.org/authors/?q=ai:gomez.sergio-alejandro"Moiola, Andrea"https://zbmath.org/authors/?q=ai:moiola.andreaThis paper proposes and analyzes a space-time Trefftz discontinuous Galerkin method for the Schrödinger equation with piecewise-constant potential. The main feature of Trefftzmethods is that they seek approximations in spaces spanned by local solutions ofthe PDE considered. This typically requires nonpolynomial basis functions. Trefftz scheme allows for much faster convergence in terms of degrees of freedom than classical polynomial DG schemes.This approach to the Trefftz approximation theory is completelydifferent from that used for the Helmholtz equation. The well-posedness and quasi-optimality of theTrefftz-DG approximation for arbitrary dimensions and discrete Trefftz subspaces are proved.The error analysis for discrete subspaces spanned by complexexponentials satisfying the Schrödinger equation is presented. Some numerical experiments validatethe theoretical results presented.
Reviewer: Yan Xu (Hefei)Numerical analysis for Maxwell obstacle problems in electric shieldinghttps://zbmath.org/1491.650942022-09-13T20:28:31.338867Z"Hensel, Maurice"https://zbmath.org/authors/?q=ai:hensel.maurice"Yousept, Irwin"https://zbmath.org/authors/?q=ai:yousept.irwinThis paper discusses a finite element method for a Maxwell obstacle problem in electric shielding. The approach relies on the leapfrog time-stepping and the Nedelec edge elements in which no additional nonlinear solver is required for the computation of the discrete evolutionary variational inequality of Ampere-Maxwell type. \(L^1\) and \(L^2\) stability are discussed and several numerical experiments are included.
Reviewer: Marius Ghergu (Dublin)Non-symmetric isogeometric FEM-BEM couplingshttps://zbmath.org/1491.651332022-09-13T20:28:31.338867Z"Elasmi, Mehdi"https://zbmath.org/authors/?q=ai:elasmi.mehdi"Erath, Christoph"https://zbmath.org/authors/?q=ai:erath.christoph"Kurz, Stefan"https://zbmath.org/authors/?q=ai:kurz.stefanSummary: We present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting of two disjoint domains. We consider the Finite Element Method in the bounded domains to simulate possibly non-linear materials. The Boundary Element Method is applied in unbounded or thin domains where the material behavior is linear. The isogeometric framework allows to combine different design and analysis tools: first, we consider the same type of NURBS parameterizations for an exact geometry representation and second, we use the numerical analysis for the Galerkin approximation. Moreover, it facilitates to perform \(h\)- and \(p\)-refinements. For the sake of analysis, we consider the framework of strongly monotone and Lipschitz continuous operators to ensure well-posedness of the coupled system. Furthermore, we provide a priori error estimates. We additionally show an improved convergence behavior for the errors in functionals of the solution that may double the rate under certain assumptions. Numerical examples conclude the work which illustrate the theoretical results.Multiscale scattering in nonlinear Kerr-type mediahttps://zbmath.org/1491.651482022-09-13T20:28:31.338867Z"Maier, Roland"https://zbmath.org/authors/?q=ai:maier.roland|maier.roland.1"Verfürth, Barbara"https://zbmath.org/authors/?q=ai:verfurth.barbaraSummary: We propose a multiscale approach for a nonlinear Helmholtz problem with possible oscillations in the Kerr coefficient, the refractive index, and the diffusion coefficient. The method does not rely on structural assumptions on the coefficients and combines the multiscale technique known as Localized Orthogonal Decomposition with an adaptive iterative approximation of the nonlinearity. We rigorously analyze the method in terms of well-posedness and convergence properties based on suitable assumptions on the initial data and the discretization parameters. Numerical examples illustrate the theoretical error estimates and underline the practicability of the approach.Coupled iterative analysis for stationary inductionless magnetohydrodynamic system based on charge-conservative finite element methodhttps://zbmath.org/1491.651542022-09-13T20:28:31.338867Z"Zhang, Xiaodi"https://zbmath.org/authors/?q=ai:zhang.xiaodi"Ding, Qianqian"https://zbmath.org/authors/?q=ai:ding.qianqianSummary: This paper considers charge-conservative finite element approximation and three coupled iterations of stationary inductionless magnetohydrodynamics equations in Lipschitz domain. Using a mixed finite element method, we discretize the hydrodynamic unknowns by stable velocity-pressure finite element pairs, discretize the current density and electric potential by \(\boldsymbol{H}(\operatorname{div},\varOmega)\times L^2(\varOmega)\)-comforming finite element pairs. The well-posedness of this formula and the optimal error estimate are provided. In particular, we show that the error estimates for the velocity, the current density and the pressure are independent of the electric potential. With this, we propose three coupled iterative methods: Stokes, Newton and Oseen iterations. Rigorous analysis of convergence and stability for different iterative schemes are provided, in which we improve the stability conditions for both Stokes and Newton iterative method. Numerical results verify the theoretical analysis and show the applicability and effectiveness of the proposed methods.An integral equation formulation of the \(N\)-body dielectric spheres problem. II: Complexity analysishttps://zbmath.org/1491.651652022-09-13T20:28:31.338867Z"Bramas, Bérenger"https://zbmath.org/authors/?q=ai:bramas.berenger"Hassan, Muhammad"https://zbmath.org/authors/?q=ai:hassan.muhammad"Stamm, Benjamin"https://zbmath.org/authors/?q=ai:stamm.benjaminSummary: This article is the second in a series of two papers concerning the mathematical study of a boundary integral equation of the second kind that describes the interaction of \(N\) dielectric spherical particles undergoing mutual polarisation. The first article presented the numerical analysis of the Galerkin method used to solve this boundary integral equation and derived \(N\)-independent convergence rates for the induced surface charges and total electrostatic energy. The current article will focus on computational aspects of the algorithm. We provide a convergence analysis of the iterative method used to solve the underlying linear system and show that the number of liner solver iterations required to obtain a solution is independent of \(N\). Additionally, we present two linear scaling solution strategies for the computation of the approximate induced surface charges. Finally, we consider a series of numerical experiments designed to validate our theoretical results and explore the dependence of the numerical errors and computational cost of solving the underlying linear system on different system parameters.
For Part I, see [\textit{M. Hassan} and \textit{B. Stamm}, ESAIM, Math. Model. Numer. Anal. 55, 65--102 (2021; Zbl 1491.65170)].On the inverse problem for Channell collisionless plasma equilibriahttps://zbmath.org/1491.760982022-09-13T20:28:31.338867Z"Allanson, Oliver"https://zbmath.org/authors/?q=ai:allanson.oliver"Troscheit, Sascha"https://zbmath.org/authors/?q=ai:troscheit.sascha"Neukirch, Thomas"https://zbmath.org/authors/?q=ai:neukirch.thomasSummary: Vlasov-Maxwell equilibria are described by the self-consistent solutions of the time-independent Maxwell equations for the real-space dynamics of electromagnetic fields and the Vlasov equation for the phase-space dynamics of particle distribution functions (DFs) in a collisionless plasma. These two systems (macroscopic and microscopic) are coupled via the source terms in Maxwell's equations, which are sums of velocity-space `moment' integrals of the particle DF. This paper considers a particular subset of solutions of the broad plasma physics problem: `the inverse problem for collisionless equilibria' (IPCE), viz. \textit{`given information regarding the macroscopic configuration of a collisionless plasma equilibrium, what self-consistent equilibrium DFs exist?'} We introduce the constants of motion approach to IPCE using the assumptions of a `modified Maxwellian' DF, and a strictly neutral and spatially one-dimensional plasma, and this is consistent with `\textit{P. J. Channell}'s method' [``Exact Vlasov-Maxwell equilibria with sheared magnetic fields'', Phys. Fluids 19, No. 10, 1541--1545 (1976; \url{doi:10.1063/1.861357})]. In such circumstances, IPCE formally reduces to the inversion of Weierstrass transformations [\textit{G. G. Bilodeau}, Duke Math. J. 29, 293--308 (1962; Zbl 0154.38003)]. These are the same transformations that feature in the initial value problem for the heat/diffusion equation. We discuss the various mathematical conditions that a candidate solution of IPCE must satisfy. One method that can be used to invert the Weierstrass transform is expansions in Hermite polynomials. Building on the results of \textit{O. Allanson} et al. [``From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials'', J. Plasma Phys. 82, No. 3, Article ID 905820306, 28 p. (2016; \url{doi:10.1017/S0022377816000519})], we establish under what circumstances a solution obtained by these means converges and allows velocity moments of all orders. Ever since the seminal work by \textit{I. B. Bernstein} et al. [Phys. Rev., II. Ser. 108, 546--550 (1957; Zbl 0081.44904)] on `stationary' electrostatic plasma waves, the necessary quality of non-negativity has been noted as a feature that any candidate solution of IPCE will not \textit{a priori} satisfy. We discuss this problem in the context of Channell equilibria, for magnetized plasmas.Fourier theory in optics and optical information processinghttps://zbmath.org/1491.780012022-09-13T20:28:31.338867Z"Yatagai, Toyohiko"https://zbmath.org/authors/?q=ai:yatagai.toyohikoPublisher's description: Fourier analysis is one of the most important concepts when you apply physical ideas to engineering issues. This book provides a comprehensive understanding of Fourier transform and spectral analysis in optics, image processing, and signal processing. Written by a world renowned author, this book looks to unify the readers understanding of principles of optics, information processing and measurement. This book describes optical imaging systems through a linear system theory. The book also provides an easy understanding of Fourier transform and system theory in optics. It also provides background of optical measurement and signal processing. Finally, the author also provides a systematic approach to learning many signal processing techniques in optics. The book is intended for researchers, industry professionals, and graduate level students in optics and information processing.Nine equilibrium points of four point charges on the planehttps://zbmath.org/1491.780022022-09-13T20:28:31.338867Z"Lee, Tsung-Lin"https://zbmath.org/authors/?q=ai:lee.tsung-lin"Tsai, Ya-Lun"https://zbmath.org/authors/?q=ai:tsai.ya-lunSummary: We find a specific configuration for four point charges on the plane and show, with charge values in a small region, there are nine equilibrium points on the same plane, which reaches the claimed upper bound of Maxwell's conjecture. A procedure of computing bifurcation curves is presented for assisting in locating the region in the parameter space yielding the nine equilibrium points.Propagation of a terahertz Bessel vortex beam through a homogeneous magnetized plasma slabhttps://zbmath.org/1491.780032022-09-13T20:28:31.338867Z"Li, Haiying"https://zbmath.org/authors/?q=ai:li.haiying"Ding, Wei"https://zbmath.org/authors/?q=ai:ding.wei"Liu, Jiawei"https://zbmath.org/authors/?q=ai:liu.jiawei"Ying, Ci"https://zbmath.org/authors/?q=ai:ying.ci"Bai, Lu"https://zbmath.org/authors/?q=ai:bai.lu"Wu, Zhensen"https://zbmath.org/authors/?q=ai:wu.zhensenSummary: This paper provides an analytic method to study propagation characteristics of a linearly polarized Bessel vortex beam through a homogeneous magnetized plasma slab. The incident Bessel vortex beam, as well as the reflected, transmitted and internal fields are expanded in terms of cylindrical vector wave functions (CVWFs). The effects of plasma thickness, electron density and magnetic induction strength on the contour profiles of the reflected and transmitted beams and orbital angular momentum (OAM) spectra are analyzed and discussed in detail. In particular, the magnetic induction strength has a significant impact on the polarization of the transmitted beam, but not on OAM state distribution. The channel capacity of THz OAM multiplexing decreases with an increase of plasma thickness and electron density.Two-dimensional resistive-wall impedance with finite thickness: its mathematical structures and their physical meaningshttps://zbmath.org/1491.780042022-09-13T20:28:31.338867Z"Shobuda, Yoshihiro"https://zbmath.org/authors/?q=ai:shobuda.yoshihiroSummary: When the skin depth is greater than the chamber thickness for relativistic beams, the two-dimensional longitudinal resistive-wall impedance of a cylindrical chamber with a finite thickness decreases proportionally to the frequency. The phenomenon is commonly interpreted as electromagnetic fields leaking out of the chamber over a frequency range. However, the relationship between the wall current on the chamber and the leakage fields from the chamber is unclear because the naive resistive-wall impedance formula does not dynamically express how the wall current converts to the leakage fields when the skin depth exceeds the chamber thickness. A prestigious textbook[1] re-expressed the resistive-wall impedance via a parallel circuit model with the resistive-wall and inductive terms to provide a dynamic picture of the phenomenon. However, there are some flaws in the formula. This study highlights them from a fundamental standpoint, and provides a more appropriate and rigorous picture of the longitudinal resistive-wall impedance with finite thickness. To demonstrate their physical meaning, we re-express the longitudinal impedance for non-relativistic beams, as well as the transverse resistive-wall impedance including space charge impedance based on a parallel circuit model.Time-averaged potential for molecular ions in three-dimensional radio frequency trapshttps://zbmath.org/1491.780052022-09-13T20:28:31.338867Z"Rudyi, Semyon"https://zbmath.org/authors/?q=ai:rudyi.semyon"Rozhdestvensky, Yuri"https://zbmath.org/authors/?q=ai:rozhdestvensky.yuriSummary: This study deals with distinctive features of forming an effective potential for molecular ions and diatomic structures in threedimensional radio-frequency traps. A simple model is proposed, which demonstrates the transition from vibration dynamics of micromotion and micro-rotation to the time-averaged pseudopotential and rotation potential. It shows the existence of equilibrium states of a dimer molecule, which determine the stable orientation of an ion within the space of a three-dimensional Paul ion trap. Stable states and orbits for symmetrical and asymmetrical configurations were found.Propagation characteristics of non-diffracting Lommel beams in a gradient-index mediumhttps://zbmath.org/1491.780062022-09-13T20:28:31.338867Z"Hui, Yuanfei"https://zbmath.org/authors/?q=ai:hui.yuanfei"Cui, Zhiwei"https://zbmath.org/authors/?q=ai:cui.zhiwei"Song, Pan"https://zbmath.org/authors/?q=ai:song.pan(no abstract)Numerical model for atmospheric microwave absorptionhttps://zbmath.org/1491.780072022-09-13T20:28:31.338867Z"Kies, Abdelkader"https://zbmath.org/authors/?q=ai:kies.abdelkader"Dib, Anis S. Amine"https://zbmath.org/authors/?q=ai:dib.anis-s-amine"Belbachir, Abdelhafid"https://zbmath.org/authors/?q=ai:belbachir.abdelhafid"Bouamrane, Rachid"https://zbmath.org/authors/?q=ai:bouamrane.rachid(no abstract)Asymptotics for 2D whispering gallery modes in optical micro-disks with radially varying indexhttps://zbmath.org/1491.780082022-09-13T20:28:31.338867Z"Balac, Stéphane"https://zbmath.org/authors/?q=ai:balac.stephane"Dauge, Monique"https://zbmath.org/authors/?q=ai:dauge.monique"Moitier, Zoïs"https://zbmath.org/authors/?q=ai:moitier.zoisSummary: Whispering gallery modes [WGM] are resonant modes displaying special features: they concentrate along the boundary of the optical cavity at high polar frequencies and they are associated with complex scattering resonances very close to the real axis. As a classical simplification of the full Maxwell system, we consider 2D Helmholtz equations governing transverse electric or magnetic modes. Even in this 2D framework, very few results provide asymptotic expansion of WGM resonances at high polar frequency \(m\to\infty\) for cavities with radially varying optical index. In this work, using a direct Schrödinger analogy, we highlight three typical behaviors in such optical micro-disks, depending on the sign of an `effective curvature' that takes into account the radius of the disk and the values of the optical index and its derivative. Accordingly, this corresponds to abruptly varying effective potentials (step linear or step harmonic) or more classical harmonic potentials, leading to three distinct asymptotic expansions for ground state energies. Using multiscale expansions, we design a unified procedure to construct families of quasi-resonances and associate quasi-modes that have the WGM structure and satisfy eigenequations modulo a super-algebraically small residual \(\mathscr{O}(m^{-\infty})\). We show using the black box scattering approach that quasi-resonances are \(\mathscr{O}(m^{-\infty})\) close to true resonances.Hybridization of the rigorous coupled-wave approach with transformation optics for electromagnetic scattering by a surface-relief gratinghttps://zbmath.org/1491.780092022-09-13T20:28:31.338867Z"Civiletti, B. J."https://zbmath.org/authors/?q=ai:civiletti.benjamin-j"Lakhtakia, A."https://zbmath.org/authors/?q=ai:lakhtakia.akhlesh"Monk, P. B."https://zbmath.org/authors/?q=ai:monk.peter-bThe authors combine transformation optics with the rigorous coupled-wave approach, in view to study the time-harmonic Maxwell equations in a spatial domain that contains a grating, being invariant in one dimension (and so that the chosen constitutive properties allow the reduction of the full Maxwell system to a 2D Helmholtz equation for each linear polarization state). The existence of solution to the original scattering problem is obtained. A convergence analysis was included for a discretized form of the transformed problem (with respect to two different parameters), and the uniqueness of solution of this discretized problem is obtained. A numerical example was presented as a test of the convergence theory, allowing also some comparison with other known methods.
Reviewer: Luis Filipe Pinheiro de Castro (Aveiro)Defect reconstruction from magnetic flux leakage measurements employing modified cuckoo search algorithmhttps://zbmath.org/1491.780102022-09-13T20:28:31.338867Z"Zhang, Daqian"https://zbmath.org/authors/?q=ai:zhang.daqian"Huang, Chen"https://zbmath.org/authors/?q=ai:huang.chen"Fei, Jiyou"https://zbmath.org/authors/?q=ai:fei.jiyouSummary: Accurate and efficient estimation for defect profile of magnetic flux leakage (MFL) signals is important for nondestructive evaluation in industry. To improve the accuracy of defect profile reconstruction, an improved reconstruction method based on modified cuckoo search (CS), called MCS, is proposed in this paper. Firstly, a novel single-dimension updating evolution strategy is proposed to avoid the interference between multiple dimensions, which can make full use of the appropriate nest position in the historical search. Secondly, an adaptive multi-strategy difference evolution is introduced into the evolution process to improve the diversity and efficiency of CS algorithm. The proportion factor of each strategy in multi-strategy difference evolution is adjusted dynamically according to the value of the objective fitness. Finally, various MFL signals are selected to verify the effectiveness of the proposed MCS algorithm. The experiment results illustrate that the proposed method has high performance on the quality of the solution and robustness for noise.Effect of temperature sensitive ion channels on the single and multilayer network behavior of an excitable media with electromagnetic inductionhttps://zbmath.org/1491.780112022-09-13T20:28:31.338867Z"Karthikeyan, Anitha"https://zbmath.org/authors/?q=ai:karthikeyan.anitha"Moroz, Irene"https://zbmath.org/authors/?q=ai:moroz.irene-m"Rajagopal, Karthikeyan"https://zbmath.org/authors/?q=ai:rajagopal.karthikeyan"Duraisamy, Prakash"https://zbmath.org/authors/?q=ai:duraisamy.prakashSummary: The dynamical behavior of the neurons directly depends on the transition from resting to spiking states. These transitions show different types of bifurcations and has different spiking periods. The transitions are also affected by the temperature exposure of the ionic channels. To understand such effects, we investigate the Morris-Lecar (ML) neuron model with temperature affected calcium, potassium and leak current channels. The presented ML model is considered with electromagnetic field coupling considering a simple cubic memristor flux relation. Firstly the basic dynamical properties of the ML model is analyzed considering the current temperature as the control parameter. The temperature affected ionic channels in the ML model leads to various types of oscillations from periodic spiking to chaotic bursting. These bifurcation patterns are well discussed with corresponding Lyapunov exponents. To study the wave propagation in the temperature dependent ML model (TDML), we have constructed two different types of network structure. In the first a simple lattice network is considered with the local nodes of the TDML neurons and the temperature effects on the wave propagation is studied individually for the three channels. In the second type of network, we have considered inter coupled three lattice layers of TDML neurons. This discussion is subdivided in to two cases and in the first case the layers are constructed such that the first, second and third layers having temperature affected calcium, potassium and leaky current channels respectively. In the second case we considered only one channel to have temperature effects and the others have no temperature affected ion channels. The wave propagation phenomenon in both the types of network is analyzed considering the current temperature as the control parameter.Triggering recollisions with XUV pulses: imprint of recolliding periodic orbitshttps://zbmath.org/1491.780122022-09-13T20:28:31.338867Z"Dubois, J."https://zbmath.org/authors/?q=ai:dubois.jonathan-l|dubois.jean-luc|dubois.jean-guy|dubois.jean-emile|dubois.j-m|dubois.jerome|dubois.jacques-emile|dubois.jacques-o|dubois.jacque-octave|dubois.joel"Jorba, À."https://zbmath.org/authors/?q=ai:jorba.angelSummary: We consider an electron in an atom driven by an infrared (IR) elliptically polarized laser field after its ionization by an ultrashort extreme ultraviolet (XUV) pulse. We find that, regardless of the atom species and the laser ellipticity, there exists XUV parameters for which the electron returns to its parent ion after ionizing, i.e., undergoes a recollision. This shows that XUV pulses trigger efficiently recollisions in atoms regardless of the ellipticity of the IR field. The XUV parameters for which the electron undergoes a recollision are obtained by studying the location of recolliding periodic orbits (RPOs) in phase space. The RPOs and their linear stability are followed and analyzed as a function of the intensity and ellipticity of the IR field. We determine the relation between the RPOs identified here and the ones found in the literature and used to interpret other types of highly nonlinear phenomena for low elliptically and circularly polarized IR fields.Floquet engineering of electric polarization with two-frequency drivehttps://zbmath.org/1491.780132022-09-13T20:28:31.338867Z"Ikeda, Yuya"https://zbmath.org/authors/?q=ai:ikeda.yuya"Kitamura, Sota"https://zbmath.org/authors/?q=ai:kitamura.sota"Morimoto, Takahiro"https://zbmath.org/authors/?q=ai:morimoto.takahiroSummary: Electric polarization is a geometric phenomenon in solids and has a close relationship to the symmetry of the system. Here we propose a mechanism to dynamically induce and manipulate electric polarization by using an external light field. Specifically, we show that application of bicircular lights controls the rotational symmetry of the system and can generate electric polarization. To this end, we use Floquet theory to study a system subjected to a two-frequency drive. We derive an effective Hamiltonian with high-frequency expansions, for which the electric polarization is computed with the Berry phase formula. We demonstrate the dynamical control of polarization for a one-dimensional Su-Shrieffer-Heeger chain, a square lattice model, and a honeycomb lattice model.Nonlinear propagation of coupled surface TE and leaky TM electromagnetic waveshttps://zbmath.org/1491.780142022-09-13T20:28:31.338867Z"Smirnov, Yury"https://zbmath.org/authors/?q=ai:smirnov.yury-g"Smolkin, Eugene"https://zbmath.org/authors/?q=ai:smolkin.eugeneSummary: Propagation of the coupled electromagnetic wave, which is a superposition of TE surface and TM leaky waves, in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium is studied (if the permittivity is linear, the coupled wave does not exist). Nonlinear coupled TE-TM wave is characterised by two (independent) frequencies and two (coupled) propagation constants (propagation constants). The physical problem is reduced to a nonlinear two-parameter transmission eigenvalue problem for Maxwell's equations. Existence of coupled TE-TM waves is proved. Intervals of localisation of propagation constants are found.Lax pair, conservation laws, Darboux transformation and localized waves of a variable-coefficient coupled Hirota system in an inhomogeneous optical fiberhttps://zbmath.org/1491.780152022-09-13T20:28:31.338867Z"Yang, Dan-Yu"https://zbmath.org/authors/?q=ai:yang.danyu"Tian, Bo"https://zbmath.org/authors/?q=ai:tian.bo"Qu, Qi-Xing"https://zbmath.org/authors/?q=ai:qu.qixing"Zhang, Chen-Rong"https://zbmath.org/authors/?q=ai:zhang.chen-rong"Chen, Su-Su"https://zbmath.org/authors/?q=ai:chen.su-su"Wei, Cheng-Cheng"https://zbmath.org/authors/?q=ai:wei.cheng-chengSummary: Optical fiber communication plays an important role in the modern communication. In this paper, we investigate a variable-coefficient coupled Hirota system which describes the vector optical pulses in an inhomogeneous optical fiber. With respect to the complex wave envelopes, we construct a Lax pair and a Darboux transformation, both different from the existing ones. Infinitely-many conservation laws are derived based on our Lax pair. We obtain the one/two-fold bright-bright soliton solutions, one/two-fold bright-dark soliton solutions and one/two-fold breather solutions via our Darboux transformation. When \(\alpha(t)\), \(\beta(t)\) and \(\delta(t)\) are the trigonometric functions, we present the bright-bright soliton, bright-dark soliton and breather which are all periodic along the propagation direction, where \(\alpha(t)\), \(\beta(t)\) and \(\delta(t)\) represent the group velocity dispersion, third-order dispersion and nonlinear terms of the self-phase modulation and cross-phase modulation. Interactions between the two bright-bright soliton, two bright-dark solitons and two breathers are presented. Bound state of the two bright-bright solitons is formed. Widths and velocities of the two bright-bright solitons do not change but their amplitudes change after their interaction via the asymptotic analysis. Periods of the bright-dark solitons decrease when the periods of the trigonometric \(\alpha(t)\), \(\beta(t)\) and \(\delta(t)\) decrease.Effects of electric field on multiple vibrational resonances in Hindmarsh-Rose neuronal systemshttps://zbmath.org/1491.780162022-09-13T20:28:31.338867Z"Wang, Guowei"https://zbmath.org/authors/?q=ai:wang.guowei"Yu, Dong"https://zbmath.org/authors/?q=ai:yu.dong"Ding, Qianming"https://zbmath.org/authors/?q=ai:ding.qianming"Li, Tianyu"https://zbmath.org/authors/?q=ai:li.tianyu"Jia, Ya"https://zbmath.org/authors/?q=ai:jia.yaSummary: The effects of electric field on vibrational resonance in single Hindmarsh-Rose (HR) neuron and coupled HR neurons system are investigated by using Fourier coefficient, respectively. It is found that the multiple vibrational resonances (MVR) can be observed in a single HR neuron model no matter the electric field is considered or not, and the electric field weakens the MVR. When bidirectional coupling between two HR neurons is considered, the occurrence of MVR can also be detected, it is very interesting to observe that the electric field can enhance the MVR. The higher the frequency of the low-frequency signal is, the less the number of resonance peaks of the system response to the low-frequency signal will be. Moreover, the local anti-resonance is also observed when appropriate parameters are selected. The effects of coupling strength and other system parameters on Fourier coefficient are also illustrated here. The systems manifesting MVR have better capacity for detecting and propagating signals.FXRS: fast X-ray spectrum-simulator theory and software implementationhttps://zbmath.org/1491.780172022-09-13T20:28:31.338867Z"Chirilǎ, Ciprian C."https://zbmath.org/authors/?q=ai:chirila.ciprian-c"Ha, T. M. H."https://zbmath.org/authors/?q=ai:ha.t-m-hSummary: We propose a simple, computationally efficient scheme for an X-ray spectrum simulator. The theoretical models describing the physical processes involved are employed in our Monte Carlo software in a coherent way, paving the way for straightforward future improvements. Our results compare satisfactorily to experimental results from literature and to results from dedicated simulation software. The simplicity, excellent statistical errors, and short execution time of our code recommend it for intensive use in X-ray generation simulations.Higher-dimensional supersymmetric microlaser arrayshttps://zbmath.org/1491.810342022-09-13T20:28:31.338867Z"Qiao, Xingdu"https://zbmath.org/authors/?q=ai:qiao.xingdu"Midya, Bikashkali"https://zbmath.org/authors/?q=ai:midya.bikashkali"Gao, Zihe"https://zbmath.org/authors/?q=ai:gao.zihe"Zhang, Zhifeng"https://zbmath.org/authors/?q=ai:zhang.zhifeng"Zhao, Haoqi"https://zbmath.org/authors/?q=ai:zhao.haoqi"Wu, Tianwei"https://zbmath.org/authors/?q=ai:wu.tianwei"Yim, Jieun"https://zbmath.org/authors/?q=ai:yim.jieun"Agarwal, Ritesh"https://zbmath.org/authors/?q=ai:agarwal.ritesh"Litchinitser, Natalia M."https://zbmath.org/authors/?q=ai:litchinitser.natalia-m"Feng, Liang"https://zbmath.org/authors/?q=ai:feng.liangSummary: The nonlinear scaling of complexity with the increased number of components in integrated photonics is a major obstacle impeding large-scale, phase-locked laser arrays. Here, we develop a higher-dimensional supersymmetry formalism for precise mode control and nonlinear power scaling. Our supersymmetric microlaser arrays feature phase-locked coherence and synchronization of all of the evanescently coupled microring lasers -- collectively oscillating in the fundamental transverse supermode -- which enables high-radiance, small-divergence, and single-frequency laser emission with a two-orders-of-magnitude enhancement in energy density. We also demonstrate the feasibility of structuring high-radiance vortex laser beams, which enhance the laser performance by taking full advantage of spatial degrees of freedom of light. Our approach provides a route for designing large-scale integrated photonic systems in both classical and quantum regimes.Gamma-convergence results for nematic elastomer bilayers: relaxation and actuationhttps://zbmath.org/1491.820212022-09-13T20:28:31.338867Z"Cesana, Pierluigi"https://zbmath.org/authors/?q=ai:cesana.pierluigi"León Baldelli, Andrés A."https://zbmath.org/authors/?q=ai:leon-baldelli.andres-aSummary: We compute effective energies of thin bilayer structures composed of soft nematic elastic liquid crystals in various geometrical regimes and functional configurations. Our focus is on elastic foundations composed of an isotropic layer attached to a nematic substrate where order-strain interaction results in complex opto-mechanical instabilities activated \textit{via} coupling through the common interface. Allowing out-of-plane displacements, we compute Gamma-limits for vanishing thickness which exhibit spontaneous stress relaxation and shape-morphing behaviour. This extends the plane strain modelling of the authors [Math. Models Methods Appl. Sci. 28, No. 14, 2863--2904 (2018; Zbl 1411.49008)], and shows the asymptotic emergence of fully coupled active macroscopic nematic foundations. Subsequently, we focus on actuation and compute asymptotic configurations of an active plate on nematic foundation interacting with an applied electric field. From the analytical standpoint, the presence of an electric field and its associated electrostatic work turns the total energy non-convex and non-coercive. We show that equilibrium solutions are min-max points of the system, that min-maximising sequences pass to the limit and, that the limit system can exert mechanical work under applied electric fields.Gravity in the infrared and effective nonlocal modelshttps://zbmath.org/1491.830072022-09-13T20:28:31.338867Z"Belgacem, Enis"https://zbmath.org/authors/?q=ai:belgacem.enis"Dirian, Yves"https://zbmath.org/authors/?q=ai:dirian.yves"Finke, Andreas"https://zbmath.org/authors/?q=ai:finke.andreas"Foffa, Stefano"https://zbmath.org/authors/?q=ai:foffa.stefano"Maggiore, Michele"https://zbmath.org/authors/?q=ai:maggiore.michele(no abstract)Existence of new singularities in Einstein-aether theoryhttps://zbmath.org/1491.830182022-09-13T20:28:31.338867Z"Chan, R."https://zbmath.org/authors/?q=ai:chan.raymond-hon-fu|chan.roy|chan.ringo|chan.roberto|chan.roath|chan.ray"da Silva, M. F. A."https://zbmath.org/authors/?q=ai:da-silva.m-f-a"Satheeshkumar, V. H."https://zbmath.org/authors/?q=ai:satheeshkumar.v-h(no abstract)Beyond limber: efficient computation of angular power spectra for galaxy clustering and weak lensinghttps://zbmath.org/1491.830202022-09-13T20:28:31.338867Z"Fang, Xiao"https://zbmath.org/authors/?q=ai:fang.xiao.1|fang.xiao"Krause, Elisabeth"https://zbmath.org/authors/?q=ai:krause.elisabeth"Eifler, Tim"https://zbmath.org/authors/?q=ai:eifler.tim"MacCrann, Niall"https://zbmath.org/authors/?q=ai:maccrann.niall(no abstract)The effect of nonlinear electrodynamics on Joule-Thomson expansion of a 5-dimensional charged AdS black hole in Einstein-Gauss-Bonnet gravityhttps://zbmath.org/1491.830282022-09-13T20:28:31.338867Z"Assrary, M."https://zbmath.org/authors/?q=ai:assrary.m"Sadeghi, J."https://zbmath.org/authors/?q=ai:sadeghi.jafar|sadeghi.jonathan|sadeghi.javad"Zomorrodian, M. E."https://zbmath.org/authors/?q=ai:zomorrodian.mohammad-ebrahimSummary: We have studied in this paper the Joule-Thomson expansion of a new charged AdS black hole with a nonlinear electrodynamics in framework of Einstein-Gauss-Bonnet gravity in AdS space. We investigated effects of mass (\(m\)), electric charge (\(q\)), GB coupling constant (\(\alpha\)) and nonlinear electrodynamics parameter (\(k\)) on Joule-Thomson expansion by depicting different graphs. The fact that inversion temperature tends to decrease by increasing \(k\), is in contrast to the effect of electric charge. The divergent point as well as the zero point of Joule-Thomson coefficient are also discussed. Results show that, this black hole exhibits a phase transition similar to that of van der Waals system. Furthermore, the isonthalpic curve is obtained and an interesting dependence of these curves on charge and nonlinear electrodynamics parameter is revealed. In \(T\)-\(P\) graphs, the cooling region shrinks with charge, while this region expands both with mass and with nonlinear electrodynamics parameter. Our study shows that nonlinear electrodynamics parameter plays an important role in Joule Thomson expansion.Buchdahl compactness limit and gravitational field energyhttps://zbmath.org/1491.830312022-09-13T20:28:31.338867Z"Dadhich, Naresh"https://zbmath.org/authors/?q=ai:dadhich.naresh(no abstract)Nonlinear-Maxwell-Yukawa de-Sitter black hole thermodynamics in a cavity. II: Grand canonical ensemblehttps://zbmath.org/1491.830332022-09-13T20:28:31.338867Z"El Moumni, Hasan"https://zbmath.org/authors/?q=ai:el-moumni.hasan"Khalloufi, Jamal"https://zbmath.org/authors/?q=ai:khalloufi.jamalSummary: Considering the grand canonical ensemble, we first discuss the thermodynamics of a generalized nonlinearly-charged-dS black hole enclosed in a finite spherical cavity. Such consideration means that the temperature and the potential on the wall of the cavity are fixed. Afterward, we focus on the Maxwell-Yukawa-dS black holes as a special case of investigation. The complete phase structure and stability are probed within the grand potential and the heat capacity. Our study reveals that the electric potential plays a key role in the phase portrait. Indeed, in the small values of the electric potential, the system undergoes a Hawking-Page transition and we found both phases the small and large branches. While, when the electric potential becomes relevant the large black hole phase disappears. In the end, we briefly discuss the relevant case associated with the extremal black hole one.
For Part I, see [the authors, ibid. 973, Article ID 115593, 21 p. (2021; Zbl 1480.83075)].Spontaneous radiation of black holeshttps://zbmath.org/1491.830362022-09-13T20:28:31.338867Z"Zeng, Ding-fang"https://zbmath.org/authors/?q=ai:zeng.ding-fangSummary: We provide an explicitly hermitian hamiltonian description for the spontaneous radiation of black holes, which is a many-level, multiple-degeneracy generalization of the usual Janeys-Cummings model for two-level atoms. We show that under single-particle radiation and standard Wigner-Wiesskopf approximation, our model yields exactly thermal type power spectrum as hawking radiation requires. While in the many-particle radiation cases, numeric methods allow us to follow the evolution of microscopic state of a black hole exactly, from which we can get the firstly increasing then decreasing entropy variation trend for the radiation particles just as the Page-curve exhibited. Basing on this model analysis, we claim that two ingredients are necessary for resolutions of the information missing puzzle, a spontaneous radiation like mechanism for the production of hawking particles and proper account of the macroscopic superposition happening in the full quantum description of a black hole radiation evolution and, the working logic of replica wormholes is an effect account of this latter ingredient.
As the basis for our interpretation of black hole Hawking radiation as their spontaneous radiation, we also provide a fully atomic like inner structure models for their microscopic states definition and origins of their Bekenstein-Hawking entropy, that is, exact solution families to the Einstein equation sourced by matter constituents oscillating across the central point and their quantization. Such a first quantization model for black holes' microscopic state is non necessary for our spontaneous radiation description, but has advantages comparing with other alternatives, such as string theory fuzzball or brick wall models.Capturing non-Gaussianity of the large-scale structure with weighted skew-spectrahttps://zbmath.org/1491.830602022-09-13T20:28:31.338867Z"Dizgah, Azadeh Moradinezhad"https://zbmath.org/authors/?q=ai:dizgah.azadeh-moradinezhad"Lee, Hayden"https://zbmath.org/authors/?q=ai:lee.hayden"Schmittfull, Marcel"https://zbmath.org/authors/?q=ai:schmittfull.marcel"Dvorkin, Cora"https://zbmath.org/authors/?q=ai:dvorkin.cora(no abstract)Multipoles of the relativistic galaxy bispectrumhttps://zbmath.org/1491.850042022-09-13T20:28:31.338867Z"de Weerd, Eline M."https://zbmath.org/authors/?q=ai:de-weerd.eline-m"Clarkson, Chris"https://zbmath.org/authors/?q=ai:clarkson.chris-a"Jolicoeur, Sheean"https://zbmath.org/authors/?q=ai:jolicoeur.sheean"Maartens, Roy"https://zbmath.org/authors/?q=ai:maartens.roy"Umeh, Obinna"https://zbmath.org/authors/?q=ai:umeh.obinna(no abstract)Gaussian process estimation of transition redshifthttps://zbmath.org/1491.850052022-09-13T20:28:31.338867Z"Jesus, J. F."https://zbmath.org/authors/?q=ai:jesus.jose-f"Valentim, R."https://zbmath.org/authors/?q=ai:valentim.r"Escobal, A. A."https://zbmath.org/authors/?q=ai:escobal.a-a"Pereira, S. H."https://zbmath.org/authors/?q=ai:pereira.saulo-h(no abstract)Cosmographic analysis of redshift drifthttps://zbmath.org/1491.850062022-09-13T20:28:31.338867Z"Lobo, Francisco S. N."https://zbmath.org/authors/?q=ai:lobo.francisco-s-n"Mimoso, José Pedro"https://zbmath.org/authors/?q=ai:mimoso.jose-pedro"Visser, Matt"https://zbmath.org/authors/?q=ai:visser.matt(no abstract)