Recent zbMATH articles in MSC 82https://zbmath.org/atom/cc/822024-09-27T17:47:02.548271ZWerkzeugGraphical representations of lattice spin modelshttps://zbmath.org/1541.000452024-09-27T17:47:02.548271Z"Duminil-Copin, Hugo"https://zbmath.org/authors/?q=ai:duminil-copin.hugo(no abstract)Investigating Banhatti indices on the molecular graph and the line graph of glass with M-polynomial approachhttps://zbmath.org/1541.051772024-09-27T17:47:02.548271Z"Tousi, Jaber Ramezani"https://zbmath.org/authors/?q=ai:tousi.jaber-ramezani"Ghods, Masoud"https://zbmath.org/authors/?q=ai:ghods.masoudSummary: Topological indices are numerical values related to a chemical structure that describes the correlation of chemical structure with different physical properties and chemical reactions. Glass has wide applications in architecture, tableware, optics, and optoelectronics.
In this article, first, the mathematical relationship between M-polynomial and Banhatti indices such as \(K\)-Banhatti, \(\delta\)-Banhatti, and hyper \(\delta\)-Banhatti indices are obtained. Then using M-polynomial, Banhatti indices are calculated.The sequential conformable Langevin-type differential equations and their applications to the RLC electric circuit problemshttps://zbmath.org/1541.340092024-09-27T17:47:02.548271Z"Aydin, M."https://zbmath.org/authors/?q=ai:aydin.mustafa"Mahmudov, N. I."https://zbmath.org/authors/?q=ai:mahmudov.nazim-idrisogluSummary: In this paper, the sequential conformable Langevin-type differential equation is studied. A representation of a solution consisting of the newly defined conformable bivariate Mittag-Leffler function to its nonhomogeneous and linear version is obtained via the conformable Laplace transforms' technique. Also, existence and uniqueness of a global solution to its nonlinear version are obtained. The existence and uniqueness of solutions are shown with respect to the weighted norm defined in compliance with (conformable) exponential function. The concept of the Ulam-Hyers stability of solutions is debated based on the fixed-point approach. The LRC electrical circuits are presented as an application to the described system. Simulated and numerical instances are offered to instantiate our abstract findings.A new monotonicity formula for the spatially homogeneous Landau equation with Coulomb potential and its applicationshttps://zbmath.org/1541.351092024-09-27T17:47:02.548271Z"Desvillettes, Laurent"https://zbmath.org/authors/?q=ai:desvillettes.laurent"He, Ling-Bing"https://zbmath.org/authors/?q=ai:he.lingbing"Jiang, Jin-Cheng"https://zbmath.org/authors/?q=ai:jiang.jin-chengSummary: We describe a time-dependent functional involving the relative entropy and \(\dot{H}^1 \) the seminorm, which decreases along solutions to the spatially homogeneous Landau equation with Coulomb potential. The study of this monotone functional sheds light on the competition between dissipation and nonlinearity for this equation. It enables us to obtain new results concerning regularity/blowup issues for the Landau equation with Coulomb potential.Longtime behavior of homoenergetic solutions in the collision dominated regime for hard potentialshttps://zbmath.org/1541.353332024-09-27T17:47:02.548271Z"Kepka, Bernhard"https://zbmath.org/authors/?q=ai:kepka.bernhardSummary: We consider a particular class of solutions to the Boltzmann equation which are referred to as homoenergetic solutions. They describe the dynamics of a dilute gas due to collisions and the action of either a shear, a dilation or a combination of both. More precisely, we study the case in which the shear is dominant compared with the dilation and the collision operator has homogeneity \(\gamma >0\). We prove that solutions with initially high temperature remain close and converge to a Maxwellian distribution with temperature going to infinity. Furthermore, we give precise asymptotic formulas for the temperature. The proof relies on an ansatz which is motivated by a Hilbert-type expansion. We consider both noncutoff and cutoff kernels.Incompressible Navier-Stokes-Fourier limit of 3D stationary Boltzmann equationhttps://zbmath.org/1541.353342024-09-27T17:47:02.548271Z"Wu, Lei"https://zbmath.org/authors/?q=ai:wu.lei.1"Ouyang, Zhimeng"https://zbmath.org/authors/?q=ai:ouyang.zhimengSummary: We consider the 3D stationary Boltzmann equation in convex domains with diffuse-reflection boundary condition. We rigorously derive the steady incompressible Navier-Stokes-Fourier system and justify the asymptotic convergence as the Knudsen number \({\varepsilon}\) shrinks to zero. The proof is based on an intricate analysis of boundary layers with geometric correction and focuses on technical difficulties caused by the singularity in collision kernel \(k(v,v')\) and the perturbed remainder estimates.The optimal \(L^2\) decay rate of the velocity for the general FENE dumbbell modelhttps://zbmath.org/1541.353482024-09-27T17:47:02.548271Z"Luo, Zhaonan"https://zbmath.org/authors/?q=ai:luo.zhaonan"Luo, Wei"https://zbmath.org/authors/?q=ai:luo.wei.2"Yin, Zhaoyang"https://zbmath.org/authors/?q=ai:yin.zhaoyangSummary: In this paper we mainly study large time behavior for the strong solutions of the finite extensible nonlinear elastic (FENE) dumbbell model. The sharp \(L^2\) decay rate was obtained on the co-rotational case. We prove that the optimal \(L^2\) decay rate of the velocity of the general FENE dumbbell model is \((1+t)^{-\frac{d}{4}}\) with \(d \geq 2\). Our obtained result is sharp and improves considerably the previous result in [\textit{W. Luo} and \textit{Z. Yin}, Arch. Ration. Mech. Anal. 224, No. 1, 209--231 (2017; Zbl 1366.35134)].Formation of singularities in plasma ion dynamicshttps://zbmath.org/1541.353652024-09-27T17:47:02.548271Z"Bae, Junsik"https://zbmath.org/authors/?q=ai:bae.junsik"Choi, Junho"https://zbmath.org/authors/?q=ai:choi.junho"Kwon, Bongsuk"https://zbmath.org/authors/?q=ai:kwon.bongsukSummary: We study the formation of singularity for the Euler-Poisson system equipped with the Boltzmann relation, which describes the dynamics of ions in an electrostatic plasma. In general, it is known that smooth solutions to nonlinear hyperbolic equations fail to exist globally in time. We establish criteria for \(C^1\) blow-up of the Euler-Poisson system, both for the isothermal and pressureless cases. In particular, our blow-up condition for the pressureless model does not require that the gradient of velocity is negatively large. In fact, our result particularly implies that the smooth solutions can break down even if the gradient of initial velocity is trivial. For the isothermal case, we prove that smooth solutions leave \(C^1\) class in a finite time when the gradients of the Riemann functions are initially large.
{{\copyright} 2024 IOP Publishing Ltd \& London Mathematical Society}Propagation and energy of the dressed solitons in the Thomas-Fermi magnetoplasmahttps://zbmath.org/1541.353752024-09-27T17:47:02.548271Z"El-Monier, S. Y."https://zbmath.org/authors/?q=ai:el-monier.s-y"Atteya, A."https://zbmath.org/authors/?q=ai:atteya.aSummary: A theoretical investigation is presented for dust-acoustic (DA) waves in a collisionless Thomas-Fermi magnetoplasma. The plasma system consists of electrons, ions, and negatively charged dust grains, all existing in a quantizing magnetic field. The Korteweg-de Vries (KdV) and KdV type equations are derived by using the reductive perturbation method. The solutions of these evolved equations are obtained. The contribution of higher-order corrections to the DA is investigated. The electric field and the soliton energy were also derived. The K-dV and dressed soliton energies are depleted as the dust temperature and magnetic field increase. But they magnify as obliqueness increases. The present results are beneficial in understanding the waves propagating in Thomas-Fermi magnetoplasma that are applicable for high-intensity laser-solid matter interaction experiments and astrophysical compact objects such as white dwarfs.Interaction of two soliton waves in plasma including electrons with Kappa-Cairns distribution functionhttps://zbmath.org/1541.353862024-09-27T17:47:02.548271Z"Mirzaei, M."https://zbmath.org/authors/?q=ai:mirzaei.mozhgan|mirzaei.mostafa|mirzaei.mahbube|mirzaei.mohammad-javad|mirzaei.mehdi|mirzaei.mahmood.1|mirzaei.masoud|mirzaei.majid|mirzaei.maryam|mirzaei.mohsen|mirzaei.masaud"Motevalli, S. M."https://zbmath.org/authors/?q=ai:motevalli.s-mSummary: The interaction of positron acoustic soliton waves (PASWs) with the arbitrary collision angle in plasma including cold fluid positrons, stationary ions and electrons with Kappa-Cairns (K-C) distribution function have been studied. The equations of Korteweg-de Vries (KdV) and the phase shifts are obtained by employing the extended Poincaré-Lighthill-Kuo (PLK) method for the two colliding waves. The influences of parameters of the K-C distribution function (\(\kappa\) and \(\alpha\)), the collision angle \(\theta\) and the proportion of the ion (electron) and positron unperturbed densities (\(\beta_i(\beta_e)\)) on the phase shifts are investigated.Lie symmetry analysis, optimal system, symmetry reductions and analytic solutions for a \((2+1)\)-dimensional generalized nonlinear evolution system in a fluid or a plasmahttps://zbmath.org/1541.354052024-09-27T17:47:02.548271Z"Zhou, Tian-Yu"https://zbmath.org/authors/?q=ai:zhou.tian-yu"Tian, Bo"https://zbmath.org/authors/?q=ai:tian.bo"Shen, Yuan"https://zbmath.org/authors/?q=ai:shen.yuan.5"Cheng, Chong-Dong"https://zbmath.org/authors/?q=ai:cheng.chong-dongSummary: Nonlinear evolution equations are used to describe such nonlinear phenomena as the solitons, travelling waves and breathers in fluid mechanics, plasma physics and optics. In this paper, we investigate a \((2+1)\)-dimensional generalized nonlinear evolution system in a fluid or a plasma. Via the Lie symmetry analysis, we acquire the Lie point symmetry generators and Lie symmetry groups of that system. Via the optimal system method, we derive the optimal system of the 1-dimensional subalgebras. Based on the symmetry generators in that optimal system, we give some symmetry reductions for the \((2+1)\)-dimensional generalized nonlinear evolution system. Finally, via those symmetry reductions, we acquire some soliton, rational-type and power-series solutions.Simulation study of dust magnetosonic excitations in a magnetized dusty plasmahttps://zbmath.org/1541.354402024-09-27T17:47:02.548271Z"Singla, Sunidhi"https://zbmath.org/authors/?q=ai:singla.sunidhi"Chandra, S."https://zbmath.org/authors/?q=ai:chandra.soumen|chandra.suresh.1|chandra.shiva|chandra.shalini|chandra.sarthak|chandra.satish|chandra.subodh|chandra.sanjeev|chandra.susheel|chandra.sujan|chandra.shekhar-s|chandra.suryansh|chandra.swarniv|chandra.samarth|chandra.sushil|chandra.sudip-ratan|chandra.sumir|chandra.subha|chandra.subhash-ajay|chandra.sharat|chandra.sarvesh|chandra.souvik|chandra.saroj-kumar|chandra.sanjay|chandra.saket|chandra.saurabh"Saini, N. S."https://zbmath.org/authors/?q=ai:saini.nareshpal-singhSummary: A theoretical investigation is made to study the properties of dust magnetosonic (DMS) solitons in a magnetized electron-ion-dust plasma that contains negative polarity warm dust grains, and inertialess ions as well as electrons. By using reductive perturbation technique (RPT), the Korteweg-de Vries (KdV) equation is derived. There is the formation of only positive potential DMS solitons in the high plasma-\(\beta\) limit. The effects of plasma parameters, viz., plasma-\(\beta\), electron to ion temperature ratio and dust to electron density ratio on the characteristics of DMS solitons are also studied numerically. Furthermore, we have analysed the head-on collision of DMS solitary waves and subsequent evolution of stationary structures using INSAT FORK code. Results of this investigation might be useful for understanding the nonlinear disturbances in space plasmas especially in Earth's magnetosphere region and are also useful in understanding the energy transport phenomena of nonlinear structures.Scattering, random phase and wave turbulencehttps://zbmath.org/1541.354542024-09-27T17:47:02.548271Z"Faou, Erwan"https://zbmath.org/authors/?q=ai:faou.erwan"Mouzard, Antoine"https://zbmath.org/authors/?q=ai:mouzard.antoineSummary: We start from the remark that in wave turbulence theory, exemplified by the cubic two-dimensional Schrödinger equation (NLS) on the real plane, the regularity of the resonant manifold is linked with dispersive properties of the equation and thus with scattering phenomena. In contrast with classical analysis starting with a dynamics on a large periodic box, we propose to study NLS set on the real plane using the dispersive effects, by considering the time evolution operator in various time scales for deterministic and random initial data. By considering periodic functions embedded in the whole space by gaussian truncation, this allows explicit calculations and we identify two different regimes where the operators converges towards the kinetic operator but with different form of convergence.Classification and soliton for a generalized fourth-order dispersive nonlinear Schrödinger equation in a Heisenberg spin chainhttps://zbmath.org/1541.354682024-09-27T17:47:02.548271Z"Yang, Deniu"https://zbmath.org/authors/?q=ai:yang.deniu(no abstract)Multi-fold binary Darboux transformation and mixed solitons of a three-component Gross-Pitaevskii system in the spinor Bose-Einstein condensatehttps://zbmath.org/1541.354712024-09-27T17:47:02.548271Z"Zhang, C.-R."https://zbmath.org/authors/?q=ai:zhang.cairong|zhang.chuanrong|zhang.chunrui|zhang.chunru|zhang.chaoran|zhang.canrong|zhang.chunrui.1|zhang.chenrui|zhang.changrong|zhang.chaorui|zhang.chen-rong|zhang.chengzhao-richard|zhang.chengrui|zhang.changrui"Tian, B."https://zbmath.org/authors/?q=ai:tian.baochuan|tian.bao|tian.bo|tian.baoxian|tian.baolin|tian.baoguang|tian.boping|tian.baofeng|tian.baijun|tian.binbin|tian.beping|tian.baoyu|tian.bailing|tian.baoyuang|tian.baodan|tian.baoping|tian.bin|tian.beiyi|tian.boshi|tian.beihang|tian.boyu|tian.baoguo|tian.bing|tian.baoliang|tian.bowen"Qu, Q.-X."https://zbmath.org/authors/?q=ai:qu.qiuxia|qu.qixing"Yuan, Y.-Q."https://zbmath.org/authors/?q=ai:yuan.yin-quan|yuan.yu-qiang|yuan.yeqing|yuan.yu-quan"Wei, C.-C."https://zbmath.org/authors/?q=ai:wei.cheng-cheng|wei.changcheng|wei.chin-chung|wei.chia-chen|wei.chongchong|wei.chiu-chiSummary: The Bose-Einstein-condensation applications give rise to the superfluidity in the liquid helium and superconductivity in the metals. In this paper, we work on a three-component Gross-Pitaevskii system, which describes the matter waves in an spin-1 spinor Bose-Einstein condensate. We construct a multi-fold binary Darboux transformation with the zero seed solutions to describe the three vertical spin projection of the spin-1 spinor BEC, which is different from all the existing Darboux-type ones for the same system, and derive three types of the exponential-and-rational mixed soliton solutions associated with two conjugate complex eigenvalues. For such mixed solitons, we give their asymptotic expressions, indicating that they consist of the Ieda-Miyakawa-Wadati (IMW)-polar-state or IMW-ferromagnetic solitons but possess the time-dependent velocities. Asymptotically and graphically, interaction mechanisms between the mixed and exponential solitons are classified in six cases, and we exhibit the inelastic and elastic interactions through calculating the modifications of the polarization matrices and phase shifts for the two interacting solitons. We find that both the IMW-polar-state solitons, including the mixed and exponential solitons, can not alter the other soliton's intensity distribution during the interaction, while the mixed or exponential soliton in the IMW-ferromagnetic state does.The formation of invariant exact optical soliton solutions of Landau-Ginzburg-Higgs equation via Khater analytical approachhttps://zbmath.org/1541.354742024-09-27T17:47:02.548271Z"Faridi, Waqas Ali"https://zbmath.org/authors/?q=ai:faridi.waqas-ali"AlQahtani, Salman A."https://zbmath.org/authors/?q=ai:al-qahtani.salman-aSummary: This work aims to enhance our comprehension of the dynamical features of the nonlinear Landau-Ginzburg-Higgs evolution equation, which provides a theoretical framework for identifying various phenomena, such as the formation of superconducting states and the spontaneous breakdown of symmetries. When symmetry breaking is involved in phase transitions in particle physics or condensed matter systems, the Landau-Ginzburg-Higgs model combines the ideas of the Landau-Ginzburg theory and the Higgs mechanism. The equation plays a crucial role in characterizing the Higgs field and its related particles, including Higgs boson. In a standard model of the particle physics, Higgs mechanism explains precisely how mass is acquired. The Lie invariance requirements are taken into account by the symmetry generators. The method produces a 3-dimensional Lie algebra of the Landau-Ginzburg-Higgs model with translational symmetry (dilation or scaling) and translations in the space and the time associated with the mass and energy conservation. It is shown to be the optimal sub-algebraic system after similarity reductions are also performed. The next wave transformation method reduces the governing system to ordinary differential equations and yields a large number of exact travelling wave solutions. The Khater approach is used to solve an ordinary differential equation and investigate the closed-form analytical travelling wave solutions for the considered diffusive system. The obtained results include a singular, mixed singular, periodic, mixed trigonometric, complex combo, trigonometric, mixed hyperbolic, plane, and combined bright-dark soliton solution. The results of the sensitivity analysis demonstrate how vulnerable the suggested equation is to various initial conditions. The findings are visually displayed in contour, three-dimensional, and two-dimensional forms to emphasize the features of pulse propagation.Long time gyrokinetic equationshttps://zbmath.org/1541.354772024-09-27T17:47:02.548271Z"Cheverry, Christophe"https://zbmath.org/authors/?q=ai:cheverry.christophe"Farhat, Shahnaz"https://zbmath.org/authors/?q=ai:farhat.shahnazSummary: The aim of this text is to elucidate the oscillating patterns
(see [\textit{C. Cheverry}, ``Mathematical perspectives in plasma turbulence'', Res. Rep. Math. 2, No. 2 (2018), see also \url{HAL:hal-01617652}])
which are generated in a toroidal plasma by a strong external magnetic field and a nonzero electric field. It is also to justify and then study new modulation equations which are valid for longer times than before. Oscillating coherent structures are induced by the collective motions of charged particles which satisfy a system of ODEs implying a large parameter, the gyrofrequency \(\varepsilon^{-1}\gg 1\). By exploiting the properties of underlying integrable systems, we can complement the KAM picture
(see [\textit{G. Benettin} and \textit{P. Sempio}, Nonlinearity 7, No. 1, 281--303 (1994; Zbl 0856.70010);
\textit{M. Braun}, SIAM Rev. 23, 61--93 (1981; Zbl 0479.76128)])
and go beyond the classical results about gyrokinetics
(see [\textit{M. Bostan}, Multiscale Model. Simul. 8, No. 5, 1923--1957 (2010; Zbl 1220.35176);
\textit{A. J. Brizard} and \textit{T. S. Hahm}, Rev. Mod. Phys. 79, No. 2, 421--468 (2007; Zbl 1205.76309)]).
The purely magnetic situation was addressed by
\textit{C. Cheverry} [Commun. Math. Phys. 338, No. 2, 641--703 (2015; Zbl 1333.35290); J. Differ. Equations 262, No. 3, 2987--3033 (2017; Zbl 1358.35194)].
We are concerned here with the numerous additional difficulties due to the influence of a nonzero electric field.Sufficient conditions for the existence of minimizing harmonic maps with axial symmetry in the small-average regimehttps://zbmath.org/1541.354782024-09-27T17:47:02.548271Z"Di Fratta, Giovanni"https://zbmath.org/authors/?q=ai:di-fratta.giovanni"Slastikov, Valeriy V."https://zbmath.org/authors/?q=ai:slastikov.valeriy-v"Zarnescu, Arghir D."https://zbmath.org/authors/?q=ai:zarnescu.arghir-daniSummary: The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional defined on the space of vector fields \(H^1 (S, T)\), where \(S\) and \(T\) are surfaces of revolution. The energy functional we consider is closely related to a reduced model in the variational theory of micromagnetism for the analysis of observable magnetization states in curved thin films. We show that axially symmetric minimizers always exist, and if the target surface \(T\) is never flat, then any coexisting minimizer must have line symmetry. Thus, the minimization problem reduces to the computation of an optimal one-dimensional profile. We also provide a necessary and sufficient condition for energy minimizers to be axially symmetric.Invariant Gibbs measures for the three dimensional cubic nonlinear wave equationhttps://zbmath.org/1541.355022024-09-27T17:47:02.548271Z"Bringmann, Bjoern"https://zbmath.org/authors/?q=ai:bringmann.bjorn"Deng, Yu"https://zbmath.org/authors/?q=ai:deng.yu"Nahmod, Andrea R."https://zbmath.org/authors/?q=ai:nahmod.andrea-r"Yue, Haitian"https://zbmath.org/authors/?q=ai:yue.haitianSummary: We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional cubic wave equation, which is also known as the hyperbolic \(\Phi^4_3\)-model. This result is the hyperbolic counterpart to seminal works on the parabolic \(\Phi^4_3\)-model by \textit{M. Hairer} [Invent. Math. 198, No. 2, 269--504 (2014; Zbl 1332.60093)] and \textit{M. Hairer} and \textit{K. Matetski} [Ann. Probab. 46, No. 3, 1651--1709 (2018; Zbl 1406.60094)].
The heart of the matter lies in establishing local in time existence and uniqueness of solutions on the statistical ensemble, which is achieved by using a para-controlled ansatz for the solution, the analytical framework of the random tensor theory, and the combinatorial molecule estimates.
The singularity of the Gibbs measure with respect to the Gaussian free field brings out a new caloric representation of the Gibbs measure and a synergy between the parabolic and hyperbolic theories embodied in the analysis of heat-wave stochastic objects. Furthermore from a purely hyperbolic standpoint our argument relies on key new ingredients that include a hidden cancellation between sextic stochastic objects and a new bilinear random tensor estimate.Existence and uniqueness of mass conserving solutions to the coagulation, multi-fragmentation equations with compactly supported kernelshttps://zbmath.org/1541.355032024-09-27T17:47:02.548271Z"Das, Arijit"https://zbmath.org/authors/?q=ai:das.arijit"Saha, Jitraj"https://zbmath.org/authors/?q=ai:saha.jitrajSummary: In this article, the existence result of a solution to continuous nonlinear, initial value problem is studied. In particular, we consider a special type of problem representing the time evolution of particle number density due to the coagulation, multi-fragmentation events among the particles present in a system. The existence theorem is proved with the kinetic kernels having compact support. The proof of the main theorem is based on the contraction mapping principle. Furthermore, the mass conservation property of the existed solution is also investigated.
For the entire collection see [Zbl 1521.76009].Diffusion of a collisionless gashttps://zbmath.org/1541.355042024-09-27T17:47:02.548271Z"Kozlov, V. V."https://zbmath.org/authors/?q=ai:kozlov.valerii-vasilievich|kozlov.viktor-vladimirovich|kozlov.viktor-vyacheslavovichSummary: We study a diffusion-type equation for the density of a collisionless relativistic gas (Jüttner gas). The rate of diffusion propagation turns out to be finite. We consider problems of the existence and uniqueness of solutions of this equation, as well as some of its generalized solutions.Spin solitons in spin-1 Bose-Einstein condensateshttps://zbmath.org/1541.355052024-09-27T17:47:02.548271Z"Meng, Ling-Zheng"https://zbmath.org/authors/?q=ai:meng.ling-zheng"Qin, Yan-Hong"https://zbmath.org/authors/?q=ai:qin.yanhong"Zhao, Li-Chen"https://zbmath.org/authors/?q=ai:zhao.li-chenSummary: Vector solitons in Bose-Einstein condensates are usually investigated analytically with identical intra- and interatomic interactions (for an integrable model). We obtain six families of exact spin soliton solutions for nonintegrable cases, which can be used to describe spin-1 Bose-Einstein condensates. The stability analyses and numerical simulations indicate that three families of spin solitons are robust against spin-dependent interactions and white noise. We further investigate the motion of these stable spin solitons driven by external linear potentials. Their moving trajectories demonstrate that the spin solitons admit a negative-positive mass transition. Some splitting and diffusing behaviors can emerge during the motion of a spin soliton that are absent in spin-\(1/2\) systems. The collisions between spin solitons are exhibited with varying relative velocity and phase. The nonintegrable properties of the systems can give rise to weak amplitude and location oscillations after collision. These stable spin soliton excitations can be used to study the negative inertial mass of solitons, the dynamics of soliton-impurity systems, and the spin dynamics in Bose-Einstein condensates.Soliton based director deformation in a twist grain boundary liquid crystalhttps://zbmath.org/1541.355062024-09-27T17:47:02.548271Z"Saravanan, M."https://zbmath.org/authors/?q=ai:saravanan.moorthi"Senjudarvannan, R."https://zbmath.org/authors/?q=ai:senjudarvannan.rSummary: We investigate the director dynamics of a twist grain boundary liquid crystal under the one constant approximation for the different elastic constants representing the various deformation present in the liquid crystal medium. The free energy density is deduced to a higher-order vector nonlinear partial differential equation by balancing the torque experienced by the nematic molecules under a viscous field and the molecular field arises due to the presence of elastic constants. Upon employing the stereographic projection method we further reduced the vector nonlinear differential equation into a complex scalar nonlinear partial differential equation. We obtain a series of localized solutions for the complex scalar nonlinear partial differential equation through the standard tanh method.Formation, propagation, and excitation of matter solitons and rogue waves in chiral BECs with a current nonlinearity trapped in external potentialshttps://zbmath.org/1541.355072024-09-27T17:47:02.548271Z"Song, Jin"https://zbmath.org/authors/?q=ai:song.jin"Yan, Zhenya"https://zbmath.org/authors/?q=ai:yan.zhenya(no abstract)Well-posedness and singularity formation for Vlasov-Riesz systemhttps://zbmath.org/1541.355082024-09-27T17:47:02.548271Z"Choi, Young-Pil"https://zbmath.org/authors/?q=ai:choi.young-pil"Jeong, In-Jee"https://zbmath.org/authors/?q=ai:jeong.in-jeeSummary: We investigate the Cauchy problem for the Vlasov-Riesz system, which is a Vlasov equation featuring an interaction potential generalizing previously studied cases, including the Coulomb \(\Phi = (- \Delta)^{-1}\rho \), Manev \((- \Delta)^{-1} + (- \Delta)^{-\frac12} \), and pure Manev \((- \Delta)^{-\frac12}\) potentials. For the first time, we extend the local theory of classical solutions to potentials more singular than that for the Manev. Then, we obtain finite-time singularity formation for solutions with various attractive interaction potentials, extending the well-known blow-up result for attractive Vlasov-Poisson for \(d\ge4 \). Our local well-posedness and singularity formation results extend to cases when linear diffusion and damping in velocity are present.The plasma-charge model in a convex domainhttps://zbmath.org/1541.355092024-09-27T17:47:02.548271Z"Wu, Jingpeng"https://zbmath.org/authors/?q=ai:wu.jingpengSummary: The aim of this paper is to study the initial-boundary value problems of a Vlasov type system in a convex domain, so called the plasma-charge model, in which there are two kinds of singular sets, one caused by the boundary effect, the other by the heavy point charges. We prove the local existence of classical solutions for the case that the point charges are moving and global existence of classical solutions for the case that the point charges are fixed away from the boundary. The crucial tools are the extended Velocity Lemma for the plasma-charge model and the Pfaffelmoser's method developed by
\textit{H. J. Hwang} and \textit{J. J. L. Velázquez} [Arch. Ration. Mech. Anal. 195, No. 3, 763--796 (2010; Zbl 1218.35235)] and
\textit{C. Marchioro} et al. [Arch. Ration. Mech. Anal. 201, No. 1, 1--26 (2011; Zbl 1321.76081)].
In the Pfaffelmoser's argument, a new idea is that the plasma particles can only be close to one of the singular sets during the time interval \([t-\delta,t]\) with small length \(\delta\), which allows us to obtain the global existence for the fixed point charges case by adapting the techniques established by
\textit{H. J. Hwang} et al. [Discrete Contin. Dyn. Syst. 33, No. 2, 723--737 (2013; Zbl 1271.82026)] and
\textit{H. J. Hwang} and \textit{J. J. L. Velázquez} [Arch. Ration. Mech. Anal. 195, No. 3, 763--796 (2010; Zbl 1218.35235)] and
Marchioro et al. [loc. cit.]
to the corresponding singular sets respectively.
{{\copyright} 2024 IOP Publishing Ltd \& London Mathematical Society}Kinetic compartmental models driven by opinion dynamics: vaccine hesitancy and social influencehttps://zbmath.org/1541.355102024-09-27T17:47:02.548271Z"Bondesan, Andrea"https://zbmath.org/authors/?q=ai:bondesan.andrea"Toscani, Giuseppe"https://zbmath.org/authors/?q=ai:toscani.giuseppe"Zanella, Mattia"https://zbmath.org/authors/?q=ai:zanella.mattiaSummary: We propose a kinetic model for understanding the link between opinion formation phenomena and epidemic dynamics. The recent pandemic has brought to light that vaccine hesitancy can present different phases and temporal and spatial variations, presumably due to the different social features of individuals. The emergence of patterns in societal reactions permits to design and predict the trends of a pandemic. This suggests that the problem of vaccine hesitancy can be described in mathematical terms, by suitably coupling a kinetic compartmental model for the spreading of an infectious disease with the evolution of the personal opinion of individuals, in the presence of leaders. The resulting model makes it possible to predict the collective compliance with vaccination campaigns as the pandemic evolves and to highlight the best strategy to set up for maximizing the vaccination coverage. We conduct numerical investigations which confirm the ability of the model to describe different phenomena related to the spread of an epidemic.Wigner- and marchenko-Pastur-type limit theorems for Jacobi processeshttps://zbmath.org/1541.600132024-09-27T17:47:02.548271Z"Auer, Martin"https://zbmath.org/authors/?q=ai:auer.martin"Voit, Michael"https://zbmath.org/authors/?q=ai:voit.michael"Woerner, Jeannette H. C."https://zbmath.org/authors/?q=ai:woerner.jeannette-h-cSummary: We study Jacobi processes \((X_t)_{t\geq 0}\) on \([-1,1]^N\) and \([1,\infty [^N\) which are motivated by the Heckman-Opdam theory and associated integrable particle systems. These processes depend on three positive parameters and degenerate in the freezing limit to solutions of deterministic dynamical systems. In the compact case, these models tend for \(t\rightarrow \infty\) to the distributions of the \(\beta\)-Jacobi ensembles and, in the freezing case, to vectors consisting of ordered zeros of one-dimensional Jacobi polynomials. We derive almost sure analogues of Wigner's semicircle and Marchenko-Pastur limit laws for \(N\rightarrow \infty\) for the empirical distributions of the \(N\) particles on some local scale. We there allow for arbitrary initial conditions, which enter the limiting distributions via free convolutions. These results generalize corresponding stationary limit results in the compact case for \(\beta\)-Jacobi ensembles and, in the deterministic case, for the empirical distributions of the ordered zeros of Jacobi polynomials. The results are also related to free limit theorems for multivariate Bessel processes, \(\beta\)-Hermite and \(\beta\)-Laguerre ensembles, and the asymptotic empirical distributions of the zeros of Hermite and Laguerre polynomials for \(N\rightarrow \infty\).Existence of geometric ergodic periodic measures of stochastic differential equationshttps://zbmath.org/1541.600372024-09-27T17:47:02.548271Z"Feng, Chunrong"https://zbmath.org/authors/?q=ai:feng.chunrong"Zhao, Huaizhong"https://zbmath.org/authors/?q=ai:zhao.huaizhong"Zhong, Johnny"https://zbmath.org/authors/?q=ai:zhong.johnnyThe paper works out sufficient conditions for the existence, uniqueness and geometric convergence of a periodic measure for time-periodic Markovian processes on a locally compact metric space. The main results are applied to weakly dissipative stochastic differential equations (SDEs), Langevin equations (SDEs with additive noise) and gradient systems. The Fokker-Planck equation for the associated probability density of the periodic measure with physically relevant applications is referred to.
In passing, we note that periodic measures are the time-periodic counterpart to invariant measures for stochastic dynamical systems in order to characterize long-term periodic behavior of them. The concept of stochastic resonance is related to their investigation as well.
Reviewer: Henri Schurz (Carbondale)Optimization of escape kinetics by reflecting and resettinghttps://zbmath.org/1541.600562024-09-27T17:47:02.548271Z"Capała, Karol"https://zbmath.org/authors/?q=ai:capala.karol"Dybiec, Bartłomiej"https://zbmath.org/authors/?q=ai:dybiec.bartlomiejSummary: Stochastic restarting is a strategy of starting anew. Incorporation of the resetting to the random walks can result in a decrease in the mean first passage time due to the ability to limit unfavorably meandering, sub-optimal trajectories. In this paper, we examine how stochastic resetting influences escape dynamics from the \((-\operatorname{\infty},1)\) interval in the presence of the single-well power-law \(|x |^\kappa\) potentials with \(\kappa>0\). Examination of the mean first passage time is complemented by the analysis of the coefficient of variation, which provides a robust and reliable indicator assessing the efficiency of stochastic resetting. The restrictive nature of resetting is compared to placing a reflective boundary in the system at hand. In particular, for each potential, the position of the reflecting barrier giving the same mean first passage time as the optimal resetting rate is determined. Finally, in addition to reflecting, we compare the effectiveness of other resetting strategies with respect to optimization of the mean first passage time.
{\copyright 2023 American Institute of Physics}Feynman-Kac equation for Brownian non-Gaussian polymer diffusionhttps://zbmath.org/1541.600672024-09-27T17:47:02.548271Z"Zhou, Tian"https://zbmath.org/authors/?q=ai:zhou.tian"Wang, Heng"https://zbmath.org/authors/?q=ai:wang.heng|wang.heng.1"Deng, Weihua"https://zbmath.org/authors/?q=ai:deng.weihuaSummary: The motion of the polymer center of mass (CM) is driven by two stochastic terms that are Gaussian white noise generated by standard thermal stirring and chain polymerization processes, respectively. It can be described by the Langevin equation and is Brownian non-Gaussian by calculating the kurtosis. We derive the forward Fokker-Planck equation governing the joint distribution of the motion of CM and the chain polymerization process. The backward Fokker-Planck equation governing only the probability density function (PDF) of CM position for a given number of monomers is also derived. We derive the forward and backward Feynman-Kac equations for the functional distribution of the motion of the CM, respectively, and present some of their applications, which are validated by a deep learning method based on backward stochastic differential equations (BSDEs), i.e. the deep BSDE method.
{{\copyright} 2024 IOP Publishing Ltd}Temporal correlation in the inverse-gamma polymerhttps://zbmath.org/1541.600822024-09-27T17:47:02.548271Z"Basu, Riddhipratim"https://zbmath.org/authors/?q=ai:basu.riddhipratim"Seppäläinen, Timo"https://zbmath.org/authors/?q=ai:seppalainen.timo"Shen, Xiao"https://zbmath.org/authors/?q=ai:shen.xiaoSummary: Understanding the decay of correlations in time for (1+1)-dimensional polymer models in the KPZ universality class has been a challenging topic. Following numerical studies by physicists, concrete conjectures were formulated by \textit{P. L. Ferrari} and \textit{H. Spohn} [SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 074, 23 p. (2016; Zbl 1344.60095)] in the context of planar exponential last passage percolation. These have mostly been resolved by various authors. In the context of positive temperature lattice models, however, these questions have remained open. We consider the time correlation problem for the exactly solvable inverse-gamma polymer in \(\mathbb{Z}^2\). We establish, up to constant factors, upper and lower bounds on the correlation between free energy functions for two polymers rooted at the origin (droplet initial condition) when the endpoints are either close together or far apart. We find the same exponents as predicted in [loc. cit.]. Our arguments rely on the understanding of stationary polymers, coupling, and random walk comparison. We use recently established moderate deviation estimates for the free energy. In particular, we do not require asymptotic analysis of complicated exact formulae.On the rate of normal approximation for Poisson continuum percolationhttps://zbmath.org/1541.600832024-09-27T17:47:02.548271Z"Lo, Tiffany Y. Y."https://zbmath.org/authors/?q=ai:lo.tiffany-y-y"Xia, Aihua"https://zbmath.org/authors/?q=ai:xia.aihuaSummary: It is known that the cardinality of the largest cluster of a percolating Poisson process restricted to a large finite box is asymptotically normal. In this note, we establish a rate of convergence for the statement. As each point in the largest cluster is determined by points as far as the diameter of the box, known results in the literature of normal approximation for Poisson functionals appear to be inapplicable. To disentangle the long-range dependence of the largest cluster, we use the fact that the second largest cluster has comparatively shorter range of dependence to restrict the range of dependence, apply a recent result of \textit{L. H. Y. Chen} et al. [Ann. Appl. Probab. 31, No. 6, 2881--2923 (2021; Zbl 1484.60025)] to obtain a Berry-Esseen type bound for the normal approximation of the number of points belonging to clusters that have a restricted range of dependence, and then estimate the gap between this quantity and the cardinality of the largest cluster.Detecting structured signals in Ising modelshttps://zbmath.org/1541.621052024-09-27T17:47:02.548271Z"Deb, Nabarun"https://zbmath.org/authors/?q=ai:deb.nabarun"Mukherjee, Rajarshi"https://zbmath.org/authors/?q=ai:mukherjee.rajarshi"Mukherjee, Sumit"https://zbmath.org/authors/?q=ai:mukherjee.sumit"Yuan, Ming"https://zbmath.org/authors/?q=ai:yuan.mingSummary: In this paper we study the effect of dependence on detecting a class of signals in Ising models, where the signals are present in a structured way. Examples include Ising models on lattices, and mean-field type Ising models (Erdős-Rényi, Random regular, and dense graphs). Our results rely on correlation decay and mixing type behavior for Ising models, and demonstrate the beneficial behavior of criticality in detection of strictly lower signals. As a by-product of our proof technique, we develop sharp control on mixing and spin-spin correlation for several mean-field type Ising models in all regimes of temperature-which might be of independent interest.Nonasymptotic bounds for suboptimal importance samplinghttps://zbmath.org/1541.650052024-09-27T17:47:02.548271Z"Hartmann, Carsten"https://zbmath.org/authors/?q=ai:hartmann.carsten"Richter, Lorenz"https://zbmath.org/authors/?q=ai:richter.lorenzSummary: Importance sampling is a popular variance reduction method for Monte Carlo estimation, where an evident question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically possible, in practice only suboptimal proposal distributions are available and it can often be observed numerically that those can reduce statistical performance significantly, leading to large relative errors and therefore counteracting the original intention. Previous analysis on importance sampling has often focused on asymptotic arguments that work well in a large deviations regime. In this article, we provide lower and upper bounds on the relative error in a nonasymptotic setting. They depend on the deviation of the actual proposal from optimality, and we thus identify potential robustness issues that importance sampling may have, especially in high dimensions. We particularly focus on path sampling problems for diffusion processes with nonvanishing noise, for which generating good proposals comes with additional technical challenges. We provide numerous numerical examples that support our findings and demonstrate the applicability of the derived bounds.Finite difference approximations of the spatially homogeneous Fokker-Planck-Landau equationhttps://zbmath.org/1541.650752024-09-27T17:47:02.548271Z"Wollman, Stephen"https://zbmath.org/authors/?q=ai:wollman.stephenSummary: Finite difference methods are developed for approximating the spatially homogeneous Fokker-Planck-Landau equation for Coulomb collisions. The numerical methods apply the Fast Fourier Transform to improve time efficiency. Computational work is then done to compare the numerical approximations using FFT with the numerical method of
\textit{S. Wollman} [J. Comput. Appl. Math. 324, 173--203 (2017; Zbl 1365.65199)]. In addition, some computations are done to verify the theoretical rate of convergence of the FPL equation proved in
[\textit{R. M. Strain} and \textit{Y. Guo}, Arch. Ration. Mech. Anal. 187, No. 2, 287--339 (2008; Zbl 1130.76069)].A non-parametric gradient-based shape optimization approach for solving inverse problems in directed self-assembly of block copolymershttps://zbmath.org/1541.650812024-09-27T17:47:02.548271Z"Bochkov, Daniil"https://zbmath.org/authors/?q=ai:bochkov.daniil"Gibou, Frederic"https://zbmath.org/authors/?q=ai:gibou.fredericSummary: We consider the inverse problem of finding guiding pattern shapes that result in desired self-assembly morphologies of block copolymer melts. Specifically, we model polymer self-assembly using the self-consistent field theory and derive, in a non-parametric setting, the sensitivity of the dissimilarity between the desired and the actual morphologies to arbitrary perturbations in the guiding pattern shape. The sensitivity is then used for the optimization of the confining pattern shapes such that the dissimilarity between the desired and the actual morphologies is minimized. The efficiency and robustness of the proposed gradient-based algorithm are demonstrated in a number of examples related to templating vertical interconnect accesses (VIA).A fast algebraic multigrid solver and accurate discretization for highly anisotropic heat flux. I: Open field lineshttps://zbmath.org/1541.651152024-09-27T17:47:02.548271Z"Wimmer, Golo A."https://zbmath.org/authors/?q=ai:wimmer.golo-a"Southworth, Ben S."https://zbmath.org/authors/?q=ai:southworth.ben-s"Gregory, Thomas J."https://zbmath.org/authors/?q=ai:gregory.thomas-j"Tang, Xian-Zhu"https://zbmath.org/authors/?q=ai:tang.xian-zhuSummary: We present a novel solver technique for the anisotropic heat flux equation, aimed at the high level of anisotropy seen in magnetic confinement fusion plasmas. Such problems pose two major challenges: (i) discretization accuracy and (ii) efficient implicit linear solvers. We simultaneously address each of these challenges by constructing a new finite element discretization with excellent accuracy properties, tailored to a novel solver approach based on algebraic multigrid (AMG) methods designed for advective operators. We pose the problem in a mixed formulation, introducing the directional temperature gradient as an auxiliary variable. The temperature and auxiliary fields are discretized in a scalar discontinuous Galerkin space with upwinding principles used for discretizations of advection. We demonstrate the proposed discretization's superior accuracy over other discretizations of anisotropic heat flux, achieving error \(1000\times\) smaller for anisotropy ratio of \(10^9\), for \textit{closed field lines.} The block matrix system is reordered and solved in an approach where the two advection operators are inverted using AMG solvers based on approximate ideal restriction, which is particularly efficient for upwind discontinuous Galerkin discretizations of advection. To ensure that the advection operators are nonsingular, in this paper we restrict ourselves to considering open (acyclic) magnetic field lines for the linear solvers. We demonstrate fast convergence of the proposed iterative solver in highly anisotropic regimes where other diffusion-based AMG methods fail.A linearizing-decoupling finite element method with stabilization for the Peterlin viscoelastic modelhttps://zbmath.org/1541.651162024-09-27T17:47:02.548271Z"Xia, Lekang"https://zbmath.org/authors/?q=ai:xia.lekang"Zhou, Guanyu"https://zbmath.org/authors/?q=ai:zhou.guanyuSummary: We propose a linearizing-decoupling finite element method for the nonstationary diffusive Peterlin viscoelastic system with shear-dependent viscosity modeling the incompressible polymeric fluid flow, where the equation of the conformation tensor \(\boldsymbol{C}\) contains a diffusion term with a tiny diffusion coefficient \(\epsilon\). By using the stabilizing terms \(\alpha_1^{-1} \Delta (\boldsymbol{u}^{n+1} - \boldsymbol{u}^n)\) and \(\alpha_2^{-1} \Delta (\boldsymbol{C}^{n+1} - \boldsymbol{C}^n)\), at every time level, the velocity \(\boldsymbol{u}\) and each component \(C_{ij}\) of the conformation tensor \(\boldsymbol{C}\) can be computed in parallel by our scheme. We obtain the error estimate \(C(\tau + h^2)\) for the P2/P1/P2 element, where the constant \(C\) depends on the norm of the solution but is not explicitly related to the reciprocal of \(\epsilon\). We conduct several numerical simulations and compute the experimental convergence rates to compare with the theoretical results.Numerical study of transient Wigner-Poisson model for RTDs: numerical method and its applicationshttps://zbmath.org/1541.651212024-09-27T17:47:02.548271Z"Jiang, Haiyan"https://zbmath.org/authors/?q=ai:jiang.haiyan"Lu, Tiao"https://zbmath.org/authors/?q=ai:lu.tiao"Yao, Wenqi"https://zbmath.org/authors/?q=ai:yao.wenqi"Zhang, Weitong"https://zbmath.org/authors/?q=ai:zhang.weitongSummary: The system of transient Wigner-Poisson equations (TWPEs) is a common model to describe carrier transport in quantum devices. In this paper, we design a second-order semi-implicit time integration scheme for TWPEs with the inflow boundary conditions, and a hybrid sinc-Galerkin/finite-difference method [\textit{H. Jiang} et al., J. Comput. Appl. Math. 409, Article ID 114152, 12 p. (2022; Zbl 1487.81086)] is applied for the spatial discretization. The fully-discretized system is rigorously proved to be unconditionally \(L^2\)-stable, and the computational cost is comparable with that of the second-order explicit Runge-Kutta scheme (ERK2). The numerical method is applied to study a double-barrier resonant tunneling diode (RTD), where representative characteristics of RTDs, including the resonant tunneling effect, bistability and the intrinsic high-frequency current oscillation, are simulated successfully.A second-order \(\mathrm{SO}(3)\)-preserving and energy-stable scheme for orthonormal frame gradient flow model of biaxial nematic liquid crystalshttps://zbmath.org/1541.651292024-09-27T17:47:02.548271Z"Wang, Hanbin"https://zbmath.org/authors/?q=ai:wang.hanbin"Xu, Jie"https://zbmath.org/authors/?q=ai:xu.jie.4"Yang, Zhiguo"https://zbmath.org/authors/?q=ai:yang.zhiguoThe paper addresses the challenge of developing a numerical scheme for the gradient flow of biaxial nematic liquid crystals that preserves the orthonormal frame structure and maintains energy stability. Biaxial nematic liquid crystals, unlike their uniaxial counterparts, exhibit spontaneous non-axisymmetric local anisotropy, which has important implications for various technological applications including in semiconductors. The mathematical modelling of these materials involves complex, nonlinear systems governed by the orthonormal frame gradient flow.
To tackle this problem, the authors develop a novel second-order generalised rotational discrete gradient scheme. This method reformulates the original gradient flow system into an equivalent generalised rotational form, facilitating the development of a discrete gradient approximation that adheres to the energy difference relation. The scheme is notable for strictly maintaining the orthonormality of the tensor field and ensuring energy dissipation at the discrete level, independent of the time step sizes.
The methods employed include a detailed mathematical formulation of the biaxial liquid crystal energy functional, followed by the development of a generalised rotational form of the gradient flow system. The discrete gradient scheme is implemented using a time-centered Crank-Nicolson method, and an inexact Newton-Krylov iterative solver is used to handle the nonlinearities in the system. The scheme's robustness is further enhanced by a time-adaptive strategy that dynamically adjusts the time step sizes based on the evolution of the system's energy, thereby improving computational efficiency.
The main findings of the manuscript demonstrate the efficacy of the proposed scheme through extensive numerical experiments. The authors provide numerical results that validate the accuracy, efficiency, unconditional stability, and \(\mathrm{SO}(3)\)-preserving properties of the scheme. The simulations reveal that the scheme can handle highly anisotropic derivative terms and strong nonlinear couplings effectively. The results highlight the ability of the biaxial orthonormal frame gradient flow model to capture complex, non-axisymmetric local anisotropies that are not represented by uniaxial models.
In conclusion, this research makes a significant contribution to the field of computational modelling of liquid crystals, particularly in the context of biaxial nematic phases. The proposed scheme not only advances the numerical approximation techniques for such systems but also sets a foundation for future work in the computational study of liquid crystals with complex elastic properties. This study is pivotal for researchers and practitioners involved in the modelling and simulation of anisotropic materials, providing a robust and efficient tool for exploring the dynamics of biaxial nematic liquid crystals.
Reviewer: Denys Dutykh (Le Bourget-du-Lac)Langevin dynamics for adaptive inverse reinforcement learning of stochastic gradient algorithmshttps://zbmath.org/1541.683172024-09-27T17:47:02.548271Z"Krishnamurthy, Vikram"https://zbmath.org/authors/?q=ai:krishnamurthy.vikram"Yin, George"https://zbmath.org/authors/?q=ai:yin.george-gangSummary: Inverse reinforcement learning (IRL) aims to estimate the reward function of optimizing agents by observing their response (estimates or actions). This paper considers IRL when noisy estimates of the gradient of a reward function generated by multiple stochastic gradient agents are observed. We present a generalized Langevin dynamics algorithm to estimate the reward function \(R(\theta)\); specifically, the resulting Langevin algorithm asymptotically generates samples from the distribution proportional to \(\exp(R(\theta))\). The proposed adaptive IRL algorithms use kernel-based passive learning schemes. We also construct multi-kernel passive Langevin algorithms for IRL which are suitable for high dimensional data. The performance of the proposed IRL algorithms are illustrated on examples in adaptive Bayesian learning, logistic regression (high dimensional problem) and constrained Markov decision processes. We prove weak convergence of the proposed IRL algorithms using martingale averaging methods. We also analyze the tracking performance of the IRL algorithms in non-stationary environments where the utility function \(R(\theta)\) has a hyper-parameter that jump changes over time as a slow Markov chain which is not known to the inverse learner. In this case, martingale averaging yields a Markov switched diffusion limit as the asymptotic behavior of the IRL algorithm.Mechanically manipulated in-plane electric currents and thermal control in piezoelectric semiconductor filmshttps://zbmath.org/1541.740602024-09-27T17:47:02.548271Z"Zhang, Gongye"https://zbmath.org/authors/?q=ai:zhang.gongye"Kong, Xueqian"https://zbmath.org/authors/?q=ai:kong.xueqian"Mi, Changwen"https://zbmath.org/authors/?q=ai:mi.changwenSummary: This study explores the new findings of in-plane mechanical forces on electric currents and thermal control in piezoelectric semiconductors. The thermo-electro-elastic theory is considered based on the thermo-piezoelectricity theory and drift-diffusion theory for semiconductors. A two-dimensional nonlinear model for in-plane deformations of piezoelectric semiconductor films is developed, where thermo-elastic, pyroelectric and thermoelectric couplings are involved. The newly developed nonlinear equations are directly solved based on the finite element method, while linearized equations derived from the nonlinear theory and corresponding analytical solutions are also obtained as a reference for validation. Our findings indicate that the in-plane mechanical forces exerted on piezoelectric semiconductors significantly influence both currents and thermal fluxes through piezoelectric coupling. Specifically, the angle of in-plane mechanical force relative to the c-axis significantly impacts the currents, with the potential to suppress, enhance or alter the direction, thereby affecting the temperature field. Based on these findings, an application simulation that focuses on mechanically induced current manipulation and thermal control is introduced and realized.Unsteady boundary layer flow and heat transfer over a stretching sheet with a convective boundary condition in a nanofluidhttps://zbmath.org/1541.760302024-09-27T17:47:02.548271Z"Mansur, Syahira"https://zbmath.org/authors/?q=ai:mansur.syahira"Ishak, Anuar"https://zbmath.org/authors/?q=ai:ishak.anuarSummary: The heat transfer characteristics of an unsteady boundary layer flow of a nanofluid past a stretching sheet with a convective surface boundary condition are studied. Numerical solutions to the governing equations are obtained using a shooting method. The results are found for the reduced Nusselt number as well as the temperature profiles for some values of the unsteadiness parameter, convective parameter, thermophoresis parameter, Brownian motion parameter and Lewis number. The results indicate that the reduced Nusselt number is lower for higher values of the unsteadiness parameter, thermophoresis parameter, Brownian motion parameter and Lewis number. However, the reduced Nusselt number increases with increasing values of the convective parameter.
For the entire collection see [Zbl 1388.00025].Boundary layer flow and heat transfer past a shrinking sheet in a copper-water nanofluidhttps://zbmath.org/1541.760682024-09-27T17:47:02.548271Z"Aleng, Nur Liyana"https://zbmath.org/authors/?q=ai:aleng.nur-liyana"Bachok, Norfifah"https://zbmath.org/authors/?q=ai:bachok.norfifah"Arifin, Norihan Md."https://zbmath.org/authors/?q=ai:arifin.norihan-md"Ishak, Anuar"https://zbmath.org/authors/?q=ai:ishak.anuarSummary: The problem of laminar fluid flow which results from the shrinking of a flat surface in a water-based copper (Cu) nanofluid is considered in this study. The model used for the nanofluid incorporates the effect of the nanoparticles volume fraction. The governing partial differential equations are transformed into ordinary differential equations by similarity transformations. The transformed equations are solved numerically by using a shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles and temperature profiles are presented for different values of the governing parameters. The analysis reveals the conditions for the existence of the steady boundary layer flow due to shrinking of the sheet and it is found that when the mass suction parameter exceeds a certain critical value, steady flow is possible. Dual solutions for the velocity and temperature distributions are obtained. With increasing values of the nanoparticles volume fraction, the skin friction and the heat transfer coefficient increase.
For the entire collection see [Zbl 1388.00025].Mixed convection boundary-layer flow near the stagnation-point on a vertical surface in a banofluidhttps://zbmath.org/1541.760812024-09-27T17:47:02.548271Z"Dasman, Anisah"https://zbmath.org/authors/?q=ai:dasman.anisah"Othman, Noor Adila"https://zbmath.org/authors/?q=ai:othman.noor-adila"Ahmad, Salimah"https://zbmath.org/authors/?q=ai:ahmad.salimah"Yacob, Nor Azizah"https://zbmath.org/authors/?q=ai:yacob.nor-azizah"Ishak, Anuar"https://zbmath.org/authors/?q=ai:ishak.anuarSummary: The steady boundary layer flow of a nanofluid near a stagnation point on a vertical surface is investigated. The velocity of the external flow is assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically using the Keller box method with the help of MATLAB software. The effects of the Brownian motion parameter, thermophoresis parameter, and Lewis number on the fluid flow, heat and mass transfer characteristics are analyzed and discussed. It is found that for assisting flow, the friction at the surface decreases with an increase in Lewis number while it decreases with increasing Brownian motion and thermophoresis parameters. However, the effects of Lewis number for the opposing flow showed a different trend. Moreover, increasing the Brownian motion parameter, the thermophoresis parameter and the Lewis number are to decrease the heat transfer rate at the surface for both assisting and opposing flows, but on the other hand increase the mass transfer rate at the surface.
For the entire collection see [Zbl 1388.00025].Mixed convection flow about a solid sphere with constant heat flux embedded in a porous medium filled by a nanofluid: Buongiorno-Darcy modelhttps://zbmath.org/1541.760822024-09-27T17:47:02.548271Z"Tham, Leony"https://zbmath.org/authors/?q=ai:tham.leony"Nazar, Roslinda"https://zbmath.org/authors/?q=ai:nazar.roslinda-mohd"Pop, Ioan"https://zbmath.org/authors/?q=ai:pop.ioan.1Summary: The laminar mixed convection boundary layer flow about a solid sphere in a nanofluid, which is maintained at a constant surface heat flux, has been studied via the nanofluid Buongiorno model and porous medium Darcy model for both cases of a heated and cooled sphere. The resulting system of nonlinear partial differential equations is solved numerically using an implicit finite-difference scheme known as the Keller box method. The solutions for the flow and heat transfer characteristics are evaluated numerically and studied for various values of the governing parameters, namely the Brownian motion parameter, thermophoresis parameter and mixed convection parameter. It is found that the boundary layer separates from the sphere for some negative values of the mixed convection parameter (opposing flow), and increasing the mixed convection parameter delays the boundary layer separation and the separation can be completely suppressed for sufficiently large values of the mixed convection parameter.
For the entire collection see [Zbl 1388.00025].Plasma theory. An advanced guide for graduate studentshttps://zbmath.org/1541.761062024-09-27T17:47:02.548271Z"Rozhansky, Vladimir"https://zbmath.org/authors/?q=ai:rozhansky.vladimirPublisher's description: This textbook, based on the author's classroom-tested lecture course, helps graduate students master the advanced plasma theory needed to unlock results at the forefront of current research. It is structured around a two semester course, beginning with kinetic theory and transport processes, while the second semester is devoted to plasma dynamics, including MHD theory, equilibrium, and stability. More advanced problems such as neoclassical theory, stochastization of the magnetic field lines, and edge plasma physics are also considered, and each chapter ends with an illustrative example which demonstrates a concrete application of the theory. The distinctive feature of this book is that, unlike most other advanced plasma science texts, phenomena in both low and high temperature plasma are considered simultaneously so that theory of slightly ionized and fully ionized plasmas is presented holistically. This book will therefore be ideal as a classroom text or self-study guide for a wide cohort of graduate students working in different areas like nuclear fusion, gas discharge physics, low temperature plasma applications, astrophysics, and more. It is also a useful reference for more seasoned researchers.Calculation of partition function of Ising model on quantum computerhttps://zbmath.org/1541.810422024-09-27T17:47:02.548271Z"Laba, H. P."https://zbmath.org/authors/?q=ai:laba.h-p"Tkachuk, V. M."https://zbmath.org/authors/?q=ai:tkachuk.volodymyr-mSummary: We study the partition function of the Ising model on a graph with the help of quantum computing. The Boltzmann factor is modeled on a quantum computer as a trace of some evolution operator with effective Hamiltonian over ancilla spins (qubits) corresponding to graph links. We propose two methods for this which are based on effective Hamiltonian with three-spin interaction and on two-spin interaction. The limit of small temperatures allows us to find the ground state of the system that is related to the discrete combinatorial optimization problem. The partition function of the Ising model for two-spin clusters is calculated on IBM's quantum computer. The possibility of finding ground state is also demonstrated for two-spin clusters.Homological quantum rotor codes: logical qubits from torsionhttps://zbmath.org/1541.810482024-09-27T17:47:02.548271Z"Vuillot, Christophe"https://zbmath.org/authors/?q=ai:vuillot.christophe"Ciani, Alessandro"https://zbmath.org/authors/?q=ai:ciani.alessandro"Terhal, Barbara M."https://zbmath.org/authors/?q=ai:terhal.barbara-mSummary: We formally define homological quantum rotor codes which use multiple quantum rotors to encode logical information. These codes generalize homological or CSS quantum codes for qubits or qudits, as well as linear oscillator codes which encode logical oscillators. Unlike for qubits or oscillators, homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code, depending on the homology of the underlying chain complex. In particular, a code based on the chain complex obtained from tessellating the real projective plane or a Möbius strip encodes a qubit. We discuss the distance scalling for such codes which can be more subtle than in the qubit case due to the concept of logical operator spreading by continuous stabilizer phase-shifts. We give constructions of homological quantum rotor codes based on 2D and 3D manifolds as well as products of chain complexes. Superconducting devices being composed of islands with integer Cooper pair charges could form a natural hardware platform for realizing these codes: we show that the \(0 - \pi\) qubit as well as Kitaev's current-mirror qubit -- also known as the Möbius strip qubit -- are indeed small examples of such codes and discuss possible extensions.Spectral and dynamical contrast on highly correlated Anderson-type modelshttps://zbmath.org/1541.810542024-09-27T17:47:02.548271Z"Matos, Rodrigo"https://zbmath.org/authors/?q=ai:matos.rodrigo"Mavi, Rajinder"https://zbmath.org/authors/?q=ai:mavi.rajinder"Schenker, Jeffrey"https://zbmath.org/authors/?q=ai:schenker.jeffrey-hSummary: We study spectral and dynamical properties of random Schrödinger operators \(H_{\text{Vert}}=-A_{\mathbb{G}_{\text{Vert}}}+V_{\omega }\) and \(H_{\text{Diag}}=-A_{\mathbb{G}_{\text{Diag}}}+V_{\omega }\) on certain two-dimensional graphs \({\mathbb{G}_{\text{Vert}}}\) and \({\mathbb{G}_{\text{Diag}}} \). Differently from the standard Anderson model, the random potentials are not independent but, instead, are constant along any vertical line, i.e \(V_{\omega }(\boldsymbol{n})=\omega (n_1)\), for \(\boldsymbol{n}=(n_1,n_2)\). In particular, the potentials studied here exhibit long range correlations. We present examples where geometric changes to the underlying graph, combined with high disorder, have a significant impact on the spectral and dynamical properties of the operators, leading to contrasting behaviors for the ``diagonal'' and ``vertical'' models. Moreover, the ``vertical'' model exhibits a sharp phase transition within its (purely) absolutely continuous spectrum. This is captured by the notions of transient and recurrent components of the absolutely continuous spectrum, introduced by \textit{J. E. Avron} and \textit{B. Simon} [J. Funct. Anal. 43, 1--31 (1981; Zbl 0488.47021)].Topology of 2D Dirac operators with variable mass and an application to shallow-water waveshttps://zbmath.org/1541.810552024-09-27T17:47:02.548271Z"Rossi, Sylvain"https://zbmath.org/authors/?q=ai:rossi.sylvain"Tarantola, Alessandro"https://zbmath.org/authors/?q=ai:tarantola.alessandroSummary: A Dirac operator on the plane with constant (positive) mass is a Chern insulator, sitting in class D of the Kitaev table. Despite its simplicity, this system is topologically ill-behaved: the non-compact Brillouin zone prevents definition of a bulk invariant, and naively placing the model on a manifold with boundary results in violations of the bulk-edge correspondence (BEC). We overcome both issues by letting the mass spatially vary in the vertical direction, interpolating between the original model and its negative-mass counterpart. Proper bulk and edge indices can now be defined. They are shown to coincide, thereby embodying BEC.
The shallow-water model exhibits the same illnesses as the 2D massive Dirac. Identical problems suggest identical solutions, and indeed extending the approach above to this setting yields proper indices and another instance of BEC.
{{\copyright} 2024 The Author(s). Published by IOP Publishing Ltd}Bethe ansatz solutions and hidden \(sl(2)\) algebraic structure for a class of quasi-exactly solvable systemshttps://zbmath.org/1541.810712024-09-27T17:47:02.548271Z"Li, Siyu"https://zbmath.org/authors/?q=ai:li.siyu"Marquette, Ian"https://zbmath.org/authors/?q=ai:marquette.ian"Zhang, Yao-Zhong"https://zbmath.org/authors/?q=ai:zhang.yaozhongSummary: The construction of analytic solutions for quasi-exactly solvable systems is an interesting problem. We revisit a class of models for which the odd solutions were largely missed previously in the literature: the anharmonic oscillator, the singular anharmonic oscillator, the generalized quantum isotonic oscillator, non-polynomially deformed oscillator, and the Schrödinger system from the kink stability analysis of \(\phi^6\)-type field theory. We present a systematic and unified treatment for the odd and even sectors of these models. We find generic closed-form expressions for constraints to the allowed model parameters for quasi-exact solvability, the corresponding energies and wavefunctions. We also make progress in the analysis of solutions to the Bethe ansatz equations in the spaces of model parameters and provide insight into the curves/surfaces of the allowed parameters in the parameter spaces. Most previous analyses in this aspect were on a case-by-case basis and restricted to the first excited states. We present analysis of the solutions (i.e. roots) of the Bethe ansatz equations for higher excited states (up to levels \(n=30\) or 50). The shapes of the root distributions change drastically across different regions of model parameters, illustrating phenomena analogous to phase transition in context of integrable models. Furthermore, we also obtain the \(sl(2)\) algebraization for the class of models in their respective even and odd sectors in a unified way.On the set of reduced states of translation invariant, infinite quantum systemshttps://zbmath.org/1541.810822024-09-27T17:47:02.548271Z"Blakaj, Vjosa"https://zbmath.org/authors/?q=ai:blakaj.vjosa"Wolf, Michael M."https://zbmath.org/authors/?q=ai:wolf.michael-marc|mclean-wolf.michaelSummary: The set of two-body reduced states of translation invariant, infinite quantum spin chains can be approximated from inside and outside using matrix product states and marginals of finite systems, respectively. These lead to hierarchies of algebraic approximations that become tight only in the limit of infinitely many auxiliary variables. We show that this is necessarily so for any algebraic ansatz by proving that the set of reduced states is not semialgebraic. We also provide evidence that additional elementary transcendental functions cannot lead to a finitary description.Ladder operators with no vacuum, their coherent states, and an application to graphenehttps://zbmath.org/1541.810842024-09-27T17:47:02.548271Z"Bagarello, F."https://zbmath.org/authors/?q=ai:bagarello.fabioSummary: In literature ladder operators of different nature exist. The most famous are those obeying canonical (anti-) commutation relations, but they are not the only ones. In our knowledge, all ladder operators have a common feature: the lowering operators annihilate a non zero vector, the \textit{vacuum}. This is connected to the fact that operators of these kind are often used in factorizing some positive operators, or some operators which are bounded from below. This is the case, of course, of the harmonic oscillator, but not only. In this paper we discuss what happens when considering lowering operators with no vacua. In particular, after a general analysis of this situation, we propose a possible construction of coherent states, and we apply our construction to graphene.Exact renormalization groups and transportation of measureshttps://zbmath.org/1541.810972024-09-27T17:47:02.548271Z"Shenfeld, Yair"https://zbmath.org/authors/?q=ai:shenfeld.yairSummary: This note provides a new perspective on Polchinski's exact renormalization group, by explaining how it gives rise, via the multiscale Bakry-Émery criterion, to Lipschitz transport maps between Gaussian free fields and interacting quantum and statistical field theories. Consequently, many functional inequalities can be verified for the latter field theories, going beyond the current known results.Flow equation and fermion gap in the holographic superconductorshttps://zbmath.org/1541.811472024-09-27T17:47:02.548271Z"Yuk, Taewon"https://zbmath.org/authors/?q=ai:yuk.taewon"Sin, Sang-Jin"https://zbmath.org/authors/?q=ai:sin.sang-jinSummary: We reconsider the fermion spectral function in the presence of the Cooper pair condensation and identified the interaction type of complex scalar and fermion, which gives consistent results with the expected s-wave superconductor for the first time. We derive the matrix Riccati equation, which allows the precise calculation of the fermion spectral function. Apart from the gap structure, we studied the effect of the chemical potential and the density and compared it with the BCS theory. We found that two theories give similar results in small chemical potential but very different ones in the high-density case, which we attribute to the correlation effect.The Gross-Neveu-Yukawa archipelagohttps://zbmath.org/1541.811612024-09-27T17:47:02.548271Z"Erramilli, Rajeev S."https://zbmath.org/authors/?q=ai:erramilli.rajeev-s"Iliesiu, Luca V."https://zbmath.org/authors/?q=ai:iliesiu.luca-v"Kravchuk, Petr"https://zbmath.org/authors/?q=ai:kravchuk.petr"Liu, Aike"https://zbmath.org/authors/?q=ai:liu.aike"Poland, David"https://zbmath.org/authors/?q=ai:poland.david"Simmons-Duffin, David"https://zbmath.org/authors/?q=ai:simmons-duffin.davidSummary: We perform a bootstrap analysis of a mixed system of four-point functions of bosonic and fermionic operators in parity-preserving 3d CFTs with \(O(N)\) global symmetry. Our results provide rigorous bounds on the scaling dimensions of the \(O(N)\)-symmetric Gross-Neveu-Yukawa (GNY) fixed points, constraining these theories to live in isolated islands in the space of CFT data. We focus on the cases \(N = 1, 2, 4, 8\), which have applications to phase transitions in condensed matter systems, and compare our bounds to previous analytical and numerical results.Hot and dense QCD shear viscosity at leading loghttps://zbmath.org/1541.812062024-09-27T17:47:02.548271Z"Danhoni, Isabella"https://zbmath.org/authors/?q=ai:danhoni.isabella"Moore, Guy D."https://zbmath.org/authors/?q=ai:moore.guy-dSummary: The leading-order weak-coupling shear viscosity of QCD was computed almost 20 years ago, and the extension to next-to-leading order is 4 years old. But these results have never been applied at finite baryon chemical potential \(\mu\), despite the fact that intermediate-energy heavy ion collisions and merging neutron stars may explore the Quark-Gluon Plasma in a regime where baryon chemical potentials are large. Here we extend the leading-log shear viscosity calculation to finite \(\mu\), and we argue that the convergence of the weak-coupling expansion, while questionable for achievable plasmas, should be better at \(\mu > T\) than at \(\mu = 0\).Self-dual solutions of a field theory model of two linked ringshttps://zbmath.org/1541.812162024-09-27T17:47:02.548271Z"Taklimi, Neda Abbasi"https://zbmath.org/authors/?q=ai:taklimi.neda-abbasi"Ferrari, Franco"https://zbmath.org/authors/?q=ai:ferrari.franco"Piątek, Marcin R."https://zbmath.org/authors/?q=ai:piatek.marcin-rSummary: In this work the connection established in [\textit{F. Ferrari}, Phys. Lett., A 323, No. 5--6, 351--359 (2004; Zbl 1118.81346); \textit{F. Ferrari} et al., Nucl. Phys., B 945, Article ID 114673, 35 p. (2019; Zbl 1430.82016)] between a model of two linked polymers rings with fixed Gaussian linking number forming a 4-plat and the statistical mechanics of non-relativistic anyon particles is explored. The excluded volume interactions have been switched off and only the interactions of entropic origin arising from the topological constraints are considered. An interpretation from the polymer point of view of the field equations that minimize the energy of the model in the limit in which one of the spatial dimensions of the 4-plat becomes very large is provided. It is shown that the self-dual contributions are responsible for the long-range interactions that are necessary for preserving the global topological properties of the system during the thermal fluctuations. The non self-dual part is also related to the topological constraints, and takes into account the local interactions acting on the monomers in order to prevent the breaking of the polymer lines. It turns out that the energy landscape of the two linked rings is quite complex. Assuming as a rough approximation that the monomer densities of half of the 4-plat are constant, at least two points of energy minimum are found. Classes of non-trivial self-dual solutions of the self-dual field equations are derived. One of these classes is characterized by densities of monomers that are the squared modulus of holomorphic functions. The second class is obtained under some assumptions that allow to reduce the self-dual equations to an analog of the Gouy-Chapman equation for the charge distribution of ions in a double layer capacitor. In the present case, the spatial distribution of the electric potential of the ions is replaced by the spatial distribution of the fictitious magnetic fields associated with the presence of the topological constraints. In the limit in which two of the spatial dimensions are large in comparison with the third one, we provide exact formulas for the conformations of the monomer densities of the 4-plat by using the elliptic, hyperbolic and trigonometric solutions of the sinh-Gordon and cosh-Gordon equations which have been used for instance in the construction of classical string solutions in AdS3 and dS3 [\textit{I. Bakas} and \textit{G. Pastras}, J. High Energy Phys. 2016, No. 7, Paper No. 70, 53 p. (2016; Zbl 1390.81407)].Spectral approximation scheme for a hybrid, spin-density Kohn-Sham density-functional theory in an external (nonuniform) magnetic field and a collinear exchange-correlation energyhttps://zbmath.org/1541.812222024-09-27T17:47:02.548271Z"Melgaard, M."https://zbmath.org/authors/?q=ai:melgaard.michael|melgard.m"Syrjanen, V. J. J."https://zbmath.org/authors/?q=ai:syrjanen.v-j-jSummary: We provide a mathematical justification of a spectral approximation scheme known as spectral binning for the Kohn-Sham spin density-functional theory in the presence of an external (nonuniform) magnetic field and a collinear exchange-correlation energy term. We use an extended density-only formulation for modeling the magnetic system. No current densities enter the description in this formulation, but the particle density is split into different spin components. By restricting the exchange-correlation energy functional to be of a collinear LSDA form, we prove a series of results which enable us to mathematically justify the spectral binning scheme using the method of Gamma-convergence, in conjunction with auxiliary steps involving recasting the electrostatic potentials, justifying the spectral approximation by making a spectral decomposition of the Hamiltonian and ``linearizing'' the latter Hamiltonian.Infinite critical Boson induced non-Fermi liquid in \(d = 3 - \epsilon\) dimensionshttps://zbmath.org/1541.812252024-09-27T17:47:02.548271Z"Pan, Zhiming"https://zbmath.org/authors/?q=ai:pan.zhiming"Zhang, Xiao-Tian"https://zbmath.org/authors/?q=ai:zhang.xiaotianSummary: We study the fermion-boson coupled system in \(d = 3 - \epsilon\) space dimensions near the quantum phase transition; infinite many boson modes locating on a sphere become critical simultaneously, which is dubbed ``critical boson surface'' (CBS). The fermions on the Fermi surface can be scattered to nearby points locating on a boson ring in the low-energy limit. The large number of the boson scattering channels \(N\) renders the well-known Landau damping effect largely suppressed. We propose an effective theory for a single point on the Fermi surface and the associated critical boson ring induced by the boson scattering channels. Based on the effective model, one-loop renormalization group analysis is performed with asymptotic \(\epsilon\)-expansion. The fermion self-energy and Yukawa interaction vertex are dressed with \(\epsilon\) poles and are largely enhanced due to the presence of critical boson ring. The imaginary part of the self-energy exhibits a linear-in frequency dependence and the real part gives a vanishing quasiparticle weight in the low-energy limit, which signatures the celebrated ``marginal Fermi liquid'' behavior. We find a novel non-Fermi liquid fixed point, at which the critical properties show features associated with the CBS.Effect of the three-body interactions on the reduction of the exchange dipolar termhttps://zbmath.org/1541.812272024-09-27T17:47:02.548271Z"Kouidri, Smain"https://zbmath.org/authors/?q=ai:kouidri.smainSummary: We focus our study on the effect of the exchange dipolar term in the absence/presence of three-body interactions for the Bose dipolar gas using two approximations firstly that of Hartree-Fock-Bogoliubov Popov (HFB-P) where the anomalous density is totally neglected and secondly the generalized Hartree-Fock-Bogoliubov (GHFB) approximation which takes it into account. The aim is to determine the three densities: the condensed density, the non-condensed density and the anomalous density \textit{via} different aspect ratios. The analyze of the comportment of the exchange dipolar term as a function of \(\frac{T}{T_c}\) and the role of the effect of three-body interactions played in the treatment of this physical quantity and more particularly the collective excitation modes take place in this work.Quantum heat machines enabled by twisted geometryhttps://zbmath.org/1541.820012024-09-27T17:47:02.548271Z"Filgueiras, Cleverson"https://zbmath.org/authors/?q=ai:filgueiras.cleverson"Rojas, Moises"https://zbmath.org/authors/?q=ai:rojas.moises"Silva, Edilberto O."https://zbmath.org/authors/?q=ai:silva.edilberto-o"Romero, Carlos"https://zbmath.org/authors/?q=ai:romero.carlos-santiuste|romero.carlos|romero.carlos-barronSummary: In this paper, we analyze the operation of an Otto cycle heat machine driven by a non-interacting two-dimensional electron gas on a twisted geometry. We show that due to both the energy quantization on this structure and the adiabatic transformation of the number of complete twists per unit length of a helicoid, the machine performance in terms of output work, efficiency, and operation mode can be altered. We consider the deformations as in a spring, which is either compressed or stretched from its resting position. The realization of classically inconceivable Otto machines, with an incompressible sample, can be realized as well. The energy-level spacing of the system is the quantity that is being either compressed or stretched. These features are due to the existence of an effective geometry-induced quantum potential which is of pure quantum-mechanical origin.Connection probabilities of multiple FK-Ising interfaceshttps://zbmath.org/1541.820022024-09-27T17:47:02.548271Z"Feng, Yu"https://zbmath.org/authors/?q=ai:feng.yu"Peltola, Eveliina"https://zbmath.org/authors/?q=ai:peltola.eveliina"Wu, Hao"https://zbmath.org/authors/?q=ai:wu.hao.2Summary: We find the scaling limits of a general class of boundary-to-boundary connection probabilities and multiple interfaces in the critical planar FK-Ising model, thus verifying predictions from the physics literature. We also discuss conjectural formulas using Coulomb gas integrals for the corresponding quantities in general critical planar random-cluster models with cluster-weight \({q \in [1,4)}\). Thus far, proofs for convergence, including ours, rely on discrete complex analysis techniques and are beyond reach for other values of \(q\) than the FK-Ising model \((q=2)\). Given the convergence of interfaces, the conjectural formulas for other values of \(q\) could be verified similarly with relatively minor technical work. The limit interfaces are variants of \(\mathrm{SLE}_\kappa\) curves (with \(\kappa = 16/3\) for \(q=2\)). Their partition functions, that give the connection probabilities, also satisfy properties predicted for correlation functions in conformal field theory (CFT), expected to describe scaling limits of critical random-cluster models. We verify these properties for all \(q \in [1,4)\), thus providing further evidence of the expected CFT description of these models.Villain model with long-range couplingshttps://zbmath.org/1541.820032024-09-27T17:47:02.548271Z"Giachetti, Guido"https://zbmath.org/authors/?q=ai:giachetti.guido"Defenu, Nicolò"https://zbmath.org/authors/?q=ai:defenu.nicolo"Ruffo, Stefano"https://zbmath.org/authors/?q=ai:ruffo.stefano"Trombettoni, Andrea"https://zbmath.org/authors/?q=ai:trombettoni.andreaSummary: The nearest-neighbor Villain, or periodic Gaussian, model is a useful tool to understand the physics of the topological defects of the two-dimensional nearest-neighbor \(XY\) model, as the two models share the same symmetries and are in the same universality class. The long-range counterpart of the two-dimensional \(XY\) has been recently shown to exhibit a non-trivial critical behavior, with a complex phase diagram including a range of values of the power-law exponent of the couplings decay, \(\sigma\), in which there are a magnetized, a disordered and a critical phase [\textit{G. Giachetti} et al., Phys. Rev. Lett. 127, No. 15, Article ID 156801, 7 p. (2021; \url{doi:10.1103/PhysRevLett.127.156801})]. Here we address the issue of whether the critical behavior of the two-dimensional \(XY\) model with long-range couplings can be described by the Villain counterpart of the model. After introducing a suitable generalization of the Villain model with long-range couplings, we derive a set of renormalization-group equations for the vortex-vortex potential, which differs from the one of the long-range \(XY\) model, signaling that the decoupling of spin-waves and topological defects is no longer justified in this regime. The main results are that for \(\sigma < 2\) the two models no longer share the same universality class. Remarkably, within a large region of its the phase diagram, the Villain model is found to behave similarly to the one-dimensional Ising model with \(1/r^2\) interactions.Multicriticality in Yang-Lee edge singularityhttps://zbmath.org/1541.820042024-09-27T17:47:02.548271Z"Lencsés, Máté"https://zbmath.org/authors/?q=ai:lencses.mate"Miscioscia, Alessio"https://zbmath.org/authors/?q=ai:miscioscia.alessio"Mussardo, Giuseppe"https://zbmath.org/authors/?q=ai:mussardo.giuseppe"Takács, Gábor"https://zbmath.org/authors/?q=ai:takacs.gaborSummary: In this paper we study the non-unitary deformations of the two-dimensional Tricritical Ising Model obtained by coupling its two spin \(\mathbb{Z}_2\) odd operators to imaginary magnetic fields. Varying the strengths of these imaginary magnetic fields and adjusting correspondingly the coupling constants of the two spin \(\mathbb{Z}_2\) even fields, we establish the presence of two universality classes of infrared fixed points on the critical surface. The first class corresponds to the familiar Yang-Lee edge singularity, while the second class to its tricritical version. We argue that these two universality classes are controlled by the conformal non-unitary minimal models \(\mathcal{M}(2, 5)\) and \(\mathcal{M}(2, 7)\) respectively, which is supported by considerations based on \(\boldsymbol{PT}\) symmetry and the corresponding extension of Zamolodchikov's \(c\)-theorem, and also verified numerically using the truncated conformal space approach. Our results are in agreement with a previous numerical study of the lattice version of the Tricritical Ising Model [\textit{G. von Gehlen}, Int. J. Mod. Phys. B 8, No. 25--26, 3507--3529 (1994; \url{doi:10.1142/S0217979294001494}), see also Zbl 0877.60087]. We also conjecture the classes of universality corresponding to higher non-unitary multicritical points obtained by perturbing the conformal unitary models with imaginary coupling magnetic fields.Monotonicity of the scalar curvature of the quantum exponential family for transverse-field Ising chainshttps://zbmath.org/1541.820052024-09-27T17:47:02.548271Z"Nakamura, Takemi"https://zbmath.org/authors/?q=ai:nakamura.takemiThe authors investigate the monotonicity property of the scalar curvature of the quantum exponential family within simple physical systems, namely transverse-field Ising chains of various sizes. The study reveales that the monotonicity breaks down for chains of finite sizes, while it appears to hold for non-interacting or infinite-size chains. These results indicate that finite-size effects can manifest in the curvature due to monotonicity with respect to majorization.
For the entire collection see [Zbl 1528.53002].
Reviewer: Utkir A. Rozikov (Tashkent)Estimation of information theoretic measures on the Ising modelhttps://zbmath.org/1541.820062024-09-27T17:47:02.548271Z"Razak, Fatimah Abdul"https://zbmath.org/authors/?q=ai:razak.fatimah-abdul"Jensen, Henrik Jeldtoft"https://zbmath.org/authors/?q=ai:jensen.henrik-jeldtoftSummary: Information theoretic measures are especially of interest to complex systems since these are typically strongly interconnected. We propose looking at these measures in the context of statistical mechanics, the setting being the Ising model. The model is famous for the ability to replicate critical transition with simple nearest neighbour interactions. Complex systems whose main characteristic consist in essential collective behaviour takes into account instances when the whole system is interdependent and may benefit from investigations on the Ising Model. We simulate the Ising model with the Metropolis Monte Carlo algorithm and estimate these measures using time average values of the simulations with interesting results.
For the entire collection see [Zbl 1388.00025].Gibbs properties of the Bernoulli field on inhomogeneous trees under the removal of isolated siteshttps://zbmath.org/1541.820072024-09-27T17:47:02.548271Z"Henning, Florian"https://zbmath.org/authors/?q=ai:henning.florian"Külske, Christof"https://zbmath.org/authors/?q=ai:kulske.christof"Schubert, Niklas"https://zbmath.org/authors/?q=ai:schubert.niklasSummary: We consider the i.i.d. Bernoulli field \(\mu_p\) with occupation density \(p\in(0,1)\) on a possibly non-regular countably infinite tree with bounded degrees. For large \(p\), we show that the quasilocal Gibbs property, i.e. compatibility with a suitable quasilocal specification, is lost under the deterministic transformation which removes all isolated ones and replaces them by zeros, while a quasilocal specification does exist at small \(p\). \par Our results provide an example for an independent field in a spatially non-homogeneous setup which loses the quasilocal Gibbs property under a local deterministic transformation.Density of states for the Anderson model on nested fractalshttps://zbmath.org/1541.820082024-09-27T17:47:02.548271Z"Balsam, Hubert"https://zbmath.org/authors/?q=ai:balsam.hubert"Kaleta, Kamil"https://zbmath.org/authors/?q=ai:kaleta.kamil"Olszewski, Mariusz"https://zbmath.org/authors/?q=ai:olszewski.mariusz"Pietruska-Pałuba, Katarzyna"https://zbmath.org/authors/?q=ai:pietruska-paluba.katarzynaLet \(\mathfrak{K}^{\infty}\) be a planar unbounded simple nested fractal with the Good Labeling Property and let \( \mathfrak{L}\) be the associated Laplacian. The authors propose and study the random Anderson operator \(H^\omega = H_0 + V^\omega\), acting in \(L^2(\mathfrak{K}^{\infty},\mu )\) with the kinetic term \(H_0\) takes the form \(\phi(-\mathfrak{L}),\) for a sufficiently regular operator monotone function \(\phi,\) and \(V^\omega\) is the operator of multiplication by a function that is called a fractal alloy-type potential. The main goal of this paper is to establish the existence and then to study asymptotic properties of the integrated density of states of the operator \(H^\omega.\)
Reviewer: Nasir N. Ganikhodjaev (Tashkent)Low-dimensional reduction of the non-abelian quantum synchronization models on the unitary grouphttps://zbmath.org/1541.820092024-09-27T17:47:02.548271Z"Kim, Dohyun"https://zbmath.org/authors/?q=ai:kim.dohyun.2"Kim, Jeongho"https://zbmath.org/authors/?q=ai:kim.jeonghoSummary: We present a low-dimensional reduction of the non-Abelian synchronization models on the unitary group, when the initial configuration has special structures. We first consider the microscopic model, and show that the dynamics can be reduced to the \(n \)-copies of the one-dimensional Kuramoto systems, if the initial data can be represented by simultaneously diagonalizable matrices. Then, we extend the dimensional reduction to the kinetic synchronization model on \(\mathbf{U}(n) \), when the initial distribution belongs to a special family of functions called a \textit{class function}. Under this condition, a solution to the kinetic equation can be reduced to a solution to the Kuramoto-like dynamics on the \(n \)-dimensional torus \(\mathbb{T}^n \). Using these dimensional reductions and the relationship between the Kuramoto models, we establish a novel general synchronization framework for the non-Abelian synchronization models.Hypocoercivity and global hypoellipticity for the kinetic Fokker-Planck equation in \(H^k\) spaceshttps://zbmath.org/1541.820102024-09-27T17:47:02.548271Z"Zhang, Chaoen"https://zbmath.org/authors/?q=ai:zhang.chaoenSummary: The purpose of this paper is to extend the hypocoercivity results for the kinetic Fokker-Planck equation in \(H^1\) space in \textit{C. Villani}'s memoir [Hypocoercivity. Providence, RI: American Mathematical Society (AMS) (2009; Zbl 1197.35004)] to higher order Sobolev spaces. As in the \(L^2\) and \(H^1\) setting, there is lack of coercivity in \(H^k\) for the associated operator. To remedy this issue, we shall modify the usual \(H^k\) norm with certain well-chosen mixed terms and with suitable coefficients which are constructed by induction on \(k \). In parallel, a similar strategy but with coefficients depending on time (c.f. [\textit{F. Hérau}, J. Funct. Anal. 244, No. 1, 95--118 (2007; Zbl 1120.35016)]), usually referred as Hérau's method, can be employed to prove global hypoellipticity in \(H^k \). The exponents in our regularity estimates are optimal in short time. Moreover, as in our recent work [the author et al., J. Math. Pures Appl. (9) 150, 1--23 (2021; Zbl 1480.60235)], the general results here can be applied in the mean-field setting to get estimates independent of the dimension; in particular, an application to the Curie-Weiss model is presented.Uniform-in-time propagation of chaos for kinetic mean field Langevin dynamicshttps://zbmath.org/1541.820112024-09-27T17:47:02.548271Z"Chen, Fan"https://zbmath.org/authors/?q=ai:chen.fan"Lin, Yiqing"https://zbmath.org/authors/?q=ai:lin.yiqing"Ren, Zhenjie"https://zbmath.org/authors/?q=ai:ren.zhenjie"Wang, Songbo"https://zbmath.org/authors/?q=ai:wang.songboSummary: We study the kinetic mean field Langevin dynamics under the functional convexity assumption of the mean field energy functional. Using hypocoercivity, we first establish the exponential convergence of the mean field dynamics and then show the corresponding \(N\)-particle system converges exponentially in a rate uniform in \(N\) modulo a small error. Finally we study the short-time regularization effects of the dynamics and prove its uniform-in-time propagation of chaos property in both the Wasserstein and entropic sense. Our results can be applied to the training of two-layer neural networks with momentum and we include the numerical experiments.Interface layers and coupling conditions on networks for linearized kinetic BGK equationhttps://zbmath.org/1541.820122024-09-27T17:47:02.548271Z"Akramov, Ikrom"https://zbmath.org/authors/?q=ai:akramov.ikrom"Borsche, Raul"https://zbmath.org/authors/?q=ai:borsche.raul"Eckhard, Nils"https://zbmath.org/authors/?q=ai:eckhard.nils"Klar, Axel"https://zbmath.org/authors/?q=ai:klar.axelSummary: We consider a linearized kinetic BGK equation and the associated acoustic system on a network. Coupling conditions for the macroscopic equations are derived from the kinetic conditions via an asymptotic analysis near the nodes of the network. This analysis leads to the consideration of a fixpoint problem involving the solutions of kinetic half-space problems. This work extends the procedure developed in [the second and fourth author, SIAM J. Sci. Comput. 40, No. 3, A1784--A1808 (2018; Zbl 1394.82008)], where coupling conditions for a simplified BGK model have been derived. Numerical comparisons between different coupling conditions confirm the accuracy of the proposed approximation.Hermitian and non-Hermitian higher-order topological states in mechanical metamaterialshttps://zbmath.org/1541.820132024-09-27T17:47:02.548271Z"Tian, Yuping"https://zbmath.org/authors/?q=ai:tian.yuping"Tan, Zhuhua"https://zbmath.org/authors/?q=ai:tan.zhuhua"Zhang, Wei"https://zbmath.org/authors/?q=ai:zhang.wei.300Summary: Higher-order topological insulators exhibit clear hierarchical boundary states, providing an amazing platform for robust wave manipulations in mechanical or acoustic systems. Recently, this theory has been extended to non-Hermiticity-induced higher-order topology, which enables actively controllable topological transport. Nevertheless, most related studies focus on the non-Hermitian quadrupole topology, associated with the coexistence of negative and positive couplings to constitute a \(\pi\)-flux lattice, which hindered the realizations in classical wave systems. Here, we propose a novel tight-binding model without negative couplings, which supports non-Hermiticity-induced higher-order topological states. In the Hermitian case, the middle band gaps host the vanishing bulk polarization and the associated topology is dependent only upon the associated edge polarization. By introducing the external loss as non-Hermitian components, we reveal that therein the trivial structures can also host topological corner states, featured by the quantized nonzero edge polarizations in the biorthogonal basis. Furthermore, such a topological phase transition induced by non-Hermiticity can be realized for almost all of our lattices, except for the isotropic case where the middle band gaps never open. Basing on the theoretical design, we map the lattice models into the mechanical metamaterials to access the analogous higher-order topology in the elastic wave systems for both Hermitian and non-Hermitian physics. The simulated band structures match well with theoretical solutions. And the robust higher-order topological states are also identified. Our work paves the way to implement the non-Hermitian higher-order topology and offers the possibility for wave manipulations in non-Hermitian systems.A proof of finite crystallization via stratificationhttps://zbmath.org/1541.820142024-09-27T17:47:02.548271Z"Friedrich, Manuel"https://zbmath.org/authors/?q=ai:friedrich.manuel"Kreutz, Leonard"https://zbmath.org/authors/?q=ai:kreutz.leonard-cAuthors' abstract: We devise a new technique to prove two-dimensional crystallization results in the square lattice for finite particle systems. We apply this strategy to energy minimizers of configurational energies featuring two-body short-ranged particle interactions and three-body angular potentials favoring bond-angles of the square lattice. To each configuration, we associate its bond graph which is then suitably modified by identifying chains of successive atoms. This method, called \textit{stratification}, reduces the crystallization problem to a simple minimization that corresponds to a proof via slicing of the isoperimetric inequality in $\ell^1$. As a byproduct, we also prove a fluctuation estimate for minimizers of the configurational energy, known as the $n^{3/4}$-law
Reviewer: Xingbin Pan (Shanghai)An unconditionally stable threshold dynamics method for the Willmore flowhttps://zbmath.org/1541.820152024-09-27T17:47:02.548271Z"Hu, Shengqing"https://zbmath.org/authors/?q=ai:hu.shengqing.1"Lin, Zijie"https://zbmath.org/authors/?q=ai:lin.zijie"Wang, Dong"https://zbmath.org/authors/?q=ai:wang.dong.13"Wang, Xiao-Ping"https://zbmath.org/authors/?q=ai:wang.xiaopingSummary: In this paper, we propose a threshold dynamics method for the Willmore flow with a new kernel constructed based on the combination of a Gaussian kernel and a Cosine function. We show the consistency of the method by asymptotic analysis and construct a Lyapunov functional to show the unconditional stability of the proposed method. Compare to previous work, no artificial parameters are required for the construction of the kernel. Numerical experiments including area preservation or perimeter preservation are performed to show the effectiveness of the method.Integrability in the chiral model of magic angleshttps://zbmath.org/1541.820162024-09-27T17:47:02.548271Z"Becker, Simon"https://zbmath.org/authors/?q=ai:becker.simon"Humbert, Tristan"https://zbmath.org/authors/?q=ai:humbert.tristan"Zworski, Maciej"https://zbmath.org/authors/?q=ai:zworski.maciejAuthors' abstract: Magic angles in the chiral model of twisted bilayer graphene are parameters for which the chiral version of the Bistritzer-MacDonald Hamiltonian exhibits a flat band at energy zero. We compute the sums over powers of (complex) magic angles and use that to show that the set of magic angles is infinite. We also provide a new proof of the existence of the first real magic angle, showing also that the corresponding flat band has minimal multiplicity for the simplest possible choice of potentials satisfying all symmetries. These results indicate (though do not prove) a hidden integrability of the chiral model.
Reviewer: Xingbin Pan (Shanghai)On the theory of superconductivityhttps://zbmath.org/1541.820172024-09-27T17:47:02.548271Z"Ginzburg, V. L."https://zbmath.org/authors/?q=ai:ginzburg.vitaly-l"Landau, L. D."https://zbmath.org/authors/?q=ai:landau.lev-d(no abstract)From a magnetoacoustic system to a J-T black hole: a little trip down memory lanehttps://zbmath.org/1541.830602024-09-27T17:47:02.548271Z"Williams, Floyd L."https://zbmath.org/authors/?q=ai:williams.floyd-l(no abstract)Renormalisation group improvement in the stochastic formalismhttps://zbmath.org/1541.831602024-09-27T17:47:02.548271Z"Hardwick, Robert J."https://zbmath.org/authors/?q=ai:hardwick.robert-j"Markkanen, Tommi"https://zbmath.org/authors/?q=ai:markkanen.tommi"Nurmi, Sami"https://zbmath.org/authors/?q=ai:nurmi.samiSummary: We investigate compatibility between the stochastic infrared (IR) resummation of light test fields on inflationary spacetimes and renormalisation group running of the ultraviolet (UV) physics. Using the Wilsonian approach, we derive improved stochastic Langevin and Fokker-Planck equations which consistently include the renormalisation group effects. With the exception of stationary solutions, these differ from the naive approach of simply replacing the classical potential in the standard stochastic equations with the renormalisation group improved potential. Using this new formalism, we exemplify the IR dynamics with the Yukawa theory during inflation, illustrating the differences between the consistent implementation of the UV running and the naive approach.Conditions for (no) eternal inflationhttps://zbmath.org/1541.831862024-09-27T17:47:02.548271Z"Rudelius, Tom"https://zbmath.org/authors/?q=ai:rudelius.tomSummary: We construct analytic and numerical solutions of the Fokker-Planck equation that arises in the context of stochastic inflation. We use these solutions to derive necessary conditions for eternal inflation on the higher derivatives of the scalar field potential and examine the prospects for eternal inflation in a variety of popular models. We note similarities between the conditions needed to avoid eternal inflation and several recently-proposed Swampland criteria, which leads us to speculate on the possibility that the de Sitter Swampland conjectures should be viewed as approximate consequences of a No Eternal Inflation principle.Statistical mechanical approach of complex networks with weighted linkshttps://zbmath.org/1541.901082024-09-27T17:47:02.548271Z"Oliveira, Rute"https://zbmath.org/authors/?q=ai:oliveira.rute"Brito, Samuraí"https://zbmath.org/authors/?q=ai:brito.samurai"da Silva, Luciano R."https://zbmath.org/authors/?q=ai:da-silva.luciano-r"Tsallis, Constantino"https://zbmath.org/authors/?q=ai:tsallis.constantinoSummary: Systems that consist of many localized constituents interacting with each other can be represented by complex networks. Consistently, network science has become highly popular in vast fields focusing on natural, artificial and social systems. We numerically analyze the growth of \(d\)-dimensional geographic networks (characterized by the index \(\alpha_\mathrm{G} \geq 0; d = 1, 2, 3, 4)\) whose links are weighted through a predefined random probability distribution, namely \(P(w) \propto e^{-|w-w_c|/\tau}, w\) being the weight \((w_c \geq 0; \tau > 0)\). In this model, each site has an evolving degree \(k_i\) and a local energy \(\varepsilon\equiv \sum^{k_i}_{j=1} w_{ij}/2 (i = 1, 2, \dots, N)\) that depend on the weights of the links connected to it. Each newly arriving site links to one of the pre-existing ones through preferential attachment given by the probability \(\Pi_{ij} \equiv \varepsilon_i/d^{\alpha_\mathrm{A}}_{ij}(\alpha_\mathrm{A} \geqslant 0)\), where \(d_{ij}\) is the Euclidean distance between the sites. Short- and long-range interactions respectively correspond to \(\alpha_\mathrm{A}/d > 1\) and \(0 \leq \alpha_\mathrm{A}/d \leq 1; \alpha_\mathrm{A}/d \rightarrow \infty\) corresponds to interactions between close neighbors, and \(\alpha_\mathrm{A}/d \rightarrow 0\) corresponds to infinitely-ranged interactions. The site energy distribution \(p(\varepsilon)\) corresponds to the usual degree distribution \(p(k)\) as the particular instance \((w_c, \tau)\) = (1, 0). We numerically verify that the corresponding connectivity distribution \(p(\varepsilon)\) converges, when \(\alpha_\mathrm{A}/d \rightarrow \infty\), to the weight distribution \(P(w)\) for infinitely wide distributions (i.e. \(\tau \rightarrow \infty, \forall w_\mathrm{c})\) as well as for \(w_\mathrm{c} \rightarrow 0, \forall \tau\). Finally, we show that \(p(\varepsilon)\) is well approached by the \(q\)-exponential distribution \(e_q^{-\beta_q|\varepsilon-w'_\mathrm{c}|} [0 \leqslant w'_\mathrm{c}(w_\mathrm{c}, \alpha_\mathrm{A}/d) \leqslant w_\mathrm{c}]\), which optimizes the nonadditive entropy \(S_q\) under simple constraints; \(q\) depends only on \(\alpha_\mathrm{A}/d\), thus exhibiting universality.The stabilization of random Boolean networks through edge immunizationhttps://zbmath.org/1541.901102024-09-27T17:47:02.548271Z"Wang, Jiannan"https://zbmath.org/authors/?q=ai:wang.jiannan"Wei, Wei"https://zbmath.org/authors/?q=ai:wei.wei.8"Gao, Qing"https://zbmath.org/authors/?q=ai:gao.qing"Zheng, Zhiming"https://zbmath.org/authors/?q=ai:zheng.zhimingSummary: The stability of random Boolean networks (RBNs) has aroused continuous interest due to its close relationship with genetic regulatory systems. In this paper, we aim to stabilize RBNs through immunization of a minimum set of influential edges. By formulizing network stability with edge-based Hamming distance, we exploit the cavity method with the assumption of locally tree-like topology and find that the stability of RBNs is determined by the largest eigenvalue of weighted non-backtracking matrix. Combined with the collective influence theory in optimal percolation research, we quantify the contribution of each edge to the largest eigenvalue and propose an efficient edge immunization strategy. As validation we perform numerical simulations on both synthetic and real-world networks. Results show that the proposed strategy outperforms the other benchmarks and achieves stabilization with fewer immune edges. In addition, we also find that the top influential edges are rarely the most connected, which emphasizes the significance of global network topology rather than local connections. Our work sheds light on the stabilization of RBNs, and moreover, provides necessary theoretical guidance to the targeted therapy of genetic diseases.Binary and ternary structures of the evolutions in the universe \((2\times 3\times 2\times \ldots\)-world). IV: The entropy description of evolutionhttps://zbmath.org/1541.920572024-09-27T17:47:02.548271Z"Ławrynowicz, Maria"https://zbmath.org/authors/?q=ai:lawrynowicz.maria"Nowak-Kȩpczyk, Małgorzata"https://zbmath.org/authors/?q=ai:nowak-kepczyk.malgorzata"Suzuki, Osamu"https://zbmath.org/authors/?q=ai:suzuki.osamuSummary: This is the fourth part of the papers which is written under the same title [the third author, ibid. 69, No. 1, 11--23 (2019; Zbl 1538.92032); ibid. 69, No. 1, 25--31 (2019; Zbl 1538.92033); the authors, ibid. 70, No. 1, 11--41 (2020; Zbl 1541.92056)]. In the first and second parts, we have seen that binary and ternary structures can describe evolutions of systems, for example, quarks, atoms, galaxies, RNA, DNA and languages. In the third paper, we have given the evolution of languages and shown that it has an intimate connection to that in physics. In this part we shall develop a ``general evolution theory'' for the systems with binary and ternary structures at first. Then we will show how evolutionary systems create so called complexity systems as the border of the evolutionary system. We consider the evolution based on the following principle:
\textbf{The principle of evolution}
\begin{itemize}
\item[(1)] Every system in this universe must obey the law of increase of entropy (Boltzmann's principle) [\textit{C. Tsallis}, Introduction to nonextensive statistical mechanics. Approaching a complex world. Berlin: Springer (2009; Zbl 1172.82004)].
\item[(2)] Evolutionary systems perform against the Boltzmann principle (Schrödinger's principle or Bergson's philosophy) [\textit{H. Bergson}, Levolution creatrice. Presses Universitaires de France (1907)].
\end{itemize}Persistence in perturbed contact models in continuumhttps://zbmath.org/1541.920712024-09-27T17:47:02.548271Z"Pirogov, Sergey"https://zbmath.org/authors/?q=ai:pirogov.sergei-a"Zhizhina, Elena"https://zbmath.org/authors/?q=ai:zhizhina.elena-anatolevnaSummary: Can a local disaster lead to extinction? We answer this question in this work. In the paper \textit{E. A. Zhizhina} and \textit{S. A. Pirogov} [Probl. Inf. Transm. 59, No. 2, 128--145 (2023; Zbl 1530.92198); translation from Probl. Peredachi Inf. 59, No. 2, 63--82 (2023)] we considered contact processes on locally compact metric spaces with state dependent birth and death rates and formulated sufficient conditions on the rates that ensure the existence of invariant measures. One of the crucial conditions in [loc. cit.] was the critical regime condition, which meant the existence of a balance between birth and death rates in average. In the present work, we reject the criticality condition and suppose that the balance condition is violated. This implies that the evolution of the correlation functions of the contact model under consideration is determined by a nonlocal convolution type operator perturbed by a (negative) potential. We show that local peaks in mortality do not typically lead to extinction. We prove that a family of invariant measures exists even without the criticality condition and these measures can be described using the Feynman-Kac formula.