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On spectral gaps of growth-fragmentation semigroups in higher moment spaces Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-29 Mustapha Mokhtar-Kharroubi, Jacek Banasiak
We present a general approach to proving the existence of spectral gaps and asynchronous exponential growth for growth-fragmentation semigroups in moment spaces \begin{document}$ L^{1}( \mathbb{R} _{+};\ x^{\alpha }dx) $\end{document} and \begin{document}$ L^{1}( \mathbb{R} _{+};\ \left( 1+x\right) ^{\alpha }dx) $\end{document} for unbounded total fragmentation rates and continuous growth rates \begin{document}$
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Large friction-high force fields limit for the nonlinear Vlasov–Poisson–Fokker–Planck system Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-29 José A. Carrillo, Young-Pil Choi, Yingping Peng
We provide a quantitative asymptotic analysis for the nonlinear Vlasov–Poisson–Fokker–Planck system with a large linear friction force and high force-fields. The limiting system is a diffusive model with nonlocal velocity fields often referred to as aggregation-diffusion equations. We show that a weak solution to the Vlasov–Poisson–Fokker–Planck system strongly converges to a strong solution to the
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A toy model for the relativistic Vlasov-Maxwell system Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-29 Jonathan Ben-Artzi, Stephen Pankavich, Junyong Zhang
The global-in-time existence of classical solutions to the relativistic Vlasov-Maxwell (RVM) system in three space dimensions remains elusive after nearly four decades of mathematical research. In this note, a simplified "toy model" is presented and studied. This toy model retains one crucial aspect of the RVM system: the phase-space evolution of the distribution function is governed by a transport
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Sharp decay estimates for the Vlasov-Poisson and Vlasov-Yukawa systems with small data Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-29 Xianglong Duan
In this paper, we present sharp decay estimates for small data solutions to the following two systems: the Vlasov-Poisson (V-P) system in dimension 3 or higher and the Vlasov-Yukawa (V-Y) system in dimension 2 or higher. We rely on a modification of the vector field method for transport equation as developed by Smulevici in 2016 for the Vlasov-Poisson system. Using the Green's function in particular
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The Boltzmann-Grad limit for the Lorentz gas with a Poisson distribution of obstacles Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-28 François Golse
In this note, we propose a slightly different proof of Gallavotti's theorem ["Statistical Mechanics: A Short Treatise", Springer, 1999, pp. 48-55] on the derivation of the linear Boltzmann equation for the Lorentz gas with a Poisson distribution of obstacles in the Boltzmann-Grad limit.
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Global hypocoercivity of kinetic Fokker-Planck-Alignment equations Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-28 Roman Shvydkoy
In this note we establish hypocoercivity and exponential relaxation to the Maxwellian for a class of kinetic Fokker-Planck-Alignment equations arising in the studies of collective behavior. Unlike previously known results in this direction that focus on convergence near Maxwellian, our result is global for hydrodynamically dense flocks, which has several consequences. In particular, if communication
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Kinetic equations for processes on co-evolving networks Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-26 Martin Burger
The aim of this paper is to derive macroscopic equations for processes on large co-evolving networks, examples being opinion polarization with the emergence of filter bubbles or other social processes such as norm development. This leads to processes on graphs (or networks), where both the states of particles in nodes as well as the weights between them are updated in time. In our derivation we follow
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The inviscid limit for the 2D Navier-Stokes equations in bounded domains Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-24 Claude W. Bardos, Trinh T. Nguyen, Toan T. Nguyen, Edriss S. Titi
We prove the inviscid limit for the incompressible Navier-Stokes equations for data that are analytic only near the boundary in a general two-dimensional bounded domain. Our proof is direct, using the vorticity formulation with a nonlocal boundary condition, the explicit semigroup of the linear Stokes problem near the flatten boundary, and the standard wellposedness theory of Navier-Stokes equations
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Kinetic Fokker-Planck and Landau equations with specular reflection boundary condition Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-24 Hongjie Dong, Yan Guo, Timur Yastrzhembskiy
We establish existence of finite energy weak solutions to the kinetic Fokker-Planck equation and the linear Landau equation near Maxwellian, in the presence of specular reflection boundary condition for general domains. Moreover, by using a method of reflection and the \begin{document}$ S_p $\end{document} estimate of [7], we prove regularity in the kinetic Sobolev spaces \begin{document}$ S_p $\end{document}
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Phase mixing for solutions to 1D transport equation in a confining potential Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-24 Sanchit Chaturvedi, Jonathan Luk
Consider the linear transport equation in 1D under an external confining potential \begin{document}$ \Phi $\end{document}: \begin{document}$ \begin{equation*} {\partial}_t f + v {\partial}_x f - {\partial}_x \Phi {\partial}_v f = 0. \end{equation*} $\end{document} For \begin{document}$ \Phi = \frac {x^2}2 + \frac { \varepsilon x^4}2 $\end{document} (with \begin{document}$ \varepsilon >0 $\end{document}
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Linear instability of Vlasov-Maxwell systems revisited-A Hamiltonian approach Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-10 Zhiwu Lin
We consider linear stability of steady states of 1\begin{document}$ \frac{1}{2} $\end{document} and 3DVlasov-Maxwell systems for collisionless plasmas. The linearized systems canbe written as separable Hamiltonian systems with constraints. By using ageneral theory for separable Hamiltonian systems, we recover the sharp linearstability criteria obtained previously by different approaches. Moreover,
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From kinetic to fluid models of liquid crystals by the moment method Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-10 Pierre Degond, Amic Frouvelle, Jian-Guo Liu
This paper deals with the convergence of the Doi-Navier-Stokes model of liquid crystals to the Ericksen-Leslie model in the limit of the Deborah number tending to zero. While the literature has investigated this problem by means of the Hilbert expansion method, we develop the moment method, i.e. a method that exploits conservation relations obeyed by the collision operator. These are non-classical
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On time decay for the spherically symmetric Vlasov-Poisson system Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-01 Jack Schaeffer
A collisionless plasma is modeled by the Vlasov-Poisson system. Solutions in three space dimensions that have smooth, compactly supported initial data with spherical symmetry are considered. An improved field estimate is presented that is based on decay estimates obtained by Illner and Rein. Then some estimates are presented that ensure only particles with sufficiently small velocity can be found within
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Instantaneous smoothing and exponential decay of solutions for a degenerate evolution equation with application to Boltzmann's equation Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-01 Fedor Nazarov,Kevin Zumbrun
We establish an instantaneous smoothing property for decaying solutions on the half-line \begin{document}$ (0, +\infty) $\end{document} of certain degenerate Hilbert space-valued evolution equations arising in kinetic theory, including in particular the steady Boltzmann equation. Our results answer the two main open problems posed by Pogan and Zumbrun in their treatment of \begin{document}$ H^1 $\end{document}
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On time decay for the spherically symmetric Vlasov-Poisson system Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-01 Jack Schaeffer
A collisionless plasma is modeled by the Vlasov-Poisson system. Solutions in three space dimensions that have smooth, compactly supported initial data with spherical symmetry are considered. An improved field estimate is presented that is based on decay estimates obtained by Illner and Rein. Then some estimates are presented that ensure only particles with sufficiently small velocity can be found within
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Thermalization of a rarefied gas with total energy conservation: Existence, hypocoercivity, macroscopic limit Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-01 Gianluca Favre,Marlies Pirner,Christian Schmeiser
The thermalization of a gas towards a Maxwellian velocity distribution with the background temperature is described by a kinetic relaxation model. The sum of the kinetic energy of the gas and the thermal energy of the background are conserved, and the heat flow in the background is governed by the Fourier law. For the coupled nonlinear system of the kinetic and the heat equation, existence of solutions
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On regular solutions and singularity formation for Vlasov/Navier-Stokes equations with degenerate viscosities and vacuum Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-01 Young-Pil Choi,Jinwook Jung
We analyze the Vlasov equation coupled with the compressible Navier–Stokes equations with degenerate viscosities and vacuum. These two equations are coupled through the drag force which depends on the fluid density and the relative velocity between particle and fluid. We first establish the existence and uniqueness of local-in-time regular solutions with arbitrarily large initial data and a vacuum
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A moment closure based on a projection on the boundary of the realizability domain: Extension and analysis Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-01 Teddy Pichard
A closure relation for moments equations in kinetic theory was recently introduced in [38], based on the study of the geometry of the set of moments. This relation was constructed from a projection of a moment vector toward the boundary of the set of moments and corresponds to approximating the underlying kinetic distribution as a sum of a chosen equilibrium distribution plus a sum of purely anisotropic
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A Lie algebra-theoretic approach to characterisation of collision invariants of the Boltzmann equation for general convex particles Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-01 Mark Wilkinson
By studying scattering Lie groups and their associated Lie algebras, we introduce a new method for the characterisation of collision invariants for physical scattering families associated to smooth, convex hard particles in the particular case that the collision invariant is of class \begin{document}$ \mathscr{C}^{1} $\end{document}. This work extends that of Saint-Raymond and Wilkinson (Communications
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Local conditional regularity for the Landau equation with Coulomb potential Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-01 Immanuel Ben Porat
This paper studies the regularity of Villani solutions of the space homogeneous Landau equation with Coulomb interaction in dimension 3. Specifically, we prove that any such solution belonging to the Lebesgue space \begin{document}$ L_{t}^{\infty}L_{v}^{q} $\end{document} with \begin{document}$ q>3 $\end{document} in an open cylinder \begin{document}$ (0,S)\times B $\end{document}, where \begin{document}$
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Optimal non-symmetric Fokker-Planck equation for the convergence to a given equilibrium Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-01 Anton Arnold,Beatrice Signorello
This paper is concerned with finding Fokker-Planck equations in \begin{document}$ \mathbb{R}^d $\end{document} with the fastest exponential decay towards a given equilibrium. For a prescribed, anisotropic Gaussian we determine a non-symmetric Fokker-Planck equation with linear drift that shows the highest exponential decay rate for the convergence of its solutions towards equilibrium. At the same time
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Uncertainty quantification in hierarchical vehicular flow models Kinet. Relat. Models (IF 1.0) Pub Date : 2022-01-01 Michael Herty,Elisa Iacomini
We consider kinetic vehicular traffic flow models of BGK type [24]. Considering different spatial and temporal scales, those models allow to derive a hierarchy of traffic models including a hydrodynamic description. In this paper, the kinetic BGK–model is extended by introducing a parametric stochastic variable to describe possible uncertainty in traffic. The interplay of uncertainty with the given
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A lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles Kinet. Relat. Models (IF 1.0) Pub Date : 2021-12-21 Luís Simão Ferreira
In this paper, we proceed as suggested in the final section of [2] and prove a lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles. This bound turns out to be around \begin{document}$ 0.02 $\end{document}, which is already physically meaningful, and we perform Monte Carlo simulations to provide a better empirical estimate for this value via entropy production
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Lagrangian dual framework for conservative neural network solutions of kinetic equations Kinet. Relat. Models (IF 1.0) Pub Date : 2021-12-21 Hyung Ju Hwang, Hwijae Son
In this paper, we propose a novel conservative formulation for solving kinetic equations via neural networks. More precisely, we formulate the learning problem as a constrained optimization problem with constraints that represent the physical conservation laws. The constraints are relaxed toward the residual loss function by the Lagrangian duality. By imposing physical conservation properties of the
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A kinetic chemotaxis model with internal states and temporal sensing Kinet. Relat. Models (IF 1.0) Pub Date : 2021-12-20 Zhi-An Wang
By employing the Fourier transform to derive key a priori estimates for the temporal gradient of the chemical signal, we establish the existence of global solutions and hydrodynamic limit of a chemotactic kinetic model with internal states and temporal gradient in one dimension, which is a system of two transport equations coupled to a parabolic equation proposed in [4].
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A neural network closure for the Euler-Poisson system based on kinetic simulations Kinet. Relat. Models (IF 1.0) Pub Date : 2021-12-20 Léo Bois, Emmanuel Franck, Laurent Navoret, Vincent Vigon
This work deals with the modeling of plasmas, which are ionized gases. Thanks to machine learning, we construct a closure for the one-dimensional Euler-Poisson system valid for a wide range of collisional regimes. This closure, based on a fully convolutional neural network called V-net, takes as input the whole spatial density, mean velocity and temperature and predicts as output the whole heat flux
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Diffusion limit and the optimal convergence rate of the Vlasov-Poisson-Fokker-Planck system Kinet. Relat. Models (IF 1.0) Pub Date : 2021-12-17 Mingying Zhong
In the present paper, we study the diffusion limit of the classical solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system with initial data near a global Maxwellian. We prove the convergence and establish the optimal convergence rate of the global strong solution to the VPFP system towards the solution to the drift-diffusion-Poisson system based on the spectral analysis with precise estimation
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The fragmentation equation with size diffusion: Small and large size behavior of stationary solutions Kinet. Relat. Models (IF 1.0) Pub Date : 2021-11-03 Philippe Laurençot, Christoph Walker
The small and large size behavior of stationary solutions to the fragmentation equation with size diffusion is investigated. It is shown that these solutions behave like stretched exponentials for large sizes, the exponent in the exponential being solely given by the behavior of the overall fragmentation rate at infinity. In contrast, the small size behavior is partially governed by the daughter fragmentation
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Macroscopic descriptions of follower-leader systems Kinet. Relat. Models (IF 1.0) Pub Date : 2021-11-18 Sara Bernardi, Gissell Estrada-Rodriguez, Heiko Gimperlein, Kevin J. Painter
The fundamental derivation of macroscopic model equations to describe swarms based on microscopic movement laws and mathematical analyses into their self-organisation capabilities remains a challenge from the perspective of both modelling and analysis. In this paper we clarify relevant continuous macroscopic model equations that describe follower-leader interactions for a swarm where these two populations
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Uniform-in-time continuum limit of the lattice Winfree model and emergent dynamics Kinet. Relat. Models (IF 1.0) Pub Date : 2021-11-18 Seung-Yeal Ha, Myeongju Kang, Bora Moon
We study a uniform-in-time continuum limit of the lattice Winfree model(LWM) and its asymptotic dynamics which depends on system functions such as natural frequency function and coupling strength function. The continuum Winfree model(CWM) is an integro-differential equation for the temporal evolution of Winfree phase field. The LWM describes synchronous behavior of weakly coupled Winfree oscillators
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Uniform lifetime for classical solutions to the Hot, Magnetized, Relativistic Vlasov Maxwell system Kinet. Relat. Models (IF 1.0) Pub Date : 2021-12-06 Dayton Preissl, Christophe Cheverry, Slim Ibrahim
This article is devoted to the kinetic description in phase space of magnetically confined plasmas. It addresses the problem of stability near equilibria of the Relativistic Vlasov Maxwell system. We work under the Glassey-Strauss compactly supported momentum assumption on the density function $ f(t,\cdot) $. Magnetically confined plasmas are characterized by the presence of a strong external magnetic
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Magnetic confinement for the 2D axisymmetric relativistic Vlasov-Maxwell system in an annulus Kinet. Relat. Models (IF 1.0) Pub Date : 2021-11-25 Jin Woo Jang, Robert M. Strain, Tak Kwong Wong
Although the nuclear fusion process has received a great deal of attention in recent years, the amount of mathematical analysis that supports the stability of the system seems to be relatively insufficient. This paper deals with the mathematical analysis of the magnetic confinement of the plasma via kinetic equations. We prove the global wellposedness of the Vlasov-Maxwell system in a two-dimensional
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Global existence of small displacement solutions for Hookean incompressible viscoelasticity in 3D Kinet. Relat. Models (IF 1.0) Pub Date : 2021-11-22 Boyan Jonov, Paul Kessenich, Thomas C. Sideris
The initial value problem for incompressible Hookean viscoelastic motion in three space dimensions has global strong solutions with small displacements.
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Pointwise bounds for the Green's function for the Neumann-Laplace operator in $ \text{R}^3 $ Kinet. Relat. Models (IF 1.0) Pub Date : 2021-11-22 David Hoff
We derive pointwise bounds for the Green's function and its derivatives for the Laplace operator on smooth bounded sets in \begin{document}$ {\bf R}^3 $\end{document} subject to Neumann boundary conditions. The proofs require only ordinary calculus, scaling arguments and the most basic facts of \begin{document}$ L^2 $\end{document}-Sobolev space theory.
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The Einstein-Vlasov system in maximal areal coordinates---Local existence and continuation Kinet. Relat. Models (IF 1.0) Pub Date : 2021-11-22 Sebastian Günther, Gerhard Rein
We consider the spherically symmetric, asymptotically flat Einstein-Vlasov system in maximal areal coordinates. The latter coordinates have been used both in analytical and numerical investigations of the Einstein-Vlasov system [3,8,18,19], but neither a local existence theorem nor a suitable continuation criterion has so far been established for the corresponding nonlinear system of PDEs. We close
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Kinetic description of stable white dwarfs Kinet. Relat. Models (IF 1.0) Pub Date : 2021-11-05 Juhi Jang, Jinmyoung Seok
In this paper, we study fermion ground states of the relativistic Vlasov-Poisson system arising in the semiclassical limit from relativistic quantum theory of white dwarfs. We show that fermion ground states of the three dimensional relativistic Vlasov-Poisson system exist for subcritical mass, the mass density of such fermion ground states satisfies the Chandrasekhar equation for white dwarfs, and
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Glassey-Strauss representation of Vlasov-Maxwell systems in a Half Space Kinet. Relat. Models (IF 1.0) Pub Date : 2021-11-05 Yunbai Cao, Chanwoo Kim
Following closely the classical works [5]-[7] by Glassey, Strauss, and Schaeffer, we present a version of the Glassey-Strauss representation for the Vlasov-Maxwell systems in a 3D half space when the boundary is the perfect conductor.
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Towards a further understanding of the dynamics in the excitatory NNLIF neuron model: Blow-up and global existence Kinet. Relat. Models (IF 1.0) Pub Date : 2021-08-23 Pierre Roux, Delphine Salort
The Nonlinear Noisy Leaky Integrate and Fire (NNLIF) model is widely used to describe the dynamics of neural networks after a diffusive approximation of the mean-field limit of a stochastic differential equation. In previous works, many qualitative results were obtained: global existence in the inhibitory case, finite-time blow-up in the excitatory case, convergence towards stationary states in the
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A criterion for asymptotic preserving schemes of kinetic equations to be uniformly stationary preserving Kinet. Relat. Models (IF 1.0) Pub Date : 2021-08-23 Casimir Emako, Farah Kanbar, Christian Klingenberg, Min Tang
In this work we are interested in the stationary preserving property of asymptotic preserving (AP) schemes for kinetic models. We introduce a criterion for AP schemes for kinetic equations to be uniformly stationary preserving (SP). Our key observation is that as long as the Maxwellian of the distribution function can be updated explicitly, such AP schemes are also SP. To illustrate our observation
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Boltzmann-type equations for multi-agent systems with label switching Kinet. Relat. Models (IF 1.0) Pub Date : 2021-08-23 Nadia Loy, Andrea Tosin
In this paper, we propose a Boltzmann-type kinetic description of mass-varying interacting multi-agent systems. Our agents are characterised by a microscopic state, which changes due to their mutual interactions, and by a label, which identifies a group to which they belong. Besides interacting within and across the groups, the agents may change label according to a state-dependent Markov-type jump
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BGK models for inert mixtures: Comparison and applications Kinet. Relat. Models (IF 1.0) Pub Date : 2021-09-23 Sebastiano Boscarino, Seung Yeon Cho, Maria Groppi, Giovanni Russo
Consistent BGK models for inert mixtures are compared, first in their kinetic behavior and then versus the hydrodynamic limits that can be derived in different collision-dominated regimes. The comparison is carried out both analytically and numerically, for the latter using an asymptotic preserving semi-Lagrangian scheme for the BGK models. Application to the plane shock wave in a binary mixture of
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The delayed Cucker-Smale model with short range communication weights Kinet. Relat. Models (IF 1.0) Pub Date : 2021-09-23 Zili Chen, Xiuxia Yin
Various flocking results have been established for the delayed Cucker-Smale model, especially in the long range communication case. However, the short range communication case is more realistic due to the limited communication ability. In this case, the non-flocking behavior can be frequently observed in numerical simulations. Furthermore, it has potential applications in many practical situations
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Relativistic BGK model for massless particles in the FLRW spacetime Kinet. Relat. Models (IF 1.0) Pub Date : 2021-09-23 Byung-Hoon Hwang, Ho Lee, Seok-Bae Yun
In this paper, we address the Cauchy problem for the relativistic BGK model proposed by Anderson and Witting for massless particles in the Friedmann-Lemaȋtre-Robertson-Walker (FLRW) spacetime. We first derive the explicit form of the Jüttner distribution in the FLRW spacetime, together with a set of nonlinear relations that leads to the conservation laws of particle number, momentum, and energy for
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Inelastic Boltzmann equation driven by a particle thermal bath Kinet. Relat. Models (IF 1.0) Pub Date : 2021-06-17 Rafael Sanabria
We consider the spatially inhomogeneous Boltzmann equation for inelastic hard-spheres, with constant restitution coefficient $ \alpha\in(0,1) $, under the thermalization induced by a host medium with fixed $ e\in(0,1] $ and a fixed Maxwellian distribution. When the restitution coefficient $ \alpha $ is close to 1 we prove existence and uniqueness of global solutions considering the close-to-equilibrium
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Density dependent diffusion models for the interaction of particle ensembles with boundaries Kinet. Relat. Models (IF 1.0) Pub Date : 2021-06-17 Jennifer Weissen, Simone Göttlich, Dieter Armbruster
The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction potential that leads to a coherent motion where all particles move in the same direction with the same speed known as a flock. Interaction of the flock with boundaries
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Lower bound for the Boltzmann equation whose regularity grows tempered with time Kinet. Relat. Models (IF 1.0) Pub Date : 2021-06-17 Ling-Bing He, Jie Ji, Ling-Xuan Shao
As a first step towards the general global-in-time stability for the Boltzmann equation with soft potentials, in the present work, we prove the quantitative lower bounds for the equation under the following two assumptions, which stem from the available energy estimates, i.e. (ⅰ). the hydrodynamic quantities (local mass, local energy, and local entropy density) are bounded (from below or from above)
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A spectral study of the linearized Boltzmann operator in \begin{document}$ L^2 $\end{document}-spaces with polynomial and Gaussian weights Kinet. Relat. Models (IF 1.0) Pub Date : 2021-06-23 Pierre Gervais
The spectrum structure of the linearized Boltzmann operator has been a subject of interest for over fifty years and has been inspected in the space $ L^2\left( {\mathbb R}^d, \exp(|v|^2/4)\right) $ by B. Nicolaenko [27] in the case of hard spheres, then generalized to hard and Maxwellian potentials by R. Ellis and M. Pinsky [13], and S. Ukai proved the existence of a spectral gap for large frequencies
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Heterogeneous discrete kinetic model and its diffusion limit Kinet. Relat. Models (IF 1.0) Pub Date : 2021-06-29 Ho-Youn Kim, Yong-Jung Kim, Hyun-Jin Lim
A revertible discrete velocity kinetic model is introduced when the environment is spatially heterogeneous. It is proved that the parabolic scale singular limit of the model exists and satisfies a new heterogeneous diffusion equation that depends on the diffusivity and the turning frequency together. An energy functional is introduced which takes into account spatial heterogeneity in the velocity field
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Pencil-beam approximation of fractional Fokker-Planck Kinet. Relat. Models (IF 1.0) Pub Date : 2021-06-29 Guillaume Bal, Benjamin Palacios
We consider the modeling of light beams propagating in highly forward-peaked turbulent media by fractional Fokker-Planck equations and their approximations by fractional Fermi pencil beam models. We obtain an error estimate in a 1-Wasserstein distance for the latter model showing that beam spreading is well captured by the Fermi pencil-beam approximation in the small diffusion limit.
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Incompressible Navier-Stokes-Fourier limit from the Landau equation Kinet. Relat. Models (IF 1.0) Pub Date : 2021-05-14 Mohamad Rachid
In this work, we provide a result on the derivation of the incompressible Navier-Stokes-Fourier system from the Landau equation for hard, Maxwellian and moderately soft potentials. To this end, we first investigate the Cauchy theory associated to the rescaled Landau equation for small initial data. Our approach is based on proving estimates of some adapted Sobolev norms of the solution that are uniform
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Global strong solutions in \begin{document}$ {\mathbb{R}}^3 $\end{document} for ionic Vlasov-Poisson systems Kinet. Relat. Models (IF 1.0) Pub Date : 2021-05-07 Megan Griffin-Pickering, Mikaela Iacobelli
Systems of Vlasov-Poisson type are kinetic models describing dilute plasma. The structure of the model differs according to whether it describes the electrons or positively charged ions in the plasma. In contrast to the electron case, where the well-posedness theory for Vlasov-Poisson systems is well established, the well-posedness theory for ion models has been investigated more recently. In this
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Mathematical modelling of charge transport in graphene heterojunctions Kinet. Relat. Models (IF 1.0) Pub Date : 2021-03-03 Luigi Barletti, Giovanni Nastasi, Claudia Negulescu, Vittorio Romano
A typical graphene heterojunction device can be divided into two classical zones, where the transport is basically diffusive, separated by a "quantum active region" (e.g., a locally gated region), where the charge carriers are scattered according to the laws of quantum mechanics. In this paper we derive a mathematical model of such a device, where the classical regions are described by drift-diffusion
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A mean-field limit of the particle swarmalator model Kinet. Relat. Models (IF 1.0) Pub Date : 2021-03-03 Seung-Yeal Ha, Jinwook Jung, Jeongho Kim, Jinyeong Park, Xiongtao Zhang
We present a mean-field limit of the particle swarmalator model introduced in [46] with singular communication weights. For a mean-field limit, we employ a probabilistic approach for the propagation of molecular chaos and suitable cut-offs in singular terms, which results in the validation of the mean-field limit. We also provide a local-in-time well-posedness of strong and weak solutions to the derived
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On group symmetries of the hydrodynamic equations for rarefied gas Kinet. Relat. Models (IF 1.0) Pub Date : 2021-02-23 Alexander V. Bobylev, Sergey V. Meleshko
The invariant group transformations of three-dimensional hydrodynamic equations derived from the Boltzmann equation are studied. Three levels (with respect to the Knudsen number) of hydrodynamic description are considered and compared: (a) Euler equations, (b) Navier-Stokes equations, (c) Generalized Burnett equations (GBEs), which replace the original (ill-posed) Burnett equations. The main attention
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Polytropic gas modelling at kinetic and macroscopic levels Kinet. Relat. Models (IF 1.0) Pub Date : 2021-02-23 Vladimir Djordjić, Milana Pavić-Čolić, Nikola Spasojević
In this paper, we consider the kinetic model of continuous type describing a polyatomic gas in two different settings corresponding to a different choice of the functional space used to define macroscopic quantities. Such a model introduces a single continuous variable supposed to capture all the phenomena related to the more complex structure of a polyatomic molecule. In particular, we provide a direct
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A model of cultural evolution in the context of strategic conflict Kinet. Relat. Models (IF 1.0) Pub Date : 2021-03-17 Misha Perepelitsa
We consider a model of cultural evolution for a strategy selection in a population of individuals who interact in a game theoretic framework. The evolution combines individual learning of the environment (population strategy profile), reproduction, proportional to the success of the acquired knowledge, and social transmission of the knowledge to the next generation. A mean-field type equation is derived
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Macroscopic limit of the kinetic Bloch equation Kinet. Relat. Models (IF 1.0) Pub Date : 2021-03-17 Kamel Hamdache, Djamila Hamroun
This work concerns the existence of solution of the kinetic spinor Boltzmann equation as well as the asymptotic behavior of such solution when $ \varepsilon \to 0 $, that is when the time relaxation of the spin-flip collisions is very small in comparison to the time relaxation parameter of the collisions with no spin reversal. Due to the lack of regularity of the weak solution, the switching term $
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Mathematical modelling of collagen fibres rearrangement during the tendon healing process Kinet. Relat. Models (IF 1.0) Pub Date : 2021-01-27 José Antonio Carrillo, Martin Parisot, Zuzanna Szymańska
Tendon injuries present a clinical challenge to modern medicine as they heal slowly and rarely is there full restoration to healthy tendon structure and mechanical strength. Moreover, the process of healing is not fully elucidated. To improve understanding of tendon function and the healing process, we propose a new model of collagen fibres rearrangement during tendon healing. The model consists of
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Shadow Lagrangian dynamics for superfluidity Kinet. Relat. Models (IF 1.0) Pub Date : 2021-01-27 Patrick Henning, Anders M. N. Niklasson
Motivated by a similar approach for Born-Oppenheimer molecular dynamics, this paper proposes an extended "shadow" Lagrangian density for quantum states of superfluids. The extended Lagrangian contains an additional field variable that is forced to follow the wave function of the quantum state through a rapidly oscillating extended harmonic oscillator. By considering the adiabatic limit for large frequencies
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Emergent dynamics of a thermodynamic Cucker-Smale ensemble on complete Riemannian manifolds Kinet. Relat. Models (IF 1.0) Pub Date : 2021-01-27 Hyunjin Ahn, Seung-Yeal Ha, Woojoo Shim
We study emergent collective behaviors of a thermodynamic Cucker-Smale (TCS) ensemble on complete smooth Riemannian manifolds. For this, we extend the TCS model on the Euclidean space to a complete smooth Riemannian manifold by adopting the work [30] for a CS ensemble, and provide a sufficient framework to achieve velocity alignment and thermal equilibrium. Compared to the model proposed in [30], our