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On two properties of the Fisher information Kinet. Relat. Models (IF 1.38) Pub Date : 2020-11-20 Nicolas Rougerie
Alternative proofs for the superadditivity and the affinity (in the large system limit) of the usual and some fractional Fisher informations of a probability density of many variables are provided. They are consequences of the fact that such informations can be interpreted as quantum kinetic energies.
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Superposition principle and schemes for measure differential equations Kinet. Relat. Models (IF 1.38) Pub Date : 2020-11-20 Fabio Camilli; Giulia Cavagnari; Raul De Maio; Benedetto Piccoli
Measure Differential Equations (MDE) describe the evolution of probability measures driven by probability velocity fields, i.e. probability measures on the tangent bundle. They are, on one side, a measure-theoretic generalization of ordinary differential equations; on the other side, they allow to describe concentration and diffusion phenomena typical of kinetic equations. In this paper, we analyze
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Evolutionary game theory in mixed strategies: From microscopic interactions to kinetic equations Kinet. Relat. Models (IF 1.38) Pub Date : 2020-11-20 Juan Pablo Pinasco; Mauro Rodriguez Cartabia; Nicolas Saintier
In this work we propose a kinetic formulation for evolutionary game theory for zero sum games when the agents use mixed strategies. We start with a simple adaptive rule, where after an encounter each agent increases by a small amount $ h $ the probability of playing the successful pure strategy used in the match. We derive the Boltzmann equation which describes the macroscopic effects of this microscopical
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Collisional sheath solutions of a bi-species Vlasov-Poisson-Boltzmann boundary value problem Kinet. Relat. Models (IF 1.38) Pub Date : 2020-11-20 Mehdi Badsi
The mathematical description of the interaction between a collisional plasma and an absorbing wall is a challenging issue. In this paper, we propose to model this interaction by considering a stationary bi-species Vlasov-Poisson-Boltzmann boundary value problem with boundary conditions that are consistent with the physics. In particular, we show that the wall potential can be uniquely determined from
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Navier-Stokes limit of globally hyperbolic moment equations Kinet. Relat. Models (IF 1.38) Pub Date : 2020-12-28 Zhiting Ma
This paper is concerned with the Navier-Stokes limit of a class of globally hyperbolic moment equations from the Boltzmann equation. we show that the Navier-Stokes equations can be formally derived from the hyperbolic moment equations for various different collision mechanisms. Furthermore, the formal limit is justified rigorously by using an energy method. It should be noted that the hyperbolic moment
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A semigroup approach to the convergence rate of a collisionless gas Kinet. Relat. Models (IF 1.38) Pub Date : 2020-09-02 Armand Bernou
We study the rate of convergence to equilibrium for a collisionless (Knudsen) gas enclosed in a vessel in dimension $ n \in \{2,3\} $. By semigroup arguments, we prove that in the $ L^1 $ norm, the polynomial rate of convergence $ \frac{1}{(t+1)^{n-}} $ given in [25], [17] and [18] can be extended to any $ C^2 $ domain, with standard assumptions on the initial data. This is to our knowledge, the first
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Averaging of highly-oscillatory transport equations Kinet. Relat. Models (IF 1.38) Pub Date : 2020-09-02 Philippe Chartier; Nicolas Crouseilles; Mohammed Lemou; Florian Méhats
In this paper, we develop a new strategy aimed at obtaining high-order asymptotic models for transport equations with highly-oscillatory solutions. The technique relies upon recent developments averaging theory for ordinary differential equations, in particular normal form expansions in the vanishing parameter. Noteworthy, the result we state here also allows for the complete recovery of the exact
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Confined steady states of the relativistic Vlasov–Maxwell system in an infinitely long cylinder Kinet. Relat. Models (IF 1.38) Pub Date : 2020-09-02 Jörg Weber
The time evolution of a collisionless plasma is modeled by the relativistic Vlasov–Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. In this work, the setting is two and one-half dimensional, that is, the distribution functions of the particles species are independent of the third space dimension. We consider the case that the plasma
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On the entropic property of the Ellipsoidal Statistical model with the prandtl number below 2/3 Kinet. Relat. Models (IF 1.38) Pub Date : 2020-09-02 Shigeru Takata; Masanari Hattori; Takumu Miyauchi
Entropic property of the Ellipsoidal Statistical model with the Prandtl number Pr below 2/3 is discussed. Although 2/3 is the lower bound of Pr for the H theorem to hold unconditionally, it is shown that the theorem still holds even for $ \mathrm{Pr}<2/3 $, provided that anisotropy of stress tensor satisfies a certain criterion. The practical tolerance of that criterion is assessed numerically by the
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Global existence theorem for a model governing the motion of two cell populations Kinet. Relat. Models (IF 1.38) Pub Date : 2020-09-24 Brock C. Price; Xiangsheng Xu
This article is concerned with the existence of a weak solution to the initial boundary problem for a cross-diffusion system which arises in the study of two cell population growth. The mathematical challenge is due to the fact that the coefficient matrix is non-symmetric and degenerate in the sense that its determinant is $ 0 $. The existence assertion is established by exploring the fact that the
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Derivative estimates for screened Vlasov-Poisson system around Penrose-stable equilibria Kinet. Relat. Models (IF 1.38) Pub Date : 2020-09-24 Trinh T. Nguyen
In this paper, we establish derivative estimates for the Vlasov-Poisson system with screening interactions around Penrose-stable equilibria on the phase space $ {\mbox{Re }}^d_x\times {\mbox{Re }}_v^d $, with dimension $ d\ge 3 $. In particular, we establish the optimal decay estimates for higher derivatives of the density of the perturbed system, precisely like the free transport, up to a log correction
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An anisotropic interaction model with collision avoidance Kinet. Relat. Models (IF 1.38) Pub Date : 2020-09-29 Claudia Totzeck
In this article an anisotropic interaction model avoiding collisions is proposed. Starting point is a general isotropic interacting particle system, as used for swarming or follower-leader dynamics. An anisotropy is induced by rotation of the force vector resulting from the interaction of two agents. In this way the anisotropy is leading to a smooth evasion behaviour. In fact, the proposed model generalizes
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A moment closure based on a projection on the boundary of the realizability domain: 1D case Kinet. Relat. Models (IF 1.38) Pub Date : 2020-09-29 Teddy Pichard
This work aims to develop and test a projection technique for the construction of closing equations of moment systems. One possibility to define such a closure consists in reconstructing an underlying kinetic distribution from a vector of moments, then expressing the closure based on this reconstructed function.Exploiting the geometry of the realizability domain, i.e. the set of moments of positive
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Kinetic modelling of colonies of myxobacteria Kinet. Relat. Models (IF 1.38) Pub Date : 2020-09-29 Sabine Hittmeir; Laura Kanzler; Angelika Manhart; Christian Schmeiser
A new kinetic model for the dynamics of myxobacteria colonies on flat surfaces is derived formally, and first analytical and numerical results are presented. The model is based on the assumption of hard binary collisions of two different types: alignment and reversal. We investigate two different versions: a) realistic rod-shaped bacteria and b) artificial circular shaped bacteria called Maxwellian
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BGK model of the multi-species Uehling-Uhlenbeck equation Kinet. Relat. Models (IF 1.38) Pub Date : 2020-09-29 Gi-Chan Bae; Christian Klingenberg; Marlies Pirner; Seok-Bae Yun
We propose a BGK model of the quantum Boltzmann equation for gas mixtures. We also provide a sufficient condition that guarantees the existence of equilibrium coefficients so that the model shares the same conservation laws and $ H $-theorem with the quantum Boltzmann equation. Unlike the classical BGK for gas mixtures, the equilibrium coefficients of the local equilibriums for quantum multi-species
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Opinion formation systems via deterministic particles approximation Kinet. Relat. Models (IF 1.38) Pub Date : 2020-09-29 Simone Fagioli; Emanuela Radici
We propose an ODE-based derivation for a generalized class of opinion formation models either for single and multiple species (followers, leaders, trolls). The approach is purely deterministic and the evolution of the single opinion is determined by the competition between two mechanisms: the opinion diffusion and the compromise process. Such deterministic approach allows to recover in the limit an
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Kinetic formulation of a 2 × 2 hyperbolic system arising in gas chromatography Kinet. Relat. Models (IF 1.38) Pub Date : 2020-08-04 Christian Bourdarias; Marguerite Gisclon; Stéphane Junca
A particular 2x2 hyperbolic system commonly used in the context of gas-solid chromatography is reformulated as a single kinetic equation using an additional kinetic variable. A kinetic numerical scheme is built from this new formulation and its behavior is tested on solving the Riemann problem in different configurations leading to single or composite waves.
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Quantitative Local Sensitivity estimates for the random kinetic Cucker-Smale Model with Chemotactic Movement Kinet. Relat. Models (IF 1.38) Pub Date : 2020-08-04 Seung-Yeal Ha; Bora Moon
In this paper, we present quantitative local sensitivity estimates for the kinetic chemotaxis Cucker-Smale(CCS) equation with random inputs. In the absence of random inputs, the kinetic CCS model exhibits velocity alignment under suitable structural assumptions on the turning kernel and reaction term despite of the random effect due to a turning operator. We provide a global existence of a regular
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On the transport operators arising from linearizing the Vlasov-Poisson or Einstein-Vlasov system about isotropic steady states Kinet. Relat. Models (IF 1.38) Pub Date : 2020-08-04 Gerhard Rein; Christopher Straub
If the Vlasov-Poisson or Einstein-Vlasov system is linearized about an isotropic steady state, a linear operator arises the properties of which are relevant in the linear as well as nonlinear stability analysis of the given steady state. We prove that when defined on a suitable Hilbert space and equipped with the proper domain of definition this transport operator $ {\mathcal T} $ is skew-adjoint,
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Analytic smoothing effect for the nonlinear Landau equation of Maxwellian molecules Kinet. Relat. Models (IF 1.38) Pub Date : 2020-08-04 Yoshinori Morimoto; Chao-Jiang Xu
We consider the Cauchy problem of the nonlinear Landau equation of Maxwellian molecules, under the perturbation frame work to global equilibrium. We show that if $ H^r_x(L^2_v), r >3/2 $ norm of the initial perturbation is small enough, then the Cauchy problem of the nonlinear Landau equation admits a unique global solution which becomes analytic with respect to both position $ x $ and velocity $ v
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On the generic complete synchronization of the discrete Kuramoto model Kinet. Relat. Models (IF 1.38) Pub Date : 2020-08-04 Woojoo Shim
We study the emergent behavior of discrete-time approximation of the finite-dimensional Kuramoto model. Compared to Zhang and Zhu's recent work in [38], we do not rely on the consistency of one-step foward Euler scheme but analyze the discrete model directly to obtain sharper and more explicit result. More precisely, we present the optimal condition for the convergence and order preserving for identical
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Stability of a non-local kinetic model for cell migration with density dependent orientation bias Kinet. Relat. Models (IF 1.38) Pub Date : 2020-08-04 Nadia Loy; Luigi Preziosi
The aim of the article is to study the stability of a non-local kinetic model proposed in [17], that is a kinetic model for cell migration taking into account the non-local sensing performed by a cell in order to decide its direction and speed of movement. We show that pattern formation results from modulation of one non-dimensional parameter that depends on the tumbling frequency, the sensing radius
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Gelfand-Shilov smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off Kinet. Relat. Models (IF 1.38) Pub Date : 2020-08-04 Wei-Xi Li; Lvqiao Liu
In this work we consider the Cauchy problem for the spatially inhomogeneous non-cutoff Boltzmann equation. For any given solution belonging to weighted Sobolev space, we will show it enjoys at positive time the Gelfand-Shilov smoothing effect for the velocity variable and Gevrey regularizing properties for the spatial variable. This improves the result of Lerner-Morimoto-Pravda-Starov-Xu [J. Funct
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Weak dissipative solutions to a free-boundary problem for finitely extensible bead-spring chain molecules: Variable viscosity coefficients Kinet. Relat. Models (IF 1.38) Pub Date : 2020-08-04 Donatella Donatelli; Tessa Thorsen; Konstantina Trivisa
We investigate the global existence of weak solutions to a free boundary problem governing the evolution of finitely extensible bead-spring chains in dilute polymers. The free boundary in the present context is defined with regard to a density threshold of $ \rho = 1, $ below which the fluid is modeled as compressible and above which the fluid is modeled as incompressible. The present article focuses
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On the Cucker-Smale ensemble with \begin{document}$ q $\end{document}-closest neighbors under time-delayed communications Kinet. Relat. Models (IF 1.38) Pub Date : 2020-05-06 Jiu-Gang Dong; Seung-Yeal Ha; Doheon Kim
We study time-asymptotic interplay between time-delayed communication and Cucker-Smale (C-S) velocity alignment. For this, we present two sufficient frameworks for the asymptotic flocking to the continuous and discrete C-S models with $ q $-closest neighbors in the presence of time-delayed communications. Communication time-delays result from the finite-propagation speed of information and they are
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A Petrov-Galerkin spectral method for the inelastic Boltzmann equation using mapped Chebyshev functions Kinet. Relat. Models (IF 1.38) Pub Date : 2020-05-06 Jingwei Hu; Jie Shen; Yingwei Wang
We develop in this paper a Petrov-Galerkin spectral method for the inelastic Boltzmann equation in one dimension. Solutions to such equations typically exhibit heavy tails in the velocity space so that domain truncation or Fourier approximation would suffer from large truncation errors. Our method is based on the mapped Chebyshev functions on unbounded domains, hence requires no domain truncation.
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Strong solutions for the Alber equation and stability of unidirectional wave spectra Kinet. Relat. Models (IF 1.38) Pub Date : 2020-05-06 Agissilaos G. Athanassoulis; Gerassimos A. Athanassoulis; Mariya Ptashnyk; Themistoklis Sapsis
The Alber equation is a moment equation for the nonlinear Schrödinger equation, formally used in ocean engineering to investigate the stability of stationary and homogeneous sea states in terms of their power spectra. In this work we present the first well-posedness theory for the Alber equation with the help of an appropriate equivalent reformulation. Moreover, we show linear Landau damping in the
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Angular moments models for rarefied gas dynamics. Numerical comparisons with kinetic and Navier-Stokes equations Kinet. Relat. Models (IF 1.38) Pub Date : 2020-05-06 Sébastien Guisset
Angular moments models based on a minimum entropy problem have been largely used to describe the transport of photons [14] or charged particles [18]. In this communication the $ M_1 $ and $ M_2 $ angular moments models are presented for rarefied gas dynamics applications. After introducing the models studied, numerical simulations carried out in various collisional regimes are presented and illustrate
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Slow flocking dynamics of the Cucker-Smale ensemble with a chemotactic movement in a temperature field Kinet. Relat. Models (IF 1.38) Pub Date : 2020-05-06 Seung-Yeal Ha; Doheon Kim; Weiyuan Zou
We study slow flocking phenomenon arising from the dynamics of Cucker-Smale (CS) ensemble with chemotactic movements in a self-consistent temperature field. For constant temperature field, our situation reduces to the previous CS model with chemotactic movements. When a large CS ensemble with chemotactic movements is placed in a self-consistent temperature field, the dynamics of the CS ensemble can
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Asymptotic flocking in the Cucker-Smale model with reaction-type delays in the non-oscillatory regime Kinet. Relat. Models (IF 1.38) Pub Date : 2020-05-06 Jan Haskovec; Ioannis Markou
We study a variant of the Cucker-Smale system with reaction-type delay. Using novel backward-forward and stability estimates on appropriate quantities we derive sufficient conditions for asymptotic flocking of the solutions. These conditions, although not explicit, relate the velocity fluctuation of the initial datum and the length of the delay. If satisfied, they guarantee monotone decay (i.e., non-oscillatory
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Well-posedness for boundary value problems for coagulation-fragmentation equations Kinet. Relat. Models (IF 1.38) Pub Date : 2020-05-06 Iñigo U. Erneta
We investigate a coagulation-fragmentation equation with boundary data, establishing the well-posedness of the initial value problem when the coagulation kernels are bounded at zero and showing existence of solutions for the singular kernels relevant in the applications. We determine the large time asymptotic behavior of solutions, proving that solutions converge exponentially fast to zero in the absence
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Local well-posedness of the Boltzmann equation with polynomially decaying initial data Kinet. Relat. Models (IF 1.38) Pub Date : 2020-05-06 Christopher Henderson; Stanley Snelson; Andrei Tarfulea
We consider the Cauchy problem for the spatially inhomogeneous non-cutoff Boltzmann equation with polynomially decaying initial data in the velocity variable. We establish short-time existence for any initial data with this decay in a fifth order Sobolev space by working in a mixed $ L^2 $ and $ L^\infty $ space that allows to compensate for potential moment generation and obtaining new estimates on
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