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Kinetic and Related Models (KRM)

ISSN 1937-5093(print) ISSN 1937-5077(online)	Current volume Go	Journal archive Go	Advanced Search
	KRM is now SCI-E, covered in Science Citation Index-Expanded (SCIE) including the Web of Science ISI Alerting Service Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES). KRM publishes high quality papers of original research in the areas of kinetic equations spanning from mathematical theory to numerical analysis, simulations and modelling. It includes studies on models arising from physics, engineering, finance, biology, human and social sciences, together with their related fields such as fluid models, interacting particle systems and quantum systems. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time. KRM was launched in 2008 as a quarterly publication in March, June, September and December. It is edited by a group of energetic leaders to guarantee the journal's highest standard and closest link to the scientific communities. A unique feature of this journal is its streamlined review process and rapid publication. Authors are kept informed throughout the process through direct and personal communication between the authors and editors.

TOP 10 Most Read Articles in KRM, May 2012

1	Existence and sharp localization in velocity of small-amplitude Boltzmann shocks Volume 2, Number 4, Pages: 667 - 705, 2009 Guy Métivier and K. Zumbrun Abstract Full Text Related Articles Using a weighted $H^s$-contraction mapping argument based on the macro-micro decomposition of Liu and Yu, we give an elementary proof of existence, with sharp rates of decay and distance from the Chapman-Enskog approximation, of small-amplitude shock profiles of the Boltzmann equation with hard-sphere potential, recovering and slightly sharpening results obtained by Caflisch and Nicolaenko using different techniques. A key technical point in both analyses is that the linearized collision operator $L$ is negative definite on its range, not only in the standard square-root Maxwellian weighted norm for which it is self-adjoint, but also in norms with nearby weights. Exploring this issue further, we show that $L$ is negative definite on its range in a much wider class of norms including norms with weights asymptotic nearly to a full Maxwellian rather than its square root. This yields sharp localization in velocity at near-Maxwellian rate, rather than the square-root rate obtained in previous analyses.
2	A maximum entropy principle based closure method for macro-micro models of polymeric materials Volume 1, Number 2, Pages: 171 - 184, 2008 Yunkyong Hyon, José A. Carrillo, Qiang Du and Chun Liu Abstract Full Text Related Articles We consider the finite extensible nonlinear elasticity (FENE) dumbbell model in viscoelastic polymeric fluids. We employ the maximum entropy principle for FENE model to obtain the solution which maximizes the entropy of FENE model in stationary situations. Then we approximate the maximum entropy solution using the second order terms in microscopic configuration field to get an probability density function (PDF). The approximated PDF gives a solution to avoid the difficulties caused by the nonlinearity of FENE model. We perform the moment-closure approximation procedure with the PDF approximated from the maximum entropy solution, and compute the induced macroscopic stresses. We also show that the moment-closure system satisfies the energy dissipation law. Finally, we show some numerical simulations to verify the PDF and moment-closure system.
3	Celebrating Cercignani's conjecture for the Boltzmann equation Volume 4, Number 1, Pages: 277 - 294, 2011 Laurent Desvillettes, Clément Mouhot and Cédric Villani Abstract References Full Text Related Articles Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s.
4	Qualitative analysis of the generalized Burnett equations and applications to half--space problems Volume 1, Number 2, Pages: 295 - 312, 2008 Marzia Bisi, Maria Paola Cassinari and Maria Groppi Abstract Full Text Related Articles The Generalized Burnett Equations, very recently introduced by Bobylev [3,4], are tested versus Fluid--Dynamic applications, considering the classical steady evaporation/condensation problem. By means of the methods of the qualitative theory of dynamical systems, comparison is made to other kinetic and hydrodynamic models, and indications on an appropriate choice of the disposable parameters are obtained.
5	Orientation waves in a director field with rotational inertia Volume 2, Number 1, Pages: 1 - 37, 2009 Giuseppe Alì and John K. Hunter Abstract Full Text Related Articles We study a variational system of nonlinear hyperbolic partial differential equations that describes the propagation of orientation waves in a director field with rotational inertia and potential energy given by the Oseen-Frank energy from the continuum theory of nematic liquid crystals. There are two types of waves, which we call splay and twist waves, respectively. Weakly nonlinear splay waves are described by the quadratically nonlinear Hunter-Saxton equation. In this paper, we derive a new cubically nonlinear asymptotic equation that describes weakly nonlinear twist waves. This equation provides a surprising representation of the Hunter-Saxton equation, and like the Hunter-Saxton equation it is completely integrable. There are analogous cubically nonlinear representations of the Camassa-Holm and Degasperis-Procesi equations. Moreover, two different, but compatible, variational principles for the Hunter-Saxton equation arise from a single variational principle for the primitive director field equations in the two different limits for splay and twist waves. We also use the asymptotic equation to analyze a one-dimensional initial value problem for the director-field equations with twist-wave initial data.
6	Analytical and numerical investigations of refined macroscopic traffic flow models Volume 3, Number 2, Pages: 311 - 333, 2010 Michael Herty and Reinhard Illner Abstract Full Text Related Articles We continue research on generalized macroscopic models of conservation type as started in [15]. In this paper we keep the characteristic (for traffic) non-locality removed in [15] by Taylor expansion and discuss the merits and problems of such an expansion. We observe that the models satisfy maximum principles and conclude that "triggers'' are needed in order to cause traffic jams (braking waves) in traffic guided by such models. Several such triggers are introduced and discussed. The models are refined further in order to properly address non-monotonic (in speed) traffic regimes, and the inclusion of an individual reaction time is discussed in the context of a braking wave. A number of numerical experiments are conducted to exhibit our findings.
7	On a family of finite-difference schemes with approximate transparent boundary conditions for a generalized 1D Schrödinger equation Volume 2, Number 1, Pages: 151 - 179, 2009 Bernard Ducomet, Alexander Zlotnik and Ilya Zlotnik Abstract Full Text Related Articles We consider a 1D Schrödinger equation with variable coefficients on the half-axis. We study a family of two-level symmetric finite-difference schemes with a three-point parameter dependent averaging in space. This family includes a number of particular schemes. The schemes are coupled to an approximate transparent boundary condition (TBC). We prove two stability bounds with respect to initial data and a free term in the main equation, under suitable conditions on an operator of the approximate TBC. We also consider the family of schemes on an infinite mesh in space. We derive and analyze the discrete TBC allowing to restrict these schemes to a finite mesh and prove the stability conditions for it. Numerical examples are also included.
8	On the Kac model for the Landau equation Volume 4, Number 1, Pages: 333 - 344, 2011 Evelyne Miot, Mario Pulvirenti and Chiara Saffirio Abstract References Full Text Related Articles We introduce a $N$-particle system which approximates, in the mean-field limit, the solutions of the Landau equation with Coulomb singularity. This model plays the same role as the Kac's model for the homogeneous Boltzmann equation. We use compactness arguments following [11].
9	Modelling and simulation of a solar updraft tower Volume 2, Number 1, Pages: 191 - 204, 2009 Ingenuin Gasser Abstract Full Text Related Articles A new model for a solar updraft tower is presented. It is based on a one-dimensional description of the fully transient gasdynamics in an updraft power plant from the outer end of the collector to the top of the tower. All the main physical effects are included. The model is derived from basic gasdynamic equations, a low Mach number asymptotics is performed and numerical simulations are shown.
10	Semilagrangian schemes applied to moving boundary problems for the BGK model of rarefied gas dynamics Volume 2, Number 1, Pages: 231 - 250, 2009 Giovanni Russo and Francis Filbet Abstract Full Text Related Articles In this paper we present a new semilagrangian scheme for the numerical solution of the BGK model of rarefied gas dynamics, in a domain with moving boundaries, in view of applications to Micro Electro Mechanical Systems (MEMS). The source term is treated implicitly, which makes the scheme Asymptotic Preserving in the limit of small Knudsen number. Because of its Lagrangian nature, no stability restriction is posed on the CFL number, which is determined only by accuracy requirements. The method is tested on a one dimensional piston problem. The solution for small Knudsen number is compared with the results obtained by the numerical solution of the Euler equation of gas dynamics.

2011 Impact Factor.677