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KRM is covered in Science Citation Index (SCI), 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.
We are proud to announce that Pierre Degond, one of the
editorsinchief of KRM, received the "JacquesLouis Lions
Prize 2013". Please refer to the following link for this good
news:
http://www.academiesciences.fr/activite/prix/laureat_lions.pdf
Archived in Portico 
TOP 10 Most Read Articles in KRM, February 2015
1 
Existence and sharp localization in velocity
of smallamplitude 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
macromicro decomposition of Liu and Yu, we give an elementary proof
of existence, with sharp rates of decay and distance from the
ChapmanEnskog approximation, of smallamplitude shock profiles of
the Boltzmann equation with hardsphere 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 squareroot Maxwellian
weighted norm for which it is selfadjoint, 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 nearMaxwellian rate, rather than the squareroot rate
obtained in previous analyses.

2 
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.

3 
Analysis and simulations of a refined flocking and swarming model of CuckerSmale type
Volume 4, Number 1, Pages: 1  16, 2011
Martial Agueh,
Reinhard Illner
and Ashlin Richardson
Abstract
References
Full Text
Related Articles
The CuckerSmale model for flocking or swarming of birds or insects is generalized to scenarios
where a typical bird will be subject to a) a friction force term driving it to fly at optimal speed,
b) a repulsive short range force to avoid collisions, c) an attractive "flocking" force computed
from the birds seen by each bird inside its vision cone, and d) a "boundary" force which will
entice birds to search for and return to the flock if they find themselves at some distance from the
flock. We introduce these forces in detail, discuss the required cutoffs and their implications and
show that there are natural bounds in velocity space. Wellposedness of the initial value problem
is discussed in spaces of measurevalued functions. We conclude with a series of numerical simulations.

4 
Discrete transparent boundary conditions for the Schrodinger equation  a compact higher order scheme
Volume 1, Number 1, Pages: 101  125, 2008
Maike Schulte
and Anton Arnold
Abstract
Full Text
Related Articles
We consider the twodimensional timedependent Schrödinger equation with the new compact ninepoint scheme in space and the CrankNicolson difference scheme in time. For the resulting difference equation we derive discrete transparent boundary conditions in order to get highly accurate solutions for open boundary problems. Numerical experiments illustrate the perfect absorption of outgoing wave independently of their impact angle at the boundary. Finally, we apply inhomogeneous discrete transparent boundary conditions to the transient simulation of quantum waveguides.

5 
Analysis of a model for wealth redistribution
Volume 1, Number 1, Pages: 1  27, 2008
Daniel Matthes
and Giuseppe Toscani
Abstract
Full Text
Related Articles
A recent application of the kinetic theory for many particle systems
is the description of the redistribution of wealth among trading agents in a simple market economy.
This paper provides an analytical investigation of
the particular model with quenched saving propensities,
which has been introduced by Chakrabarti, Chatterjee and Manna [11].
We prove uniqueness and dynamical stability of the stationary solution
to the underlying Boltzmann equation,
and provide estimates on the rate of equilibration.
As one main result,
we obtain that realistic steady wealth distributions with Pareto tail
are only algebraically stable in this framework.

6 
On the plasmacharge model
Volume 3, Number 2, Pages: 241  254, 2010
Silvia Caprino
and Carlo Marchioro
Abstract
Full Text
Related Articles
We consider a system made of a positive VlasovPoisson plasma and $N$ positive charges in $\R^2$, interacting among themselves and with the plasma via the Coulomb force. We prove an existence and uniqueness theorem for the system in case the charges are initially apart from the plasma.

7 
Kinetic approach to deflagration processes in a recombination reaction
Volume 4, Number 1, Pages: 259  276, 2011
Fiammetta Conforto,
Maria Groppi,
Roberto Monaco
and Giampiero Spiga
Abstract
References
Full Text
Related Articles
Steady onedimensional flame structure is investigated in a binary gas mixture made up by diatomic molecules and atoms, which undergo an irreversible exothermic twosteps reaction, a recombination process followed by inelastic scattering (deexcitation). A kinetic model at the Boltzmann level, accounting for chemical encounters as well as for mechanical collisions, is proposed and its main features are analyzed. In the case of collision dominated regime with slow recombination and fast deexcitation, the model is the starting point for a consistent derivation,
via suitable asymptotic expansion of ChapmanEnskog type, of reactive fluiddynamic NavierStokes equations. The resulting set of ordinary differential equations for the smooth steady deflagration profile is investigated in the frame of the qualitative theory of dynamical systems, and numerical results for the flame eigenvalue and for the main macroscopic observables are presented and briefly commented on for illustrative purposes.

8 
Fastreaction limit for the inhomogeneous AizenmanBak model
Volume 1, Number 1, Pages: 127  137, 2008
José A. Carrillo,
Laurent Desvillettes
and Klemens Fellner
Abstract
Full Text
Related Articles
Solutions of the spatially inhomogeneous diffusive\linebreak AizenmannBak
model for clustering within a bounded domain with homogeneous
Neumann boundary conditions are shown to stabilize, in the fast
reaction limit, towards local equilibria determined by their
monomer density. Moreover, the sequence of monomer densities
converges to the solution of a nonlinear diffusion equation whose
nonlinearity depends on the sizedependent diffusion coefficient.
Initial data are assumed to be integrable, bounded and with a
certain number of moments in size. The number density of clusters
for the solutions is assumed to verify uniform bounds away from
zero and infinity independently of the scale parameter.

9 
Regularity criteria for the magnetohydrodynamic equations with partial viscous terms and the Leray$\alpha$MHD
model
Volume 2, Number 2, Pages: 293  305, 2009
Jishan Fan
and Tohru Ozawa
Abstract
Full Text
Related Articles
We prove some regularity conditions for the MHD equations with
partial viscous terms and the Leray$\alpha$MHD model. Since the
solutions to the Leray$\alpha$MHD model are smoother than that of
the original MHD equations, we are able to obtain better regularity
conditions in terms of the magnetic field $B$ only.

10 
Rigorous validity of the Boltzmann equation for a thin layer of a rarefied gas
Volume 3, Number 2, Pages: 281  297, 2010
Raffaele Esposito
and Mario Pulvirenti
Abstract
Full Text
Related Articles
We consider a thin layer of a rarified gas modeled by a large hardsphere system and show that, as long as the thickness of the layer is much larger than the interaction length, the limiting behavior is described, at least for short times, by a Boltzmann equation with twodimensional position variable and threedimensional velocity.
By the analysis of the Lorentz gas we argue that, if the thickness of the layer is of the same order of the interaction length, this is not the case.

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