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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.
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TOP 10 Most Read Articles in KRM, March 2017
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 
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.

4 
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.

5 
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 meanfield 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].

6 
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.

7 
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.

8 
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.

9 
On a continuous mixed strategies model for evolutionary game theory
Volume 4, Number 1, Pages: 187  213, 2011
Astridh Boccabella,
Roberto Natalini
and Lorenzo Pareschi
Abstract
References
Full Text
Related Articles
We consider an integrodifferential model for evolutionary game
theory which describes the evolution of a population adopting
mixed strategies. Using a reformulation based on the first
moments of the solution, we prove some analytical properties of
the model and global estimates. The asymptotic behavior and the
stability of solutions in the case of two strategies is analyzed
in details. Numerical schemes for two and three strategies which
are able to capture the correct equilibrium states are also
proposed together with several numerical examples.

10 
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.

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