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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, May 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 
A maximum entropy principle based closure method for macromicro 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 momentclosure approximation procedure with the PDF
approximated from the maximum entropy solution, and compute the
induced macroscopic stresses. We also show that the momentclosure
system satisfies the energy dissipation law. Finally, we show some
numerical simulations to verify the PDF and momentclosure 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 halfspace 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 FluidDynamic 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 OseenFrank
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 HunterSaxton 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 HunterSaxton equation, and
like the HunterSaxton equation it is completely integrable.
There are analogous cubically nonlinear representations of the CamassaHolm
and DegasperisProcesi equations.
Moreover, two different, but compatible, variational principles for the HunterSaxton
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 onedimensional initial value problem for the
directorfield equations with twistwave 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) nonlocality 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 nonmonotonic (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 finitedifference 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 halfaxis.
We study a family of twolevel symmetric finitedifference schemes with a threepoint 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 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].

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 onedimensional 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.

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