Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics And Kinetic Limit For A System Of Noiseless D-Dimensional
  Vicsek-Type Particles   We analyze the continuous time evolution of a $d$-dimensional system of $N$
self propelled particles with a kinematic constraint on the velocities inspired
by the original Vicsek's one \cite{VCB-JCS}. Interactions among particles are
specified by a pairwise potential in such a way that the velocity of any given
particle is updated to the weighted average velocity of all those particles
interacting with it. The weights are given in terms of the interaction rate
function. When the size of the system is fixed, we show the existence of an
invariant manifold in the phase space and prove its exponential asymptotic
stability. In the kinetic limit we show that the particle density satisfies a
nonlinear kinetic equation of Vlasov type, under suitable conditions on the
interaction. We study the qualitative behaviour of the solution and we show
that the Boltzmann-Vlasov entropy is strictly decreasing in time.

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The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph