737 research outputs found
Kinetic hierarchy and propagation of chaos in biological swarm models
We consider two models of biological swarm behavior. In these models, pairs
of particles interact to adjust their velocities one to each other. In the
first process, called 'BDG', they join their average velocity up to some noise.
In the second process, called 'CL', one of the two particles tries to join the
other one's velocity. This paper establishes the master equations and BBGKY
hierarchies of these two processes. It investigates the infinite particle limit
of the hierarchies at large time-scale. It shows that the resulting kinetic
hierarchy for the CL process does not satisfy propagation of chaos. Numerical
simulations indicate that the BDG process has similar behavior to the CL
process
Celebrating Cercignani's conjecture for the Boltzmann equation
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.Comment: This paper is dedicated to the memory of the late Carlo Cercignani,
powerful mind and great scientist, one of the founders of the modern theory
of the Boltzmann equation. 24 pages. V2: correction of some typos and one
ref. adde
Complete characterization of convergence to equilibrium for an inelastic Kac model
Pulvirenti and Toscani introduced an equation which extends the Kac
caricature of a Maxwellian gas to inelastic particles. We show that the
probability distribution, solution of the relative Cauchy problem, converges
weakly to a probability distribution if and only if the symmetrized initial
distribution belongs to the standard domain of attraction of a symmetric stable
law, whose index is determined by the so-called degree of
inelasticity, , of the particles: . This result is
then used: (1) To state that the class of all stationary solutions coincides
with that of all symmetric stable laws with index . (2) To determine
the solution of a well-known stochastic functional equation in the absence of
extra-conditions usually adopted
Comment on "Why quantum mechanics cannot be formulated as a Markov process"
In the paper with the above title, D. T. Gillespie [Phys. Rev. A 49, 1607,
(1994)] claims that the theory of Markov stochastic processes cannot provide an
adequate mathematical framework for quantum mechanics. In conjunction with the
specific quantum dynamics considered there, we give a general analysis of the
associated dichotomic jump processes. If we assume that Gillespie's
"measurement probabilities" \it are \rm the transition probabilities of a
stochastic process, then the process must have an invariant (time independent)
probability measure. Alternatively, if we demand the probability measure of the
process to follow the quantally implemented (via the Born statistical
postulate) evolution, then we arrive at the jump process which \it can \rm be
interpreted as a Markov process if restricted to a suitable duration time.
However, there is no corresponding Markov process consistent with the
event space assumption, if we require its existence for all times .Comment: Latex file, resubm. to Phys. Rev.
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On Visible Homelessness and the Micro-Aesthetics of Public Space
In this article, we investigate the circumstances that have produced the current municipal regulatory approach to homelessness in the City of Melbourne, Victoria, and the ways in which visibly homeless people are policed through a micro-aesthetics of their presence in public space, which involves the monitoring of their bodily demeanour and their physical possessions. Our study contributes to and draws from a range of debates, including studies of the governmental conjunction of poverty and crime, analysis of the co-implication of law and spatiality, research on the criminalisation of homelessness and homeless people, and the burgeoning criminological interest in the significance of the visual field for our understandings of crime and criminality. This article recounts how homelessness, public space and questions of aesthetics have recently coalesced in debates about the regulation of homelessness in the public space of Melbourneâs city centre. It approaches the issues through comparative consideration of genres of municipal management frameworks in other jurisdictions, detailed textual consideration of the Protocol on Homelessness in the City of Melbourne and an empirical study of visible homelessness in the public places of central Melbourne
Self-similarity and power-like tails in nonconservative kinetic models
In this paper, we discuss the large--time behavior of solution of a simple
kinetic model of Boltzmann--Maxwell type, such that the temperature is time
decreasing and/or time increasing. We show that, under the combined effects of
the nonlinearity and of the time--monotonicity of the temperature, the kinetic
model has non trivial quasi-stationary states with power law tails. In order to
do this we consider a suitable asymptotic limit of the model yielding a
Fokker-Planck equation for the distribution. The same idea is applied to
investigate the large-time behavior of an elementary kinetic model of economy
involving both exchanges between agents and increasing and/or decreasing of the
mean wealth. In this last case, the large-time behavior of the solution shows a
Pareto power law tail. Numerical results confirm the previous analysis
A glutathione conjugate of hepoxilin A3: formation and action in the rat central nervous system.
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