694 research outputs found
From the Boltzmann equation to fluid mechanics on a manifold
We apply the Chapman-Enskog procedure to derive hydrodynamic equations on an
arbitrary surface from the Boltzmann equation on the surface
Direct simulation for a homogenous gas
A probabilistic analysis of the direct simulation of a homogeneous gas is
given. A hierarchy of equations similar to the BBGKY hierarchy for the reduced
probability densities is derived. By invoking the molecular chaos assumption,
an equation similar to the Boltzmann equation for the single particle
probability density and the corresponding H-theorem is derived
Quantum Kinetic Evolution of Marginal Observables
We develop a rigorous formalism for the description of the evolution of
observables of quantum systems of particles in the mean-field scaling limit.
The corresponding asymptotics of a solution of the initial-value problem of the
dual quantum BBGKY hierarchy is constructed. Moreover, links of the evolution
of marginal observables and the evolution of quantum states described in terms
of a one-particle marginal density operator are established. Such approach
gives the alternative description of the kinetic evolution of quantum
many-particle systems to generally accepted approach on basis of kinetic
equations.Comment: 18 page
Towards a relativistic statistical theory
In special relativity the mathematical expressions, defining physical
observables as the momentum, the energy etc, emerge as one parameter (light
speed) continuous deformations of the corresponding ones of the classical
physics. Here, we show that the special relativity imposes a proper one
parameter continuous deformation also to the expression of the classical
Boltzmann-Gibbs-Shannon entropy. The obtained relativistic entropy permits to
construct a coherent and selfconsistent relativistic statistical theory [Phys.
Rev. E {\bf 66}, 056125 (2002); Phys. Rev. E {\bf 72}, 036108 (2005)],
preserving the main features (maximum entropy principle, thermodynamic
stability, Lesche stability, continuity, symmetry, expansivity, decisivity,
etc.) of the classical statistical theory, which is recovered in the classical
limit. The predicted distribution function is a one-parameter continuous
deformation of the classical Maxwell-Boltzmann distribution and has a simple
analytic form, showing power law tails in accordance with the experimental
evidence.Comment: Physica A (2006). Proof correction
Statistical kinetic treatment of relativistic binary collisions
In particle-based algorithms, the effect of binary collisions is commonly
described in a statistical way, using Monte Carlo techniques. It is shown that,
in the relativistic regime, stringent constraints should be considered on the
sampling of particle pairs for collision, which are critical to ensure
physically meaningful results, and that nonrelativistic sampling criteria
(e.g., uniform random pairing) yield qualitatively wrong results, including
equilibrium distributions that differ from the theoretical J\"uttner
distribution. A general procedure for relativistically consistent algorithms is
provided, and verified with three-dimensional Monte Carlo simulations, thus
opening the way to the numerical exploration of the statistical properties of
collisional relativistic systems.Comment: Accepted for publication as a Rapid Communication in Phys. Rev.
Continuum description of finite-size particles advected by external flows. The effect of collisions
The equation of the density field of an assembly of macroscopic particles
advected by a hydrodynamic flow is derived from the microscopic description of
the system. This equation allows to recognize the role and the relative
importance of the different microscopic processes implicit in the model: the
driving of the external flow, the inertia of the particles, and the collisions
among them.
The validity of the density description is confirmed by comparisons of
numerical studies of the continuum equation with Direct Simulation Monte Carlo
(DSMC) simulations of hard disks advected by a chaotic flow. We show that the
collisions have two competing roles: a dispersing-like effect and a clustering
effect (even for elastic collisions). An unexpected feature is also observed in
the system: the presence of collisions can reverse the effect of inertia, so
that grains with lower inertia are more clusterized.Comment: Final (strongly modified) version accepted in PRE; 6 pages, 3 figure
The Enskog Process
The existence of a weak solution to a McKean-Vlasov type stochastic
differential system corresponding to the Enskog equation of the kinetic theory
of gases is established under natural conditions. The distribution of any
solution to the system at each fixed time is shown to be unique. The existence
of a probability density for the time-marginals of the velocity is verified in
the case where the initial condition is Gaussian, and is shown to be the
density of an invariant measure.Comment: 38 page
A new approach to quantitative propagation of chaos for drift, diffusion and jump processes
This paper is devoted the the study of the mean field limit for many-particle
systems undergoing jump, drift or diffusion processes, as well as combinations
of them. The main results are quantitative estimates on the decay of
fluctuations around the deterministic limit and of correlations between
particles, as the number of particles goes to infinity. To this end we
introduce a general functional framework which reduces this question to the one
of proving a purely functional estimate on some abstract generator operators
(consistency estimate) together with fine stability estimates on the flow of
the limiting nonlinear equation (stability estimates). Then we apply this
method to a Boltzmann collision jump process (for Maxwell molecules), to a
McKean-Vlasov drift-diffusion process and to an inelastic Boltzmann collision
jump process with (stochastic) thermal bath. To our knowledge, our approach
yields the first such quantitative results for a combination of jump and
diffusion processes.Comment: v2 (55 pages): many improvements on the presentation, v3: correction
of a few typos, to appear In Probability Theory and Related Field
Corrigendum to “Abnormal brain connectivity in first-episode psychosis: A diffusion MRI tractography study of the corpus callosum” [NeuroImage 35 (2007) 458–466]
STRUCTURAL AND STEREOSPECIFIC REQUIREMENTS FOR THE NUCLEOSIDE-TRIGGERED GERMINATION OF BACILLUS-CEREUS SPORES
A selection of adenosine analogues was tested for their ability to trigger germination of Bacillus cereus NCIB 8122 spores. The germination-inducing activity was governed by the structural properties of the sugar rather than the base moieties of the nucleosides. Among the sugar-modified analogues, only those containing a 2'-deoxy-D-ribose moiety promoted spore germination. Requirements for a specific molecular structure of the base were not clearly identified, although the highest activity was observed when substituents were inserted at position 6 of the purine ring. All the base-modified analogues, even those such as coformycin and 2'-deoxycoformycin with an expanded base ring, retained the germination-inducing activity of adenosine. However, of the two 2'-deoxycoformycin diastereoisomers characterized by an asymmetric carbon atom at position 8 of the homopurine ring, only the 8S-isomer induced germination, thus indicating that stereospecific configuration of the inducer, at least in the case of 2'-deoxycoformycin, appears to be essential for the initiation of spore germination. The differences in the germination-inducing activity of the various analogues tested were not affected significantly by spore activation at different temperatures, although the higher the activation temperature, the lower was the concentration of each analogue required for maximum germination
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