308 research outputs found
Level Set Approach to Reversible Epitaxial Growth
We generalize the level set approach to model epitaxial growth to include
thermal detachment of atoms from island edges. This means that islands do not
always grow and island dissociation can occur. We make no assumptions about a
critical nucleus. Excellent quantitative agreement is obtained with kinetic
Monte Carlo simulations for island densities and island size distributions in
the submonolayer regime.Comment: 7 pages, 9 figure
Velocity fluctuations and hydrodynamic diffusion in sedimentation
We study non-equilibrium velocity fluctuations in a model for the
sedimentation of non-Brownian particles experiencing long-range hydrodynamic
interactions. The complex behavior of these fluctuations, the outcome of the
collective dynamics of the particles, exhibits many of the features observed in
sedimentation experiments. In addition, our model predicts a final relaxation
to an anisotropic (hydrodynamic) diffusive state that could be observed in
experiments performed over longer time ranges.Comment: 7 pages, 5 EPS figures, EPL styl
On Strong Convergence to Equilibrium for the Boltzmann Equation with Soft Potentials
The paper concerns - convergence to equilibrium for weak solutions of
the spatially homogeneous Boltzmann Equation for soft potentials (-4\le
\gm<0), with and without angular cutoff. We prove the time-averaged
-convergence to equilibrium for all weak solutions whose initial data have
finite entropy and finite moments up to order greater than 2+|\gm|. For the
usual -convergence we prove that the convergence rate can be controlled
from below by the initial energy tails, and hence, for initial data with long
energy tails, the convergence can be arbitrarily slow. We also show that under
the integrable angular cutoff on the collision kernel with -1\le \gm<0, there
are algebraic upper and lower bounds on the rate of -convergence to
equilibrium. Our methods of proof are based on entropy inequalities and moment
estimates.Comment: This version contains a strengthened theorem 3, on rate of
convergence, considerably relaxing the hypotheses on the initial data, and
introducing a new method for avoiding use of poitwise lower bounds in
applications of entropy production to convergence problem
Global Hilbert Expansion for the Vlasov-Poisson-Boltzmann System
We study the Hilbert expansion for small Knudsen number for the
Vlasov-Boltzmann-Poisson system for an electron gas. The zeroth order term
takes the form of local Maxwellian: $ F_{0}(t,x,v)=\frac{\rho_{0}(t,x)}{(2\pi
\theta_{0}(t,x))^{3/2}} e^{-|v-u_{0}(t,x)|^{2}/2\theta_{0}(t,x)},\text{\
}\theta_{0}(t,x)=K\rho_{0}^{2/3}(t,x).t=0u_00\leq t\leq \varepsilon
^{-{1/2}\frac{2k-3}{2k-2}},\rho_{0}(t,x) u_{0}(t,x)\gamma=5/3$
Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with integrable angular cross section
This paper focuses on the study of existence and uniqueness of distributional
and classical solutions to the Cauchy Boltzmann problem for the soft potential
case assuming integrability of the angular part of the collision
kernel (Grad cut-off assumption). For this purpose we revisit the
Kaniel--Shinbrot iteration technique to present an elementary proof of
existence and uniqueness results that includes large data near a local
Maxwellian regime with possibly infinite initial mass. We study the propagation
of regularity using a recent estimate for the positive collision operator given
in [3], by E. Carneiro and the authors, that permits to study such propagation
without additional conditions on the collision kernel. Finally, an
-stability result (with ) is presented assuming the
aforementioned condition.Comment: 19 page
The Moment Guided Monte Carlo method for the Boltzmann equation
In this work we propose a generalization of the Moment Guided Monte Carlo
method developed in [11]. This approach permits to reduce the variance of the
particle methods through a matching with a set of suitable macroscopic moment
equations. In order to guarantee that the moment equations provide the correct
solutions, they are coupled to the kinetic equation through a non equilibrium
term. Here, at the contrary to the previous work in which we considered the
simplified BGK operator, we deal with the full Boltzmann operator. Moreover, we
introduce an hybrid setting which permits to entirely remove the resolution of
the kinetic equation in the limit of infinite number of collisions and to
consider only the solution of the compressible Euler equation. This
modification additionally reduce the statistical error with respect to our
previous work and permits to perform simulations of non equilibrium gases using
only a few number of particles. We show at the end of the paper several
numerical tests which prove the efficiency and the low level of numerical noise
of the method.Comment: arXiv admin note: text overlap with arXiv:0908.026
Optimal time decay of the non cut-off Boltzmann equation in the whole space
In this paper we study the large-time behavior of perturbative classical
solutions to the hard and soft potential Boltzmann equation without the angular
cut-off assumption in the whole space \threed_x with \DgE. We use the
existence theory of global in time nearby Maxwellian solutions from
\cite{gsNonCutA,gsNonCut0}. It has been a longstanding open problem to
determine the large time decay rates for the soft potential Boltzmann equation
in the whole space, with or without the angular cut-off assumption
\cite{MR677262,MR2847536}. For perturbative initial data, we prove that
solutions converge to the global Maxwellian with the optimal large-time decay
rate of O(t^{-\frac{\Ndim}{2}+\frac{\Ndim}{2r}}) in the
L^2_\vel(L^r_x)-norm for any .Comment: 31 pages, final version to appear in KR
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Particle Simulation of Coulomb Collisions: Comparing the Methods of Takizuka & Abe and Nanbu
The interactions of charged particles in a plasma are in a plasma is governed by the long-range Coulomb collision. We compare two widely used Monte Carlo models for Coulomb collisions. One was developed by Takizuka and Abe in 1977, the other was developed by Nanbu in 1997. We perform deterministic and stochastic error analysis with respect to particle number and time step. The two models produce similar stochastic errors, but Nanbu's model gives smaller time step errors. Error comparisons between these two methods are presented
Screened and Unscreened Phases in Sedimenting Suspensions
A coarse-grained stochastic hydrodynamical description of velocity and
concentration fluctuations in steadily sedimenting suspensions is constructed,
and analyzed using self-consistent and renormalization group methods. We find
that there exists a dynamical, non-equilibrium phase transition from an
"unscreened" phase in which we recover the Caflisch-Luke (R.E. Caflisch and
J.H.C. Luke, Phys. Fluids 28, 759 (1985)) divergence of the velocity variance
to a "screened" phase where the velocity fluctuations have a finite correlation
length growing as where is the particle volume fraction,
in agreement with Segr\`e et. al. (Phys. Rev. Lett. 79, 2574 (1997)) and the
velocity variance is independent of system size. Detailed predictions are made
for the correlation function in both phases and at the transition.Comment: 4 pages, revtex 1 figur
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