397 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
The Mean-Field Limit for Solid Particles in a Navier-Stokes Flow
We propose a mathematical derivation of Brinkman's force for a cloud of
particles immersed in an incompressible fluid. Our starting point is the Stokes
or steady Navier-Stokes equations set in a bounded domain with the disjoint
union of N balls of radius 1/N removed, and with a no-slip boundary condition
for the fluid at the surface of each ball. The large N limit of the fluid
velocity field is governed by the same (Navier-)Stokes equations in the whole
domain, with an additional term (Brinkman's force) that is (minus) the total
drag force exerted by the fluid on the particle system. This can be seen as a
generalization of Allaire's result in [Arch. Rational Mech. Analysis 113
(1991), 209-259] who treated the case of motionless, periodically distributed
balls. Our proof is based on slightly simpler, though similar homogenization
techniques, except that we avoid the periodicity assumption and use instead the
phase-space empirical measure for the particle system. Similar equations are
used for describing the fluid phase in various models for sprays
Decrypting Integrins by Mixed-Solvent Molecular Dynamics Simulations
Integrins are a family of α/β heterodimeric cell surface adhesion receptors which are capable of transmitting signals bidirectionally across membranes. They are known for their therapeutic potential in a wide range of diseases. However, the development of integrin-targeting medications has been impacted by unexpected downstream effects including unwanted agonist-like effects. Allosteric modulation of integrins is a promising approach to potentially overcome these limitations. Applying mixed-solvent molecular dynamics (MD) simulations to integrins, the current study uncovers hitherto unknown allosteric sites within the integrin α I domains of LFA-1 (αLβ2; CD11a/CD18), VLA-1 (α1β1; CD49a/CD29), and Mac-1 (αMβ2, CD11b/CD18). We show that these pockets are putatively accessible to small-molecule modulators. The findings reported here may provide opportunities for the design of novel allosteric integrin inhibitors lacking the unwanted agonism observed with earlier as well as current integrin-targeting drugs.</p
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$
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
Sequential quasi-Monte Carlo: Introduction for Non-Experts, Dimension Reduction, Application to Partly Observed Diffusion Processes
SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for
filtering and related sequential problems. Gerber and Chopin (2015) introduced
SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two
objectives: (a) to introduce Sequential Monte Carlo to the QMC community, whose
members are usually less familiar with state-space models and particle
filtering; (b) to extend SQMC to the filtering of continuous-time state-space
models, where the latent process is a diffusion. A recurring point in the paper
will be the notion of dimension reduction, that is how to implement SQMC in
such a way that it provides good performance despite the high dimension of the
problem.Comment: To be published in the proceedings of MCMQMC 201
A Continuum Description of Rarefied Gas Dynamics (I)--- Derivation From Kinetic Theory
We describe an asymptotic procedure for deriving continuum equations from the
kinetic theory of a simple gas. As in the works of Hilbert, of Chapman and of
Enskog, we expand in the mean flight time of the constituent particles of the
gas, but we do not adopt the Chapman-Enskog device of simplifying the formulae
at each order by using results from previous orders. In this way, we are able
to derive a new set of fluid dynamical equations from kinetic theory, as we
illustrate here for the relaxation model for monatomic gases. We obtain a
stress tensor that contains a dynamical pressure term (or bulk viscosity) that
is process-dependent and our heat current depends on the gradients of both
temperature and density. On account of these features, the equations apply to a
greater range of Knudsen number (the ratio of mean free path to macroscopic
scale) than do the Navier-Stokes equations, as we see in the accompanying
paper. In the limit of vanishing Knudsen number, our equations reduce to the
usual Navier-Stokes equations with no bulk viscosity.Comment: 16 page
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