509 research outputs found
Concentration of Hydrogen in the Upper Atmosphere of the Earth in the 300-600 Km Altitude Range According to Ionospheric Data
Concentration of hydrogen in upper atmosphere according to ionospheric dat
Diffusive transport in two-dimensional nematics
We discuss a dynamical theory for nematic liquid crystals describing the
stage of evolution in which the hydrodynamic fluid motion has already
equilibrated and the subsequent evolution proceeds via diffusive motion of the
orientational degrees of freedom. This diffusion induces a slow motion of
singularities of the order parameter field. Using asymptotic methods for
gradient flows, we establish a relation between the Doi-Smoluchowski kinetic
equation and vortex dynamics in two-dimensional systems. We also discuss moment
closures for the kinetic equation and Landau-de Gennes-type free energy
dissipation
Limit shapes for Gibbs ensembles of partitions
We explicitly compute limit shapes for several grand canonical Gibbs
ensembles of partitions of integers. These ensembles appear in models of
aggregation and are also related to invariant measures of zero range and
coagulation-fragmentation processes. We show, that all possible limit shapes
for these ensembles fall into several distinct classes determined by the
asymptotics of the internal energies of aggregates
Coalescing particle systems and applications to nonlinear Fokker–Planck equations
We study a stochastic particle system with a logarithmically-singular
inter-particle interaction potential which allows for inelastic particle
collisions. We relate the squared Bessel process to the evolution of localized
clusters of particles, and develop a numerical method capable of detecting
collisions of many point particles without the use of pairwise computations, or
very refined adaptive timestepping. We show that when the system is in an
appropriate parameter regime, the hydrodynamic limit of the empirical mass
density of the system is a solution to a nonlinear Fokker-Planck equation, such
as the Patlak-Keller-Segel (PKS) model, or its multispecies variant. We then
show that the presented numerical method is well-suited for the simulation of
the formation of finite-time singularities in the PKS, as well as PKS pre- and
post-blow-up dynamics. Additionally, we present numerical evidence that blow-up
with an increasing total second moment in the two species Keller-Segel system
occurs with a linearly increasing second moment in one component, and a
linearly decreasing second moment in the other component
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