1,833 research outputs found
Stochastic vortex method for forced three-dimensional Navier--Stokes equations and pathwise convergence rate
We develop a McKean-Vlasov interpretation of Navier-Stokes equations with
external force field in the whole space, by associating with local mild
-solutions of the 3d-vortex equation a generalized nonlinear diffusion
with random space-time birth that probabilistically describes creation of
rotation in the fluid due to nonconservativeness of the force. We establish a
local well-posedness result for this process and a stochastic representation
formula for the vorticity in terms of a vector-weighted version of its law
after its birth instant. Then we introduce a stochastic system of 3d vortices
with mollified interaction and random space-time births, and prove the
propagation of chaos property, with the nonlinear process as limit, at an
explicit pathwise convergence rate. Convergence rates for stochastic
approximation schemes of the velocity and the vorticity fields are also
obtained. We thus extend and refine previous results on the probabilistic
interpretation and stochastic approximation methods for the nonforced equation,
generalizing also a recently introduced random space-time-birth particle method
for the 2d-Navier-Stokes equation with force.Comment: Published in at http://dx.doi.org/10.1214/09-AAP672 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Transport properties of heavy particles in high Reynolds number turbulence
The statistical properties of heavy particle trajectories in high Reynolds
numbers turbulent flows are analyzed. Dimensional analysis assuming Kolmogorov
scaling is compared with the result of numerical simulation using a synthetic
turbulence advecting field. The non-Markovian nature of the fluid velocity
statistics along the solid particle trajectories is put into evidence, and its
relevance in the derivation of Lagrangian transport models is discussed.Comment: 30 pages, 11 eps figures included. To appear in Physics of Fluid
A Class of Nonperturbative Configurations in Abelian-Higgs Models: Complexity from Dynamical Symmetry Breaking
We present a numerical investigation of the dynamics of symmetry breaking in
both Abelian and non-Abelian Higgs models in three spatial
dimensions. We find a class of time-dependent, long-lived nonperturbative field
configurations within the range of parameters corresponding to type-1
superconductors, that is, with vector masses () larger than scalar masses
(). We argue that these emergent nontopological configurations are related
to oscillons found previously in other contexts. For the Abelian-Higgs model,
our lattice implementation allows us to map the range of parameter space -- the
values of -- where such configurations exist and to
follow them for times t \sim \O(10^5) m^{-1}. An investigation of their
properties for -symmetric models reveals an enormously rich structure
of resonances and mode-mode oscillations reminiscent of excited atomic states.
For the SU(2) case, we present preliminary results indicating the presence of
similar oscillonic configurations.Comment: 21 pages, 19 figures, prd, revte
Weakly Interacting, Dilute Bose Gases in 2D
This article surveys a number of theoretical problems and open questions in
the field of two-dimensional dilute Bose gases with weak repulsive
interactions. In contrast to three dimensions, in two dimensions the formation
of long-range order is prohibited by the Bogoliubov-Hohenberg theorem, and
Bose-Einstein condensation is not expected to be realized. Nevertheless, first
experimental indications supporting the formation of the condensate in low
dimensional systems have been recently obtained. This unexpected behaviour
appears to be due to the non-uniformity, introduced into a system by the
external trapping potential. Theoretical predictions, made for homogeneous
systems, require therefore careful reexamination.
We survey a number of popular theoretical treatments of the dilute weakly
interacting Bose gas and discuss their regions of applicability. The
possibility of Bose-Einstein condensation in a two-dimensional gas, the
validity of perturbative t-matrix approximation and diluteness condition are
issues that we discuss in detail.Comment: Survey, 25 pages RMP style, revised version, refs added, some changes
made, accepted for publication in Rev. Mod. Phy
Corrections to the Law of Mass Action and Properties of the Asymptotic State for Reversible Diffusion-Limited Reactions
On example of diffusion-limited reversible
reactions we re-examine two fundamental concepts of classical chemical kinetics
- the notion of "Chemical Equilibrium" and the "Law of Mass Action". We
consider a general model with distance-dependent reaction rates, such that any
pair of particles, performing standard random walks on sites of a
-dimensional lattice and being at a distance apart of each other at
time moment , may associate forming a particle at the rate .
In turn, any randomly moving particle may spontaneously dissociate at the
rate into a geminate pair of s "born" at a distance
apart of each other. Within a formally exact approach based on Gardiner's
Poisson representation method we show that the asymptotic state
attained by such diffusion-limited reactions is generally \textit{not a true
thermodynamic equilibrium}, but rather a non-equilibrium steady-state, and that
the Law of Mass Action is invalid. The classical concepts hold \text{only} in
case when the ratio does not depend on for any .Comment: 30 pages, 2 figure
Theory and applications of free-electron vortex states
Both classical and quantum waves can form vortices: with helical phase fronts
and azimuthal current densities. These features determine the intrinsic orbital
angular momentum carried by localized vortex states. In the past 25 years,
optical vortex beams have become an inherent part of modern optics, with many
remarkable achievements and applications. In the past decade, it has been
realized and demonstrated that such vortex beams or wavepackets can also appear
in free electron waves, in particular, in electron microscopy. Interest in
free-electron vortex states quickly spread over different areas of physics:
from basic aspects of quantum mechanics, via applications for fine probing of
matter (including individual atoms), to high-energy particle collision and
radiation processes. Here we provide a comprehensive review of theoretical and
experimental studies in this emerging field of research. We describe the main
properties of electron vortex states, experimental achievements and possible
applications within transmission electron microscopy, as well as the possible
role of vortex electrons in relativistic and high-energy processes. We aim to
provide a balanced description including a pedagogical introduction, solid
theoretical basis, and a wide range of practical details. Special attention is
paid to translate theoretical insights into suggestions for future experiments,
in electron microscopy and beyond, in any situation where free electrons occur.Comment: 87 pages, 34 figure
Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators
Bosonic topological insulators (BTI) in three dimensions are
symmetry-protected topological phases (SPT) protected by time-reversal and
boson number conservation {symmetries}. BTI in three dimensions were first
proposed and classified by the group cohomology theory which suggests two
distinct root states, each carrying a index. Soon after, surface
anomalous topological orders were proposed to identify different root states of
BTI, which even leads to a new BTI root state beyond the group cohomology
classification. In this paper, we propose a universal physical mechanism via
\textit{vortex-line condensation} {from} a 3d superfluid to achieve all {three}
root states. It naturally produces bulk topological quantum field theory (TQFT)
description for each root state. Topologically ordered states on the surface
are \textit{rigorously} derived by placing TQFT on an open manifold, which
allows us to explicitly demonstrate the bulk-boundary correspondence. Finally,
we generalize the mechanism to symmetries and discuss potential SPT
phases beyond the group cohomology classification.Comment: ReVTeX 4.1 (published version
Evolutionary games on graphs
Game theory is one of the key paradigms behind many scientific disciplines
from biology to behavioral sciences to economics. In its evolutionary form and
especially when the interacting agents are linked in a specific social network
the underlying solution concepts and methods are very similar to those applied
in non-equilibrium statistical physics. This review gives a tutorial-type
overview of the field for physicists. The first three sections introduce the
necessary background in classical and evolutionary game theory from the basic
definitions to the most important results. The fourth section surveys the
topological complications implied by non-mean-field-type social network
structures in general. The last three sections discuss in detail the dynamic
behavior of three prominent classes of models: the Prisoner's Dilemma, the
Rock-Scissors-Paper game, and Competing Associations. The major theme of the
review is in what sense and how the graph structure of interactions can modify
and enrich the picture of long term behavioral patterns emerging in
evolutionary games.Comment: Review, final version, 133 pages, 65 figure
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