1,278 research outputs found
Sticky Particles and Stochastic Flows
Gaw\c{e}dzki and Horvai have studied a model for the motion of particles
carried in a turbulent fluid and shown that in a limiting regime with low
levels of viscosity and molecular diffusivity, pairs of particles exhibit the
phenomena of stickiness when they meet. In this paper we characterise the
motion of an arbitrary number of particles in a simplified version of their
model
Large Deviations for Brownian Intersection Measures
We consider independent Brownian motions in . We assume that and . Let denote the intersection measure of the
paths by time , i.e., the random measure on that assigns to any
measurable set the amount of intersection local time of the
motions spent in by time . Earlier results of Chen \cite{Ch09} derived
the logarithmic asymptotics of the upper tails of the total mass
as . In this paper, we derive a large-deviation principle for the
normalised intersection measure on the set of positive measures
on some open bounded set as before exiting . The
rate function is explicit and gives some rigorous meaning, in this asymptotic
regime, to the understanding that the intersection measure is the pointwise
product of the densities of the normalised occupation times measures of the
motions. Our proof makes the classical Donsker-Varadhan principle for the
latter applicable to the intersection measure.
A second version of our principle is proved for the motions observed until
the individual exit times from , conditional on a large total mass in some
compact set . This extends earlier studies on the intersection
measure by K\"onig and M\"orters \cite{KM01,KM05}.Comment: To appear in "Communications on Pure and Applied Mathematics
Direct Force In High Momentum Limit of QCD For Proton Physics
An explicit construction of the proton wave function is outlined in the high
momentum limit of QCD dominated by a direct force, one generated by
hooking the ends of a vertex to 3 distinct vertices, thus
making up a -shaped diagram (see fig.1). The high degree of symmetry
thus involved ensures that the wave function is a mixture of
and components, rather than the traditional and
type. Some results of this paradigm shift are offered.Comment: 6 pages, Presented at 4th International Symposium on Symmetries in
Subatomic Physics at NTU, Taipei, 200
Comparison of simulated longitudinal profiles of hadronic air showers with MASS2 balloon data
The KASKADE and CORSIKA air shower generators are compared to the data
collected by MASS2 balloon experiment in 1991. The test of longitudinal profile
for proton, helium and muon flux production provide good constraints on these
air shower generators. KASKADE and CORSIKA especially with the new simulator
UrQMD for low energies are found to fit these data well. This study is limited
to a comparison of longitudinal profiles and therefore does not provide
constraints on the overall shower development.Comment: to be published in Astroparticle Physic
Pathwise uniqueness of the squared Bessel and CIR processes with skew reflection on a deterministic time dependent curve
We investigate pathwise uniqueness for the squared Bessel and
Cox-Ingersoll-Ross processes with additional reflection term that is multiplied
by some real number strictly between minus one and one. The reflection term is
the symmetric local time of the corresponding processes at a deterministic time
dependent curve.Comment: Structured introduction and modified Section
Self-intersection local times of random walks: Exponential moments in subcritical dimensions
Fix , not necessarily integer, with . We study the -fold
self-intersection local time of a simple random walk on the lattice up
to time . This is the -norm of the vector of the walker's local times,
. We derive precise logarithmic asymptotics of the expectation of
for scales that are bounded from
above, possibly tending to zero. The speed is identified in terms of mixed
powers of and , and the precise rate is characterized in terms of
a variational formula, which is in close connection to the {\it
Gagliardo-Nirenberg inequality}. As a corollary, we obtain a large-deviation
principle for for deviation functions satisfying
t r_t\gg\E[\|\ell_t\|_p]. Informally, it turns out that the random walk
homogeneously squeezes in a -dependent box with diameter of order to produce the required amount of self-intersections. Our main tool is
an upper bound for the joint density of the local times of the walk.Comment: 15 pages. To appear in Probability Theory and Related Fields. The
final publication is available at springerlink.co
Electron attachment rates for PAH anions in the ISM and dark molecular clouds: dependence on their chemical properties
CONTEXT: The attachment of free electrons to polycondensed aromatic ring
molecules (PAHs) is studied for the variety of these molecules with different
numbers of condensed rings and over a broad range of electron temperatures,
using a multichannel quantum scattering approach. The calculations of the
relevant cross sections are used in turn to model the corresponding attachment
rates for each of the systems under study, and these rates are parametrized as
a function of temperature using a commonly employed expression for two-body
processes in the interstellar medium (ISM). AIM: The scope of this work is to
use first principles to establish the influence of chemical properties on the
efficiency of the electron-attachment process for PAHs. METHODS: Quantum
multichannel scattering methods are employed to generate the relevant cross
sections, hence the attachment rates, using integral elastic cross sections
computed over a broad range of relevant energies, from threshold up to 1000 K
and linking the attachment to low-energy resonant collisions. RESULTS: The
rates obtained for the present molecules are found to markedly vary within the
test ensemble of the present work and to be lower than the earlier values used
for the entire class of PAHs anions, when modelling their evolutions in ISM
environments. The effects of such differences on the evolutions of chemical
networks that include both PAH and PAH- species are analysed in some detail and
related to previous calculations.Comment: accepted to be published on A&
Invariant densities for dynamical systems with random switching
We consider a non-autonomous ordinary differential equation on a smooth
manifold, with right-hand side that randomly switches between the elements of a
finite family of smooth vector fields. For the resulting random dynamical
system, we show that H\"ormander type hypoellipticity conditions are sufficient
for uniqueness and absolute continuity of an invariant measure.Comment: 16 pages; we replaced our original article to point out and close a
gap in the discussion of the Lorenz system in Section 7 (see Remark 2); this
gap is only present in the journal version of this article --- it wasn't
present in the previous arxiv versio
Self-intersection local time of planar Brownian motion based on a strong approximation by random walks
The main purpose of this work is to define planar self-intersection local
time by an alternative approach which is based on an almost sure pathwise
approximation of planar Brownian motion by simple, symmetric random walks. As a
result, Brownian self-intersection local time is obtained as an almost sure
limit of local averages of simple random walk self-intersection local times. An
important tool is a discrete version of the Tanaka--Rosen--Yor formula; the
continuous version of the formula is obtained as an almost sure limit of the
discrete version. The author hopes that this approach to self-intersection
local time is more transparent and elementary than other existing ones.Comment: 36 pages. A new part on renormalized self-intersection local time has
been added and several inaccuracies have been corrected. To appear in Journal
of Theoretical Probabilit
Magnetization reversal by injection and transfer of spin: experiments and theory
Reversing the magnetization of a ferromagnet by spin transfer from a current,
rather than by applying a magnetic field, is the central idea of an extensive
current research. After a review of our experiments of current-induced
magnetization reversal in Co/Cu/Co trilayered pillars, we present the model we
have worked out for the calculation of the current-induced torque and the
interpretation of the experiments
- …