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 $p$ independent Brownian motions in $\R^d$. We assume that $p\geq 2$ and $p(d-2)<d$. Let $\ell_t$ denote the intersection measure of the $p$ paths by time $t$, i.e., the random measure on $\R^d$ that assigns to any measurable set $A\subset \R^d$ the amount of intersection local time of the motions spent in $A$ by time $t$. Earlier results of Chen \cite{Ch09} derived the logarithmic asymptotics of the upper tails of the total mass $\ell_t(\R^d)$ as $t\to\infty$. In this paper, we derive a large-deviation principle for the normalised intersection measure $t^{-p}\ell_t$ on the set of positive measures on some open bounded set $B\subset\R^d$ as $t\to\infty$ before exiting $B$. 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 $p$ 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 $B$, conditional on a large total mass in some compact set $U\subset B$. 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 qqqqqq 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 $qqq$ force, one generated by hooking the ends of a $ggg$ vertex to 3 distinct ${\bar q}gq$ vertices, thus making up a $Y$-shaped diagram (see fig.1). The high degree of $S_3$ symmetry thus involved ensures that the $qqq$ wave function is a mixture of $56, 0^+$ and $20,1^+$ components, rather than the traditional $56, 0^+$ and $70, 0^+$ 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 $p>1$, not necessarily integer, with $p(d-2)<d$. We study the $p$-fold self-intersection local time of a simple random walk on the lattice $\Z^d$ up to time $t$. This is the $p$-norm of the vector of the walker's local times, $\ell_t$. We derive precise logarithmic asymptotics of the expectation of $\exp\{\theta_t \|\ell_t\|_p\}$ for scales $\theta_t>0$ that are bounded from above, possibly tending to zero. The speed is identified in terms of mixed powers of $t$ and $\theta_t$, 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 $\|\ell_t\|_p/(t r_t)$ for deviation functions $r_t$ satisfying t r_t\gg\E[\|\ell_t\|_p]. Informally, it turns out that the random walk homogeneously squeezes in a $t$-dependent box with diameter of order $\ll t^{1/d}$ 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