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

Dispersion and collapse in stochastic velocity fields on a cylinder

The dynamics of fluid particles on cylindrical manifolds is investigated. The velocity field is obtained by generalizing the isotropic Kraichnan ensemble, and is therefore Gaussian and decorrelated in time. The degree of compressibility is such that when the radius of the cylinder tends to infinity the fluid particles separate in an explosive way. Nevertheless, when the radius is finite the transition probability of the two-particle separation converges to an invariant measure. This behavior is due to the large-scale compressibility generated by the compactification of one dimension of the space

Uniform shrinking and expansion under isotropic Brownian flows

We study some finite time transport properties of isotropic Brownian flows. Under a certain nondegeneracy condition on the potential spectral measure, we prove that uniform shrinking or expansion of balls under the flow over some bounded time interval can happen with positive probability. We also provide a control theorem for isotropic Brownian flows with drift. Finally, we apply the above results to show that under the nondegeneracy condition the length of a rectifiable curve evolving in an isotropic Brownian flow with strictly negative top Lyapunov exponent converges to zero as $t\to \infty$ with positive probability

Ergodic properties of a model for turbulent dispersion of inertial particles

We study a simple stochastic differential equation that models the dispersion of close heavy particles moving in a turbulent flow. In one and two dimensions, the model is closely related to the one-dimensional stationary Schroedinger equation in a random delta-correlated potential. The ergodic properties of the dispersion process are investigated by proving that its generator is hypoelliptic and using control theory

A stochastic perturbation of inviscid flows

We prove existence and regularity of the stochastic flows used in the stochastic Lagrangian formulation of the incompressible Navier-Stokes equations (with periodic boundary conditions), and consequently obtain a \holderspace{k}{\alpha} local existence result for the Navier-Stokes equations. Our estimates are independent of viscosity, allowing us to consider the inviscid limit. We show that as $\nu \to 0$, solutions of the stochastic Lagrangian formulation (with periodic boundary conditions) converge to solutions of the Euler equations at the rate of $O(\sqrt{\nu t})$.Comment: 13 pages, no figures

Charge Carrier Extraction in Organic Solar Cells Governed by Steady-State Mobilities

Charge transport in organic photovoltaic (OPV) devices is often characterized by steady-state mobilities. However, the suitability of steady-state mobilities to describe charge transport has recently been called into question, and it has been argued that dispersion plays a significant role. In this paper, the importance of the dispersion of charge carrier motion on the performance of organic photovoltaic devices is investigated. An experiment to measure the charge extraction time under realistic operating conditions is set up. This experiment is applied to different blends and shows that extraction time is directly related to the geometrical average of the steady-state mobilities. This demonstrates that under realistic operating conditions the steady-state mobilities govern the charge extraction of OPV and gives a valuable insight in device performance

Uncertainty-modulated attentional capture: Outcome variance increases attentional priority

Our prior experiences shape the way that we prioritize information from the environment for further processing, analysis, and action. We show in three experiments that this process of attentional prioritization is critically modulated by the degree of uncertainty in these previous experiences. Participants completed a visual search task in which they made a saccade to a target to earn a monetary reward. The color of a colorsingleton distractor in the search array signaled the reward outcome(s) that were available, with different degrees of variance (uncertainty). Participants were never required to look at the colored distractor, and doing so would slow their response to the target. Nevertheless, across all experiments, participants were more likely to look at distractors associated with high outcome variance versus low outcome variance. This pattern was observed when all distractors had equal expected value (Experiment 1), when the difference in variance was opposed by a difference in expected value (i.e., the high-variance distractor had a low expected value, and vice versa: Experiment 2), and when high- and low-variance distractors were paired with the maximum-value outcome on an equal proportion of trials (Experiment 3). Our findings demonstrate that experience of prediction error plays a fundamental role in guiding “attentional exploration,” wherein priority is driven by the potential for a stimulus to reduce future uncertainty through a process of learning, as opposed to maximizing current information gain.info:eu-repo/semantics/publishedVersio

Interacting Arrays of Steps and Lines in Random Media

The phase diagram of two interacting planar arrays of directed lines in random media is obtained by a renormalization group analysis. The results are discussed in the contexts of the roughening of reconstructed crystal surfaces, and the pinning of flux line arrays in layered superconductors. Among the findings are a glassy flat phase with disordered domain structures, a novel second-order phase transition with continuously varying critical exponents, and the generic disappearance of the glassy ``super-rough'' phases found previously for a single array.Comment: 4 pages, REVTEX 3.0, uses epsf,multicol, 3 .eps-figures, submitted to PR

Stochastic Lagrangian Particle Approach to Fractal Navier-Stokes Equations

In this article we study the fractal Navier-Stokes equations by using stochastic Lagrangian particle path approach in Constantin and Iyer \cite{Co-Iy}. More precisely, a stochastic representation for the fractal Navier-Stokes equations is given in terms of stochastic differential equations driven by L\'evy processes. Basing on this representation, a self-contained proof for the existence of local unique solution for the fractal Navier-Stokes equation with initial data in \mW^{1,p} is provided, and in the case of two dimensions or large viscosity, the existence of global solution is also obtained. In order to obtain the global existence in any dimensions for large viscosity, the gradient estimates for L\'evy processes with time dependent and discontinuous drifts is proved.Comment: 19 page