We describe a technique for deconvolving the stochastic motion of particles from large-scale fluid flow in a dynamic environment such as that found in living cells. The method leverages the separation of timescales to subtract out the persistent component of motion from single-particle trajectories. The mean-squared displacement of the resulting trajectories is rescaled so as to enable robust e...

Abstract. We consider a continuous-time branching random walk on the integer lattice Zd (d > 1) with a finite number of branching sources, or catalysts. The random walk is assumed to be spatially homogeneous and irreducible. The branching mechanism at each catalyst, being independent of the random walk, is governed by a Markov branching process. The quantities of interest are the local numbers ...

The zero-mean circular complex Gaussian field statistics of a random medium are experimentally demonstrated in the optical domain, thus verifying this key assumption of statistical optics. Using a frequency-tunable laser source in a fixed-path-length interferometer, we obtain optical field fluctuations in the time and frequency domains that clearly show that the ensemble-averaged temporal inten...

We have studied both experimentally and numerically the dynamic effect of nonlinearity on lasing in disordered medium. The third-order nonlinearity not only changes the frequency and size of lasing modes, but also modifies the laser emission intensity and laser pulse width. When the nonlinear response time is longer than the lifetime of the lasing mode, the nonlinearity changes the laser output...

2 Diffusive limit for a particle in a random flow 7 2.1 Diffusion of a particle in a time-dependent random flow . . . . . . . . . . . . . . . . 7 2.1.1 The central limit theorem, purely time-dependent flows, and diffusion . . . . 8 2.1.2 Using formal asymptotic expansions . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 Random flows with spatial-temporal dependence . . . . . . . . . . . . ...

An integral-differential equation is derived for the self-consistent (effective) field in the medium consisting of many small bodies randomly distributed in some region. Acoustic and electromagnetic fields are considered in such a medium. Each body has a characteristic dimension a ≪ λ, where λ is the wavelength in the free space. The minimal distance d between any of the two bodies satisfies th...

I Directed polymers A Why bother? II Hamiltonian and Randomness A Pure case B Let’s put randomness 1 Hamiltonian 2 Partition function 3 Averages C What to look for? D Size: disorder and thermal correlation 1 Free energy fluctuation 2 Our Aim 3 Digression: Self-averaging III Q.: Is disorder relevant? A Annealed average: low temperature problem B Moments of Z 1 Hamiltonian for moments 2 Bound sta...

We consider the Liouville equations with highly heterogeneous Hamiltonians and their numerical solution by a time splitting algorithm. Such equations model the density of particles evolving according to the corresponding Hamiltonian dynamics as well as the propagation of high frequency waves with a wavelength much smaller than the correlation length of the random Hamiltonian. Our main results a...

Random optical-pulse polarization switching along an active optical medium in the Λ configuration with spatially disordered occupation numbers of its lower energy sublevel pair is described using the idealized integrable Maxwell-Bloch model. Analytical results describing the light polarization-switching statistics for the single self-induced transparency pulse are compared with statistics obtai...

Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. We analyse in detail this relationship and study various distributions using stochastic calculus and functional integration.