We study the model of totally asymmetric exclusion process with generalized update, which compared to usual process, has an additional parameter enhancing clustering particles. derive exact multiparticle distributions distances travelled by particles on infinite lattice for two types initial conditions: step and alternating ones. Two different scaling limits formulas are studied. Under first as...

The localization of fluorescent microspheres is often employed for drift correction and image registration in single molecule microscopy, and is commonly carried out by fitting a point spread function to the image of the given microsphere. The mismatch between the point spread function and the image of the microsphere, however, calls into question the suitability of this localization approach. ...

We present a class of diffraction-free partially coherent beams each member which is comprised finite power, non-accelerating Airy bump residing on statistically homogeneous, Gaussian-correlated background. examine free-space propagation soft apertured realizations the proposed and show that their evolution governed by two spatial scales: coherence width background aperture size. A relative mag...

We construct a class of ℓ $\ell$ -adic local systems on A 1 $\mathbb {A}^1$ that generalizes the Airy sheaves defined by N. Katz to reductive groups. These are finite field analogues generalizations classical equation y ′ ( z ) = $y^{\prime \prime }(z)=zy(z)$ . employ geometric Langlands correspondence sought-after as eigenvalues certain rigid Hecke eigensheaves, following methods developed Hei...

This article is concerned with the numerical solution of the full dynamical von Kármán plate equations for geometrically nonlinear (large-amplitude) vibration in the simple case of a rectangular plate under periodic boundary conditions. This system is composed of three equations describing the time evolution of the transverse displacement field, as well as the two longitudinal displacements. Pa...

We investigate extended processes given by last-passage times in directed models defined using exponential variables with decaying mean. In certain cases we find the universal Airy process, but other cases lead to nonuniversal and trivial extended processes.

Modulation theory is developed for a periodic peakon solution of the Camassa-Holm equation. An explicit simple wave solution of these modulation equations is then derived; this simple wave describing the evolution into an undular bore of an initial step. The characteristic on which the expansion fan occurs (propagating at a nonlinear group velocity) has a turning point, illustrating the fact th...