Large deviations of the interface height in the Golubović-Bruinsma model of stochastic growth.

We study large deviations of the one-point height H of a stochastic interface, governed by the Golubović-Bruinsma equation, ∂_{t}h=-ν∂_{x}^{4}h+(λ/2)(∂_{x}h)^{2}+sqrt[D]ξ(x,t), where h(x,t) is the interface height at point x and time t and ξ(x,t) is the Gaussian white noise. The interface is initially flat, and H is defined by the relation h(x=0,t=T)=H. We focus on the short-time limit, T≪T_{NL}, where T_{NL}=ν^{5/7}(Dλ^{2})^{-4/7} is the characteristic nonlinear time of the system.

Probabilities of moderately atypical fluctuations of the size of a swarm of Brownian bees.

The "Brownian bees" model describes an ensemble of N= const independent branching Brownian particles. The conservation of N is provided by a modified branching process. When a particle branches into two particles, the particle which is farthest from the origin is eliminated simultaneously.

Erratum: Macroscopic fluctuation theory and first-passage properties of surface diffusion [Phys. Rev. E 93, 020102(R) (2016)].

This corrects the article DOI: 10.1103/PhysRevE.93.

Macroscopic fluctuation theory and first-passage properties of surface diffusion.

We investigate nonequilibrium fluctuations of a solid surface governed by the stochastic Mullins-Herring equation with conserved noise. This equation describes surface diffusion of adatoms accompanied by their exchange between the surface and the bulk of the solid, when desorption of adatoms is negligible. Previous works dealt with dynamic scaling behavior of the fluctuating interface.

Large Deviations of Surface Height in the Kardar-Parisi-Zhang Equation.

Using the weak-noise theory, we evaluate the probability distribution P(H,t) of large deviations of height H of the evolving surface height h(x,t) in the Kardar-Parisi-Zhang equation in one dimension when starting from a flat interface. We also determine the optimal history of the interface, conditioned on reaching the height H at time t. We argue that the tails of P behave, at arbitrary time t>0, and in a proper moving frame, as -lnP∼|H|^{5/2} and ∼|H|^{3/2}.

Survival of interacting diffusing particles inside a domain with absorbing boundary.

Suppose that a d-dimensional domain is filled with a gas of (in general, interacting) diffusive particles with density n_{0}. A particle is absorbed whenever it reaches the domain boundary. Employing macroscopic fluctuation theory, we evaluate the probability P that no particles are absorbed during a long time T.

Survival of a static target in a gas of diffusing particles with exclusion.

Let a lattice gas of constant density, described by the symmetric simple exclusion process, be brought in contact with a "target": a spherical absorber of radius R. Employing the macroscopic fluctuation theory (MFT), we evaluate the probability P(T) that no gas particle hits the target until a long but finite time T. We also find the most likely gas density history conditional on the nonhitting.

Emergence of fluctuating traveling front solutions in macroscopic theory of noisy invasion fronts.

The position of an invasion front, propagating into an unstable state, fluctuates because of the shot noise coming from the discreteness of reacting particles and stochastic character of the reactions and diffusion. A recent macroscopic theory [Meerson and Sasorov, Phys. Rev.

Nonlinear theory of nonstationary low Mach number channel flows of freely cooling nearly elastic granular gases.

We employ hydrodynamic equations to investigate nonstationary channel flows of freely cooling dilute gases of hard and smooth spheres with nearly elastic particle collisions. This work focuses on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity.

Self-similar relaxation dynamics of a fluid wedge in a Hele-Shaw cell.

Let the interface between two immiscible fluids in a Hele-Shaw cell have, at t = 0, a wedge shape. As a wedge is scale-free, the fluid relaxation dynamics are self-similar. We find the dynamic exponent of this self-similar flow and show that the interface shape is given by the solution of an unusual inverse problem of potential theory.

Scaling and self-similarity in an unforced flow of inviscid fluid trapped inside a viscous fluid in a Hele-Shaw cell.

We investigate quasi-two-dimensional relaxation, by surface tension, of a long straight stripe of inviscid fluid trapped inside a viscous fluid in a Hele-Shaw cell. Combining analytical and numerical solutions, we describe the emergence of a self-similar dumbbell shape and find nontrivial dynamic exponents that characterize scaling behavior of the dumbbell dimensions.