Tricritical Behavior in Dynamical Phase Transitions.

We identify a new scenario for dynamical phase transitions associated with time-integrated observables occurring in diffusive systems described by the macroscopic fluctuation theory. It is characterized by the pairwise meeting of first- and second-order bias-induced phase transition curves at two tricritical points. We formulate a simple, general criterion for its appearance and derive an exact Landau theory for the tricritical behavior.

Extinctions of coupled populations, and rare event dynamics under non-Gaussian noise.

The survival of natural populations may be greatly affected by environmental conditions that vary in space and time. We look at a population residing in two locations (patches) coupled by migration, in which the local conditions fluctuate in time. We report on two findings.

Occupation-time statistics of a gas of interacting diffusing particles.

The time that a diffusing particle spends in a certain region of space is known as the occupation time, or the residence time. Recently, the joint occupation-time statistics of an ensemble of noninteracting particles was addressed using the single-particle statistics. Here we employ the macroscopic fluctuation theory (MFT) to study the occupation-time statistics of many interacting particles.

Narrow Escape of Interacting Diffusing Particles.

The narrow escape problem deals with the calculation of the mean escape time (MET) of a Brownian particle from a bounded domain through a small hole on the domain's boundary. Here we develop a formalism which allows us to evaluate the nonescape probability of a gas of diffusing particles that may interact with each other. In some cases the nonescape probability allows us to evaluate the MET of the first particle.

Fluctuations of absorption of interacting diffusing particles by multiple absorbers.

We study fluctuations of particle absorption by a three-dimensional domain with multiple absorbing patches. The domain is in contact with a gas of interacting diffusing particles. This problem is motivated by living cell sensing via multiple receptors distributed over the cell surface.

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.