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Many random growth models have the property that the set of discovered sites, scaled properly, converges to some deterministic set as time grows. Such results are known as shape theorems. Typically, not much is known about the shapes. For…
Classical nucleation theory is used to estimate the free-energy barrier to nucleation of the solid phase of particles interacting via a potential which has a short-ranged attraction. Due to the high interfacial tension between the fluid and…
We study statistical relationships between bubble walls in cosmological first-order phase transitions. We consider the conditional and joint probabilities for different points on the walls to remain uncollided at given times. We use these…
For first passage percolation on $\mathbb{Z}^2$ with i.i.d. bounded edge weights, we consider the upper tail large deviation event; i.e., the rare situation where the first passage time between two points at distance $n$, is macroscopically…
Strongly first-order phase transitions, i.e., those with a large order parameter, are characterized by a considerable supercooling and high velocities of phase transition fronts. A very strong phase transition may have important…
Motivated by recent time domain experiments on ultrafast atom ionization, we analyze the transients and timescales that characterize, besides the relatively long lifetime, the decay by tunneling of a localized state. While the tunneling…
We used molecular dynamics simulations and the path sampling technique known as forward flux sampling to study homogeneous nucleation of NaCl crystals from supersaturated aqueous solutions at 298 K and 1 bar. Nucleation rates were obtained…
In population genetics, diffusions on the unit interval are often used to model the frequency path of an allele. In this setting we derive approximations for fixation probabilities, expected hitting times and the expected…
Motivated by nucleation and molecular aggregation in physical, chemical and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We…
A general theory of nucleation for colloids and macromolecules in solution is formulated within the context of fluctuating hydrodynamics. A formalism for the determination of nucleation pathways is developed and stochastic differential…
First-order phase transitions that proceed via nucleation of bubbles are described by the homogeneous nucleation theory of Langer. The nucleation rate is one of the most interesting parameters of these transitions. In previous works we have…
We summarize recent work on the consistent calculation of bubble-nucleation rates. Our approach is based on the notion of a real coarse-grained potential. The bubble-nucleation rate is calculated through an expansion around the…
The relationship between anomalous superdiffusive behavior and particle trapping probability is analyzed on a rocking ratchet potential with spatially correlated weak disorder. The trapping probability density is shown, analytically and…
The timescales of many physical, chemical, and biological processes are determined by first passage times (FPTs) of diffusion. The overwhelming majority of FPT research studies the time it takes a single diffusive searcher to find a target.…
Several simple approximations for the evolution during the nucleation period have been presented. All of them have been compared with precise numerical solution and the errors have been estimated. All relative errors are enough small.
One possible way in which phase transitions in the early universe may have ocurred is via nucleation of bubbles of the new phase (true vacuum) in the old phase (false vacuum). The technique most widely used to compute the probability of…
A new model to calculate the rate of nucleation is formulated. This model is based on the classical nucleation theory but considers also vapor depletion around the formed embryo. The key characteristic which arises in frames of this theory…
We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…
A common scenario in a variety of biological systems is that multiple particles are searching in parallel for an immobile target located in a bounded domain, and the fastest among them that arrives to the target first triggers a given…
A nonperturbative correction to the thermal nucleation rate of critical bubbles in a first order phase transition is estimated. The correction originates from large-amplitude fluctuations which may be present before the transition occurs.…