Variational approach to KPZ: Fluctuation theorems and large deviation function for entropy production.

Motivated by the time behavior of the functional arising in the variational approach to the Kardar-Parisi-Zhang (KPZ) equation, and in order to study fluctuation theorems in such a system, we have adapted a path-integral scheme that adequately fits to this kind of study dealing with unstable systems. As the KPZ system has no stationary probability distribution, we show how to proceed for obtaining detailed as well as integral fluctuation theorems. This path-integral methodology, together with the variational approach, in addition to allowing analyze fluctuation theorems, can be exploited to determine a large deviation function for entropy production.

Stochastic entropies and fluctuation theorems for a discrete one-dimensional Kardar-Parisi-Zhang system.

The statistical properties of stochastic entropies in a discrete stationary one-dimensional Kardar-Parisi-Zhang system are numerically studied. As the usual time-independent solution of the associated Fokker-Planck equation is not strictly stationary, it is necessary to transform the current variables to other variables with zero spatial mean. We resorted to discrete representations in order to prove the statistical properties of entropies, and we performed a direct test of the fluctuation theorem.

Waves of seed propagation induced by delayed animal dispersion.

We study a model of seed dispersal that considers the inclusion of an animal disperser moving diffusively, feeding on fruits and transporting the seeds, which are later deposited and capable of germination. The dynamics depends on several population parameters of growth, decay, harvesting, transport, digestion and germination. In particular, the deposition of transported seeds at places away from their collection sites produces a delay in the dynamics, whose effects are the focus of this work.

Enhanced transport through desorption-mediated diffusion.

We present a master equation approach to the study of the bulk-mediated surface diffusion mechanism in a three-dimensional confined domain. The proposed scheme allowed us to evaluate analytically a number of magnitudes that were used to characterize the efficiency of the bulk-mediated surface transport mechanism, for instance, the mean escape time from the domain, and the mean number of distinct visited sites on the confined domain boundary.

Narrow-escape-time problem: the imperfect trapping case.

We present a master equation approach to the narrow escape time (NET) problem, i.e., the time needed for a particle contained in a confining domain with a single narrow opening to exit the domain for the first time.