Emerging extreme value and Fermi-Dirac distributions in the Lévy branching and annihilating process.

We study the dynamics of the branching and annihilating process with long-range interactions. Static particles generate an offspring and annihilate upon contact. The branching distance is supposed to follow a Lévy-like power-law distribution with P(r)∝1/r^{α}.

Minimum free-energy paths for the self-organization of polymer brushes.

A methodology to calculate minimum free-energy paths based on the combination of a molecular theory and the improved string method is introduced and applied to study the self-organization of polymer brushes under poor solvent conditions. Polymer brushes in a poor solvent cannot undergo macroscopic phase separation due to the physical constraint imposed by the grafting points; therefore, they microphase separate forming aggregates. Under some conditions, the theory predicts that the homogeneous brush and the aggregates can exist as two different minima of the free energy.

Stationary and dynamic critical behavior of the contact process on the Sierpinski carpet.

We investigate the critical behavior of a stochastic lattice model describing a contact process in the Sierpinski carpet with fractal dimension d=log8/log3. We determine the threshold of the absorbing phase transition related to the transition between a statistically stationary active and the absorbing states. Finite-size scaling analysis is used to calculate the order parameter, order parameter fluctuations, correlation length, and their critical exponents.

Critical short-time dynamics in a system with interacting static and diffusive populations.

We study the critical short-time dynamical behavior of a one-dimensional model where diffusive individuals can infect a static population upon contact. The model presents an absorbing phase transition from an active to an inactive state. Previous calculations of the critical exponents based on quasistationary quantities have indicated an unusual crossover from the directed percolation to the diffusive contact process universality classes.

Universality classes of the absorbing state transition in a system with interacting static and diffusive populations.

In this work, we study the critical behavior of a one-dimensional model that mimics the propagation of an epidemic process mediated by a density of diffusive individuals which can infect a static population upon contact. We simulate the above model on linear chains to determine the critical density of the diffusive population, above which the system achieves a statistically stationary active state, as a function of two relevant parameters related to the average lifetimes of the diffusive and nondiffusive populations. A finite-size scaling analysis is employed to determine the order parameter and correlation length critical exponents.

Wave-packet dynamics in chains with delayed electronic nonlinear response.

We study the dynamics of one electron wave packet in a chain with a nonadiabatic electron-phonon interaction. The electron-phonon coupling is taken into account in the time-dependent Schrödinger equation by a delayed cubic nonlinearity. In the limit of an adiabatic coupling, the self-trapping phenomenon occurs when the nonlinearity parameter exceeds a critical value of the order of the bandwidth.

Criticality of a contact process with coupled diffusive and non-diffusive fields.

We investigate the critical behavior of a model with two coupled critical densities, one of which is diffusive. The model simulates the propagation of an epidemic process in a population, which uses the underlying lattice to leave a track of the recent disease history. We determine the critical density of the population above which the system reaches an active stationary state with a finite density of active particles.