An important application involving two-species reaction-diffusion systems relates to the problem of finding the best statistical strategy for optimizing the encounter rate between organisms. We investigate the general problem of how the encounter rate depends on whether organisms move in Lévy or Brownian random walks. By simulating a limiting generalized searcher-target model (e.g., predator-prey, mating partner, pollinator-flower), we find that Lévy walks confer a significant advantage for increasing encounter rates when the searcher is larger or moves rapidly relative to the target, and when the target density is low.

The electronic band structure, density of states, dielectric function, optical absorption, and infrared spectrum of cubic ${\text{BaSnO}}_3$ were simulated using density functional theory, within both the local density and generalized gradient approximations, LDA and GGA, respectively. Dielectric optical permittivities and polarizabilities at $\omega =0$ and $\omega =\infty$ were also estimated. Indirect band gaps E($\mathrm{R}\to \Gamma$ ) of 1.01 eV (LDA) and 0.74 eV (GGA) were found, which are smaller than the experimental one ($\approx$ 3.1 eV). A comparison of the calculated cubic ${\text{BaSnO}}_3$ band gap with those of others stannates ${\text{ASnO}}_3$ (A = Ca, Sr, Cd) already published highlights their dependence on each crystal profile. The cubic ${\text{BaSnO}}_3$ effective masses of electrons and holes were computed by parabolic fittings along different directions at the conduction band minimum and valence band maximum, being anisotropic for both electrons and holes. The experimental band gap and calculated effective masses confirm the semiconductor character of cubic ${\text{BaSnO}}_3$ . Finally, the vibrational normal modes and the infrared spectrum of cubic ${\text{BaSnO}}_3$ were obtained and assigned.

We investigate the critical behavior of a one-dimensional diffusive epidemic propagation process by means of a Monte Carlo procedure. In the model, healthy (A) and sick (B) individuals diffuse on a lattice with diffusion constants $D_A$ and $D_B,$ respectively. According to a Wilson renormalization calculation, the system presents a second-order phase transition between a steady reactive state and a vacuum state, with distinct universality classes for the cases $D_A{=D}_B$ and $D_A<D_B.$ A first-order transition has been conjectured for $D_A>D_B.$ In this work we perform a finite size scaling analysis of order parameter data at the vicinity of the critical point in dimension $d=1.\mathrm{}$ Our results show no signature of a first-order transition in the case of $D_A>D_B.$ A finite size scaling typical of second-order phase transitions fits well the data from all three regimes. We found that the correlation exponent $\nu =2\mathrm{}$ as predicted by field-theoretical arguments. Estimates for $\beta /\nu$ are given for all relevant regimes.