Research
We will address, using tools of Statistical Physics, the study of important and challenging problems in some fields of complex systems, namely fields related to disordered systems, including colloids, and granular media. To obtain the proposed objectives we will use analytical as well as numerical techniques.
In this context, an important goal of our project is to improve our current understanding of the interplay between anomalous diffusion and reaction in the limit of fast reaction rates (diffusion-controlled kinetics). To this end, analytical and numerical techniques (e.g., fractional Fokker-Planck equations and CTRW simulations) will be carried out. Some specific topics we want to address include problems where the global density of some reactant species is time-dependent due to mechanisms alien to the reaction, problems where several reactant species performing qualitatively different types of motion (e.g. anomalous and normal diffusion) coexist, and multi-species advection-reaction systems (e.g. many particle systems under the influence of an external field). In order to accomplish these goals, the development of new methods, in addition to the aforementioned ones, may become necessary.
Besides, we will study (mainly using extensive numerical simulations) the properties on- and off-equilibrium of a few, but important, disordered systems. In particular, we will try to characterize the equilibrium properties of graphene sheets with different substrates, the complex singularities (Fisher and Lee-Yang zeros) of some systems (spin glasses and diluted models), the existence or not of the Almeida-Thouless line in finite-dimensional spin models, the off-equilibrium behavior of Heisenberg spin glass, the universality class of three-dimensional diluted Potts model, and the critical properties of the Random Field Ising model.
We will also analyze certain classes of colloidal solutions which, despite their complexity, can be modeled with simple anisotropic and penetrable interactions. In what concerns granular fluids, the novel challenges to be addressed include the influence of roughness on the statistical properties of the system, the proposal and solution of a model for monodisperse gas-solid suspensions, the application of the Enskog kinetic equation for granular mixtures to problems such as stability and segregation, and the analysis of non-Newtonian steady states.