P. A. Santoro

Anomalous diffusion governed by a fractional diffusion equation and the electrical response of an electrolytic cell

The electrical response of an electrolytic cell in which the diffusion of mobile ions in the bulk is governed by a fractional diffusion equation of distributed order is analyzed. The boundary conditions at the electrodes limiting the sample are described by an integro-differential equation governing the kinetic at the interface. The analysis is carried out by supposing that the positive and negative ions have the same mobility and that the electric potential profile across the sample satisfies the Poissons equation. The results cover a rich variety of scenarios, including the ones connected to anomalous diffusion.

Analogies Between the Cracking Noise of Ethanol-Dampened Charcoal and Earthquakes

We report on an extensive characterization of the cracking noise produced by charcoal samples when dampened with ethanol. We argue that the evaporation of ethanol causes transient and irregularly distributed internal stresses that promote the fragmentation of the samples and mimic some situations found in mining processes. The results show that, in general, the most fundamental seismic laws ruling earthquakes (the Gutenberg-Richter law, the unified scaling law for the recurrence times, Omoris law, the productivity law, and Båths law) hold under the conditions of the experiment. Some discrepancies were also identified (a smaller exponent in the Gutenberg-Richter law, a stationary behavior in the aftershock rates for long times, and a double power-law relationship in the productivity law) and are related to the different loading conditions. Our results thus corroborate and elucidate the parallel between the seismic laws and fracture experiments caused by a more complex loading condition that also occurs in natural and induced seismicity (such as long-term fluid injection and gas-rock outbursts in mining processes).

Dynamics of tournaments: the soccer case

A random walk-like model is considered to discuss statistical aspects of tournaments. The model is applied to soccer leagues with emphasis on the scores. This competitive system was computationally simulated and the results are compared with empirical data from the English, the German and the Spanish leagues and showed a good agreement with them. The present approach enabled us to characterize a diffusion where the scores are not normally distributed, having a short and asymmetric tail extending towards more positive values. We argue that this non-Gaussian behavior is related with the difference between the teams and with the asymmetry of the scores system. In addition, we compared two tournament systems: the all-play-all and the elimination tournaments.

Reentrant isotropic – discotic nematic phase transition: a critical exponent study

In this work the critical exponents associated with the behavior of the macroscopic orientational order parameter are determined near the reentrant isotropic (IRE)–discotic nematic (ND) and ND–isotropic (I) phase transitions in a lyotropic mixture of potassium laurate, decanol and D2O by measurement of optical birefringence. The critical exponents found indicate that the low temperature ND–IRE phase transition is quasi‐continuous, having a critical exponent, β1∼0.17, which is markedly different from that found at the classical ND–I phase transition, β2∼0.38. The results are discussed and compared with others obtained with different lyotropic mixtures.

Anomalous Diffusion Effects on the Electrical Impedance Response of Liquid-Crystalline Systems

The electrical impedance response of six nematic liquid crystals samples is analyzed by means of an extension of the Poisson-Nernst-Planck diffusional model. This formulation includes fractional derivatives of distributed order governing the behavior of the bulk density of mobile charges, whose solutions are subjected to integro-differential equations accounting for the boundary conditions. The role of the intrinsic surface lengths involved in the adsorption-desorption phenomena at the electrodes is emphasized, in order to analyze the frequency dependence of the real and imaginary parts of the electrical impedance experimentally obtained.

Anomalous diffusion in a symbolic model

In this work, we investigate some statistical properties of symbolic sequences generated by a numerical procedure in which the symbols are repeated following the power-law probability density. In this analysis, we consider that the sum of n symbols represents the position of a particle in erratic movement. This approach reveals a rich diffusive scenario characterized by non-Gaussian distribution and, depending on the power-law exponent or the procedure used to build the walker, we may have superdiffusion, subdiffusion or usual diffusion. Additionally, we use the continuous-time random walk framework to compare the analytic results with the numerical data, thereby finding good agreement. Because of its simplicity and flexibility, this model can be a candidate for describing real systems governed by power-law probability densities.

Surface viscosity and anchoring energy effects on the relaxation of a nematic liquid crystal cell

We investigate the relaxation of the director in a nematic liquid crystal cell by considering the presence of different surface viscosities and anchoring energies on the boundaries. To face a more general problem, we also model the surfaces as characterised by time dependent easy directions which can be mechanically or optically induced in the system. In order to connect the analytical results with measurable physical quantities, the temporal behaviour of the optical path difference is established incorporating the contribution of the surface viscosity.

Nonlinear Refractive Index and Thermal Diffusivity Measurements Near the Reentrant Isotropic – Discotic Nematic Phase Transition

In this work we report on measurements, as a function of the temperature, of the nonlinear refractive indices parallel ( ) and perpendicular ( ) to the nematic director near the reentrant isotropic – discotic nematic phase transition in a lyotropic mixture of potassium laurate, decanol and D 2 O. Thermal diffusivities, parallel ( D ∥) and perpendicular ( D ⊥) to the director in this reentrant isotropic–discotic nematic phase transition, were also obtained as a function of the temperature from Z-scan experiment and interpreted through a thermal lens model. The ratios and D ∥/ D ⊥ are less than one in this nematic phase. These results are discussed in terms of structural changes in the micellar configuration which takes place in each nematic phase transition.