Transport with hard-core interaction in a chain of asymmetric cavities

In this paper we investigate the diffusion of particles inside a chain of asymmetric cavities. We are considering particles that interact through a hard--core potential and are driven by an external force. We show that the difference in the current when the force is applied to the left and to the right strongly depends on the concentration inside the cavity. We found that, when the concentration is high enough, the hard--core interaction vanishes and inverts the asymmetric effect of the cavity. We also introduce a new equation, a modification to the Fick--Jacobs equation, to describe this system analytically. Finally, we used numerical simulations to verify the analytic results, finding a good agreement between theory and simulations.Comment: XXVI IUPAP Conference on Computational Physics, CCP2014 August 11-14, 2014, Boston, Massachusetts, US

Transport in a chain of asymmetric cavities: Effects of the concentration with hard-core interaction

We studied the transport process of overdamped Brownian particles, in a chain of asymmetric cavities, interacting through a hard-core potential. When a force is applied in opposite directions a difference in the drift velocity of the particles inside the cavity can be observed. Previous works on similar systems deal with the low concentration regime, in which the interaction is irrelevant. In this case it was found that large particles show a stronger asymmetry in the drift velocity when a small force is applied, allowing for the separation of different size particles (Reguera et al., Phys. Rev. Lett 108, 020604, 2012). We found that when the interaction between particles is considered, the behavior of the system is substantially different. For example, as concentration is increased, the small particles are the ones that show a stronger asymmetry. For the case where all the particles in the system are of the same size we took advantage of the particle-vacancy analogy to predict that the left and right currents are almost equal in a region around the concentration 0.5 despite the asymmetry of the cavity

Current of interacting particles inside a channel of exponential cavities: Application of a modified Fick--Jacobs equation

The Fick--Jacobs equation has been widely studied, because of its applications in the diffusion and transport of non-interacting particles in narrow channels. It is also known that a modified version of this equation can be used to describe the same system with particles interacting through a hard-core potential. In this work we present a system that can be exactly solved using the Fick--Jacobs equation. The exact results of the particle concentration profile along the channel $n$, the current, $J$, and the mobility, $\mu$, of particles as a function of an external force are contrasted with Monte Carlo simulations results of non-interacting particles. For interacting particles the behavior of $n$, $J$ and $\mu$, obtained from the modified Fick--Jacobs equation are in agreement with numerical simulations, where the hard-core interaction is taken into account. Even more, for interacting particles the modified Fick--Jacobs equation gives comparatively more accurate results of the current difference (when a force is applied in opposite directions) than the exact result for the non-interacting ones

Study of recombination reactions of particles adsorbed on fractal and multifractal substrata

Recombination reactions of adsorbed particles on fractal and multifractal media are discussed within the framework of the random walk arguments. Theoretical results, which predict anomalous reaction orderX>2 in the low coverage regime, are checked by means of Monte Carlo simulations on two-dimensional structures and good agreement is found. Thermal desorption experiments on rough surfaces are simulated by studying temperature programmed reactions on fractal percolating clusters. For this case the simulations giveX≅2.5, i. e. the fractal reaction order is greater than the classical one (X=2). The influence of chemisorbed impurities (poison) on the recombination reaction is also studied and the reaction order is found to increase beyondX=2.5 when increasing the concentration of poison. Isothermal (recombination) desorption from energetically heterogeneous surfaces is simulated on two-dimensional substrata with multifractal distributions of activation energy of diffusion. For this caseX (withX>2) depends on the energetic heterogeneity of the substrata (X=2 for an homogeneous substratum). The obtained results point out that the fractal chemical kinetic behaviour is not only restricted to the low concentration regime, but it also covers the medium coverage regime, i.e. it holds for a monolayer surface coverageθ≦0.4 in fractal percolating clusters.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

A percolation model with disaggregation and aggregation

A model of percolation with disaggregation and aggregation (PDA) is proposed and studied by means of the Monte Carlo simulation on the square lattice. The critical concentration φc, the correlation length exponent and the fractal and spreading dimensions of the largest cluster at φc have been computed. The obtained results suggest that the PDA model belongs to the same universality class than the standard percolation model. Nevertheless, the critical concentration (φc=0.464±0.005) of the former is quite different from the critical probability (pc=0.5927) of the later model.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

Diffusion on two-dimensional percolation clusters with multifractal jump probabilities

By means of Monte Carlo simulations we studied the properties of diffusion limited recombination reactions (DLRR's) and random walks on two dimensional incipient percolation clusters with multifractal jump probabilities. We claim that, for these kind of geometric and energetic heterogeneous substrata, the long time behavior of the particle density in a DLRR is determined by a random walk exponent. It is also suggested that the exploration of a random walk is compact. It is considered a general case of intersection in d euclidean dimension of a random fractal of dimension DF and a multifractal distribution of probabilities of dimensions Dq (q real), where the two dimensional incipient percolation clusters with multifractal jump probabilities are particular examples. We argue that the object formed by this intersection is a multifractal of dimensions D'q = Dq + DF--d, for a finite interval of q.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

Renormalization group calculation for cells with inequivalent spins

We have considered a real-space renormalization group transformation for a bidimensional Ising model, carrying out approximate calculations for cells where site spins do not play the same role. The dependence on the ratio between the number of intercell and intracell nearest-neighbour interactions has also been discussed.Facultad de Ciencias Exacta