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

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

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

Patterns arising from the interaction between scalar and vectorial instabilities in two-photon resonant Kerr cavities

We study pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a nonlinear Kerr medium close to a two-photon resonance, placed inside a ring cavity with flat mirrors and driven by a coherent $\hat x$-polarized plane-wave field. In the self-focusing case, for negative detunings the pattern arises naturally from a codimension two bifurcation. For a critical value of the field intensity there are two wave numbers that become unstable simultaneously, corresponding to two Turing-like instabilities. Considered alone, one of the instabilities would originate a linearly polarized hexagonal pattern whereas the other instability is of pure vectorial origin and would give rise to an elliptically polarized stripe pattern. We show that the competition between the two wavenumbers can originate different structures, being the detuning a natural selection parameter.Comment: 21 pages, 6 figures. http://www.imedea.uib.es/PhysDep

Monte Carlo simulation with fixed steplength for diffusion processes in nonhomogeneous media

Monte Carlo simulation is one of the most important tools in the study of diffusion processes. For constant diffusion coefficients, an appropriate Gaussian distribution of particle's steplengths can generate exact results, when compared with integration of the diffusion equation. It is important to notice that the same method is completely erroneous when applied to non-homogeneous diffusion coefficients. A simple alternative, jumping at fixed steplengths with appropriate transition probabilities, produces correct results. Here, a model for diffusion of calcium ions in the neuromuscular junction of the crayfish is used as a test to compare Monte Carlo simulation with fixed and Gaussian steplength.Fil: Ruiz Barlett, María Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; ArgentinaFil: Hoyuelos, Miguel Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; ArgentinaFil: Martin, Hector Omar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentin

Diffusion on a lattice: transition rates, interactions and memory effects

We analyze diffusion of particles on a two dimensional square lattice. Each lattice site contains an arbitrary number of particles. Interactions affect particles only in the same site, and are macroscopically represented by the excess chemical potential. In a recent work, a general expression for transition rates between neighboring cells as functions of the excess chemical potential was derived. With transition rates, the mean field tracer diffusivity, $D^\text{MF}$, is immediately obtained. The tracer diffusivity, $D = D^\text{MF} f$, contains the correlation factor $f$, representing memory effects. An analysis of the joint probability of having given numbers of particles at different sites when a force is applied to a tagged particle allows an approximate expression for $f$ to be derived. The expression is applied to soft core interaction (different values for the maximum number of particles in a site are considered) and extended hard core

Defect-freezing and Defect-unbinding in the Vector Complex Ginzburg-Landau Equation

We describe the dynamical behavior found in numerical solutions of the Vector Complex Ginzburg-Landau equation in parameter values where plane waves are stable. Topological defects in the system are responsible for a rich behavior. At low coupling between the vector components, a {\sl frozen} phase is found, whereas a {\sl gas-like} phase appears at higher coupling. The transition is a consequence of a defect unbinding phenomena. Entropy functions display a characteristic behavior around the transition.Comment: 9 pages, using elsart.sty (not included). 3 figures. To appear in Computer Physics Communications (1999). Related material in http://www.imedea.uib.es/Nonlinear