Phase transition in the two-component symmetric exclusion process with open boundaries

We consider single-file diffusion in an open system with two species $A,B$ of particles. At the boundaries we assume different reservoir densities which drive the system into a non-equilibrium steady state. As a model we use an one-dimensional two-component simple symmetric exclusion process with two different hopping rates $D_A,D_B$ and open boundaries. For investigating the dynamics in the hydrodynamic limit we derive a system of coupled non-linear diffusion equations for the coarse-grained particle densities. The relaxation of the initial density profile is analyzed by numerical integration. Exact analytical expressions are obtained for the self-diffusion coefficients, which turns out to be length-dependent, and for the stationary solution. In the steady state we find a discontinuous boundary-induced phase transition as the total exterior density gradient between the system boundaries is varied. At one boundary a boundary layer develops inside which the current flows against the local density gradient. Generically the width of the boundary layer and the bulk density profiles do not depend on the two hopping rates. At the phase transition line, however, the individual density profiles depend strongly on the ratio $D_A/D_B$. Dynamic Monte Carlo simulation confirm our theoretical predictions.Comment: 26 pages, 6 figure

Amplification of Molecular Traffic Control in catalytic grains with novel channel topology design

We investigate the conditions for reactivity enhancement of catalytic processes in porous solids by use of molecular traffic control (MTC). With dynamic Monte-Carlo simulations and continuous-time master equation theory applied to the high concentration regime we obtain a quantitative description of the MTC effect for a network of intersecting single-file channels in a wide range of grain parameters and for optimal external operating conditions. Implementing the concept of MTC in models with specially designed alternating bimodal channels we find the efficiency ratio (compared with a topologically and structurally similar reference system without MTC) to be enhanced with increasing grain diameter, a property verified for the first time for an MTC system. Even for short intersection channels, MTC leads to a reactivity enhancement of up to approximately 65%. This suggests that MTC may significantly enhance the efficiency of a catalytic process for small as well as large porous particles with a suitably chosen binary channel topology.Comment: 15 pages, 12 figure

Amplication of Molecular Traffic Control in catalytic grains with novel channel topology design

We investigate the conditions for reactivity enhancement of catalytic processes in porous solids by the use of molecular traffic control (MTC). With dynamic Monte-Carlo simulations and continuous-time master equation theory applied to the high concentration regime, we obtain a quantitative description of the MTC effect for a network of intersecting single-file channels in a wide range of grain parameters and for optimal external operating conditions. Implementing the concept of MTC in models with specially designed alternating bimodal channels, we find the efficiency ratio (compared with a topologically and structurally similar reference system without MTC) to be enhanced with increasing grain diameter, a property verified for the first time for a MTC system. Even for short intersection channels, MTC leads to a reactivity enhancement of up to approximately 65%. This suggests that MTC may significantly enhance the efficiency of a catalytic process for small as well as large porous particles with a suitably chosen binary channel topology

“It’s Always Good to Ask”:A Mixed Methods Study on the Perceived Role of Sexual Health Practitioners Asking Gay and Bisexual Men About Experiences of Domestic Violence and Abuse

Development of joint displays is a valued approach to merging qualitative and quantitative findings in mixed methods research. This study aimed to illustrate a case series mixed methods display and the utility of using mixed methods for broadening our understanding of domestic violence and abuse. Using a convergent design, 532 gay and bisexual men participated in a Health and Relationship Survey in a U.K. sexual health service and 19 in an interview. Quantitative and qualitative data were analyzed separately and integrated at the level of interpretation and reporting. There were inconsistencies in perceptions and reports of abuse. Men were supportive of selective enquiry for domestic violence and abuse by practitioners (62.6%; 95% confidence interval = 58.1% to 66.7%) while being mindful of contextual factors.</p

Particle current in symmetric exclusion process with time-dependent hopping rates

In a recent study, (Jain et al 2007 Phys. Rev. Lett. 99 190601), a symmetric exclusion process with time-dependent hopping rates was introduced. Using simulations and a perturbation theory, it was shown that if the hopping rates at two neighboring sites of a closed ring vary periodically in time and have a relative phase difference, there is a net DC current which decreases inversely with the system size. In this work, we simplify and generalize our earlier treatment. We study a model where hopping rates at all sites vary periodically in time, and show that for certain choices of relative phases, a DC current of order unity can be obtained. Our results are obtained using a perturbation theory in the amplitude of the time-dependent part of the hopping rate. We also present results obtained in a sudden approximation that assumes large modulation frequency.Comment: 17 pages, 2 figure

Scaling limits of a tagged particle in the exclusion process with variable diffusion coefficient

We prove a law of large numbers and a central limit theorem for a tagged particle in a symmetric simple exclusion process in the one-dimensional lattice with variable diffusion coefficient. The scaling limits are obtained from a similar result for the current through -1/2 for a zero-range process with bond disorder. For the CLT, we prove convergence to a fractional Brownian motion of Hurst exponent 1/4.Comment: 9 page

Molecular traffic control in single-file networks with fast catalysts

As a model for molecular traffic control (MTC) we investigate the diffusion of hard core particles in crossed single-file systems. We consider a square lattice of single-files being connected to external reservoirs. The (vertical) alpha-channels, carrying only A-particles, are connected to reservoirs with constant density ra. B-particles move along the (horizontal) beta-channels, which are connected to reservoirs of density rB. We allow the irreversible transition A to B at intersections. We are interested in the stationary density profile in the alpha- and beta- channels, which is the distribution of the occupation probabilities over the lattice. We calculate the stationary currents of the system and show that for sufficiently long channels the currents (as a function of the reservoir densities) show in the limit of large transition rates non analytic behavior. The results obtained by direct solution of the master equation are verified by kinetic Monte Carlo simulations.Comment: 11 page

Billiards in a general domain with random reflections

We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain ${\mathcal D} \subset {\mathbb R}^d$ until it hits the boundary and bounces randomly inside according to some reflection law. We assume that the boundary of the domain is locally Lipschitz and almost everywhere continuously differentiable. The angle of the outgoing velocity with the inner normal vector has a specified, absolutely continuous density. We construct the discrete time and the continuous time processes recording the sequence of hitting points on the boundary and the pair location/velocity. We mainly focus on the case of bounded domains. Then, we prove exponential ergodicity of these two Markov processes, we study their invariant distribution and their normal (Gaussian) fluctuations. Of particular interest is the case of the cosine reflection law: the stationary distributions for the two processes are uniform in this case, the discrete time chain is reversible though the continuous time process is quasi-reversible. Also in this case, we give a natural construction of a chord "picked at random" in ${\mathcal D}$, and we study the angle of intersection of the process with a $(d-1)$-dimensional manifold contained in ${\mathcal D}$.Comment: 50 pages, 10 figures; To appear in: Archive for Rational Mechanics and Analysis; corrected Theorem 2.8 (induced chords in nonconvex subdomains

A review on substances and processes relevant for optical remote sensing of extremely turbid marine areas, with a focus on the Wadden Sea

The interpretation of optical remote sensing data of estuaries and tidal flat areas is hampered by optical complexity and often extreme turbidity. Extremely high concentrations of suspended matter, chlorophyll and dissolved organic matter, local differences, seasonal and tidal variations and resuspension are important factors influencing the optical properties in such areas. This review gives an overview of the processes in estuaries and tidal flat areas and the implications of these for remote sensing in such areas, using the Wadden Sea as a case study area. Results show that remote sensing research in extremely turbid estuaries and tidal areas is possible. However, this requires sensors with a large ground resolution, algorithms tuned for high concentrations of various substances and the local specific optical properties of these substances, a simultaneous detection of water colour and land-water boundaries, a very short time lag between acquisition of remote sensing and in situ data used for validation and sufficient geophysical and ecological knowledge of the area. © 2010 The Author(s)