Ratchet effect in an asymmetric two-dimensional system of Janus particles.

We consider a disk-like Janus particle self-driven by a force of constant magnitude f, but an arbitrary direction depending on the stochastic rotation of the disk. The particle diffuses in a two-dimensional channel of varying width 2h(x). We applied the procedure mapping the 2+1-dimensional Fokker-Planck equation onto the longitudinal coordinate x; the result is the Fick-Jacobs equation extended by the spatially dependent effective diffusion constant D(x) and an additional effective potential -γ(x), derived recursively within the mapping procedure.

Hydrodynamic approximations for driven dense colloidal mixtures in narrow pores.

The system of driven dense colloid mixtures is studied in one-, two-, and three-dimensional geometries. We calculate the diffusion coefficients and mobilities for each particle type, including cross-terms, in a hydrodynamic limit, using a mean-field-type approximation. The set of nonlinear diffusion equations are then solved.

Short-range and long-range correlations in driven dense colloidal mixtures in narrow pores.

The system of a driven dense colloid mixture in a tube with diameter comparable to particle size is modeled by a generalization of the asymmetric simple exclusion process (ASEP) model. The generalization goes in two directions: relaxing the exclusion constraint by allowing several (but few) particles on a site and by considering two species of particles, which differ in size and transport coefficients. We calculate the nearest-neighbor correlations using a variant of the Kirkwood approximation and show by comparison with numerical simulations that the approximation provides quite accurate results.

Dichotomic ratchet in a two-dimensional corrugated channel.

We consider a particle diffusing in a two-dimensional (2D) channel of varying width h(x). It is driven by a force of constant magnitude f but random orientation there or back along the channel. We derive the effective generalized Fick-Jacobs equation for this system, which describes the dynamics of such a particle in the longitudinal coordinate x.

Colloid particles in microfluidic inertial hydrodynamic ratchet at moderate Reynolds number.

The movement of spherical Brownian particle carried by an alternating fluid flow in a tube of periodically variable diameter is investigated. On the basis of our previous results [Phys. Rev.

Separation of dense colloidal suspensions in narrow channels: A stochastic model.

The flow of a colloidal suspension in a narrow channel of periodically varying width is described by the one-dimensional generalized asymmetric exclusion process. Each site admits multiple particle occupancy. We consider particles of two different sizes.

Hydrodynamic separation of colloidal particles in tubes: Effective one-dimensional approach.

We investigate diffusion of colloidal particles carried by flow in tubes of variable diameter and under the influence of an external field. We generalize the method mapping the three-dimensional confined diffusion onto an effective one-dimensional problem to the case of nonconservative forces and use this mapping for the problem in question. We show that in the presence of hydrodynamic drag, the lowest approximation (the Fick-Jacobs approximation) may be insufficient, and inclusion of at least the first-order correction is desirable to obtain more reliable results.

Movement of spherical colloid particles carried by flow in tubes of periodically varying diameter.

We provide analytical formulas for the movement of spherical particles in a corrugated tube, in the approximation of small amplitude of the tube diameter variation. We calculate how the particle is pushed toward the wall at some places and pulled off the wall at others. We show that this effect causes rectification of the particle movement, when the direction of the fluid flow is alternated, thus leading to the hydrodynamic ratchet effect.

Dimensional reduction of a general advection-diffusion equation in 2D channels.

Diffusion of point-like particles in a two-dimensional channel of varying width is studied. The particles are driven by an arbitrary space dependent force. We construct a general recurrence procedure mapping the corresponding two-dimensional advection-diffusion equation onto the longitudinal coordinate x.

Localization in random bipartite graphs: Numerical and empirical study.

We investigate adjacency matrices of bipartite graphs with a power-law degree distribution. Motivation for this study is twofold: first, vibrational states in granular matter and jammed sphere packings; second, graphs encoding social interaction, especially electronic commerce. We establish the position of the mobility edge and show that it strongly depends on the power in the degree distribution and on the ratio of the sizes of the two parts of the bipartite graph.

Inertial hydrodynamic ratchet: Rectification of colloidal flow in tubes of variable diameter.

We investigate analytically a microfluidic device consisting of a tube with a nonuniform but spatially periodic diameter, where a fluid driven back and forth by a pump carries colloidal particles. Although the net flow of the fluid is zero, the particles move preferentially in one direction due to the ratchet mechanism, which occurs due to the simultaneous effect of inertial hydrodynamics and Brownian motion. We show that the average current is strongly sensitive to particle size, thus facilitating colloidal particle sorting.

Modules in the metabolic network of E. coli with regulatory interactions.

We examine the modular structure of the metabolic network when combined with the regulatory network representing direct regulation of enzymes by small metabolites in E. coli. We introduce novel clustering algorithm and compare it with mainstream module detection method based on simulated annealing.

Equivalence of replica and cavity methods for computing spectra of sparse random matrices.

We show by direct calculation that the replica and cavity methods are exactly equivalent for the spectrum of an Erdős-Rényi random graph. We introduce a variational formulation based on the cavity method and use it to find approximate solutions for the density of eigenvalues. We also use this variational method for calculating spectra of sparse covariance matrices.

Interacting molecular motors: efficiency and work fluctuations.

We investigate the model of "reversible ratchet" with interacting particles, presented by us earlier [F. Slanina, EPL 84, 50009 (2008)]. We further clarify the effect of efficiency enhancement due to interaction and show that it is of energetic origin, rather than a consequence of reduced fluctuations.

Kinetics of step bunching during growth: a minimal model.

We study a minimal stochastic model of step bunching during growth on a one-dimensional vicinal surface. The formation of bunches is controlled by the preferential attachment of atoms to descending steps (inverse Ehrlich-Schwoebel effect) and the ratio d of the attachment rate to the terrace diffusion coefficient. For generic parameters (d>0) the model exhibits a very slow crossover to a nontrivial asymptotic coarsening exponent beta approximately 0.

Inelastically scattering particles and wealth distribution in an open economy.

Using the analogy with inelastic granular gases we introduce a model for wealth exchange in society. The dynamics is governed by a kinetic equation, which allows for self-similar solutions. The scaling function has a power-law tail, the exponent being given by a transcendental equation.

Glass transition in a simple stochastic model with back-reaction.

We formulate and solve a model of dynamical arrest in colloids. A particle is coupled to the bath of statistically identical particles. The dynamics is described by Langevin equation with stochastic external force described by telegraphic noise.

The rise and fall of a networked society: a formal model.

In a well networked community, there is intense social interaction, and information disseminates briskly and broadly. This is important if the environment is volatile (i.e.