Splitting probabilities and interfacial territory covered by two-dimensional and three-dimensional surface-mediated diffusion

Constructing efficient strategies for the process optimization by restart

Optimization of the mean completion time of random processes by restart is a subject of active theoretical research in statistical physics and has long found practical application in computer science. Meanwhile, one of the key issues remains largely unsolved: how to construct a restart strategy for a process whose detailed statistics are unknown to ensure that the expected completion time will reduce? Addressing this query here we propose several constructive criteria for the effectiveness of various protocols of noninstantaneous restart in the mean completion time problem and in the success probability problem. Being expressed in terms of a small number of easily estimated statistical characteristics of the original process (MAD, median completion time, low-order statistical moments of completion time), these criteria allow informed restart decision based on partial information.

Diffusion toward a nanoforest of absorbing pillars

Spiky coatings (also known as nanoforests or Fakir-like surfaces) have found many applications in chemical physics, material sciences, and biotechnology, such as superhydrophobic materials, filtration and sensing systems, and selective protein separation, to name but a few. In this paper, we provide a systematic study of steady-state diffusion toward a periodic array of absorbing cylindrical pillars protruding from a flat base. We approximate a periodic cell of this system by a circular tube containing a single pillar, derive an exact solution of the underlying Laplace equation, and deduce a simple yet exact representation for the total flux of particles onto the pillar. The dependence of this flux on the geometric parameters of the model is thoroughly analyzed. In particular, we investigate several asymptotic regimes, such as a thin pillar limit, a disk-like pillar, and an infinitely long pillar. Our study sheds light onto the trapping efficiency of spiky coatings and reveals the roles of pillar anisotropy and diffusional screening.

Theory for controlling individual self-propelled micro-swimmers by photon nudging I: directed transport

Photon nudging is a new experimental method which enables the force-free manipulation and localization of individual self-propelled artificial micro-swimmers in fluidic environments.

Bulk-mediated surface transport in the presence of bias

Surface transport, when the particle is allowed to leave the surface, travel in the bulk for some time, and then return to the surface, is referred to as bulk-mediated surface transport. Recently, we proposed a formalism that significantly simplifies analysis of bulk-mediated surface diffusion [A. M. Berezhkovskii, L. Dagdug, and S. M. Bezrukov, J. Chem. Phys. 143, 084103 (2015)]. Here this formalism is extended to bulk-mediated surface transport in the presence of bias, i.e., when the particle has arbitrary drift velocities on the surface and in the bulk. A key advantage of our approach is that the transport problem reduces to that of a two-state problem of the particle transitions between the surface and the bulk. The latter can be solved with relative ease. The formalism is used to find the Laplace transforms of the first two moments of the particle displacement over the surface in time t at arbitrary values of the particle drift velocities and diffusivities on the surface and in the bulk. This allows us to analyze in detail the time dependence of the effective drift velocity of the particle on the surface, which can be highly nontrivial.

Tuning the Flight Length of Molecules Diffusing on a Hydrophobic Surface

Transport at solid-liquid interfaces is critical to self-assembly, biosensing, and heterogeneous catalysis, but surface diffusion remains difficult to characterize and rationally manipulate, due to the inherent heterogeneity of adsorption on solid surfaces. Using single-molecule tracking, we characterized the diffusion of a fluorescent long-chain surfactant on a hydrophobic surface, which involved periods of confinement alternating with bulk-mediated "flights". The concentration of methanol in solution was varied to tune the strength of the hydrophobic surface-molecule interaction. The frequency of confinement had a nonmonotonic dependence on methanol concentration that reflected the relative influence of anomalously strong adsorption sites. By carefully accounting for the effect of this surface heterogeneity, we demonstrated that flight lengths increased monotonically as the hydrophobic attraction decreased, in agreement with theoretical predictions for bulk-mediated surface diffusion. The theory provided an accurate description of surface diffusion, despite the system being heterogeneous, and can be leveraged to optimize molecular search and assembly processes.

Overlap of two Brownian trajectories: exact results for scaling functions

We consider two random walkers starting at the same time t=0 from different points in space separated by a given distance R. We compute the average volume of the space visited by both walkers up to time t as a function of R and t and dimensionality of space d. For d<4, this volume, after proper renormalization, is shown to be expressed through a scaling function of a single variable R/√t. We provide general integral formulas for scaling functions for arbitrary dimensionality d<4. In contrast, we show that no scaling function exists for higher dimensionalities d≥4.