Related papers: Geometry-controlled kinetics
Many biological processes involve one dimensional diffusion over a correlated inhomogeneous energy landscape with a correlation length $\xi_c$. Typical examples are specific protein target location on DNA, nucleosome repositioning, or DNA…
The concept of geometry works as an overarching framework underlying a wide range of transport phenomena. Particularly, the geometric phase effect in classical and quantum heat pump has been attracting much attention in microscopic systems.…
First passage times (FPTs) are often used to study timescales in physical, chemical, and biological processes. FPTs generically describe the time it takes a random "searcher" to find a "target." In many systems, the important timescale is…
A deeper understanding of nonequilibrium phenomena is needed to reveal the principles governing natural and synthetic molecular machines. Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear…
We consider a family of controlled reaction-diffusion equations, describing the spatial spreading of an invasive biological species. For a given propagation speed $c\in{I\!\!R}$, we seek a control with minimum cost, which achieves a…
Photon transport through turbid media has typically been modeled through diffusion or telegraph equations. These models describe behavior of the average, or typical, photon with remarkable accuracy, however, we show here that they fail to…
Diffusion is a reoccurring phenomena in many fields and is affected by the geometry in which it takes place. Here we investigate the effects of geometry on diffusion in a Brick and Mortar model system. The tortuous effects are evaluated…
We present a detailed study of the effects of the initial distribution on the kinetic evolution of the irreversible reaction A+B -> 0 in one dimension. Our analytic as well as numerical work is based on a reaction-diffusion model of this…
For transport processes in geometrically restricted domains, the mean first-passage time (MFPT) admits a general scaling dependence on space parameters for diffusion, anomalous diffusion, and diffusion in disordered or fractal media. For…
Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…
Many transport processes in ecology, physics and biochemistry can be described by the average time to first find a site or exit a region, starting from an initial position. Typical mathematical treatments are based on formulations that…
For a substance diffusing on a curved surface, we obtain an explicit relation valid for very small values of the time, between the local concentration, the diffusion coefficient, the intrinsic spatial curvature and the time. We recover the…
Time-dependent $\mathcal{PT}$-symmetric quantum mechanics is featured by a varying inner-product metric and has stimulated a number of interesting studies beyond conventional quantum mechanics. In this paper, we explore geometric aspects of…
We study the dynamics of protein folding via statistical energy-landscape theory. In particular, we concentrate on the local-connectivity case with the folding progress described by the fraction of native conformations. We obtain…
Tracking the movement of tracer particles has long been a strategy for uncovering complex structures. Here, we study discrete-time random walks on finite Cayley trees to infer key parameters such as tree depth and geometric bias toward the…
We investigate first-hitting location (FHL) statistics induced by drift-diffusion processes in domains with absorbing boundaries, and examine how such boundary laws give rise to intrinsic information observables. Rather than introducing…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…
Many events in biology are triggered when a diffusing searcher finds a target, which is called a first passage time (FPT). The overwhelming majority of FPT studies have analyzed the time it takes a single searcher to find a target. However,…
We investigate a class of diffusion-controlled reactions that are initiated at the time instance when a prescribed number $K$ among $N$ particles independently diffusing in a solvent are simultaneously bound to a target region. In the…
Pattern dynamics on curved surfaces are found everywhere in nature. The geometry of surfaces have been shown to influence dynamics and play a functional role, yet a comprehensive understanding is still elusive. Here, we report for the first…