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We study the properties of ageing Scher-Montroll transport in terms of a biased subdiffusive continuous time random walk in which the waiting times between consecutive jumps of the charge carriers are distributed according to the power law probability with . As we show, the dynamical properties of the Scher-Montroll transport depend on the ageing time span between the initial preparation of the system and the start of the observation. The Scher-Montroll transport theory was originally shown to describe the photocurrent in amorphous solids in the presence of an external electric field, but it has since been used in many other fields of physical sciences, in particular also in the geophysical context for the description of the transport of tracer particles in subsurface aquifers. In the absence of ageing () the photocurrent of the classical Scher-Montroll model or the breakthrough curves in the groundwater context exhibit a crossover between two power law regimes in time with the scaling exponents and . In the presence of ageing a new power law regime and an initial plateau regime of the current emerge. We derive the different power law regimes and crossover times of the ageing Scher-Montroll transport and show excellent agreement with simulations of the process. Experimental data of ageing Scher-Montroll transport in polymeric semiconductors are shown to agree well with the predictions of our theory.
Molecular signalling in living cells occurs at low copy numbers and is thereby inherently limited by the noise imposed by thermal diffusion. The precision at which biochemical receptors can count signalling molecules is intimately related to the noise correlation time. In addition to passive thermal diffusion, messenger RNA and vesicle-engulfed signalling molecules can transiently bind to molecular motors and are actively transported across biological cells. Active transport is most beneficial when trafficking occurs over large distances, for instance up to the order of 1 metre in neurons. Here we explain how intermittent active transport allows for faster equilibration upon a change in concentration triggered by biochemical stimuli. Moreover, we show how intermittent active excursions induce qualitative changes in the noise in effectively one-dimensional systems such as dendrites. Thereby they allow for significantly improved signalling precision in the sense of a smaller relative deviation in the concentration read-out by the receptor. On the basis of linear response theory we derive the exact mean field precision limit for counting actively transported molecules. We explain how intermittent active excursions disrupt the recurrence in the molecular motion, thereby facilitating improved signalling accuracy. Our results provide a deeper understanding of how recurrence affects molecular signalling precision in biological cells and novel medical-diagnostic devices.
A single predator charging a herd of prey: effects of self volume and predator-prey decision-making
(2016)
We study the degree of success of a single predator hunting a herd of prey on a two-dimensional square lattice landscape. We explicitly consider the self volume of the prey restraining their dynamics on the lattice. The movement of both predator and prey is chosen to include an intelligent, decision making step based on their respective sighting ranges, the radius in which they can detect the other species (prey cannot recognise each other besides the self volume interaction): after spotting each other the motion of prey and predator turns from a nearest neighbour random walk into directed escape or chase, respectively. We consider a large range of prey densities and sighting ranges and compute the mean first passage time for a predator to catch a prey as well as characterise the effective dynamics of the hunted prey. We find that the prey's sighting range dominates their life expectancy and the predator profits more from a bad eyesight of the prey than from his own good eye sight. We characterise the dynamics in terms of the mean distance between the predator and the nearest prey. It turns out that effectively the dynamics of this distance coordinate can be captured in terms of a simple Ornstein–Uhlenbeck picture. Reducing the many-body problem to a simple two-body problem by imagining predator and nearest prey to be connected by an effective Hookean bond, all features of the model such as prey density and sighting ranges merge into the effective binding constant.