Subordinated Langevin Equations for Anomalous Diffusion in External Potentials - Biasing and Decoupled Forces

The role of external forces in systems exhibiting anomalous diffusion is discussed on the basis of the describing Langevin equations. Since there exist different possibilities to include the effect of an external field the concept of {\it biasing} and {\it decoupled} external fields is introduced. Complementary to the recently established Langevin equations for anomalous diffusion in a time-dependent external force-field [{\it Magdziarz et al., Phys. Rev. Lett. {\bf 101}, 210601 (2008)}] the Langevin formulation of anomalous diffusion in a decoupled time-dependent force-field is derived

Continuous Time Random Walks with Internal Dynamics and Subdiffusive Reaction-Diffusion Equations

We formulate the generalized master equation for a class of continuous time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an advection-diffusion and a jump-diffusion scheme. Based on this master equation, we also derive reaction-diffusion equations for subdiffusive chemical species, using a mean field approximation

Feynman-Kac equation for anomalous processes with space-and time-dependent forces

Invited contribution to the J. Phys. A special issue Emerging Talent

Weakly non-ergodic Statistical Physics

We find a general formula for the distribution of time averaged observables for weakly non-ergodic systems. Such type of ergodicity breaking is known to describe certain systems which exhibit anomalous fluctuations, e.g. blinking quantum dots and the sub-diffusive continuous time random walk model. When the fluctuations become normal we recover usual ergodic statistical mechanics. Examples of a particle undergoing fractional dynamics in a binding force field are worked out in detail. We briefly discuss possible physical applications in single particle experiments

A Glial Variant of the Vesicular Monoamine Transporter Is Required To Store Histamine in the Drosophila Visual System

Unlike other monoamine neurotransmitters, the mechanism by which the brain's histamine content is regulated remains unclear. In mammals, vesicular monoamine transporters (VMATs) are expressed exclusively in neurons and mediate the storage of histamine and other monoamines. We have studied the visual system of Drosophila melanogaster in which histamine is the primary neurotransmitter released from photoreceptor cells. We report here that a novel mRNA splice variant of Drosophila VMAT (DVMAT-B) is expressed not in neurons but rather in a small subset of glia in the lamina of the fly's optic lobe. Histamine contents are reduced by mutation of dVMAT, but can be partially restored by specifically expressing DVMAT-B in glia. Our results suggest a novel role for a monoamine transporter in glia that may be relevant to histamine homeostasis in other systems

Run and tumble particle under resetting:a renewal approach

We consider a particle undergoing run and tumble dynamics, in which its velocity stochastically reverses, in one dimension. We study the addition of a Poissonian resetting process occurring with rate $r$. At a reset event the particle's position is returned to the resetting site $X_r$ and the particle's velocity is reversed with probability $\eta$. The case $\eta = 1/2$ corresponds to position resetting and velocity randomization whereas $\eta =0$ corresponds to position-only resetting. We show that, beginning from symmetric initial conditions, the stationary state does not depend on $\eta$ i.e. it is independent of the velocity resetting protocol. However, in the presence of an absorbing boundary at the origin, the survival probability and mean time to absorption do depend on the velocity resetting protocol. Using a renewal equation approach, we show that the the mean time to absorption is always less for velocity randomization than for position-only resetting.Comment: 16 pages, 1 figure, version accepted in Journal of Physics