24 research outputs found
Exact two-time correlation and response functions in the one-dimensional coagulation-diffusion process by the empty-interval-particle method
The one-dimensional coagulation-diffusion process describes the strongly
fluctuating dynamics of particles, freely hopping between the nearest-neighbour
sites of a chain such that one of them disappears with probability 1 if two
particles meet. The exact two-time correlation and response function in the
one-dimensional coagulation-diffusion process are derived from the
empty-interval-particle method. The main quantity is the conditional
probability of finding an empty interval of n consecutive sites, if at distance
d a site is occupied by a particle. Closed equations of motion are derived such
that the probabilities needed for the calculation of correlators and responses,
respectively, are distinguished by different initial and boundary conditions.
In this way, the dynamical scaling of these two-time observables is analysed in
the longtime ageing regime. A new generalised fluctuation-dissipation ratio
with an universal and finite limit is proposed.Comment: 31 pages, submitted to J.Stat.Mec
Spatial clustering of interacting bugs: Levy flights versus Gaussian jumps
A biological competition model where the individuals of the same species
perform a two-dimensional Markovian continuous-time random walk and undergo
reproduction and death is studied. The competition is introduced through the
assumption that the reproduction rate depends on the crowding in the
neighborhood. The spatial dynamics corresponds either to normal diffusion
characterized by Gaussian jumps or to superdiffusion characterized by L\'evy
flights. It is observed that in both cases periodic patterns occur for
appropriate parameters of the model, indicating that the general macroscopic
collective behavior of the system is more strongly influenced by the
competition for the resources than by the type of spatial dynamics. However,
some differences arise that are discussed.Comment: This version incorporates in the text the correction published as an
Erratum in Europhysics Letters (EPL) 95, 69902 (2011) [doi:
10.1209/0295-5075/95/69902
Aging processes in reversible reaction-diffusion systems: Monte Carlo simulations
Reaction-diffusion systems with reversible reactions generically display
power-law relaxation towards chemical equilibrium. In this work we investigate
through numerical simulations aging processes that characterize the
non-equilibrium relaxation. Studying a model which excludes multiple occupancy
of a site, we find that the scaling behavior of the two-time correlation and
response functions are similar to that discovered previously in an exactly
solvable version with no restrictions on the occupation numbers. Especially, we
find that the scaling of the response depends on whether the perturbation
conserves a certain quantity or not. Our results point to a high degree of
universality in relaxation processes taking place in diffusion-limited systems
with reversible reactions.Comment: 12 pages, 4 figures included, accepted for publication in JSTA
Conformal symmetry in non-local field theories
We have shown that a particular class of non-local free field theory has
conformal symmetry in arbitrary dimensions. Using the local field theory
counterpart of this class, we have found the Noether currents and Ward
identities of the translation, rotation and scale symmetries. The operator
product expansion of the energy-momentum tensor with quasi-primary fields is
also investigated.Comment: 15 pages, V2 (Some references added) V3(published version
Interacting Brownian Motion with Resetting
We study two Brownian particles in dimension , diffusing under an
interacting resetting mechanism to a fixed position. The particles are subject
to a constant drift, which biases the Brownian particles toward each other. We
derive the steady-state distributions and study the late time relaxation
behavior to the stationary state.Comment: 13 pages, 4 figure
Diffusion under time-dependent resetting
We study a Brownian particle diffusing under a time-modulated stochastic
resetting mechanism to a fixed position. The rate of resetting r(t) is a
function of the time t since the last reset event. We derive a sufficient
condition on r(t) for a steady-state probability distribution of the position
of the particle to exist. We derive the form of the steady-state distributions
under some particular choices of r(t) and also consider the late time
relaxation behavior of the probability distribution. Finally we consider first
passage time properties for the Brownian particle to reach the origin and
derive a formula for the mean first passage time. We study optimal properties
of the mean first passage time and show that a threshold function is at least
locally optimal for the problem of minimizing the mean first passage time.Comment: 15 pages, 4 figure
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 . At a reset event the
particle's position is returned to the resetting site and the particle's
velocity is reversed with probability . The case corresponds
to position resetting and velocity randomization whereas corresponds
to position-only resetting. We show that, beginning from symmetric initial
conditions, the stationary state does not depend on 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
A mini-review of the diffusion dynamics of DNA-binding proteins: experiments and models
In the course of various biological processes, specific DNA-binding proteins must efficiently find a particular target sequence/protein or a damaged site on the DNA. DNA-binding proteins perform this task based on diffusion. Nevertheless, investigations over recent decades have found that the diffusion dynamics of DNA-binding proteins are generally complicated and, further, protein specific. In this review, we collect experimental and theoretical studies that quantify the diffusion dynamics of DNA-binding proteins and review them from the viewpoint of diffusion processes.11Nsciescopu