2,793 research outputs found
The subdiffusive target problem: Survival probability
The asymptotic survival probability of a spherical target in the presence of
a single subdiffusive trap or surrounded by a sea of subdiffusive traps in a
continuous Euclidean medium is calculated. In one and two dimensions the
survival probability of the target in the presence of a single trap decays to
zero as a power law and as a power law with logarithmic correction,
respectively. The target is thus reached with certainty, but it takes the trap
an infinite time on average to do so. In three dimensions a single trap may
never reach the target and so the survival probability is finite and, in fact,
does not depend on whether the traps move diffusively or subdiffusively. When
the target is surrounded by a sea of traps, on the other hand, its survival
probability decays as a stretched exponential in all dimensions (with a
logarithmic correction in the exponent for ). A trap will therefore reach
the target with certainty, and will do so in a finite time. These results may
be directly related to enzyme binding kinetics on DNA in the crowded cellular
environment.Comment: 6 pages. References added, improved account of previous results and
typos correcte
Weak disorder: anomalous transport and diffusion are normal yet again
Particles driven through a periodic potential by an external constant force
are known to exhibit a pronounced peak of the diffusion around a critical force
that defines the transition between locked and running states. It has recently
been shown both experimentally and numerically that this peak is greatly
enhanced if some amount of spatial disorder is superimposed on the periodic
potential. Here we show that beyond a simple enhancement lies a much more
interesting phenomenology. For some parameter regimes the system exhibits a
rich variety of behaviors from normal diffusion to superdiffusion, subdiffusion
and even subtransport.Comment: Substantial improvements in presentatio
An analytical approach to sorting in periodic potentials
There has been a recent revolution in the ability to manipulate
micrometer-sized objects on surfaces patterned by traps or obstacles of
controllable configurations and shapes. One application of this technology is
to separate particles driven across such a surface by an external force
according to some particle characteristic such as size or index of refraction.
The surface features cause the trajectories of particles driven across the
surface to deviate from the direction of the force by an amount that depends on
the particular characteristic, thus leading to sorting. While models of this
behavior have provided a good understanding of these observations, the
solutions have so far been primarily numerical. In this paper we provide
analytic predictions for the dependence of the angle between the direction of
motion and the external force on a number of model parameters for periodic as
well as random surfaces. We test these predictions against exact numerical
simulations
Multiplicative Noise: Applications in Cosmology and Field Theory
Physical situations involving multiplicative noise arise generically in
cosmology and field theory. In this paper, the focus is first on exact
nonlinear Langevin equations, appropriate in a cosmologica setting, for a
system with one degree of freedom. The Langevin equations are derived using an
appropriate time-dependent generalization of a model due to Zwanzig. These
models are then extended to field theories and the generation of multiplicative
noise in such a context is discussed. Important issues in both the cosmological
and field theoretic cases are the fluctuation-dissipation relations and the
relaxation time scale. Of some importance in cosmology is the fact that
multiplicative noise can substantially reduce the relaxation time. In the field
theoretic context such a noise can lead to a significant enhancement in the
nucleation rate of topological defects.Comment: 21 pages, LaTex, LA-UR-93-210
Synchronization of globally coupled two-state stochastic oscillators with a state dependent refractory period
We present a model of identical coupled two-state stochastic units each of
which in isolation is governed by a fixed refractory period. The nonlinear
coupling between units directly affects the refractory period, which now
depends on the global state of the system and can therefore itself become time
dependent. At weak coupling the array settles into a quiescent stationary
state. Increasing coupling strength leads to a saddle node bifurcation, beyond
which the quiescent state coexists with a stable limit cycle of nonlinear
coherent oscillations. We explicitly determine the critical coupling constant
for this transition
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