2,119 research outputs found
Optimal search strategies of space-time coupled random walkers with finite lifetimes
We present a simple paradigm for detection of an immobile target by a
space-time coupled random walker with a finite lifetime. The motion of the
walker is characterized by linear displacements at a fixed speed and
exponentially distributed duration, interrupted by random changes in the
direction of motion and resumption of motion in the new direction with the same
speed. We call these walkers "mortal creepers". A mortal creeper may die at any
time during its motion according to an exponential decay law characterized by a
finite mean death rate . While still alive, the creeper has a finite
mean frequency of change of the direction of motion. In particular, we
consider the efficiency of the target search process, characterized by the
probability that the creeper will eventually detect the target. Analytic
results confirmed by numerical results show that there is an
-dependent optimal frequency that maximizes the
probability of eventual target detection. We work primarily in one-dimensional
() domains and examine the role of initial conditions and of finite domain
sizes. Numerical results in domains confirm the existence of an optimal
frequency of change of direction, thereby suggesting that the observed effects
are robust to changes in dimensionality. In the case, explicit
expressions for the probability of target detection in the long time limit are
given. In the case of an infinite domain, we compute the detection probability
for arbitrary times and study its early- and late-time behavior. We further
consider the survival probability of the target in the presence of many
independent creepers beginning their motion at the same location and at the
same time. We also consider a version of the standard "target problem" in which
many creepers start at random locations at the same time.Comment: 18 pages, 7 figures. The title has been changed with respect to the
one in the previous versio
Universality of efficiency at maximum power
We investigate the efficiency of power generation by thermo-chemical engines.
For strong coupling between the particle and heat flows and in the presence of
a left-right symmetry in the system, we demonstrate that the efficiency at
maximum power displays universality up to quadratic order in the deviation from
equilibrium. A maser model is presented to illustrate our argument.Comment: 4 pages, 2 figure
Pulse Propagation in Chains with Nonlinear Interactions
Pulse propagation in nonlinear arrays continues to be of interest because it
provides a possible mechanism for energy transfer with little dispersion. Here
we show that common measures of pulse dispersion might be misleading; in
strongly anharmonic systems they tend to reflect a succession of extremely
narrow pulses traveling at decreasing velocities rather than the actual width
of a single pulse. We present analytic estimates for the fraction of the
initial energy that travels in the leading pulses. We also provide analytic
predictions for the leading pulse velocity in a Fermi-Pasta-Ulam beta-chain
Escape of a Uniform Random Walk from an Interval
We study the first-passage properties of a random walk in the unit interval
in which the length of a single step is uniformly distributed over the finite
range [-a,a]. For a of the order of one, the exit probabilities to each edge of
the interval and the exit time from the interval exhibit anomalous properties
stemming from the change in the minimum number of steps to escape the interval
as a function of the starting point. As a decreases, first-passage properties
approach those of continuum diffusion, but non-diffusive effects remain because
of residual discreteness effectsComment: 8 pages, 8 figures, 2 column revtex4 forma
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