1,892 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
Anomalous diffusion in a random nonlinear oscillator due to high frequencies of the noise
We study the long time behaviour of a nonlinear oscillator subject to a
random multiplicative noise with a spectral density (or power-spectrum) that
decays as a power law at high frequencies. When the dissipation is negligible,
physical observables, such as the amplitude, the velocity and the energy of the
oscillator grow as power-laws with time. We calculate the associated scaling
exponents and we show that their values depend on the asymptotic behaviour of
the external potential and on the high frequencies of the noise. Our results
are generalized to include dissipative effects and additive noise.Comment: Expanded version of Proceedings StatPhys-Kolkata V
Stochastically driven single level quantum dot: a nano-scale finite-time thermodynamic machine and its various operational modes
We describe a single-level quantum dot in contact with two leads as a
nanoscale finite-time thermodynamic machine. The dot is driven by an external
stochastic force that switches its energy between two values. In the isothermal
regime, it can operate as a rechargeable battery by generating an electric
current against the applied bias in response to the stochastic driving, and
re-delivering work in the reverse cycle. This behavior is reminiscent of the
Parrondo paradox. If there is a thermal gradient the device can function as a
work-generating thermal engine, or as a refrigerator that extracts heat from
the cold reservoir via the work input of the stochastic driving. The efficiency
of the machine at maximum power output is investigated for each mode of
operation, and universal features are identified.Comment: 4 pages, 3 figures, V2: typos corrected around eq.(12
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