324 research outputs found
Does Greed Help a Forager Survive?
We investigate the role of greed on the lifetime of a random-walking forager
on an initially resource-rich lattice. Whenever the forager lands on a
food-containing site, all the food there is eaten and the forager can hop
more steps without food before starving. Upon reaching an empty
site, the forager comes one time unit closer to starvation. The forager is also
greedy---given a choice to move to an empty or to a food-containing site in its
local neighborhood, the forager moves preferentially towards food.
Surprisingly, the forager lifetime varies non-monotonically with greed, with
different senses of the non-monotonicity in one and two dimensions. Also
unexpectedly, the forager lifetime in one dimension has a huge peak for very
negative greed.Comment: 5 pages, 4 figures, 2-column revtex format. Version 2 is expanded in
response to referee comments. For publication in PR
Starvation Dynamics of a Greedy Forager
We investigate the dynamics of a greedy forager that moves by random walking
in an environment where each site initially contains one unit of food. Upon
encountering a food-containing site, the forager eats all the food there and
can subsequently hop an additional steps without food before
starving to death. Upon encountering an empty site, the forager goes hungry and
comes one time unit closer to starvation. We investigate the new feature of
forager greed; if the forager has a choice between hopping to an empty site or
to a food-containing site in its nearest neighborhood, it hops preferentially
towards food. If the neighboring sites all contain food or are all empty, the
forager hops equiprobably to one of these neighbors. Paradoxically, the
lifetime of the forager can depend non-monotonically on greed, and the sense of
the non-monotonicity is opposite in one and two dimensions. Even more
unexpectedly, the forager lifetime in one dimension is substantially enhanced
when the greed is negative; here the forager tends to avoid food in its local
neighborhood. We also determine the average amount of food consumed at the
instant when the forager starves. We present analytic, heuristic, and numerical
results to elucidate these intriguing phenomena.Comment: 32 pages, 11 figures. Version 2: Various corrections in response to
referee reports. For publication in JSTA
Exactly solvable model of reactions on a random catalytic chain
In this paper we study a catalytically-activated A + A \to 0 reaction taking
place on a one-dimensional regular lattice which is brought in contact with a
reservoir of A particles. The A particles have a hard-core and undergo
continuous exchanges with the reservoir, adsorbing onto the lattice or
desorbing back to the reservoir. Some lattice sites possess special, catalytic
properties, which induce an immediate reaction between two neighboring A
particles as soon as at least one of them lands onto a catalytic site. We
consider three situations for the spatial placement of the catalytic sites:
regular, annealed random and quenched random. For all these cases we derive
exact results for the partition function, and the disorder-averaged pressure
per lattice site. We also present exact asymptotic results for the particles'
mean density and the system's compressibility. The model studied here furnishes
another example of a 1D Ising-type system with random multisite interactions
which admits an exact solution.Comment: 41 pages, AmsTe
On the non-equivalence of two standard random walks
We focus on two models of nearest-neighbour random walks on d-dimensional
regular hyper-cubic lattices that are usually assumed to be identical - the
discrete-time Polya walk, in which the walker steps at each integer moment of
time, and the Montroll-Weiss continuous-time random walk in which the time
intervals between successive steps are independent, exponentially and
identically distributed random variables with mean 1. We show that while for
symmetric random walks both models indeed lead to identical behaviour in the
long time limit, when there is an external bias they lead to markedly different
behaviour.Comment: 5 pages, 1 figur
Bidimensional intermittent search processes: an alternative to Levy flights strategies
Levy flights are known to be optimal search strategies in the particular case
of revisitable targets. In the relevant situation of non revisitable targets,
we propose an alternative model of bidimensional search processes, which
explicitly relies on the widely observed intermittent behavior of foraging
animals. We show analytically that intermittent strategies can minimize the
search time, and therefore do constitute real optimal strategies. We study two
representative modes of target detection, and determine which features of the
search time are robust and do not depend on the specific characteristics of
detection mechanisms. In particular, both modes lead to a global minimum of the
search time as a function of the typical times spent in each state, for the
same optimal duration of the ballistic phase. This last quantity could be a
universal feature of bidimensional intermittent search strategies
Optimally Frugal Foraging
We introduce the \emph{frugal foraging} model in which a forager performs a
discrete-time random walk on a lattice, where each site initially contains
food units. The forager metabolizes one unit of food at each step
and starves to death when it last ate steps in the past. Whenever
the forager decides to eat, it consumes all food at its current site and this
site remains empty (no food replenishment). The crucial property of the forager
is that it is \emph{frugal} and eats only when encountering food within at most
steps of starvation. We compute the average lifetime analytically as a
function of frugality threshold and show that there exists an optimal strategy,
namely, a frugality threshold that maximizes the forager lifetime.Comment: 5 pages, 3 figure
Biased Tracer Diffusion in Hard-Core Lattice Gases: Some Notes on the Validity of the Einstein Relation
In this presentation we overview some recent results on biased tracer
diffusion in lattice gases. We consider both models in which the gas particles
density is explicitly conserved and situations in which the lattice gas
particles undergo continuous exchanges with a reservoir, which case is
appropriate, e.g., to adsorbed monolayers in contact with the vapor phase. For
all these models we determine, in some cases exactly and in other ones - using
a certain decoupling approximation, the mean displacement of a tracer particle
(TP) driven by a constant external force in a dynamical background formed by
the lattice gas particles whose transition rates are symmetric. Evaluating the
TP mean displacement explicitly we are able to define the TP mobility, which
allows us to demonstrate that the Einstein relation between the TP mobility and
the diffusivity generally holds, despite the fact that in some cases diffusion
is anomalous. For models treated within the framework of the decoupling
approximation, our analytical results are confirmed by Monte Carlo simulations.
Perturbance of the lattice gas particles distribution due to the presence of a
biased TP and the form of the particle density profiles are also discussed.Comment: refs added + minor changes, to appear in: Instabilities and
Non-Equilibrium Structures IX, eds.: E.Tirapegui and O.Descalzi, (Kluwer
Academic Pub., Dordrecht), february 200
Temporal correlations of the running maximum of a Brownian trajectory
We study the correlations between the maxima and of a Brownian motion
(BM) on the time intervals and , with . We
determine exact forms of the distribution functions and , and calculate the moments and the
cross-moments with arbitrary integers and . We
show that correlations between and decay as when
, revealing strong memory effects in the statistics of the
BM maxima. We also compute the Pearson correlation coefficient , the
power spectrum of , and we discuss a possibility of extracting the
ensemble-averaged diffusion coefficient in single-trajectory experiments using
a single realization of the maximum process.Comment: 5 pages, 5 figure
The narrow escape problem revisited
The time needed for a particle to exit a confining domain through a small
window, called the narrow escape time (NET), is a limiting factor of various
processes, such as some biochemical reactions in cells. Obtaining an estimate
of the mean NET for a given geometric environment is therefore a requisite step
to quantify the reaction rate constant of such processes, which has raised a
growing interest in the last few years. In this Letter, we determine explicitly
the scaling dependence of the mean NET on both the volume of the confining
domain and the starting point to aperture distance. We show that this
analytical approach is applicable to a very wide range of stochastic processes,
including anomalous diffusion or diffusion in the presence of an external force
field, which cover situations of biological relevance.Comment: 4 pages, 1 figur
Intrinsic Friction of Monolayers Adsorbed on Solid Surfaces
We overview recent results on intrinsic frictional properties of adsorbed
monolayers, composed of mobile hard-core particles undergoing continuous
exchanges with a vapor phase. In terms of a dynamical master equation approach
we determine the velocity of a biased impure molecule - the tracer particle
(TP), constrained to move inside the adsorbed monolayer probing its frictional
properties, define the frictional forces exerted by the monolayer on the TP, as
well as the particles density distribution in the monolayer.Comment: 12 pages, 5 figures, talk at the MRS Fall 2003 Meeting, Boston,
December 1-5, 200
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