957 research outputs found
Collapse or transformation? Regeneration and innovation at the turn of the first millennium BC at Arslantepe, Turkey
Ongoing excavations at Arslantepe in south-eastern Turkey are revealing settlement continuity spanning two crucial phases at the transition from the second to the first millennium BC: the post-Hittite period and the development of Syro-Anatolian societies
Entropy production of resetting processes
Stochastic systems that undergo random restarts to their initial state have
been widely investigated in recent years, both theoretically and in
experiments. Oftentimes, however, resetting to a fixed state is impossible due
to thermal noise or other limitations. As a result, the system configuration
after a resetting event is random. Here, we consider such a resetting protocol
for an overdamped Brownian particle in a confining potential . We assume
that the position of the particle is reset at a constant rate to a random
location , drawn from a distribution . To investigate the
thermodynamic cost of resetting, we study the stochastic entropy production
. We derive a general expression for the average entropy
production for any , and the full distribution of
the entropy production for . At late times, we show that this
distribution assumes the large-deviation form , with . We
compute the rate function and the exponent for exponential
and Gaussian resetting distributions. In the latter case, we find the anomalous
exponent and show that has a first-order singularity at
a critical value of , corresponding to a real-space condensation transition.Comment: 29 pages, 6 figure
Nonlinear-Cost Random Walk: exact statistics of the distance covered for fixed budget
We consider the Nonlinear-Cost Random Walk model in discrete time introduced
in [Phys. Rev. Lett. 130, 237102 (2023)], where a fee is charged for each jump
of the walker. The nonlinear cost function is such that slow/short jumps incur
a flat fee, while for fast/long jumps the cost is proportional to the distance
covered. In this paper we compute analytically the average and variance of the
distance covered in steps when the total budget is fixed, as well as
the statistics of the number of long/short jumps in a trajectory of length ,
for the exponential jump distribution. These observables exhibit a very rich
and non-monotonic scaling behavior as a function of the variable , which
is traced back to the makeup of a typical trajectory in terms of long/short
jumps, and the resulting "entropy" thereof. As a byproduct, we compute the
asymptotic behavior of ratios of Kummer hypergeometric functions when both the
first and last arguments are large. All our analytical results are corroborated
by numerical simulations.Comment: 31 pages, 8 figure
First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension
We consider a single run-and-tumble particle (RTP) moving in one dimension.
We assume that the velocity of the particle is drawn independently at each
tumbling from a zero-mean Gaussian distribution and that the run times are
exponentially distributed. We investigate the probability distribution
of the position of the particle after runs, with . We show that
in the regime the distribution has a large deviation
form with a rate function characterized by a discontinuous derivative at the
critical value . The same is true for due to the symmetry of
. We show that this singularity corresponds to a first-order
condensation transition: for a single large jump dominates the RTP
trajectory. We consider the participation ratio of the single-run displacements
as the order parameter of the system, showing that this quantity is
discontinuous at . Our results are supported by numerical simulations
performed with a constrained Markov chain Monte Carlo algorithm.Comment: 24 pages, 10 figure
Universal survival probability for a correlated random walk and applications to records
We consider a model of space-continuous one-dimensional random walk with
simple correlation between the steps: the probability that two consecutive
steps have same sign is with . The parameter allows thus
to control the persistence of the random walk. We compute analytically the
survival probability of a walk of steps, showing that it is independent of
the jump distribution for any finite . This universality is a consequence of
the Sparre-Andersen theorem for random walks with uncorrelated and symmetric
steps. We then apply this result to derive the distribution of the step at
which the random walk reaches its maximum and the record statistics of the
walk, which show the same universality. In particular, we show that the
distribution of the number of records for a walk of steps is the same
as for a random walk with uncorrelated and
symmetrically distributed steps. We also show that in the regime where and with , this model converges to the
run-and-tumble particle, a persistent random walk often used to model the
motion of bacteria. Our theoretical results are confirmed by numerical
simulations.Comment: 28 pages, 10 figure
Servi delle Muse e canti trenodici (in margine a Eur. Ph. 1499)
In Eur. Ph. 1499 some scholars assumes μουσοπόλος as an adjective, but the occurrences of the term and the comparison with Sapph. fr. 150 V. suggest that it could be a noun; therefore, also the structure of the line should be reconsidered
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