67 research outputs found

### Application of importance sampling to the computation of large deviations in non-equilibrium processes

We present an algorithm for finding the probabilities of rare events in
nonequilibrium processes. The algorithm consists of evolving the system with a
modified dynamics for which the required event occurs more frequently. By
keeping track of the relative weight of phase-space trajectories generated by
the modified and the original dynamics one can obtain the required
probabilities. The algorithm is tested on two model systems of steady-state
particle and heat transport where we find a huge improvement from direct
simulation methods.Comment: 5 pages, 4 figures; some modification

### Dynamics of bootstrap percolation

Bootstrap percolation transition may be first order or second order, or it
may have a mixed character where a first order drop in the order parameter is
preceded by critical fluctuations. Recent studies have indicated that the mixed
transition is characterized by power law avalanches, while the continuous
transition is characterized by truncated avalanches in a related sequential
bootstrap process. We explain this behavior on the basis of a through
analytical and numerical study of the avalanche distributions on a Bethe
lattice.Comment: Proceedings of the International Workshop and Conference on
Statistical Physics Approaches to Multidisciplinary Problems, IIT Guwahati,
India, 7-13 January 200

### Accurate statistics of a flexible polymer chain in shear flow

We present exact and analytically accurate results for the problem of a
flexible polymer chain in shear flow. Under such a flow the polymer tumbles,
and the probability distribution of the tumbling times $\tau$ of the polymer
decays exponentially as $\sim \exp(-\alpha \tau/\tau_0)$ (where $\tau_0$ is the
longest relaxation time). We show that for a Rouse chain, this nontrivial
constant $\alpha$ can be calculated in the limit of large Weissenberg number
(high shear rate) and is in excellent agreement with our simulation result of
$\alpha \simeq 0.324$. We also derive exactly the distribution functions for
the length and the orientational angles of the end-to-end vector of the
polymer.Comment: 4 pages, 2 figures. Minor changes. Texts differ slightly from the PRL
published versio

### Crowding at the Front of the Marathon Packs

We study the crowding of near-extreme events in the time gaps between
successive finishers in major international marathons. Naively, one might
expect these gaps to become progressively larger for better-placing finishers.
While such an increase does indeed occur from the middle of the finishing pack
down to approximately 20th place, the gaps saturate for the first 10-20
finishers. We give a probabilistic account of this feature. However, the data
suggests that the gaps have a weak maximum around the 10th place, a feature
that seems to have a sociological origin.Comment: 5 pages, 2 figures; version 2: published manuscript with various
changes in response to referee comments and some additional improvement

### Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

We investigate the motion of a run-and-tumble particle (RTP) in one
dimension. We find the exact probability distribution of the particle with and
without diffusion on the infinite line, as well as in a finite interval. In the
infinite domain, this probability distribution approaches a Gaussian form in
the long-time limit, as in the case of a regular Brownian particle. At
intermediate times, this distribution exhibits unexpected multi-modal forms. In
a finite domain, the probability distribution reaches a steady state form with
peaks at the boundaries, in contrast to a Brownian particle. We also study the
relaxation to the steady state analytically. Finally we compute the survival
probability of the RTP in a semi-infinite domain. In the finite interval, we
compute the exit probability and the associated exit times. We provide
numerical verifications of our analytical results

### Exact Expressions for Minor Hysteresis Loops in the Random Field Ising Model on a Bethe Lattice at Zero Temperature

We obtain exact expressions for the minor hysteresis loops in the
ferromagnetic random field Ising model on a Bethe lattice at zero temperature
in the case when the driving field is cycled infinitely slowly.Comment: Replaced with the published versio

### Hysteresis in the Random Field Ising Model and Bootstrap Percolation

We study hysteresis in the random-field Ising model with an asymmetric
distribution of quenched fields, in the limit of low disorder in two and three
dimensions. We relate the spin flip process to bootstrap percolation, and show
that the characteristic length for self-averaging $L^*$ increases as $exp(exp
(J/\Delta))$ in 2d, and as $exp(exp(exp(J/\Delta)))$ in 3d, for disorder
strength $\Delta$ much less than the exchange coupling J. For system size $1 <<
L < L^*$, the coercive field $h_{coer}$ varies as $2J - \Delta \ln \ln L$ for
the square lattice, and as $2J - \Delta \ln \ln \ln L$ on the cubic lattice.
Its limiting value is 0 for L tending to infinity, both for square and cubic
lattices. For lattices with coordination number 3, the limiting magnetization
shows no jump, and $h_{coer}$ tends to J.Comment: 4 pages, 4 figure

### A Note on Limit Shapes of Minimal Difference Partitions

We provide a variational derivation of the limit shape of minimal difference partitions and discuss the link with exclusion statistic

### Record statistics in random vectors and quantum chaos

The record statistics of complex random states are analytically calculated,
and shown that the probability of a record intensity is a Bernoulli process.
The correlation due to normalization leads to a probability distribution of the
records that is non-universal but tends to the Gumbel distribution
asymptotically. The quantum standard map is used to study these statistics for
the effect of correlations apart from normalization. It is seen that in the
mixed phase space regime the number of intensity records is a power law in the
dimensionality of the state as opposed to the logarithmic growth for random
states.Comment: figures redrawn, discussion adde

### Performance Limitations of Flat Histogram Methods and Optimality of Wang-Landau Sampling

We determine the optimal scaling of local-update flat-histogram methods with
system size by using a perfect flat-histogram scheme based on the exact density
of states of 2D Ising models.The typical tunneling time needed to sample the
entire bandwidth does not scale with the number of spins N as the minimal N^2
of an unbiased random walk in energy space. While the scaling is power law for
the ferromagnetic and fully frustrated Ising model, for the +/- J
nearest-neighbor spin glass the distribution of tunneling times is governed by
a fat-tailed Frechet extremal value distribution that obeys exponential
scaling. We find that the Wang-Landau algorithm shows the same scaling as the
perfect scheme and is thus optimal.Comment: 5 pages, 6 figure

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