76 research outputs found
Statistical properties of single-file diffusion front
Statistical properties of the front of a semi-infinite system of single-file
diffusion (one dimensional system where particles cannot pass each other, but
in-between collisions each one independently follow diffusive motion) are
investigated. Exact as well as asymptotic results are provided for the
probability density function of (a) the front-position, (b) the maximum of the
front-positions, and (c) the first-passage time to a given position. The
asymptotic laws for the front-position and the maximum front-position are found
to be governed by the Fisher-Tippett-Gumbel extreme value statistics. The
asymptotic properties of the first-passage time is dominated by a
stretched-exponential tail in the distribution. The farness of the front with
the rest of the system is investigated by considering (i) the gap from the
front to the closest particle, and (ii) the density profile with respect to the
front-position, and analytical results are provided for late time behaviors.Comment: 4 revtex page
Work fluctuations for a harmonic oscillator driven by an external random force
The fluctuations of the work done by an external Gaussian random force on a
harmonic oscillator that is also in contact with a thermal bath is studied. We
have obtained the exact large deviation function as well as the complete
asymptotic forms of the probability density function. The distribution of the
work done are found to be non-Gaussian. The steady state fluctuation theorem
holds only if the ratio of the variances, of the external random forcing and
the thermal noise respectively, is less than 1/3. On the other hand, the
transient fluctuation theorem holds (asymptotically) for all the values of that
ratio. The theoretical asymptotic forms of the probability density function are
in very good agreement with the numerics as well as with an experiment.Comment: 6 pages, 4 figure
Record Statistics of Continuous Time Random Walk
The statistics of records for a time series generated by a continuous time
random walk is studied, and found to be independent of the details of the jump
length distribution, as long as the latter is continuous and symmetric.
However, the statistics depend crucially on the nature of the waiting time
distribution. The probability of finding M records within a given time duration
t, for large t, has a scaling form, and the exact scaling function is obtained
in terms of the one-sided Levy stable law. The mean of the ages of the records,
defined as , differs from t/. The asymptotic behaviour of the shortest
and the longest ages of the records are also studied.Comment: 5 pages, 3 figures; EPL published versio
Fluctuation theorem for entropy production of a partial system in the weak coupling limit
Small systems in contact with a heat bath evolve by stochastic dynamics. Here
we show that, when one such small system is weakly coupled to another one, it
is possible to infer the presence of such weak coupling by observing the
violation of the steady state fluctuation theorem for the partial entropy
production of the observed system. We give a general mechanism due to which the
violation of the fluctuation theorem can be significant, even for weak
coupling. We analytically demonstrate on a realistic model system that this
mechanism can be realized by applying an external random force to the system.
In other words, we find a new fluctuation theorem for the entropy production of
a partial system, in the limit of weak coupling.Comment: 7 pages, 3 figure
Hysteresis and Avalanches in the Random Field Ising Model
In this thesis, we discuss nonequilibrium ferromagnetic random field Ising
model (RFIM) with zero temperature Glauber single spin flip dynamics. We
briefly review the hysteresis in ferromagnets and Barkhausen effect. We discuss
some earlier results on the zero temperature RFIM. We also discuss some of the
equilibrium properties of RFIM. We setup the generating function for the
avalanche distribution for arbitrary distribution of the quenched random field
on a Bethe lattice. We explicitly calculate the probability distribution of
avalanches, for the for Bethe lattices with coordination numbers and 3,
for the special case of a rectangular distribution of the random field. We
analyse the self-consistent equations to determine the form of the avalanche
distribution for some general unimodal continuous distributions of the random
field. We derive the self-consistent equations for the magnetization on minor
hysteresis loops on a Bethe lattice, when the external field is varying
cyclically with decreasing magnitudes. We also discuss some properties of
stable configurations, when the external field is varying. We study the 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 find nontrivial dependence of the coercive field on
the coordination number of the lattice.Comment: PhD Thesis, 74 page
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