80 research outputs found
``Weather'' Records: Musings on Cold Days after a Long Hot Indian Summer
We present a simple, pedagogical introduction to the statistics of extreme
values. Motivated by a string of record high temperatures in December 1998, we
consider the distribution, averages and lifetimes for a simplified model of
such ``records.'' Our ``data'' are sequences of independent random numbers all
of which are generated from the same probability distribution. A remarkable
universality emerges: a number of results, including the lifetime histogram,
are universal, that is, independent of the underlying distribution.Comment: 14 pages, 3 figures. Invited paper for American Journal of Physic
Dynamic scaling in vacancy-mediated disordering
We consider the disordering dynamics of an interacting binary alloy with a
small admixture of vacancies which mediate atom-atom exchanges. Starting from a
perfectly phase-segregated state, the system is rapidly heated to a temperature
in the disordered phase. A suitable disorder parameter, namely, the number of
broken bonds, is monitored as a function of time. Using Monte Carlo simulations
and a coarse-grained field theory, we show that the late stages of this process
exhibit dynamic scaling, characterized by a set of scaling functions and
exponents. We discuss the universality of these exponents and comment on some
subtleties in the early stages of the disordering process.Comment: 15 pages, 6 figure
Convection cells induced by spontaneous symmetry breaking
Ubiquitous in nature, convection cells are a clear signature of systems
out-of-equilibrium. Typically, they are driven by external forces, like gravity
(in combination with temperature gradients) or shear. In this article, we show
the existence of such cells in possibly the simplest system, one that involves
only a temperature gradient. In particular, we consider an Ising lattice gas on
a square lattice, in contact with two thermal reservoirs, one at infinite
temperature and another at . When this system settles into a non-equilibrium
stationary state, many interesting phenomena exist. One of these is the
emergence of convection cells, driven by spontaneous symmetry breaking when
is set below the critical temperature.Comment: published version, 2 figures, 5 page
Extraordinary variability and sharp transitions in a maximally frustrated dynamic network
Using Monte Carlo and analytic techniques, we study a minimal dynamic network
involving two populations of nodes, characterized by different preferred
degrees. Reminiscent of introverts and extroverts in a population, one set of
nodes, labeled \textit{introverts} (), prefers fewer contacts (a lower
degree) than the other, labeled \textit{extroverts} (). As a starting point,
we consider an \textit{extreme} case, in which an simply cuts one of its
links at random when chosen for updating, while an adds a link to a random
unconnected individual (node). The model has only two control parameters,
namely, the number of nodes in each group, and ). In the steady
state, only the number of crosslinks between the two groups fluctuates, with
remarkable properties: Its average () remains very close to 0 for all
or near its maximum () if
. At the transition (), the fraction
wanders across a substantial part of , much like a pure random walk.
Mapping this system to an Ising model with spin-flip dynamics and unusual
long-range interactions, we note that such fluctuations are far greater than
those displayed in either first or second order transitions of the latter.
Thus, we refer to the case here as an `extraordinary transition.' Thanks to the
restoration of detailed balance and the existence of a `Hamiltonian,' several
qualitative aspects of these remarkable phenomena can be understood
analytically.Comment: 6 pages, 3 figures, accepted for publication in EP
A Lattice Gas Coupled to Two Thermal Reservoirs: Monte Carlo and Field Theoretic Studies
We investigate the collective behavior of an Ising lattice gas, driven to
non-equilibrium steady states by being coupled to {\em two} thermal baths.
Monte Carlo methods are applied to a two-dimensional system in which one of the
baths is fixed at infinite temperature. Both generic long range correlations in
the disordered state and critical poperties near the second order transition
are measured. Anisotropic scaling, a key feature near criticality, is used to
extract and some critical exponents. On the theoretical front, a
continuum theory, in the spirit of Landau-Ginzburg, is presented. Being a
renormalizable theory, its predictions can be computed by standard methods of
-expansions and found to be consistent with simulation data. In
particular, the critical behavior of this system belongs to a universality
class which is quite {\em different} from the uniformly driven Ising model.Comment: 21 pages, 15 figure
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