``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

Network Evolution Induced by the Dynamical Rules of Two Populations

We study the dynamical properties of a finite dynamical network composed of two interacting populations, namely; extrovert ($a$) and introvert ($b$). In our model, each group is characterized by its size ($N_a$ and $N_b$) and preferred degree ($\kappa_a$ and $\kappa_b\ll\kappa_a$). The network dynamics is governed by the competing microscopic rules of each population that consist of the creation and destruction of links. Starting from an unconnected network, we give a detailed analysis of the mean field approach which is compared to Monte Carlo simulation data. The time evolution of the restricted degrees \moyenne{k_{bb}} and \moyenne{k_{ab}} presents three time regimes and a non monotonic behavior well captured by our theory. Surprisingly, when the population size are equal $N_a=N_b$, the ratio of the restricted degree \theta_0=\moyenne{k_{ab}}/\moyenne{k_{bb}} appears to be an integer in the asymptotic limits of the three time regimes. For early times (defined by $t<t_1=\kappa_b$) the total number of links presents a linear evolution, where the two populations are indistinguishable and where $\theta_0=1$. Interestingly, in the intermediate time regime (defined for $t_1<t<t_2\propto\kappa_a$ and for which $\theta_0=5$), the system reaches a transient stationary state, where the number of contacts among introverts remains constant while the number of connections is increasing linearly in the extrovert population. Finally, due to the competing dynamics, the network presents a frustrated stationary state characterized by a ratio $\theta_0=3$.Comment: 21 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 $T$. 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 $T$ is set below the critical temperature.Comment: published version, 2 figures, 5 page

Energy flux near the junction of two Ising chains at different temperatures

We consider a system in a non-equilibrium steady state by joining two semi-infinite Ising chains coupled to thermal reservoirs with {\em different} temperatures, $T$ and $T^{\prime}$. To compute the energy flux from the hot bath through our system into the cold bath, we exploit Glauber heat-bath dynamics to derive an exact equation for the two-spin correlations, which we solve for $T^{\prime}=\infty$ and arbitrary $T$. We find that, in the $T'=\infty$ sector, the in-flux occurs only at the first spin. In the $T<\infty$ sector (sites $x=1,2,...$), the out-flux shows a non-trivial profile: $F(x)$. Far from the junction of the two chains, $F(x)$ decays as $e^{-x/\xi}$, where $\xi$ is twice the correlation length of the {\em equilibrium} Ising chain. As $T\rightarrow 0$, this decay crosses over to a power law ($x^{-3}$) and resembles a "critical" system. Simulations affirm our analytic results.Comment: 6 pages, 4 figures, submitted to EP

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