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

Fluctuations and correlations in population models with age structure

We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent death probability, as well as a variable reproduction probability for each individual as a function of age. We first solve for the steady-state of the model in mean field theory, before developing analytic techniques to compute Gaussian fluctuation corrections around the mean field fixed point. Our computations are found to be in good agreement with Monte-Carlo simulations. Finally we discuss how similar methods may be applied to fluctuations in continuous time population models.Comment: 4 page

Saddles, Arrows, and Spirals: Deterministic Trajectories in Cyclic Competition of Four Species

Population dynamics in systems composed of cyclically competing species has been of increasing interest recently. Here, we investigate a system with four or more species. Using mean field theory, we study in detail the trajectories in configuration space of the population fractions. We discover a variety of orbits, shaped like saddles, spirals, and straight lines. Many of their properties are found explicitly. Most remarkably, we identify a collective variable which evolves simply as an exponential: $\mathcal{Q}e^{\lambda t}$, where $\lambda$ is a function of the reaction rates. It provides information on the state of the system for late times (as well as for $t\rightarrow -\infty$). We discuss implications of these results for the evolution of a finite, stochastic system. A generalization to an arbitrary number of cyclically competing species yields valuable insights into universal properties of such systems.Comment: 15 pages, 5 figures, submitted to Physical Review

Roughening transition, surface tension and equilibrium droplet shapes in a two-dimensional Ising system

The exact surface tension for all angles and temperatures is given for the two-dimensional square Ising system with anisotropic nearest-neighbour interactions. Using this in the Wulff construction, droplet shapes are computed and illustrated. Letting temperature approach zero allows explicit study of the roughening transition in this model. Results are compared with those of the solid-on-solid approximation

Comment on `Renormalization-Group Calculation of the Dependence on Gravity of the Surface Tension and Bending Rigidity of a Fluid Interface'

It is shown that the interface model introduced in Phys. Rev. Lett. 86, 2369 (2001) violates fundamental symmetry requirements for vanishing gravitational acceleration $g$, so that its results cannot be applied to critical properties of interfaces for $g\to 0$.Comment: A Comment on a recent Letter by J.G. Segovia-L\'opez and V. Romero-Roch\'{\i}n, Phys. Rev. Lett.86, 2369 (2001). Latex file, 1 page (revtex

Study of the superconducting properties of the Bi-Ca-Sr-Cu-O system

High Temperature Superconductivity in the Bi-Ca-Sr-Cu-O System has been observed and has attracted considerable attention in 1988. The 80 K superconductivity phase has been identified to have a composition of Bi2CaSr2Cu2Ox, while the 110 K phase as reported in the literature has a possible composition of Bi2Ca2Sr2Cu3Ox. Researchers present here a study of the electrical properties of bulk samples of the slowly cooled and rapidly quenched 2:1:2:2 system. The samples used in this study were prepared from appropriate amounts of Bi2O3, CuO, SrCO3, CaCO3