Refined Simulations of the Reaction Front for Diffusion-Limited Two-Species Annihilation in One Dimension

Extensive simulations are performed of the diffusion-limited reaction A$+$B$\to 0$ in one dimension, with initially separated reagents. The reaction rate profile, and the probability distributions of the separation and midpoint of the nearest-neighbour pair of A and B particles, are all shown to exhibit dynamic scaling, independently of the presence of fluctuations in the initial state and of an exclusion principle in the model. The data is consistent with all lengthscales behaving as $t^{1/4}$ as $t\to\infty$. Evidence of multiscaling, found by other authors, is discussed in the light of these findings.Comment: Resubmitted as TeX rather than Postscript file. RevTeX version 3.0, 10 pages with 16 Encapsulated Postscript figures (need epsf). University of Geneva preprint UGVA/DPT 1994/10-85

Are Currency Crises Low-State Equilibria? An Empirical, Three-Interest-Rate Model

Suppose that the dynamics of the macroeconomy were given by (partly) random fluctuations between two equilibria: "good" and "bad." One would interpret currency crises (or recessions) as a shift from the good equilibrium to the bad. In this paper, the authors specify a dynamic investment-savings-aggregate-supply (IS-AS) model, determine its closed-form solution, and examine numerically its comparative statics. The authors estimate the model via maximum likelihood, using data for Argentina, Canada, and Turkey. Since the data show no support for the multiple-equilibrium explanation of fluctuations, the authors cast doubt on the third-generation models of currency crisis.Uncertainty and monetary policy

The Reaction-Diffusion Front for A+B→∅A+B \to\emptyset in One Dimension

We study theoretically and numerically the steady state diffusion controlled reaction $A+B\rightarrow\emptyset$, where currents $J$ of $A$ and $B$ particles are applied at opposite boundaries. For a reaction rate $\lambda$, and equal diffusion constants $D$, we find that when $\lambda J^{-1/2} D^{-1/2}\ll 1$ the reaction front is well described by mean field theory. However, for $\lambda J^{-1/2} D^{-1/2}\gg 1$, the front acquires a Gaussian profile - a result of noise induced wandering of the reaction front center. We make a theoretical prediction for this profile which is in good agreement with simulation. Finally, we investigate the intrinsic (non-wandering) front width and find results consistent with scaling and field theoretic predictions.Comment: 11 pages, revtex, 4 separate PostScript figure

Critical Temperature of a Trapped Bose Gas: Mean-Field Theory and Fluctuations

We investigate the possibilities of distinguishing the mean-field and fluctuation effects on the critical temperature of a trapped Bose gas with repulsive interatomic interactions. Since in a direct measurement of the critical temperature as a function of the number of trapped atoms these effects are small compared to the ideal gas results, we propose to observe Bose-Einstein condensation by adiabatically ramping down the trapping frequency. Moreover, analyzing this adiabatic cooling scheme, we show that fluctuation effects can lead to the formation of a Bose condensate at frequencies which are much larger than those predicted by the mean-field theory.Comment: 4 pages of ReVTeX and 3 figures. Submitted to Physical Review

Decay Process for Three - Species Reaction - Diffusion System

We propose the deterministic rate equation of three-species in the reaction - diffusion system. For this case, our purpose is to carry out the decay process in our three-species reaction-diffusion model of the form $A+B+C\to D$. The particle density and the global reaction rate are also shown analytically and numerically on a two-dimensional square lattice with the periodic boundary conditions. Especially, the crossover of the global reaction rate is discussed in both early-time and long-time regimes.Comment: 6 pages, 3 figures, Late

Black hole quasinormal modes using the asymptotic iteration method

In this article we show that the asymptotic iteration method (AIM) allows one to numerically find the quasinormal modes of Schwarzschild and Schwarzschild de Sitter (SdS) black holes. An added benefit of the method is that it can also be used to calculate the Schwarzschild anti-de Sitter (SAdS) quasinormal modes for the case of spin zero perturbations. We also discuss an improved version of the AIM, more suitable for numerical implementation.Comment: 10 pages, LaTeX; references added; substantially expanded versio

Graviton emission from simply rotating Kerr-de Sitter black holes: Transverse traceless tensor graviton modes

In this article we present results for tensor graviton modes (in seven dimensions and greater, $n\geq 3$) for greybody factors of Kerr-dS black holes and for Hawking radiation from simply rotating (n+4)-dimensional Kerr black holes. Although there is some subtlety with defining the Hawking temperature of a Kerr-dS black hole, we present some preliminary results for emissions assuming the standard Hawking normalization and a Bousso-Hawking-like normalization.Comment: 12 pages, 18 figure

Angular Eigenvalues of Higher-Dimensional Kerr-(A)dS Black Holes with Two Rotations

In this paper, following the work of Chen, L\"u and Pope, we present the general metric for Kerr-(A)dS black holes with two rotations. The corresponding Klein-Gordon equation is separated explicitly, from which we develop perturbative expansions for the angular eigenvalues in powers of the rotation parameters with $D\geq 6$.Comment: 10 pages, no figures. To appear in the proceedings of 2011 Shanghai Asia-Pacific School and Workshop on Gravitatio