Quantum Mechanics and Leggett's Inequalities

We show that when the proper description of the behaviour of individual photons or spin 1/2 particles in a spherically symmetric entangled pair is done through the use of the density matrix, the Leggett's inequality is not violated by quantum mechanics.Comment: 7 pages, no figures. A missing global sign in the r.h.s. of eq. (4.10) in section 4 of version 1 (v1) invalidates the conclusion of that particular section, which is then suppressed in the present version (v2

Ecological Invasion, Roughened Fronts, and a Competitor's Extreme Advance: Integrating Stochastic Spatial-Growth Models

Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An ecologically superior invader and a resident species compete for space preemptively. Our general model includes the basic contact process and a variant of the Eden model as special cases. We employ the concept of a "roughened" front to quantify effects of discreteness and stochasticity on invasion; we emphasize the probability distribution of the front-runner's relative position. That is, we analyze the location of the most advanced invader as the extreme deviation about the front's mean position. We find that a class of models with different assumptions about neighborhood interactions exhibit universal characteristics. That is, key features of the invasion dynamics span a class of models, independently of locally detailed demographic rules. Our results integrate theories of invasive spatial growth and generate novel hypotheses linking habitat or landscape size (length of the invading front) to invasion velocity, and to the relative position of the most advanced invader.Comment: The original publication is available at www.springerlink.com/content/8528v8563r7u2742

On a free boundary problem for a two-species weak competition system

[[abstract]]We study a Lotka–Volterra type weak competition model with a free boundary in a one-dimensional habitat. The main objective is to understand the asymptotic behavior of two competing species spreading via a free boundary. We also provide some sufficient conditions for spreading success and spreading failure, respectively. Finally, when spreading successfully, we provide an estimate to show that the spreading speed (if exists) cannot be faster than the minimal speed of traveling wavefront solutions for the competition model on the whole real line without a free boundary.[[incitationindex]]SCI[[booktype]]紙本[[booktype]]電子