This paper is devoted to the study of semilinear degenerate elliptic boundary value problems arising in combustion theory which obey the simple Arrhenius rate law and a general Newton law of heat exchange. We prove that ignition and extinction phenomena occur in the stable steady temperature profile at some critical values of a dimensionless rate of heat production. 2000 Mathematics Subject Cla...

The purpose of this article is to trace the origins of the Arrhenius equation and, in the light of the extensive data on the temperature dependence of reaction rates, assembled in just over a century of experimental endeavor, to assess in what ways its status has changed over the period since it was first proposed. The systematic study of the kinetics of chemical reactions commenced ( I ) mid-w...

In a preceding paper, Langer and Mukhopadhyay [Phys. Rev. E 77, 061505 (2008)] studied the diffusive motion of a tagged molecule in an heterogeneous glass-forming liquid at temperatures just above a glass transition. Among other features of this system, we postulated a relation between heterogeneity and stretched-exponential decay of correlations, and we also confirmed that systems of this kind...

We test the applicability of a living polymerization theory to describe cooperative string-like particle rearrangement clusters (strings) observed in simulations of a coarse-grained polymer melt. The theory quantitatively describes the interrelation between the average string length L, configurational entropy Sconf, and the order parameter for string assembly Φ without free parameters. Combinin...