This paper addresses the question of change of decay rate from exponential to algebraic for diffusive evolution equations. We show how the behaviour of the spectrum of the Dirichlet Laplacian in the two cases yields the passage from exponential decay in bounded domains to algebraic decay or no decay at all in the case of unbounded domains. It is well known that such rates of decay exist: the pu...

We show that at a second order phase transition, of 4 φ like system, a necessary condition for stretched exponential decay of the time dependent structure factor is obeyed. Using the ideas presented in this proof a crude estimate of the decay of the structure factor is obtained and shown to yield stretched exponential decay under very reasonable conditions.

The fluorescence decay in fluorescence lifetime imaging (FLIM) is typically fitted to a multi-exponential model with discrete lifetimes. The interaction between fluorophores in heterogeneous samples (e.g. biological tissue) can, however, produce complex decay characteristics that do not correspond to such models. Although they appear to provide a better fit to fluorescence decay data than the a...

We consider homogeneous solutions of the Vlasov—Fokker—Planck equation in plasma theory proving that they reach the equilibrium with a time exponential rate in various norms. By Csiszar—Kullback inequality, strong ̧1-convergence is a consequence of the ‘sharp’ exponential decay of relative entropy and relative Fisher information. To prove exponential strong decay in Sobolev spaces Hk, k*0, we ta...

We present results on dynamical processes that exhibit a stretched exponential relaxation. When the relaxation is a result of two competing exponential processes, the size of the system, although macroscopic, play a dominant role. There exist a crossover time t× that depends logarithmically on the size of the system, above which, the relaxation changes from a stretched exponential to a simple e...

Influence of several operating conditions on luminance decay in a green organic light-emitting diode with tris (8-hydrooxyquinoline) aluminum (Alq3) has been investigated by the analysis of its luminance decay curves. The conditions varied were operating current mode (DC or pulse) and environmental temperature (25–120 oC). The decay curves measured were analyzed by fitting the curves to stretch...

Several important aspects of fluorescence decay analysis are addressed and tested against new experimental measurements. A simulated-annealing method is described for deconvoluting the instrument response function from a measured fluorescence decay to yield the true decay, which is more convenient for subsequent fitting. The method is shown to perform well against the conventional approach, whi...

The advection and diffusion of a passive scalar is investigated for a map of the 2-torus. The map is chaotic, and the limit of almost-uniform stretching is considered. This allows an analytic understanding of the transition from a phase of constant scalar variance (for short times) to exponential decay (for long times). This transition is embodied in a short superexponential phase of decay. The...

We present novel Bayesian methods for the analysis of exponential decay data that exploit the evidence carried by every detected decay event and enables robust extension to advanced processing. Our algorithms are presented in the context of fluorescence lifetime imaging microscopy (FLIM) and particular attention has been paid to model the time-domain system (based on time-correlated single phot...