A realistic description of the kinetics of excited-state proton transfer to solvent ~PTTS! involves several simultaneous processes. Perhaps most well-studied is the reversibility of this diffusion-influenced reaction, leading to the t asymptotic decay of the initially bound state. This shows that the solvated geminate proton may recombine with the base adiabatically, in the excited electronic s...

There are many situations in which a strong electromagnetic field may be approximated as a fixed background. Going beyond this approximation, i.e. accounting for the back-reaction of quantum process on the field, is however challenging. Here we develop an approach to this problem which is a straightforward extension of background field methods. The approach follows from the observation that sca...

Abstract. In this paper, we propose to use the tailored-finite-point method (TFPM) for a type of steady-state reaction-diffusion problems in two dimensions. Three tailored finite point schemes are constructed for the given problem. Our finite point method has been tailored to some particular properties of the problem. Therefore, our TFPM satisfies the discrete maximum principle automatically. W...

We study the following nonlinear elliptic equation 8 < : u ? u + (e u R e u ? 1 jj) = 0 in ; @u @ = 0 on @; where is a smooth bounded domain in R 2. This equation arises in the study of stationary solutions of a chemotaxis system proposed by Keller and Segel. Under the condition that > jj ? 1 ; 6 = 4m for m = 1; 2; :::, where 1 is the rst (nonzero) eigenvalue of ? under the Neumann boundary con...

In this paper, we present a rigorous proof of the quasi– steady–state approximation (QSSA) used in chemistry, in two different settings: the first one corresponds to reaction–diffusion equations, while the second one is devoted to ODEs, with a particular attention to the effect of temperature.

The photodynamics of bacteriorhodopsin were studied by transient absorption and gain measurements after excitation with femtosecond pulses at 620 nm. With probing pulses at longer wavelengths (A> 770 nm) the previously reported formation of the J intermediate (with a time constant of 500f 100 fs) was confirmed. With probing pulses around 700 nm, a faster process with a relaxation time of 200 rt...