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...

Finite time singularity formation in a fourth order nonlinear parabolic partial differential equation (PDE) is analyzed. The PDE is a variant of a ubiquitous model found in the field of microelectromechanical systems (MEMS) and is studied on a one-dimensional (1D) strip and the unit disc. The solution itself remains continuous at the point of singularity while its higher derivatives diverge, a ...

For most mechanisms of chemical reactions and molecular photophysical processes the time evolution of the concentration of the intervening species cannot be obtained analytically. The pre-equilibrium approximation is one of several useful approximation methods that allow the derivation of explicit solutions and simplify numerical solutions. In this work, a general view of the pre-equilibrium ap...

Shraddha Sharma, Uma Divakaran, Anatoli Polkovnikov, and Amit Dutta Department of Physics, Indian Institute of Technology, Kanpur 208 016, India UM-DAE Center for Excellence in Basic Sciences, Mumbai 400 098, India Department of Physics, Boston University, 590 Commonwealth Ave., Boston, MA 02215, USA We study the slow quenching dynamics (characterized by an inverse rate, τ−1) of a onedimensiona...

A large parameter mismatch can induce amplitude death in two instantaneously coupled oscillators. Alternatively, a time delay in the coupling can induce amplitude death in two identical oscillators. We unify the mechanism of quenching of oscillation in coupled oscillators, either by a large parameter mismatch or a delay coupling, by a common lag scenario that is, surprisingly, different from th...

The inverse modeling of heat transfer involves the estimation of boundary conditions from the knowledge of thermal history inside a heat conducting body. Inverse analysis is extremely useful in modeling of contact heat transfer at interfaces of engineering surfaces during materials processing. In the present work, the one-dimensional transient heat conduction equation was inversely modeled in b...

We present a nonlinear multigrid method to solve the Cahn–Hilliard (CH) equation on nonuniform grids. The CH equation was originally proposed as a mathematical model to describe phase separation phenomena after the quenching of binary alloys. The model has the characteristics of thin diffusive interfaces. To resolve the sharp interfacial transition, we need a very fine grid, which is computatio...

Consider the parabolic problem u t div (a(u;ru)ru) = u p (1) for t > 0, x 2 R n under initial and boundary conditions u = 1, say. Since p is assumed positive, the right hand side becomes singular as u ! 0. When u reaches zero in nite or in nite time, one says that the solution quenches in nite or in nite time. This article gives a survey of results on this kind of problem and emphasizes those t...

The excited-state reversible reaction of a neutral particle and a charged particle in an external electric field is studied in three dimensions. This work extends the previous investigation for the ground-state reaction [S. Y. Reigh et al., J. Chem. Phys. 129, 234501 (2008)] to the excited-state reaction with two different lifetimes and quenching. The analytic series solutions for all the funda...

We present a detailed numerical study of the Gough & McIntyre model for the solar tachocline. This model explains the uniformity of the rotation profile observed in the bulk of the radiative zone by the presence of a large-scale primordial magnetic field confined below the tachocline by flows originating from within the convection zone. We attribute the failure of previous numerical attempts at...