Branching random motions, nonlinear hyperbolic systems and traveling waves

A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independient of random motion, and intensities of reverses are defined by a particle's current direction. A soluton of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) have a so-called McKean representation via such processes. Commonly this system possesses traveling-wave solutions. The convergence of solutions with Heaviside terminal data to the travelling waves is discussed.This Paper realizes the McKean programme for the Kolmogorov-Petrovskii-Piskunov equation in this case. The Feynman-Kac formula plays a key role.

Combining structure and dynamics: non-denaturing high-pressure effect on lysozyme in solution

Small-angle X-ray scattering (SAXS) and elastic and quasi-elastic neutron scattering techniques were used to investigate the high-pressure-induced changes on interactions, the low-resolution structure and the dynamics of lysozyme in solution. SAXS data, analysed using a global-fit procedure based on a new approach for hydrated protein form factor description, indicate that lysozyme completely maintains its globular structure up to 1500 bar, but significant modi. cations in the protein-protein interaction potential occur at approximately 600-1000 bar. Moreover, the mass density of the protein hydration water shows a clear discontinuity within this pressure range. Neutron scattering experiments indicate that the global and the local lysozyme dynamics change at a similar threshold pressure. A clear evolution of the internal protein dynamics from diffusing to more localized motions has also been probed. Protein structure and dynamics results have then been discussed in the context of protein-water interface and hydration water dynamics. According to SAXS results, the new configuration of water in the first hydration layer induced by pressure is suggested to be at the origin of the observed local mobility changes.

2-Aminopurine non-radiative decay and emission in aqueous solution: A theoretical study

The minimum energy path along the lowest-lying pi pi* excited state of 2-aminopurine was calculated to elucidate the mechanisms of radiationless decay and emission in water. The sequential Monte Carlo quantum mechanics approach with a multiconfigurational and perturbative description of the wave function was employed to compute the minimum, transition state, and conical intersection. It was found that the barrier in the potential energy surface to access the conical intersection funnel increases in aqueous environment, making the system prone to enlarge the emission yield. These results rationalize the observed enhancement of emission in 2-aminopurine upon increasing of the solvent polarity. (c) 2008 Elsevier B.V. All rights reserved.

VERY RAPIDLY VARYING BOUNDARIES IN EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS. THE CASE of A NON UNIFORMLY LIPSCHITZ DEFORMATION

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Approximate solution for non-Darcy transient film condensation in a porous medium

The problem of non-darcian transient film condensation adjacent to a vertical flat plate embedded in a porous medium has been considered. The governing equation for the boundary layer thickness was obtained by an integral method and solved approximately by the method of integral relations. It is shown that the results are in good agreement with those obtained exactly by the method of characteristics.

Approximate solution for non-darcy transient film condensation in a porous medium

The problem of non-darcian transient film condensation adjacent to a vertical flat plate embedded in a porous medium has been considered. The governing equation for the boundary layer thickness was obtained by an integral method and solved approximately by the method of integral relations. It is shown that the results are in good agreement with those obtained exactly by the method of characteristics.

Generalized integral transform solution for hydrodynamically developing non-Newtonian flows in circular tubes

ABSTRACT: The Generalized Integral Transform Technique (GITT) is applied to the solution of the momentum equations in a hydrodynamically developing laminar flow of a non-Newtonian power-law fluid inside a circular duct. A primitive variables formulation is adopted in order to avoid the singularity of the auxiliary eigenvalue problem in terms of Bessel functions at the centerline of the duct when the GITT approach is applied. Results for the velocity field and friction factor-Reynolds number product are computed for different power-law indices, which are tabulated and graphically presented as functions of the dimensionless coordinates. Critical comparisons with previous results in the literature are also performed, in order to validate the numerical codes developed in the present work and to demonstrate the consistency of the final results.

Analytical solution to the one-dimensional non-uniform absorption of solar radiation in uncoated and coated single glass panes

The analytical solution to the one-dimensional absorption–conduction heat transfer problem inside a single glass pane is presented, which correctly takes into account all the relevant physical phenomena: the appearance of multiple reflections, the spectral distribution of solar radiation, the spectral dependence of optical properties, the presence of possible coatings, the non-uniform nature of radiation absorption, and the diffusion of heat by conduction across the glass pane. Additionally to the well established and known direct absorptance αe, the derived solution introduces a new spectral quantity called direct absorptance moment βe, that indicates where in the glass pane is the absorption of radiation actually taking place. The theoretical and numerical comparison of the derived solution with existing approximate thermal models for the absorption–conduction problem reveals that the latter ones work best for low-absorbing uncoated single glass panes, something not necessarily fulfilled by modern glazings.

T-Q relation and exact solution for the XYZ chain with general non-diagonal boundary terms

We propose that the Baxter's Q-operator for the quantum XYZ spin chain with open boundary conditions is given by the j -> infinity limit of the corresponding transfer matrix with spin-j (i.e., (2j + I)-dimensional) auxiliary space. The associated T-Q relation is derived from the fusion hierarchy of the model. We use this relation to determine the Bethe Ansatz solution of the eigenvalues of the fundamental transfer matrix. The solution yields the complete spectrum of the Hamiltonian. (c) 2006 Elsevier B.V. All rights reserved.