Research for Research

Syndicate content
DIFFUSION THEORY OF REACTION RATES, I: FORMULATION AND EINSTEIN-SMOLUCHOWSKI APPROXIMATION
February 1, 1981

The diffusion model of reaction rates is rederived and extended. Only the diffusion model in position space is considered. The diffusion equations are non-dimensionalized and a number of singular perturbation problems are obtained. By using the diffusion model, a number of problems involving reaction rate theory can be treated. A new form of transition state theory is derived. Reaction rate constants, transmission coefficients, and the lifetime of the activated complex are calculated. It is also shown how absorption spectra can also be derived by use of the diffusion model.

Read More | Download Report
WKB EXPANSIONS BY PATH INTEGRALS, WITH APPLICATIONS TO THE ANHARMONIC OSCILLATOR
February 1, 1981
This paper is composed in three sections. The first section discusses linear mappings in path space and uses them to extend widely the class of functionals one can integrate. The second section studies the relationship between the equation of small disturbances and the path integral approach. The third section presents a detailed discussion of the classical and quantum-mechanical anharmonic oscillator (leading to a standard prototype field theory), as an application of the preceding material.
Read More | Download Report
STOCHASTIC MECHANICS OF MOLECULE-ION MOLECULE REACTION
February 1, 1981

This paper provides a treatment of molecule-ion molecule reactions based on stochastic mechanics. Stochastic mechanics is a semi-classical theory in which one assumes that particles move as a stochastic diffusion process. It is shown that the reaction probability and reaction rate can be determined from the solution of certain Partial Differential Equations (PDE). Asymptotic solutions of these PDE are constructed in terms of incomplete special functions. The results derived using stochastic mechanics are compared with results derived using other semi-classical approximations.

Read More | Download Report
Evaluation of Kinetic Theory Collision Integrals Using the Generalized Phase Shift Approach
February 1, 1981
This paper shows the collision integrals arising in the treatment of binary gas mixtures in applied magnetic fields to be straight forward generalizations of those partially evaluated by L.W. Hunter and R.F. Snider, and utilized by Hunter in his treatment of the effects of a magnetic field on the shear viscosity and thermal conductivity of single component diatomic gases. These collision integrals are further developed by use of the generalized phase shift formalism, which permits the evaluation of several summations and angle integrations and lead to considerable simplification of the expressions.
Read More | Download Report
THE SEMICLASSICAL EXPANSION TO THE ANHARMONIC OSCILLATOR PROPAGATOR
February 1, 1981

This paper shows how to calculate the terms of a semiclassical expansion of the quantum-mechanical propagator corresponding to a quartic anharmonic-oscillator potential.

Read More | Download Report
ON THE SEMI-CLASSICAL EXPANSION IN QUANTUM MECHANICS FOR ARBITRARY HAMILTONIANS
February 1, 1981
The purpose of this paper is to extend to a very wide class of Hamiltonians the range of validity of a well-known and oft-used expression for the semi-classical (WKB) approximation to the quantum-mechanical propagator K(q b,t b;q a, t a) or probability amplitude that a particle at q a at time t a will arrive at q b at time t b.
Read More | Download Report
FRANCK-CONDON THEORY OF CHEMICAL DYNAMICS. VI. ANGULAR DISTRIBUTIONS OF REACTION PRODUCTS
February 1, 1981
The Franck-Condon model and additional approximations are applied in this paper to determine product angular distributions of the type A + BC -> AB + C. The interest is in the relation of the anular distribution to certain features of the potential energy surface, the possibility of finding reduced variables, that is, scaling factors, with which to compare chemical reactions and the issue of the independence of angular from energy distributions of reaction products.
Read More
TEMPERATURE AND CURRENT DEPENDENCE OF DEGRADATION IN RED-EMITTING GAP LEDS
February 1, 1981

Experimental studies have been performed on several aspects of the degradation of electroluminescent quantum efficiency in Zn,0-doped GaP light emitting diodes. The dependence of degradation on stress temperature, stress current (experienced during accelerated aging) and measurement current (at which quantum efficiency is evaluated) has been empirically determined from experiments on several lots of devices. It is shown that degradation is dominated by a decrease in bulk p-side radiative recombination efficiency. The degradation of other factors (such as injection efficiency and injection ratio) contributing to the overall electroluminescent efficiency has only a secondary effect. Moreover, it is shown empirically that the dependences of degradation on temperature and stress current are separable.

Read More | Download Report
A DIFFUSION MODEL FOR GAP RED LED DEGRADATION
February 1, 1981
In this paper, the long-term degradation of GaP red Light Emitting Diodes (LEDs) is analyzed in terms of a diffusion model.
Read More | Download Report
RELAXATION AT CRITICAL POINTS, DETERMINISTIC AND STOCHASTIC THEORY
February 1, 1981

A generalized critical point is characterized by totally non-linear dynamics. The deterministic and stochastic theory of relaxation is formulated at such a point. Canonical problems are used to motivate the general solutions. In the deterministic theory, it is shown that at the critical point certain modes have polynomial (rather than exponential) growth or decay. The stochastic relaxation rates can be calculated in terms of various incomplete special functions. First, a substrate inhibited reaction (marginal type dynamical system). Second, the relaxation of a mean field ferromagnet. Third, the relaxation of a critical harmonic oscillator is considered.

Read More | Download Report