Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Institution
- Publication Type
Articles 1 - 3 of 3
Full-Text Articles in Physics
Transitional Probabilities For The Four-State Random Walk On A Lattice In The Presence Of Partially Reflecting Boundaries, Ramakrishna Janaswamy
Transitional Probabilities For The Four-State Random Walk On A Lattice In The Presence Of Partially Reflecting Boundaries, Ramakrishna Janaswamy
Ramakrishna Janaswamy
The four-state random walk (4RW) model, wherein the particle is endowed with two states of spin and two states of directional motion in each space coordinate, permits a stochastic solution of the Schrödinger equation (or the equivalent parabolic equation) without resorting to the usual analytical continuation in complex space of the particle trajectories. Analytical expressions are derived here for the various transitional probabilities in a 4RW by employing generating functions and eigenfunction expansions when the particle moves on a 1+1 space-time lattice with two-point boundary conditions. The most general case of dissimilar boundaries with partially reflecting boundary conditions is treated …
Simple Approximations For Condensational Growth, A. B. Kostinski
Simple Approximations For Condensational Growth, A. B. Kostinski
Department of Physics Publications
A simple geometric argument relating to the liquid water content of clouds is given. The phase relaxation time and the nature of the quasi-steady approximation for the diffusional growth of cloud drops are elucidated directly in terms of water vapor concentration. Spatial gradients of vapor concentration, inherent in the notion of quasi-steady growth, are discussed and we argue for an occasional reversal of the traditional point of view: rather than a drop growing in response to a given supersaturation, the observed values of the supersaturation in clouds are the result of a vapor field adjusting to droplet growth. Our perspective …
Surface Relief Profile Of Photopolymerisable Systems In A Single Illuminated Spot, Tsvetanka Babeva, Dana Mackey, Izabela Naydenova, Suzanne Martin, Vincent Toal
Surface Relief Profile Of Photopolymerisable Systems In A Single Illuminated Spot, Tsvetanka Babeva, Dana Mackey, Izabela Naydenova, Suzanne Martin, Vincent Toal
Conference Papers
The formation of surface relief profile in photopolymerisable systems when illuminated with a focused beam of light is simulated numerically using a two-way diffusion model that accounts both for monomer and short polymer chains diffusion. The concentration and spatial distribution dynamics of monomer, short and long polymer chains are calculated. It is assumed that the surface profile is a linear combination of monomer and polymer concentration with appropriate coefficients accounting for polymer shrinkage. A good agreement between the calculated and the experimentally measured profiles is observed thus demonstrating the successful application of the two way diffusion in modeling this system.