Quantum transition state theory and solving a first order master equation for complex reactions numerically

The field of chemical kinetics is an exciting and active field. The prevailing theories make a number of simplifying assumptions that do not always hold in actual cases. Another current problem concerns a development of efficient numerical algorithms for solving the master equations that arise in the description of complex reactions. The objective of the present work is to furnish a completely general and exact theory of reaction rates, in a form reminiscent of transition state theory, valid for all fluid phases and also to develop a computer program that can solve complex reactions by finding the concentrations of all participating substances as a function of time. To do so, the full quantum scattering theory is used for deriving the exact rate law, and then the resulting cumulative reaction probability is put into several equivalent forms that take into account all relativistic effects if applicable, including one that is strongly reminiscent of transition state theory, but includes corrections from scattering theory. Then two programs, one for solving complex reactions, the other for solving first order linear kinetic master equations to solve them, have been developed and tested for simple applications.

Pulsed parabolic equation model of acoustic transmission (PPEMAT)

Underwater sound is very important in the field of oceanography where it is used for remote sensing in much the same way that radar is used in atmospheric studies. One way to mathematically model sound propagation in the ocean is by using the parabolic-equation method, a technique that allows range dependent environmental parameters. More importantly, this method can model sound transmission where the source emits either a pure tone or a short pulse of sound. Based on the parabolic approximation method and using the split-step Fourier algorithm, a computer model for underwater sound propagation was designed and implemented. This computer model differs from previous models in its use of the interactive mode, structured programming, modular design, and state-of-the-art graphics displays. In addition, the model maximizes the efficiency of computer time through synchronization of loosely coupled dual processors and the design of a restart capability. Since the model is designed for adaptability and for users with limited computer skills, it is anticipated that it will have many applications in the scientific community.