Dynamic Systems Commons^™

A Mathematical Model Of The Dynamics Of An Optically Pumped Four-Level Solid State Laser System, Lila Freeman Roberts

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model of the dynamics of an optically pumped four-level solid state laser system. A general mathematical model that describes the spatial and temporal evolution of the electron populations in the laser rod as well as the development of the left and right traveling photon fluxes in the cavity is developed. The model consists of a coupled set of first order semilinear partial differential equations. While the model was developed for Titanium-doped sapphire lasers, it is applicable to three and four level lasers in general.

The analysis of the model is conducted in two …

Generalized Linear Inversion Using Tau-P Forward Modeling, Stephen Dade Walker

Graduate Theses

The Generalized Linear Inversion (GLI) method is used in conjunction with a tau-p forward model to successfully perform inversions of test and real-data examples. All data examples used are one-dimensional velocity profiles that represent several different cases. The stability of the technique is demonstrated in all the test-data sets. The use of simple models and wel1-control 1ed test data results in a minimum of iterations of the inversion process. Different levels of perturbation of the model and test-data examples are used to reveal insight into the robust nature of the inversion.

Additive Control Of Stochastic Linear Systems With Finite Horizon, Pao-Liu Chow, José-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

We consider a dynamic system whose state is governed by a linear stochastic differential equation with time-dependent coefficients. The control acts additively on the state of the system. Our objective is to minimize an integral cost which depends upon the evolution of the state and the total variation of the control process. It is proved that the optimal cost is the unique solution of an appropriate free boundary problem in a space-time domain. By using some decomposition arguments, the problems of a two-sided control, i.e. optimal corrections, and the case with constraints on the resources, i.e. finite fuel, can be …

Entropy Measures In Input-Output Analysis, Martin Zwick, Abbas Heiat

Complex Systems Faculty Publications and Presentations

Applications of Shannon's entropy measure to the matrices of technical and interdependence coefficients, to the final demand vector, and to other aspects of input- output tables are proposed. These entropy measures serve as indices of different types of economic diversity. The relevance of such indices for economic planning and for analyses of economic structural complexity and development is discussed.