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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 …

Gauge-Invariance And Quantization, Br Holstein

Barry R Holstein

Quantizing theories such as quantum electrodynamics that contain a gauge invariance are discussed via a simple pedagogical example. Canonical and path integral quantization methods are compared.

On A General Class Of Multivariate Linear Smoothing Operators, Tian-Xiao He

Tian-Xiao He

No abstract provided.

Asymptotic Properties Of Positive Summation-Integral Operators, Tian-Xiao He

Tian-Xiao He

No abstract provided.

On Minimal And Quasi-Minimal Supported Bivariate Splines, Tian-Xiao He

Tian-Xiao He

No abstract provided.

Semiclassical Treatment Of The Double Well, Br Holstein

Barry R Holstein

The double well potential V(x)= 1/4 λ(x2-α2)2 is addressed using both semiclassical path integral and instanton techniques. The basic physics of the two-state system is shown to arise, and energy levels calculated via the two methods are compared.

Comment On "Percolation In Isotropic Elastic Media.", Anthony Day, M. Thorpe

Anthony Roy Day

No abstract provided.

Efficient Application Of The Schauder-Tychonoff Theorem To Functional Perturbations Of $X^(N)=0$, William F. Trench

William F. Trench

No abstract provided.

Spectral Dimensionality Of Random Superconducting Networks, Anthony Roy Day, W. Xia, M. F. Thorpe

Anthony Roy Day

We compute the spectral dimensionality d-tilde of random superconducting-normal networks by directly examining the low-frequency density of states at the percolation threshold. We find that d-tilde=4.1±0.2 and 5.8±0.3 in two and three dimensions, respectively, which confirms the scaling relation d-tilde=2d/(2-s/ nu ), where s is the superconducting exponent and nu the correlation-length exponent for percolation. We also consider the one-dimensional problem where scaling arguments predict, and our numerical simulations confirm, that d-tilde=0. A simple argument provides an expression for the density of states of the localized high-frequency modes in this special case. We comment on the connection between our calculations …

Stability Of Networks Under Tension And Pressure, Anthony Roy Day, H. Yan, M. F. Thorpe

Anthony Roy Day

The number of zero-frequency modes of an elastic network is an important quantity in determining the stability of the network. We present a constraint-counting method for finding this number in general central-force networks that are under an external tension. The technique involves isolating the backbone and then counting constraints in the same way as for free standing networks. A detailed example of this counting is given for a random two-dimensional network subject to an external tension. The results are shown to agree with the number of zero-frequency modes as determined by a direct matrix diagonalization.