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Item Topics in Nonlinear Wave Theory With Applications(1984) Tracy, Eugene Raymond; Chen, Hsing Hen; Physics; Astronomy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)Selected topics in nonlinear wave theory are discussed and applications to the study of modulational instabilities are presented. A historical survey is given of topics relating to solitons and modulational problems. A method is then presented for generating exact periodic and quasiperiodic solutions to several nonlinear wave equations which have important physical applications. The method is then specialized for the purposes of studying the modulational instability of a plane wave solution of the nonlinear Schrodinger equation, an equation with general applicability in one dimensional modulational problems. Some numerical results obtained in conjunction with the analytic study are presented. The analytic approach explains the recurrence phenomena seen in our numerical studies, and the numerical work of other authors. The method of solution (related to the Inverse Scattering Method) is then analyzed within te context of Hamiltonian dynamics where we show that the method can be viewed as simply a pair of canonical transformations. The Abel Transformation which appears here and in the work of other authors is shown to be a special form of Liouville's Transformation to action-angle variables. The construction of closed form solutions of these nonlinear wave equations, via the solution of Jacobi's Inversion Problem, is surveyed briefly.Item Electrons and Spin Waves in Itinerant Ferromagnets(1976) Murray, Joanne; Korenman, Victor; Physics and Astronomy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)Though it is accepted that the 3-d magnetic electrons of transition metals such as nickel are itinerant, at high temperature these itinerant ferromagnets act as if the electrons were localized at lattice sites. In particular, three experimental results conflict with the Stoner itinerant model: 1) The spin band gap does not decrease with temperature as the average magnetization, but much more slowly. 2) Spin waves of short wavelength propagate above the Curie temperature. 3) Magnetic degrees of freedom play a role in determining thermodynamic properties n ear and above TC. The source of these discrepancies is the failure of Stoner theory to take into account magnetization fluctuations. In this paper, I do calculations of single particle and spin wave properties in a generalization of Stoner theory devised by R. E. Prange and V. Korenman to take account of fluctuations. In Stoner theory, electrons interact with an effective magnetic field proportional to the average magnetization, which becomes zero at the phase transition. The basic idea of the generalization of Stoner theory is that electrons are sensitive to their local environment and therefore that electronic and spin wave properties should be calculated in the presence of a local slowly fluctuating magnetization configuration. Only after calculating these properties should the fluctuations be thermally averaged. As a result, electrons interact with an effective magnetic field which is basically proportional to the magnitude of the local magnetization vector and which need not become zero at TC. Single particle properties are calculated by making a transformation to the spatially varying frame of reference of the local magnetization and doing perturbation theory with the magnetization gradients as the small perturbation parameter. We find that the spin eigenstates are approximately in or opposite to the direction of the local magnetization. Even when there is no longer a macroscopic magnetization, an energy gap is maintained between spin-split bands, the bands now being defined in terms of the local magnetization direction. The change in the energy gap from its zero temperature value is proportional only to the average square o f a magnetization gradient, a quantity which may be small even above TC. Thus we can understand that the gap changes only slowly with temperature and that the spin wave does not decay into Stoner single particle excitations even at high temperature. A free energy is found which is very similar in form to the free energy used to compute thermodynamic properties in localized models; thus we find that magnetic degrees of freedom are still important in computing thermodynamic properties above TC. It is the existence of a population difference and energy gap, rather than a macroscopic average magnetization that permits the existence of a spin flip collective excitation. We find a secular equation for the spin wave frequency in the presence of fluctuations which is very similar to the usua1 RPA secular equation, except for small perturbations proportional to the square of magnetization gradients. The corrections to the spin wave frequency and lifetime include the effect of the perturbation of single electron energies by the background, and also of the scattering of the spin wave from single particle spin-conserving excitations and from other spin waves. These corrections are quite small and allow for propagation even above TC. Thus it is a prediction of our theory that one see spin waves even above the critical temperature, so long as an appropriate Population difference maintains a locally ordered magnetization.Item Gravitational Radiation Detection(1976) Rydbeck, Gustaf H. B.; Weber, Joseph; Physics and Astronomy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)This dissertation studies resonant gravitational wave detectors and related data analysis. Different forms (strain amplitude) of the equation of motion for a medium responding to a gravitational wave are discussed in relation to the detection of such waves. Utilizing "Bayesian techniques" an optimal method for data analysis is developed. Noise and filter theory is reviewed. It is seen that the “Bayesian techniques" integrates filter theory and data analysis, providing both filter properties and optimal methods for integrating the data.(In particular the method leads to a non threshold type of analysis, and "looks for" correlation between two detectors without the use of time delay). Expressions for optimal sensitivity (and filters) of detector systems are given, including the limit of perfect sensors and electronics. The signal to noise ratio in terms of the spectral power of the gravitational radiation is derived. Long baseline interferometry is discussed. A computer program simulating a pair of Weber type detectors is developed to study different approaches to data analysis.