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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.Item Black Hole Dynamics and Gravitational Radiation in Galactic Nuclei(2009) Lauburg, Vanessa; Miller, Michael C.; Astronomy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this dissertation, we present new channels for the production of gravitational radiation sources: mergers of black holes in the nuclear star clusters found in many small galaxies, and mergers and tidal separations of black hole binaries in galaxies that host supermassive black holes. Mergers between stellar-mass black holes will be key sources of gravitational radiation for ground-based detectors. However, the rates of these events are highly uncertain, because we can not observe these binaries electromagnetically. In this work, we show that the nuclear star clusters found in the centers of small galaxies are conducive environments for black hole mergers. These clusters have large escape velocities, high stellar densities, and large numbers of black holes that will have multiple close encounters, which often lead to mergers. We present simulations of the three-body dynamics of black holes in this environment and estimate that, if many nuclear star clusters do not have supermassive black holes, tens of events per year will be detectable with Advanced LIGO. Larger galaxies that host supermassive black holes can produce extreme-mass ratio inspiral (EMRI) events, which are important sources for the future space-based detector, LISA. Here, we show that tidal separation of black hole binaries by supermassive black holes will produce a distinct class of EMRIs with near-zero eccentricities, and we estimate that rates from tidal separation could be comparable to or larger than those from the traditionally-discussed two-body capture formation scenario. Before tidal separation can occur, a binary encounters multiple stars as it sinks through the nucleus toward the supermassive black hole. In this region, velocities are high, and interactions with stars can destroy binaries through ionization. We investigate wide ranges in initial mass function and internal energy of the binaries, and find that tidal separations, mergers, and ionizations are all likely outcomes for binaries near the galactic center. Tidally separated binaries will contribute to the LISA detection rate, and mergers will produce tens of events per year for Advanced LIGO. We show, therefore, that galactic nuclei are promising hosts of gravitational wave sources for both LISA and LIGO.Item Two Dimensional Velocity Fields of Low Surface Brightness Galaxies(EDP Sciences, 2005) Kuzio de Naray, R.; McGaugh, S. S.; de Blok, W. J. G.; Bosma, A.We present high resolution two dimensional velocity fields from integral field spectroscopy along with derived rotation curves for nine low surface brightness galaxies. This is a positive step forward in terms of both data quality and number of objects studied. We fit NFW and pseudo-isothermal halo models to the observations. We find that the pseudo-isothermal halo better represents the data in most cases than the NFW halo, as the resulting concentrations are lower than would be expected for CDM.Item Studies of SOHO Comets(2008-08-20) Knight, Matthew Manning; A'Hearn, Michael F.; Astronomy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We present a study of the Kreutz, Marsden, and Kracht comets observed by SOHO including photometric reductions and analysis, numerical modeling, and physical modeling. We analyze the results of our photometric study of more than 900 lightcurves of Kreutz comets observed by SOHO. We find that they do not have a bimodal distance of peak brightness as previously reported, but instead peak from 10.5-14 solar radii (prior to perihelion), suggesting there is a continuum of compositions rather than two distinct subpopulations. The lightcurves have two rates of brightening, typically ~r^-7.3 when first observed by SOHO then rapidly transitioning to ~r^-3.8 between 20-30 solar radii. It is unclear at what distance the steeper slope begins, but it likely does not extend much beyond the SOHO field of view. We derive nuclear sizes up to ~50 meters in radius for the SOHO observed comets, with a cumulative size distribution of N(>R)~R^-2.2 for comets larger than 5 meters in radius. This size distribution cannot explain the six largest members of the family seen from the ground, suggesting that either the family is not collisionally evolved or that the distribution is not uniform around the orbit. After correcting for the changing discovery circumstances, the flux of comets reaching perihelion has increased since 1996, and the increase is seen in comets of all sizes. We consider the Marsden and Kracht comets together due to their apparent dynamical linkage. Seasonal effects of the viewing geometry make it impossible to build a characteristic lightcurve of either group. Many are seen to survive perihelion and most reach a peak brightness within ~6 hours of perihelion with no preference for peaks before or after perihelion. Most are barely above the detection threshold, and the largest is probably smaller than 30 meters in radius. Our dynamical simulations suggest that the orbital distribution of the Kracht group can be produced by low velocity fragmentation events and close approaches to Jupiter over the last 50-250 years. We construct fragmentation trees for the Marsden and Kracht groups and predict that 7-8 comets in each group may be visible on their next perihelion passage.Item The Tully-Fisher Relation for Low Surface Brightness Galaxies - Implications for Galaxy Evolution(Blackwell, 1995) Zwaan, M. A.; van der Hulst, J. M.; de Blok, W. J. G.; McGaugh, S. S.Item HI Observations of Low Surface Brightness Galaxies: Probing Low Density Galaxies(Blackwell, 1996) de Blok, W.J.G.; McGaugh, S.S.; van der Hulst, J.M.We present Very Large Array (vla) and Westerbork Synthesis Radio Telescope (wsrt) 21-cm Hi observations of 19 late-type low surface brightness (LSB) galaxies. Our main findings are that these galaxies, as well as having low surface brightnesses, have low Hi surface densities, about a factor of ~ 3 lower than in normal late-type galaxies. We show that LSB galaxies in some respects resemble the outer parts of late-type normal galaxies, but may be less evolved. LSB galaxies are more gas-rich than their high surface brightness counterparts. The rotation curves of LSB galaxies rise more slowly than those of HSB galaxies of the same luminosity, with amplitudes between 50 and 120 km s−1, and are often still increasing at the outermost measured point. The shape of the rotation curves suggests that LSB galaxies have low matter surface densities. We use the average total mass surface density of a galaxy as a measure for the evolutionary state, and show that LSB galaxies are among the least compact, least evolved galaxies. We show that both MHI/LB and Mdyn/LB depend strongly on central surface brightness, consistent with the surface brightness–mass-to-light ratio relation required by the Tully-Fisher relation. LSB galaxies are therefore slowly evolving galaxies, and may well be low surface density systems in all respects.Item The Dark and Baryonic Matter Content of Low Surface Brightness Galaxies(Blackwell, 1997) de Blok, W.J.G.; McGaugh, S.S.We present mass models of a sample of 19 low surface brightness (LSB) galaxies and compare the properties of their constituent mass components with those of a sample of high surface brightness (HSB) galaxies. We find that LSB galaxies are dark matter dominated. Their halo parameters are only slightly affected by assumptions on stellar mass-to-light ratios. Comparing LSB and HSB galaxies we find that mass models derived using the maximum disk hypothesis result in the disks of LSB galaxies having systematically higher stellar mass-to-light ratios than HSB galaxies of similar rotation velocity. This is inconsistent with all other available evidence on the evolution of LSB galaxies. We argue therefore that the maximum disk hypothesis does not provide a representative description of the LSB galaxies and their evolution. Mass models with stellar mass-to-light ratios determined by the colors and stellar velocity dispersions of galactic disks imply that LSB galaxies have dark matter halos that are more extended and less dense than those of HSB galaxies. Surface brightness is thus related to the halo properties. LSB galaxies are slowly evolving, low density and dark matter dominated galaxies.Item Simulating Observations of Dark Matter Dominated Galaxies: Towards the Optimal Halo Profile(Blackwell, 2007) de Blok, W.J.G.; Bosma, Albert Bosma; McGaugh, StacyLow Surface Brightness (LSB) galaxies are dominated by dark matter, and their rotation curves thus reflect their dark matter distribution. Recent high-resolution rotation curves suggest that their dark matter mass-density distributions are dominated by a constant-density core. This seems inconsistent with the predictions of Cold Dark Matter (CDM) models which produce halos with compact density cusps and steep mass-density profiles. However, the observationally determined mass profiles may be affected by non-circular motions, asymmetries and offsets between optical and dynamical centres, all of which tend to lower the observed slopes. Here we determine the impact of each of these effects on a variety of halo models, and compare the results with observed mass-density profiles. Our simulations suggest that no single systematic effect can reconcile the data with the cuspy CDM halos. The data are best described by a model with a soft core with an inner power-law mass-density slope ⍺ = −0.2±0.2. However, no single universal halo profile provides a completely adequate description of the data.