Browsing by Subject "Instabilities"
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Item Hydrodynamic instabilities of radiative blast waves(2013-12) Kim, In Tai; Ditmire, Todd R.We present the results from a series of experimental investigations into the hydrodynamic instabilities that occur in radiative blast waves. In particular, we examine the Vishniac instability in which the perturbation modes oscillate in time and, for certain mode numbers and polytropic index of the medium, can exhibit a growth in their amplitudes. Experiments were conducted on the GHOST laser laboratory in which a source of atomic clusters was irradiated by a 1J-2J, 115fs laser pulse to produce cylindrical blast waves. The thrust of this thesis falls into two categories. First, we analyze the effects radiative cooling has on the evolution of blast waves such as the lowering of the effective polytropic index and consequently the lowering of their deceleration parameter. Radiation from the blast wave surface results in a preheated ionization precursor in the upstream material and is indicated by a gradual decline in the electron density profile of the blast wave rather than a sharp jump. This mechanism, if strong enough, can also create a secondary shock wave to form ahead of the main blast wave. The second set of experiments investigates the temporal evolution of longitudinal perturbations induced on the blast waves by use of a transverse interferometric beam that modifies the cluster medium prior to the onset of the main pump beam. These perturbations are analyzed and compared to theory set forth in Vishniac's mechanism for oscillatory instabilities and their growth rate.Item Multidimensional multiscale dynamics of high-energy astrophysical flows(2010-05) Couch, Sean Michael; Wheeler, J. Craig; Milosavljević, Miloš; Bromm, Volker; Hoeflich, Peter; Jaffe, Daniel; Kumar, PawanAstrophysical flows have an enormous dynamic range of relevant length scales. The physics occurring on the smallest scales often influences the physics of the largest scales, and vice versa. I present a detailed study of the multiscale and multidimensional behavior of three high-energy astrophysical flows: jet-driven supernovae, massive black hole accretion, and current-driven instabilities in gamma-ray burst external shocks. Both theory and observations of core-collapse supernovae indicate these events are not spherically-symmetric; however, the observations are often modeled assuming a spherically-symmetric explosion. I present an in-depth exploration of the effects of aspherical explosions on the observational characteristics of supernovae. This is accomplished in large part by high-resolution, multidimensional numerical simulations of jet-driven supernovae. The existence of supermassive black holes in the centers of most large galaxies is a well-established fact in observational astronomy. How such black holes came to be so massive, however, is not well established. In this work, I discuss the implications of radiative feedback and multidimensional behavior on black hole accretion. I show that the accretion rate is drastically reduced relative to the Eddington rate, making it unlikely that stellar mass black holes could grow to supermassive black holes in less than a Hubble time. Finally, I discuss a mechanism by which magnetic field strength could be enhanced behind a gamma-ray burst external shock. This mechanism relies on a current-driven instability that would cause reorganization of the pre-shock plasma into clumps. Once shocked, these clumps generate vorticity in the post-shock plasma and ultimately enhance the magnetic energy via a relativistic dynamo process.Item Phase-field modeling of piezoelectrics and instabilities in dielectric elastomer composites(2011-12) Li, Wenyuan, 1982-; Landis, Chad M.; Huang, Rui; Mear, Mark; Tassoulas, John L.Ferroelectric ceramics are broadly used in applications including actuators, sensors and information storage. An understanding of the microstructual evolution and domain dynamics is vital for predicting the performance and reliability of such devices. The underlying mechanism responsible for ferroelectric constitutive response is ferroelectric domain wall motion, domain switching and the interactions of domain walls with other material defects. In this work, a combined theoretical and numerical modeling framework is developed to investigate the nucleation and growth of domains in a single crystal of ferroelectric material. The phase-field approach, applying the material electrical polarization as the order parameter, is used as the theoretical modeling framework to allow for a detailed accounting of the electromechanical processes. The finite element method is used for the numerical solution technique. In order to obtain a better understanding of the energetics of fracture within the phase-field setting, the J-integral is modified to include the energies associated with the order parameter. Also, the J- integral is applied to determine the crack-tip energy release rate for common sets of electromechanical crack-face boundary conditions. The calculations confirm that only true equilibrium states exhibit path-independence of J, and that domain structures near crack tips may be responsible for allowing positive energy release rate during purely electrical loading. The small deformation assumption is prevalent in the phase-field modeling approach, and is used in the previously described calculations. The analysis of large deformations will introduce the concept of Maxwell stresses, which are assumed to be higher order effects that can be neglected in the small deformation theory. However, in order to investigate the material response of soft dielectric elastomers undergoing large mechanical deformation and electric field, which are employed in electrically driven actuator devices, manipulators and energy harvesters, a finite deformation theory is incorporated in the phase-field model. To describe the material free energy, compressible Neo-Hookean and Gent models are used. The Jaumann rate of the polarization is used as the objective polarization rate to make the description of the dissipation frame indifferent. To illustrate the theory, electromechanical instabilities in composite materials with different inclusions will be studied using the finite element methods.Item Relativistic wave phenomena in astrophysical plasmas(2010-05) Soto Chavez, Angel Rualdo; Hazeltine, R. D. (Richard D.); Mahajan, Swadesh M.; Breizman, Boris; Dicus, Duaen A.; Gamba, IreneThe propagation and stability of waves in relativistic astrophysical plasmas is presented. Our investigation, using a relativistic two-fluid model, is different from previous relativistic fluid studies in that the plasma is treated fully relativistically, both in temperature and in directed speed. Much of this study is devoted to relativistic linear waves in pulsar pair plasmas, with a view to elucidating a possible mechanism for pulsar radio wave emission. We also study interesting nonlinear exact solutions in both relativistic and non-relativistic plasmas. Pulsar pair plasmas can support four transverse modes for parallel propagation. Two of these are electromagnetic plasma modes, which at high temperature become light waves. The remaining two are Alfvénic modes, split into a fast and a slow mode. The slow mode, always sub-luminous, is cyclotron (Alfvén) two-stream unstable at large wavelengths. We find that temperature effects, within the fluid model used, do not suppress the instability in the limit of large (finite) magnetic field. The fast Alfvén mode can be super-luminous only at large wavelengths; however, it is always sub-luminous at high temperatures. In this incompressible approximation, only the ordinary mode is present for perpendicular propagation. We discuss the implications of the unstable mode for radio emission mechanisms. For typical values, the instability is quite fast, and the waves can grow to sizable levels, such that, the magnetic modulation could act as a wiggler. The pulsar primary beam interacting with this wiggler, could drive a free electron laser (FEL) effect, yielding coherent radiation. Investigation of the FEL in this setting and demonstrating that the frequency spectral range, and luminosities, predicted by this mechanism is well within the observed range of radio frequency (and luminosity) emissions, is one of the principal results of this dissertation. It is tempting to speculate, then, that an FEL-like radiation effect could be responsible for the highly coherent radio wave emissions from pulsars. In the study of nonlinear exact solutions we have generalized the results to the incompressible Hall Magnetohydrodynamics (HMHD). We find that for cases when the plasma is weakly magnetized the frequencies of the modes decrease as the wave amplitude (effective mass) increases. For very strongly magnetized plasmas the light-like modes tend to be asymptotically linear; the frequency is unaffected by wave amplitude.