Core-collapse supernovae (CCSN) are among the most energetic explosions in the universe, liberating ~1053 erg of gravitational binding energy of the stellar core. Most of this energy ( ~99%) is emitted in neutrinos and only 1% is released as electromagnetic radiation in the visible spectrum. Energy radiated in the form of gravitational waves (GWs) is about five orders smaller. Nevertheless, this energy corresponds to a very strong GW signal and, because of this CCSN are considered as one of the prime sources of gravitational waves for interferometric detectors. Gravitational waves can give us access to the electromagnetically hidden compact inner core of supernovae. They will provide valuable information about the angular momentum distribution and the baryonic equation of state, both of which are uncertain. Furthermore, they might even help to constrain theoretically predicted SN mechanisms. Detection of GW signals and analysis of the observations will require realistic signal predi ctions from the non-parameterized relativistic numerical simulations of CCSN. This dissertation presents the gravitational wave signature of core-collapse v supernovae. Previous studies have considered either parametric models or nonexploding models of CCSN. This work presents complete waveforms, through the explosion phase, based on first-principles models for the first time. We performed 2D simulations of CCSN using the CHIMERA code for 12, 15, and 25M non-rotating progenitors. CHIMERA incorporates most of the criteria for realistic core-collapse modeling, such as multi-frequency neutrino transport coupled with relativistic hydrodynamics, eective GR potential, nuclear reaction network, and an industry-standard equation of state. / Based on the results of our simulations, I produced the most realistic gravitational waveforms including all postbounce phases of core-collapse supernovae: the prompt convection, the stationary accretion shock instability, and the corresponding explosion. Additionally, the tracer particles applied in the analysis of the GW signal reveal the origin of low-frequency component in the prompt part of gravitational waveform. Analysis of detectability of the GW signature from a Galactic event shows that the signal is within the band-pass of current and future GW observatories such as AdvLIGO, advanced Virgo, and LCGT. / by Konstantin Yakunin. / Thesis (Ph.D.)--Florida Atlantic University, 2011. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 200?. Mode of access: World Wide Web.

This thesis explores the vibrational behavior of the main components of sound production in the violin using a continuum mechanics approach. The author provides a mathematical description of the regions in the vibrating continuum, and begins to develop a system of equations governing their behavior, focusing on the air in the resonant chamber. Later chapters, contain discussion of issues involved in solving the system of equations, and examples involving both formal and numerical methods. The existence of a unique formal solution would allow mathematicians to make predictive models for sound waves of instruments based on physical characteristics such as size, shape, density and elasticity. / Graduation date: 2004

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 222-229). Available also in a digital version from Dissertation Abstracts.

Cell adhesion to a substrate or another cell plays an important role in the activities of the cell, such as cell growth, cell migration and cell signaling and communication with extracellular environment or other cells. The adhesion of the cell to the extracellular matrix also plays a vital role in life, as it involves in healing process of a wound and formation of the blood clot inside a vessel. The spread of cancer metastasis tumors inside the body is mostly dependent on the mechanisms of the cell adhesion. The current work is devoted to studying deformation and adhesion of the cell membrane mediated by receptors and ligands in order to enhance the existing models. In fact phospholipid molecules as the constructive units of the cell membrane grant sufficient in-plane continuity and fluidity to the cell membrane that it can be acceptably modeled as a continuum fluid medium. Therefore a two dimensional isotropic continuum fluid model is proposed in here for cell under implementation of membrane theory. In accordance to lack of sufficient study on direct effect of presence of receptors on membrane dilation, the developed model engages the intensity of presence of receptors with membrane deformation and adhesion. This influence is considered through introduction of spontaneous areal dilation. Another innovation is introduced regarding conception of receptor-ligand bonds formation such that a nonlinear constitutive relation is developed for binding force based on charge-induced dipole interaction, which is physically admissible. This relation becomes also enriched by considering one-to-one shielding phenomenon. Diffusion of the receptors is formulated along the membrane under the influence of receptor-receptor and receptor-ligand interactions. Then the presented models in this work are implemented to an axisymmetric configuration of a cell to study the deformation and adhesion of its membrane. Another target of this work is to clarify the impacts of variety of material, binding and diffusion constitutive factors on membrane deformation and adhesion and to declare a rational comparison among them. / Graduate / 0548 / 0346 / golestan@uvic.ca

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Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Jack B. Swift. Vita. Includes bibliographical references. Available also from UMI company.

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In this thesis, we studied three small subjects in the realm of continuum mechanics: imbibition in fluid mechanics, beam and rod buckling in solid mechanics and shell buckling at the solid-liquid interface. In chapter 2, we examined the radial imbibition into a homogenous semi-infinite porous media from a point source with infinite liquid supply. We proved that in the absence of gravity (or in the regime while gravity is negligible compared to surface tension), the shape of the wet area is a hemisphere, and the radius of the wet area evolves as a function with respect to time. This new law with respect to time has been verified by Finite Element Method simulation in software COMSOL and a series of experiments using packed glass microsphere as the porous media. We also found that even though the imbibition slows down, the flow rate through the point source remains constant. This new result for three dimensional radial imbibition complements the classic Lucas-Washburn law in one dimension and two dimensional radial imbibition in one plane. In chapter 3, we studied the elastic beam/rod buckling under lateral constraints in two dimension as well as in three dimension. For the two dimensional case with unique boundary conditions at both ends, the buckled beam can be divided into segments with alternate curved section and straight section. The curved section can be solved by the Euler beam equation. The straight sections, however, are key to the transition between different buckling modes, and the redistributed length of straight sections sets the upper limit and lower limit for the transition. We compared our theoretical model of varying straight sections with Finite Element Method simulation in software ABAQUS, and good agreements are found. We then attempted to employ this model as an explanation with qualitative feasibility for the crawling snake in horizontal plane between parallel walls, which shows unique shape like square wave. For the three dimensional buckling beam/rod confined in cylindrical constraints, three stages are found for the buckling and post buckling processes: initial two dimensional shape, three dimensional spiral/helix shape and final foldup/alpha shape. We characterized the shape at each stage, and then we calculated the transition points between the three stages using geometrical arguments for energy arguments. The theoretical analysis for three dimensional beam/rod are also complemented with Finite Element Method simulations from ABAQUS. In chapter 4, we investigated the buckling shape of solid shell filled with liquid core in two dimension and three dimension. A material model for liquid is first described that can be readily incorporated in the framework of solid mechanics. We then applied this material model in two dimensional and three dimensional Finite Element Method simulation using software ABAQUS. For the two dimensional liquid core solid shell model, a linear analysis is first performed to identify that ellipse corresponds to lowest order of buckling with smallest elastic energy. Finite Element Method simulation is then performed to determine the nonlinear post-buckling process. We discovered that two dimensional liquid core solid shell structures converge to peanut shape eventually while the evolution process is determined by two dimensionless parameters Kτ/μ and ρR^2/μτ. Amorphous shape exists before final peanut shape for certain models with specific Kτ/μ and ρR^2/μτ. The two dimensional peanut shape is also verified with Lattice Boltzmann simulations. For the three dimensional liquid core solid shell model, the post buckling shape is studied from Finite Element Method simulations in ABAQUS. Depending on the strain loading rate, the deformations show distinctive patterns. Large loading rate induces herringbone pattern on the surface of solid shell which resembles solid core solid shell structure, while small loading rate induces major concave pattern which resemble empty solid shell structure. For both two dimensional and three dimensional liquid core system, small scale ordered deformation pattern can be generated by increasing the shear stress in liquid core. In the final chapter, we summarized the discoveries in the dissertation with highlights on the role that geometry plays in all of the three subjects. Recommendations for future studies are also discussed.

As alternatives to partial differential equations (PDEs), nonlocal continuum models given in integral forms avoid the explicit use of conventional spatial derivatives and allow solutions to exhibit desired singular behavior. As an application, peridynamic models are reformulations of classical continuum mechanics that allow a natural treatment of discontinuities by replacing spatial derivatives of stress tensor with integrals of force density functions. The thesis is concerned about the mathematical perspective of nonlocal modeling and local-nonlocal coupling for fracture mechanics both theoretically and numerically. To this end, the thesis studies nonlocal diffusion models associated with ``Neumann-type'' constraints (or ``traction conditions'' in mechanics), a nonlinear peridynamic model for fracture mechanics with bond-breaking rules, and a multi-scale model with local-nonlocal coupling. In the computational studies, it is of practical interest to develop robust numerical schemes not only for the numerical solution of nonlocal models, but also for the evaluation of suitably defined derivatives of solutions. This leads to a posteriori nonlocal stress analysis for structure mechanical models.