Singularities and horizons in the collisions of gravitational waves

This thesis presents a study of the dynamical, nonlinear interaction of colliding gravitational waves, as described by classical general relativity. It is focused mainly on two fundamental questions: First, what is the general structure of the singularities and Killing-Cauchy horizons produced in the collisions of exactly plane-symmetric gravitational waves? Second, under what conditions will the collisions of almost-plane gravitational waves (waves with large but finite transverse sizes) produce singularities?

In the work on the collisions of exactly-plane waves, it is shown that Killing horizons in any plane-symmetric spacetime are unstable against small plane-symmetric perturbations. It is thus concluded that the Killing-Cauchy horizons produced by the collisions of some exactly plane gravitational waves are nongeneric, and that generic initial data for the colliding plane waves always produce "pure" spacetime singularities without such horizons. This conclusion is later proved rigorously (using the full nonlinear theory rather than perturbation theory), in connection with an analysis of the asymptotic singularity structure of a general colliding plane-wave spacetime. This analysis also proves that asymptotically the singularities created by colliding plane waves are of inhomogeneous-Kasner type; the asymptotic Kasner axes and exponents of these singularities in general depend on the spatial coordinate that runs tangentially to the singularity in the non-plane-symmetric direction.

In the work on collisions of almost-plane gravitational waves, first some general properties of single almost-plane gravitational-wave spacetimes are explored. It is shown that, by contrast with an exact plane wave, an almost-plane gravitational wave cannot have a propagation direction that is Killing; i.e., it must diffract and disperse as it propagates. It is also shown that an almost-plane wave cannot be precisely sandwiched between two null wavefronts; i.e., it must leave behind tails in the spacetime region through which it passes. Next, the occurrence of spacetime singularities in the collisions of almost-plane waves is investigated. It is proved that if two colliding, almost-plane gravitational waves are initially exactly plane-symmetric across a central region of sufficiently large but finite transverse dimensions, then their collision produces a spacetime singularity with the same local structure as in the exact-plane-wave collision. Finally, it is shown that a singularity still forms when the central regions are only approximately plane-symmetric initially. Stated more precisely, it is proved that if the colliding almost-plane waves are initially sufficiently close to being exactly plane-symmetric across a bounded central region of sufficiently large transverse dimensions, then their collision necessarily produces spacetime singularities. In this case, nothing is now known about the local and global structures of the singularities.

Gauge Invariant Spectral Cauchy Characteristic Extraction of Gravitational Waves in Computational General Relativity

We present a complete system for Spectral Cauchy characteristic extraction (Spectral CCE). Implemented in C++ within the Spectral Einstein Code (SpEC), the method employs numerous innovative algorithms to efficiently calculate the Bondi strain, news, and flux.

Spectral CCE was envisioned to ensure physically accurate gravitational wave-forms computed for the Laser Interferometer Gravitational wave Observatory (LIGO) and similar experiments, while working toward a template bank with more than a thousand waveforms to span the binary black hole (BBH) problem’s seven-dimensional parameter space.

The Bondi strain, news, and flux are physical quantities central to efforts to understand and detect astrophysical gravitational wave sources within the Simulations of eXtreme Spacetime (SXS) collaboration, with the ultimate aim of providing the first strong field probe of the Einstein field equation.

In a series of included papers, we demonstrate stability, convergence, and gauge invariance. We also demonstrate agreement between Spectral CCE and the legacy Pitt null code, while achieving a factor of 200 improvement in computational efficiency.

Spectral CCE represents a significant computational advance. It is the foundation upon which further capability will be built, specifically enabling the complete calculation of junk-free, gauge-free, and physically valid waveform data on the fly within SpEC.

Plane-strain discrete dislocation plasticity with climb-assisted glide motion of dislocations

A small-strain two-dimensional discrete dislocation plasticity (DDP) framework is developed wherein dislocation motion is caused by climb-assisted glide. The climb motion of the dislocations is assumed to be governed by a drag-type relation similar to the glide-only motion of dislocations: such a relation is valid when vacancy kinetics is either diffusion limited or sink limited. The DDP framework is employed to predict the effect of dislocation climb on the uniaxial tensile and pure bending response of single crystals. Under uniaxial tensile loading conditions, the ability of dislocations to bypass obstacles by climb results in a reduced dislocation density over a wide range of specimen sizes in the climb-assisted glide case compared to when dislocation motion is only by glide. A consequence is that, at least in a single slip situation, size effects due to dislocation starvation are reduced. By contrast, under pure bending loading conditions, the dislocation density is unaffected by dislocation climb as geometrically necessary dislocations (GNDs) dominate. However, climb enables the dislocations to arrange themselves into lower energy configurations which significantly reduces the predicted bending size effect as well as the amount of reverse plasticity observed during unloading. The results indicate that the intrinsic plasticity material length scale associated with GNDs is strongly affected by thermally activated processes and will be a function of temperature. © 2013 IOP Publishing Ltd.

In-plane critical current density measurements of straight and curved tracks in RABiTS-MOD coated conductors

Depending on the temperature and the magnitude and orientation of an external magnetic field, the critical current density, J c , of a coated conductor can be limited either by the properties of the grain boundaries or by those of the grains. In order to ascertain what governs J c under different conditions, we have measured straight and curved tracks, patterned into RABiTS-MOD samples, while a magnetic field was swept in the plane of the films. Significantly different results were obtained at different field and temperature ranges, which we were able to attribute to J c being limited by either grain boundaries or grains.

Scaling of velocity fluctuations in off-wall boundary conditions for turbulent flows

A model for off-wall boundary conditions for turbulent flow is investigated. The objective of such a model is to circumvent the need to resolve the buffer layer near the wall, by providing conditions in the logarithmic layer for the overlying flow. The model is based on the self-similarity of the flow at different heights in the logarithmic layer. It was first proposed by Mizuno and Jiménez (2013), imposing at the boundary plane a velocity field obtained on-the-fly from an overlying region. The key feature of the model was that the lengthscales of the field were rescaled to account for the self-similarity law. The model was successful at sustaining a turbulent logarithmic layer, but resulted in some disagreements in the flow statistics, compared to fully-resolved flows. These disagreements needed to be addressed for the model to be of practical application. In the present paper, a more refined, wavelength-dependent rescaling law is proposed, based on the wavelength-dependent dynamics in fully-resolved flows. Results for channel flow show that the new model eliminates the large artificial pressure fluctuations found in the previous one, and a better agreement is obtained in the bulk properties, the flow fluctuations, and their spectral distribution across the whole domain. © Published under licence by IOP Publishing Ltd.

Experimental and numerical investigations on dissolution and recrystallization processes of GaSb/InSb/GaSb under microgravity and terrestrial conditions

The effects of gravity and crystal orientation on the dissolution of GaSb into InSb melt and the recrystallization of InGaSb were investigated under microgravity condition using a Chinese recoverable satellite and under normal gravity condition on earth. To investigate the effect of gravity on the solid/liquid interface and compositional profiles. a numerical simulation was carried out. The InSb crystal melted at 525 degrees C and then a part of GaSb dissolved into the InSb melt during heating to 706 degrees C and this process led to the formation of InGaSb solution. InGaSb solidified during the cooling process. The experimental and calculation results clearly show that the shape of the solid/liquid interface and compositional profiles in the solution were significantly affected by gravity. Under microgravity, as the Ga compositional profiles were uniform in the radial direction. the interfaces were almost parallel. On the contrary, for normal gravity condition, as large amounts of Ga moved up in the upper region due to buoyancy, the dissolved zone broadened towards gravitational direction. Also. during the cooling process, needle crystals of InGaSb started appearing and the value of x of InxGa1-xSb crystals increased with the decrease of temperature. The GaSb with the (111)B plane dissolved into the InSb melt much more than that of the (111)A plane. (C) 2000 Elsevier Science B.V. All rights reserved.

Non-modal instabilities of two-dimensional disturbances in plane Couette flow of a power-law fluid

Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the "shear-thinning/shear-thickening" effect increases/decreases the amplitude of responses to external excitations and initial conditions. (C) 2010 Elsevier B.V. All rights reserved.

Instabilities and transient behaviors of a liquid film flowing down a porous inclined plane

The nonmodal linear stability of a falling film over a porous inclined plane has been investigated. The base flow is driven by gravity. We use Darcy's law to describe the flow in the porous medium. A simplified one-sided model is used to describe the fluid flow. In this model, the influence of the porous layer on the flow in the film can be identified by a parameter beta. The instabilities of a falling film have traditionally been investigated by linearizing the governing equations and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In the present paper, we have studied the linear stability of three-dimensional disturbances using the nonmodal stability theory. Particular attentions are paid to the transient behavior rather than the long time behavior of eigenmodes predicted by traditional normal mode analysis. The transient behaviors of the response to external excitations and the response to initial conditions are studied by examining the pseudospectral structures and the energy growth function G(t) Before we study the nonmodal stability of the system, we extend the results of long-wave analysis in previous works by examining the linear stabilities for streamwise and spanwise disturbances. Results show that the critical conditions of both the surface mode and the shear mode instabilities are dependent on beta for streamwise disturbances. However, the spanwise disturbances have no unstable eigenvalue. 2010 American Institute of Physics. [doi:10.1063/1.3455503]

Effects of crystal growth conditions on morphology of crystalline syndiotactic 1,2-polybutadiene

The crystalline syndiotatic 1,2-polybutadiene was synthesized with a catalyst consisting of iron acetylacetonate (Fe(acac)(3))-triisobutylaluminum (Al(i-Bu)(3))-diethyl phosphite (DEP), and the effects of crystal growth conditions on morphology of thin films of the polymer were investigated by transmission electron microscopy (TEM) and electron diffraction (ED) techniques. The polymer with melting point 179 degreesC was found to have 89.3% 1,2-content and 86.5% syndiotacticity by C-13 NMR measurement. The results of electron microscopic studies indicate that the solution-cast thin films of the syndiotatic 1,2-polybutadiene consist of lath-like lamellae with the c-axis perpendicular to the film plane, while a- and b-axes are in the film plane. The morphology of isothermally crystallized thin films of the polymer is temperature dependent. At lower crystallization temperatures (130 degreesC), a spherulitic structure consisting of flat-on lamellae is formed. With an increase in the crystallization temperature (e.g., at 140 degreesC), the spherulites and single faceted crystals coexist. At higher crystallization temperatures (150 degreesC), single crystals with a hexagonal prismatic shape are produced.

The topological behaviour of 3D null points in the Sun's corona

Brown D. S. and Priest E. R. 2001, The topological behaviour of 3D null points in the Sun's corona, Astronomy and Astrophysics, 367, 339-346

Parity-violating vertices for spin-3 gauge fields

The problem of constructing consistent parity-violating interactions for spin-3 gauge fields is considered in Minkowski space. Under the assumptions of locality, Poincaré invariance, and parity noninvariance, we classify all the nontrivial perturbative deformations of the Abelian gauge algebra. In space-time dimensions n=3 and n=5, deformations of the free theory are obtained which make the gauge algebra non-Abelian and give rise to nontrivial cubic vertices in the Lagrangian, at first order in the deformation parameter g. At second order in g, consistency conditions are obtained which the five-dimensional vertex obeys, but which rule out the n=3 candidate. Moreover, in the five-dimensional first-order deformation case, the gauge transformations are modified by a new term which involves the second de Wit-Freedman connection in a simple and suggestive way. © 2006 The American Physical Society.

The preparation of reach to grasp movements in adults with Down syndrome

The aim of this study was to determine the extent to which adults with Down syndrome (DS) are able to utilise advance information to prepare reach to grasp movements. The study comprised ten adults with DS; ten children matched to an individual in the group with DS on the basis of their intellectual ability, and twelve adult controls. The participants used their right hand to reach out and grasp illuminated perspex blocks. Four target blocks were positioned on a table surface, two to each side of the midsagittal plane. In the complete precue condition, participants were provided with information specifying the location of the target. In the partial precue condition, participants were given advance information indicating the location of the object relative to the midsagittal plane (left or right). In the null condition, advance information concerning the position of the target object was entirely ambiguous. It was found that both reaction times and movement times were greater for the participants with DS than for the adults without DS. The reaction times exhibited by individuals with DS in the complete precue condition were lower than those observed in the null condition, indicating that they had utilised advance information to prepare their movements. In the group with DS, when advance information specified only the location of the target object relative to the midline, reaction times were equivalent to those obtained when ambiguous information was given. In contrast, the adults without DS exhibited reaction times that were lower in both the complete and partial precue conditions when compared to the null condition. The pattern of results exhibited by the children was similar to that of the adults without DS. The movement times exhibited by all groups were not influenced by the precue condition. In summary, our findings indicate that individuals with DS are able to use advance information if it specifies precisely the location of the target object in order to prepare a reach to grasp movement. The group with DS were unable, however, to obtain the normal advantage of advance information specifying only one dimension of the movement goal (i.e., the position of an object relative to the body midline). (C) 2001 Elsevier Science B.V. All rights reserved.

Cold-formed steel sections with web openings subjected to web crippling under two-flange loading conditions - part I: Tests and finite element analysis

The results of 82 web crippling tests are presented, with 20 tests conducted on channel sections without web openings and 62 tests conducted on channel sections with web openings. The tests consider both end-two-flange and interior-two-flange loading conditions. In the case of the tests with web openings, the hole was located directly under the concentrated load. The concentrated load was applied through bearing plates; the effect of different bearing lengths is investigated. In addition, the cases of both flanges fastened and unfastened to the support is considered. A non-linear elasto-plastic finite element model is described, and the results compared against the laboratory test results; a good agreement was obtained in terms of both strength and failure modes.

Cold-formed steel sections with web openings subjected to web crippling under two-flange loading conditions - Part II: Parametric study and proposed design equations

A parametric study of cold-formed steel sections with web openings subjected to web crippling was undertaken using finite element analysis, to investigate the effects of web holes and cross-section sizes on the web crippling strengths of channel sections subjected to web crippling under both interior-two-flange (ITF) and end-two-flange (ETF) loading conditions. In both loading conditions, the hole was centred beneath the bearing plate. It was demonstrated that the main factors influencing the web crippling strength are the ratio of the hole depth to the flat depth of the web, and the ratio of the length of bearing plates to the flat depth of the web. In this paper, design recommendations in the form of web crippling strength reduction factors are proposed, that are conservative to both the experimental and finite element results.

Palaeoglacial and palaeoclimatic conditions in the NW Pacific, as revealed by a morphometric analysis of cirques upon the Kamchatka Peninsula

The distribution of glacial cirques upon the Kamchatka peninsula, Far Eastern Russia, is systematically mapped from satellite images and digital elevation model data. A total of 3,758 cirques are identified, 238 of which are occupied by active glaciers. The morphometry of the remaining 3,520 cirques is analysed. These cirques are found to show a very strong N bias in their azimuth (orientation), likely resulting from aspect-related variations in insolation. The strength of this N bias is considered to indicate that former glaciation upon the peninsula was often ‘marginal’, and mainly of cirque-type, with peaks extending little above regional equilibrium-line altitudes. This is supported by the fact that S and SE-facing cirques are the highest in the dataset, suggesting that glacier-cover was rarely sufficient to allow S and SE-facing glaciers to develop at low altitudes. The strength of these azimuth-related variations in cirque altitude is thought to reflect comparatively cloud-free conditions during former periods of glaciation. It is suggested that these characteristics, of marginal glaciation and comparatively cloud-free conditions, reflect the region’s former aridity, which was likely intensified at the global Last Glacial Maximum, and during earlier periods of ice advance, as a result of the development of negative pressure anomalies over the North Pacific (driven by the growth of the Laurentide Ice Sheet), combined with other factors, including an increase in the extent and duration of sea ice, a reduction in global sea levels, cooler sea surface temperatures, and the localised growth of mountain glaciers. There is published evidence to suggest extensive glaciation of the Kamchatka Peninsula at times during the Late Quaternary, yet the data presented here appears to suggest that such phases were comparatively short-lived, and that smaller cirque-type glaciers were generally more characteristic of the period.