Generalized Strong Curvature Singularities and Cosmic Censorship

A new definition of a strong curvature singularity is proposed. This definition is motivated by the definitions given by Tipler and Krolak, but is significantly different and more general. All causal geodesics terminating at these new singularities, which we call generalized strong curvature singularities, are classified into three possible types; the classification is based on certain relations between the curvature strength of the singularities and the causal structure in their neighborhood. A cosmic censorship theorem is formulated and proved which shows that only one class of generalized strong curvature singularities, corresponding to a single type of geodesics according to our classification, can be naked. Implications of this result for the cosmic censorship hypothesis are indicated.Comment: LaTeX, 11 pages, no figures, to appear in Mod. Phys. Lett.

Effects of fault interaction on moment, stress drop, and strain energy release

Solutions for collinear shear cracks are used to examine quantitatively the effects of fault slip zone interaction on determinations of moment, stress drop, and static energy release. Two models, the barrier model and the asperity model, are considered. In the asperity model, the actual distribution of strengths on a fault plane is idealized as a combination of two limiting cases: areas which slip freely at a uniform value of a residual friction stress and unbroken ligaments or ‘asperities’ across which slip occurs only at the time of a seismic event. In the barrier model, slip zones separated by unbroken ligaments (barriers) are introduced into a uniformly stressed medium to approximate the nonuniform fault propagation proposed by Das and Aki. The strain energy change due to introducing collinear slip zones or due to breaking the asperities between them is shown to be given by the usual formula for an isolated slip zone with the stress drop replaced by the effective stress. Significant interaction between slip zones occurs only if the length of the asperity is less than half the length of the slip zones. For the case of two collinear slip zones, fracture of the asperity between them is shown to cause a large moment primarily because of the additional displacement which is induced on the adjacent slip zones. For example, if the asperity length is 0.05l, where l is the length of each adjacent slip zone, then fracture of the asperity causes a moment almost 1.8 times the moment caused by introducing a slip zone of length l. For two collinear slip zones, the local stress drop due to fracture of the separating asperity is shown to become unbounded as the asperity length goes to zero, but in the same limit the stress drop averaged over the entire fault length is approximately equal to the apparent stress drop inferred for an isolated fault of the same moment and total fault length. This apparent stress drop is approximately equal (within a factor of 2 or 3) to the effective stress and hence can be used in the usual formula to give a good estimate of the strain energy change. For the barrier model, numerical results are given for the ratio of the stress drop calculated on the assumption of an isolated slip zone to the true stress drop. For example, in the case of two collinear slip zones of length l separated by a barrier of length 0.2l, this ratio is 0.5, whereas for a barrier length equal to that of the adjacent slip zones, the ratio is 0.24. Stress drop estimates become worse with increasing number of fault segments

Circularly polarized microwaves for magnetic resonance study in the GHz range: application to nitrogen-vacancy in diamonds

The ability to create time-dependent magnetic fields of controlled polarization is essential for many experiments with magnetic resonance. We describe a microstrip circuit that allows us to generate strong magnetic field at microwave frequencies with arbitrary adjusted polarization. The circuit performance is demonstrated by applying it to an optically detected magnetic resonance and Rabi nutation experiments in nitrogen-vacancy color centers in diamond. Thanks to high efficiency of the proposed microstrip circuit and degree of circular polarization of 85% it is possible to address the specific spin states of a diamond sample using a low power microwave generator.Comment: 4 pages, 7 figures, nitrogen-vacancy, microwave circular polarization, spin-state addressin

Coherent population oscillations with nitrogen-vacancy color centers in diamond

We present results of our research on two-field (two-frequency) microwave spectroscopy in nitrogen-vacancy (NV-) color centers in a diamond. Both fields are tuned to transitions between the spin sublevels of the NV- ensemble in the 3A2 ground state (one field has a fixed frequency while the second one is scanned). Particular attention is focused on the case where two microwaves fields drive the same transition between two NV- ground state sublevels (ms=0 -> ms=+1). In this case, the observed spectra exhibit a complex narrow structure composed of three Lorentzian resonances positioned at the pump-field frequency. The resonance widths and amplitudes depend on the lifetimes of the levels involved in the transition. We attribute the spectra to coherent population oscillations induced by the two nearly degenerate microwave fields, which we have also observed in real time. The observations agree well with a theoretical model and can be useful for investigation of the NV relaxation mechanisms.Comment: 17 page

Eshelby Transformations, Pore Pressure and Fluid Mass Changes, and Subsidence *

ABSTRACT: This paper is motivated by a recent analysis by Walsh (2002) of subsidence above a planar reservoir. Although the problem has been treated previously b

Final Report: Approaches to Some of the Outstanding Problems of Heterogeneous Compactive Deformation of Geomaterials

Evidence from laboratory experiments and field observations on porous rocks (and other porous materials) has indicated that compaction does not necessarily occur homogeneously, but, instead, is localized in narrow planar zones that are perpendicular to the maximum compressive stress. Because the permeability of these zones is reduced by several orders of magnitude, they present barriers to fluid flow across them. Consequently, their formation in reservoirs or aquifers can adversely affect attempts to inject or withdraw fluids, such as CO2. Because the zones are narrow, they will be difficult to detect from the surface and, as a result, it is important to understand the conditions for their formation and extension

The stabilization of slip on a narrow weakening fault zone by coupled deformation-pore fluid diffusion

The transient stabilization of rapid slip on a very narrow weakening fault zone by the coupling of the deformation with pore fluid diffusion is investigated. More specifically, the fault zone is assumed to be so narrow that it can be idealized as a planar surface and the constitutive law is specified as a relation between stress on the fault τ_(f/t) and relative slip δ. The study considers only the stabilizing effect due to the time dependent response of the fluid-infiltrated elastic material surrounding the fault: the response is elastically stiffer for load alterations which are too rapid to allow for fluid mass diffusion between neighboring material elements (undrained conditions) than for those which occur so slowly that the local pore fluid pressure is constant (drained conditions). Calculations are performed to determine the length of the precursory period (the period of self-driven accelerating slip prior to dynamic instability) by assuming that the near-peak τ_(f/t) versus δ relation is parabolic and that the far-field tectonic stress rate is constant. An important result of the calculations is that the duration of the precursory period is predicted to decrease with increasing fault length for a plausible range of material parameters. Although this appears to disagree with results based on simple dimensional considerations, the result is due to the dependence of the constitutive law on a characteristic sliding distance necessary to reduce τ_(f/t) from peak to residual value. Calculated precursor times are very short, typically less than a few days for fault lengths of 1 to 5 km, a tectonic stress rate of 0.1 bar/year, and field diffusivities of 0.1 to 1.0 m^2/sec. The results are, however, sensitive to details of the τ_(f/t) versus δ relation which are, at present, poorly known

Extension of compaction bands in porous sandstones

see Abstract Volum

Effect of the intermediate principal stress on fault strike and dip - theoretical analysis and experimental verification

see Abstract Volum