422 research outputs found
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.
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Effective Normal Stress Alteration due to Pore Pressure Changes Induced by Dynamic Slip Propagation on a Plane Between Dissimilar Materials
Recent, detailed examinations of fault zones show that walls of faults are often bordered by materials that are different from each other and from the more uniform material farther away. In addition, they show that the ultracataclastic core of mature fault zones, where slip is concentrated, is less permeable to flow across it than the adjoining material of the damage zone. Inhomogeneous slip at the interface between materials with different poroelastic properties and permeabilities causes a change in pore pressure there. Because slip causes compression on one side of the fault wall and extension on the other, the pore pressure on the fault increases substantially when the compressed side is significantly more permeable and decreases when, instead, the extended side is more permeable. This change in pore pressure alters the effective normal stress on the slip plane in a way that is analogous to the normal stress alteration in sliding between elastically dissimilar solids. The magnitude of the effect due to induced pore pressure can be comparable to or larger than that induced by sliding between elastic solids with a dissimilarity of properties consistent with seismic observations. The induced pore pressure effect is increased by increasing contrast in permeability, but the normal stress alteration due to elastic contrast increases rapidly as the rupture velocity approaches the generalized Rayleigh velocity. Because the alteration in effective normal stress due to either effect can be positive or negative, depending on the contrast in properties, the two effects can augment or offset each other.Earth and Planetary SciencesEngineering and Applied Science
A multiscale DEM-LBM analysis on permeability evolutions inside a dilatant shear band
This paper presents a multiscale analysis of a dilatant shear band using a three-dimensional discrete element method and a lattice Boltzmann/finite element hybrid scheme. In particular, three-dimensional simple shear tests are conducted via the discrete element method. A spatial homogenization is performed to recover the macroscopic stress from the micro-mechanical force chains. The pore geometries of the shear band and host matrix are quantitatively evaluated through morphology analyses and lattice Boltzmann/finite element flow simulations. Results from the discrete element simulations imply that grain sliding and rotation occur predominately with the shear band. These granular motions lead to dilation of pore space inside the shear band and increases in local permeability. While considerable anisotropy in the contact fabric is observed with the shear band, anisotropy of the permeability is, at most, modest in the assemblies composed of spherical grains
Microwave saturation spectroscopy of nitrogen-vacancy ensembles in diamond
Negatively-charged nitrogen-vacancy (NV) centers in diamond have
generated much recent interest for their use in sensing. The sensitivity
improves when the NV ground-state microwave transitions are narrow, but these
transitions suffer from inhomogeneous broadening, especially in high-density NV
ensembles. To better understand and remove the sources of broadening, we
demonstrate room-temperature spectral "hole burning" of the NV ground-state
transitions. We find that hole burning removes the broadening caused by
magnetic fields from C nuclei and demonstrate that it can be used for
magnetic-field-insensitive thermometry.Comment: Main text: 5 pages, 4 figures. Supplement: 6 pages, 3 figure
Fundamental quantum limits in ellipsometry
We establish the ultimate limits that quantum theory imposes on the accuracy
attainable in optical ellipsometry. We show that the standard quantum limit, as
usual reached when the incident light is in a coherent state, can be surpassed
with the use of appropriate squeezed states and, for tailored beams, even
pushed to the ultimate Heisenberg limit.Comment: To be published in Optics Letter
Modeling Slope Instability as Shear Rupture Propagation in a Saturated Porous Medium
When a region of intense shear in a slope is much thinner than other relevant geometric lengths, this shear failure may be approximated as localized slip, as in faulting, with strength determined by frictional properties of the sediment and effective stress normal to the failure surface. Peak and residual frictional strengths of submarine sediments indicate critical slope angles well above those of most submarine slopes—in contradiction to abundant failures. Because deformation of sediments is governed by effective stress, processes affecting pore pressures are a means of strength reduction. However, common methods of exami ning slope stability neglect dynamically variable pore pressure during failure. We examine elastic-plastic models of the capped Drucker-Prager type and derive approximate equations governing pore pressure about a slip surface when the adjacent material may deform plastically. In the process we identify an elastic-plastic hydraulic diffusivity with an evolving permeability and plastic storage term analogous to the elastic term of traditional poroelasticity. We also examine their application to a dynamically propagating subsurface rupture and find indications of downslope directivity.Earth and Planetary SciencesEngineering and Applied Science
The discrete fragmentation equations : semigroups, compactness and asynchronous exponential growth
In this paper we present a class of fragmentation semigroups which are compact in a scale of spaces defined in terms of finite higher moments. We use this compactness result to analyse the long time behaviour of such semigroups and, in particular, to prove that they have the asynchronous growth property. We note that, despite compactness, this growth property is not automatic as the fragmentation semigroups are not irreducible
Plastic Flow in Two-Dimensional Solids
A time-dependent Ginzburg-Landau model of plastic deformation in
two-dimensional solids is presented. The fundamental dynamic variables are the
displacement field \bi u and the lattice velocity {\bi v}=\p {\bi u}/\p t.
Damping is assumed to arise from the shear viscosity in the momentum equation.
The elastic energy density is a periodic function of the shear and tetragonal
strains, which enables formation of slips at large strains. In this work we
neglect defects such as vacancies, interstitials, or grain boundaries. The
simplest slip consists of two edge dislocations with opposite Burgers vectors.
The formation energy of a slip is minimized if its orientation is parallel or
perpendicular to the flow in simple shear deformation and if it makes angles of
with respect to the stretched direction in uniaxial stretching.
High-density dislocations produced in plastic flow do not disappear even if
the flow is stopped. Thus large applied strains give rise to metastable,
structurally disordered states. We divide the elastic energy into an elastic
part due to affine deformation and a defect part. The latter represents degree
of disorder and is nearly constant in plastic flow under cyclic straining.Comment: 16pages, Figures can be obtained at
http://stat.scphys.kyoto-u.ac.jp/index-e.htm
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