Time evolution of the QED vacuum in a uniform electric Field: Complete analytic solution by spinorial decomposition

Exact analytical solutions are presented for the time evolution of the density of pairs produced in the QED vacuum by a time-independent, uniform electric field. The mathematical tool used here to describe the pair production is the Dirac-Heisenberg-Wigner function introduced before [Phys. Rev. D 44, 1825 (1991)]. The initial value problem for this function is solved by decomposing the solution into a product of spinors. The equations for spinors are much simpler and are solved analytically. These calculations are nonperturbative since pair production is due to quantum-mechanical tunneling and the explicit solutions clearly exhibit their nonanalytic behavior.Comment: 6 pages, 1 figur

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

Heisenberg Uncertainty Relation for Coarse-grained Observables

We ask which is the best strategy to reveal uncertainty relations between comple- mentary observables of a continuous variable system for coarse-grained measurements. This leads to the derivation of new uncertainty relations for coarse-grained measurements that are always valid, even for detectors with low precision. These relations should be particularly relevant in experimental demonstrations of squeezing in quantum optics, quantum state reconstruction, and the development of trustworthy entanglement criteria

A note on entropic uncertainty relations of position and momentum

We consider two entropic uncertainty relations of position and momentum recently discussed in literature. By a suitable rescaling of one of them, we obtain a smooth interpolation of both for high-resolution and low-resolution measurements respectively. Because our interpolation has never been mentioned in literature before, we propose it as a candidate for an improved entropic uncertainty relation of position and momentum. Up to now, the author has neither been able to falsify nor prove the new inequality. In our opinion it is a challenge to do either one.Comment: 2 pages, 2 figures, 2 references adde

Fracture of a biopolymer gel as a viscoplastic disentanglement process

We present an extensive experimental study of mode-I, steady, slow crack dynamics in gelatin gels. Taking advantage of the sensitivity of the elastic stiffness to gel composition and history we confirm and extend the model for fracture of physical hydrogels which we proposed in a previous paper (Nature Materials, doi:10.1038/nmat1666 (2006)), which attributes decohesion to the viscoplastic pull-out of the network-constituting chains. So, we propose that, in contrast with chemically cross-linked ones, reversible gels fracture without chain scission

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

Permeability evolution during progressive development of deformation bands in porous sandstones

[1] Triaxial deformation experiments were carried out on large (0.1 m) diameter cores of a porous sandstone in order to investigate the evolution of bulk sample permeability as a function of axial strain and effective confining pressure. The log permeability of each sample evolved via three stages: (1) a linear decrease prior to sample failure associated with poroelastic compaction, (2) a transient increase associated with dynamic stress drop, and (3) a systematic quasi-static decrease associated with progressive formation of new deformation bands with increasing inelastic axial strain. A quantitative model for permeability evolution with increasing inelastic axial strain is used to analyze the permeability data in the postfailure stage. The model explicitly accounts for the observed fault zone geometry, allowing the permeability of individual deformation bands to be estimated from measured bulk parameters. In a test of the model for Clashach sandstone, the parameters vary systematically with confining pressure and define a simple constitutive rule for bulk permeability of the sample as a function of inelastic axial strain and effective confining pressure. The parameters may thus be useful in predicting fault permeability and sealing potential as a function of burial depth and faul

Measuring our universe from galaxy redshift surveys

Galaxy redshift surveys have achieved significant progress over the last couple of decades. Those surveys tell us in the most straightforward way what our local universe looks like. While the galaxy distribution traces the bright side of the universe, detailed quantitative analyses of the data have even revealed the dark side of the universe dominated by non-baryonic dark matter as well as more mysterious dark energy (or Einstein's cosmological constant). We describe several methodologies of using galaxy redshift surveys as cosmological probes, and then summarize the recent results from the existing surveys. Finally we present our views on the future of redshift surveys in the era of Precision Cosmology.Comment: 82 pages, 31 figures, invited review article published in Living Reviews in Relativity, http://www.livingreviews.org/lrr-2004-

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 $\pm \pi/4$ 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