The Singularity in Generic Gravitational Collapse Is Spacelike, Local, and Oscillatory

A longstanding conjecture by Belinskii, Khalatnikov, and Lifshitz that the singularity in generic gravitational collapse is spacelike, local, and oscillatory is explored analytically and numerically in spatially inhomogeneous cosmological spacetimes. With a convenient choice of variables, it can be seen analytically how nonlinear terms in Einstein's equations control the approach to the singularity and cause oscillatory behavior. The analytic picture requires the drastic assumption that each spatial point evolves toward the singularity as an independent spatially homogeneous universe. In every case, detailed numerical simulations of the full Einstein evolution equations support this assumption.Comment: 7 pages includes 4 figures. Uses Revtex and psfig. Received "honorable mention" in 1998 Gravity Research Foundation essay contest. Submitted to Mod. Phys. Lett.

Hunting Local Mixmaster Dynamics in Spatially Inhomogeneous Cosmologies

Heuristic arguments and numerical simulations support the Belinskii et al (BKL) claim that the approach to the singularity in generic gravitational collapse is characterized by local Mixmaster dynamics (LMD). Here, one way to identify LMD in collapsing spatially inhomogeneous cosmologies is explored. By writing the metric of one spacetime in the standard variables of another, signatures for LMD may be found. Such signatures for the dynamics of spatially homogeneous Mixmaster models in the variables of U(1)-symmetric cosmologies are reviewed. Similar constructions for U(1)-symmetric spacetimes in terms of the dynamics of generic $T^2$-symmetric spacetime are presented.Comment: 17 pages, 5 figures. Contribution to CQG Special Issue "A Spacetime Safari: Essays in Honour of Vincent Moncrief

Domain - wall - induced magnetoresistance in pseudo spin-valve/superconductor hybrid structures

We have studied the interaction between magnetism and superconductivity in a pseudo-spin-valve structure consisting of a Co/Cu/Py/Nb layer sequence. We are able to control the magnetization reversal process and monitor it by means of the giant magnetoresistance effect during transport measurements. By placing the superconducting Nb-film on the top of the permalloy (Py) electrode instead of putting it in between the two ferromagnets, we minimize the influence of spin scattering or spin accumulation onto the transport properties of Nb. Magnetotransport data reveal clear evidence that the stray fields of domain walls (DWs) in the pseudo-spin-valve influence the emerging superconductivity close to the transition temperature by the occurrence of peak-like features in the magneto-resistance characteristic. Direct comparison with magnetometry data shows that the resistance peaks occur exactly at the magnetization reversal fields of the Co and Py layers, where DWs are generated. For temperatures near the superconducting transition the amplitude of the DW-induced magnetoresistance increases with decreasing temperature, reaching values far beyond the size of the giant magnetoresistive response of our structure in the normal state.Comment: 20 pages, 4 figure

A Modified Version of the Waxman Algorithm

The iterative algorithm recently proposed by Waxman for solving eigenvalue problems, which relies on the method of moments, has been modified to improve its convergence considerably without sacrificing its benefits or elegance. The suggested modification is based on methods to calculate low-lying eigenpairs of large bounded hermitian operators or matrices

Evidence for an oscillatory singularity in generic U(1) symmetric cosmologies on T3×RT^3 \times R

A longstanding conjecture by Belinskii, Lifshitz, and Khalatnikov that the singularity in generic gravitational collapse is locally oscillatory is tested numerically in vacuum, U(1) symmetric cosmological spacetimes on $T^3 \times R$. If the velocity term dominated (VTD) solution to Einstein's equations is substituted into the Hamiltonian for the full Einstein evolution equations, one term is found to grow exponentially. This generates a prediction that oscillatory behavior involving this term and another (which the VTD solution causes to decay exponentially) should be observed in the approach to the singularity. Numerical simulations strongly support this prediction.Comment: 15 pages, Revtex, includes 12 figures, psfig. High resolution versions of figures 7, 8, 9, and 11 may be obtained from anonymous ftp to ftp://vela.acs.oakland.edu/pub/berger/u1genfig

A novel experiment searching for the lepton flavour violating decay mu -> eee

Since the discovery of neutrino oscillations it is known that lepton flavour is not conserved. Lepton flavour violating processes in the charged lepton sector have so far however eluded detection; as they are heavily suppressed in the standard model of particle physics, an observation would be a clear signal for new physics and help to understand the source of neutrino masses and CP violation. We propose a novel experiment searching for the decay mu -> eee with the aim of ultimately reaching a sensitivity of 10^-16, an improvement by four orders of magnitude compared to previous experiments. The technologies enabling this step are thin high-voltage monolithic active pixel sensors for precise tracking at high rates with a minimum of material and scintillating fibres for high resolution time measurements.Comment: 4 pages, 3 figures, contribution to NUFACT 11, XIIIth International Workshop on Neutrino Factories, Super beams and Beta beams, 1-6 August 2011, CERN and University of Genev

On the area of the symmetry orbits in T2T^2 symmetric spacetimes

We obtain a global existence result for the Einstein equations. We show that in the maximal Cauchy development of vacuum $T^2$ symmetric initial data with nonvanishing twist constant, except for the special case of flat Kasner initial data, the area of the $T^2$ group orbits takes on all positive values. This result shows that the areal time coordinate $R$ which covers these spacetimes runs from zero to infinity, with the singularity occurring at R=0.Comment: The appendix which appears in version 1 has a technical problem (the inequality appearing as the first stage of (52) is not necessarily true), and since the appendix is unnecessary for the proof of our results, we leave it out. version 2 -- clarifications added, version 3 -- reference correcte

Noise rectification by a superconducting loop with two weak links

We consider a superconducting loop with two weak links that encloses a magnetic flux. The weak links are unequal and are treated as Josephson junctions with non-sinusoidal phase dependence. We devise a model that takes into account the fluctuation of the critical currents, due to the fluctuations of the order parameter in the weak links. These fluctuations are important near the onset of superconductivity; in this regime they may significantly weaken and eventually disconnect the superconducting loop. As a consequence of these fluctuations and of the resistive noise in the junctions, the average dc voltage does not vanish. Our model can be easily extended to provide a qualitative description of a recent experiment.Comment: version accepted by PR