A Relativistic Version of the Ghirardi–Rimini–Weber Model

Carrying out a research program outlined by John S. Bell in 1987, we arrive at a relativistic version of the Ghirardi-Rimini-Weber (GRW) model of spontaneous wavefunction collapse. The GRW model was proposed as a solution of the measurement problem of quantum mechanics and involves a stochastic and nonlinear modification of the Schrödinger equation. It deviates very little from the Schrödinger equation for microscopic systems but efficiently suppresses, for macroscopic systems, superpositions of macroscopically different states. As suggested by Bell, we take the primitive ontology, or local beables, of our model to be a discrete set of space-time points, at which the collapses are centered. This set is random with distribution determined by the initial wavefunction. Our model is nonlocal and violates Bell’s inequality though it does not make use of a preferred slicing of space-time or any other sort of synchronization of spacelike separated points. Like the GRW model, it reproduces the quantum probabilities in all cases presently testable, though it entails deviations from the quantum formalism that are in principle testable. Our model works in Minkowski space-time as well as in (well-behaved) curved background space-times.     

Genericity and stability of naked singularities arising in an inhomogeneous dust collapse

In this paper, we consider an inhomogeneous dust collapse, and extend earlier works of Jhingan, Joshi, and Singh to the case where initial density and velocity distributions are finitely differentiable functions of co-moving coordinate r. We study the occurrence of naked singularities under various conditions on the derivatives of initial density and velocity distributions in marginally as well as non-marginally bound case. We then study their stability and genericity with respect to perturbations in the initial data in an appropriate topological sense.     

基于离散曲率的边折叠网格简化算法

在以往的网格简化算法中,大多是采用空间几何距离作为简化准则.几何距离能很好地控制简化后的网格与原始网格之间的误差,但在保持形状特征上相对较弱.本文提出的网格简化算法是根据网格顶点的曲率,采用边折叠的方式来减少低频区域的网格顶点密度.由于曲率能很好地刻画网格形状,故本文的算法能较好地保持原始网格的形状特征.     

Pseudofinite homogeneity, isolation, and reducibility

It has been proved (by S. M. Dudakov and M. A. Taitslin) that the reducibility of some models of a theory implies the second pseudofinite homogeneity property for this theory. We prove the converse, namely, that any theory with the first or the second pseudofinite homogeneity property has a reducible model and, therefore, possesses the second isolation property. This also proves the equivalence of the second isolation property and the second pseudofinite homogeneity property, in contrast to the first pseudofinite homogeneity property, which is more general than the first isolation property (this was established by O. V. Belegradek, A. P. Stolboushin, and M. A. Taitslin).     

Naked Singularities Formation in the Gravitational Collapse of Barotropic Spherical Fluids

The gravitational collapse of spherical, barotropic perfect fluids is analyzed here. For the first time, the final state of these systems is studied without resorting to simplifying assumptions - such as self-similarity - using a new approach based on non-linear o.d.e. techniques, and formation of naked singularities is shown to occur for solutions such that the mass function is analytic in a neighborhood of the spacetime singularity.     

Mechanism of synthesis of superheavy nuclei via the process of controlled electron-nuclear collapse

This paper presents a brief review of the existing approaches to the creation of superheavy nuclei in collisions of heavy nuclei to overcome the Coulomb barrier or through the pion condensation in a nucleus volume. A principally new approach to the creation of superheavy nuclei based on the stimulation of a self-organizing collapse of electron-nuclear systems is analyzed. For a neutral atom compressed by external forces, a threshold electron density is shown to exist. If such a density is reached, a self-organizing process of “electron downfall to the nucleus” starts. This process is exoenergic and leads to the formation of a supercompressed electron-nuclear cluster. The higher the charge of a nucleus, the lower the threshold of the external compression. It is shown that the maximum binding energy shifts during such a self-organizing collapse of the electron-nuclear system from A_opt ≈ 60 (for uncompressed substance) to the area of high mass numbers A_opt ≥ 200⋯ 2000 and could render the synthesis of superheavy nuclei to be energy-efficient. The synthesis proceeds through the absorption of other nuclei by the collapsed nucleus. It is theoretically proved that the synthesis efficiency is ensured by both the width reduction and increased transparency of the Coulomb barrier in the extremely compressed electron-nuclear system. The release of binding energy through the absorption of nuclei by the electron-nuclear collapsed clusters may result in the simultaneous emission of lighter nuclei. It is assumed that just such a mechanism of synthesis explains the creation of superheavy and other anomalous nuclei observed in the experiments carried out at the Electrodynamics Laboratory “Proton-21.”     

高压下γ'-Fe4N晶态合金的声子稳定性与磁性

利用基于密度泛函理论的第一性原理研究了高压下有序晶态γ’-Fe₄N合金的晶格动力学稳定性与磁性. 对比没有考虑磁性的γ’-Fe₄N的声子谱, 得出压力小于1 GPa时, 自发磁化诱导了铁磁相γ’-Fe₄N基态晶格动力学稳定. 压力在1.03-31.5 GPa时, Σ线上的点(0.37, 0.37, 0)、对称点X和M 上相继出现了声子谱软化现象. 压力在31.5-60.8 GPa时, 压致效应与自发磁化对诸原子的作用达到了稳定平衡, 表现出了声子谱稳定. 压力大于61.3 GPa时, 随着压力的增大压力诱导体系动力学不稳定性越强. 通过软模相变理论对于γ’-Fe₄N, 在10 GPa下的声学支声子的M点处软化现象的处理, 发现了动力学稳定的高压新相P2/m-Fe₄N. 压力小于1 GPa时高压新相P2/m-Fe₄N 是热力学稳定的相, 且磁矩与γ’-Fe₄N的磁矩几乎相同. 2.9-19 GPa时, P2/m相的焓比γ’相的焓小, 基态结构更稳定. 大于20 GPa时, 两相磁矩几乎相同.     

An analysis of pressure-induced phase transition and elastic properties of neodymium monopnictides

We have predicted the phase transition pressures and corresponding relative volume changes of two neodymium monopnictides (NdAs and NdSb) having NaCl-type structure at ambient conditions, using an improved interaction potential model (IIPM) approach. Both the compounds have been found to undergo from their initial NaCl(B1) phase to a body centered tetragonal (BCT) phase at high pressure. Our calculated results of phase transitions, volume collapses and elastic behavior of these compounds are found to be close to the experimental results. This shows that the inclusion of the three-body interaction and polarizability effect makes the present model suitable for high pressure studies.     

A K Raychaudhuri and his equation

Amal Kumar Raychaudhuri died on June 18, 2005. This essay follows the lecture which I gave in honour of this great Indian scientist and teacher on December 26, 2005 in Puri, India. Invited plenary talk delivered at the International Conference on Einstein’s Legacy in the New Millennium, December 15–22, 2005, Puri, India.     

High-speed cylindrical collapse of two perfect fluids

In this paper, the study of the gravitational collapse of cylindrically distributed two perfect fluid system has been carried out. It is assumed that the collapsing speeds of the two fluids are very large. We explore this condition by using the high-speed approximation scheme. There arise two cases, i.e., bounded and vanishing of the ratios of the pressures with densities of two fluids given by c _s , d _s . It is shown that the high-speed approximation scheme breaks down by non-zero pressures p ₁, p ₂ when c _s , d _s are bounded below by some positive constants. The failure of the high-speed approximation scheme at some particular time of the gravitational collapse suggests the uncertainty on the evolution at and after this time. In the bounded case, the naked singularity formation seems to be impossible for the cylindrical two perfect fluids. For the vanishing case, if a linear equation of state is used, the high-speed collapse does not break down by the effects of the pressures and consequently a naked singularity forms. This work provides the generalisation of the results already given by Nakao and Morisawa (Prog Theor Phys 113:73, 2005) for the perfect fluid.