Regular exact models for a nonstatic gas sphere in general relativity

Some new exact models for an expanding or a contracting gaseous sphere (i.e., the density is to vanish at the outer boundary together with the pressurep) are given. The physical properties of the models are investigated, and it is found that both the pressure and the density are positive inside the outer boundary of the sphere, and their respective gradients are negative. The density is increasing for contracting spheres, and it is decreasing for expanding spheres. It is also shown that this is the case for the pressure at any moment for the layers close to the boundary of the spheres. For these layers it is further shown that the adiabatic speed of sound is less than the speed of light, and the trace of the energy-momentum tensor is positive. The rate of change of the circumference as measured by an observer riding on the boundary of the sphere is increasing for expanding spheres and it is decreasing for collapsing spheres. We also find that the physical radius is an increasing function of comoving radial coordinate. The mass function is further shown to be positive.     

Nonlinear Stability of Boundary Layers of the Boltzmann Equation,I. The case <Emphasis Type="Italic">M</Emphasis><Superscript><Emphasis Type="Italic">∞</Emphasis></Superscript><−1

This is a continuation of the paper [15] on nonlinear boundary layers of the Boltzmann equation where the existence is established and shown to be strongly dependent on the Mach number M of the Maxwellian state at far field. In this paper, when M <–1, we will show that the linearized operator has the exponential decay in time property and therefore a bootstrapping argument yields nonlinear stability of the boundary layers.     

The Spectral Gap of the 2-D Stochastic Ising Model with Nearly Single-Spin Boundary Conditions

We establish upper bounds for the spectral gap of the stochastic Ising model at low temperature in an N×N box, with boundary conditions which are plus except for small regions at the corners which are either free or minus. The spectral gap decreases exponentially in the size of the corner regions, when these regions are of size at least of order logN. This means that removing as few as O(logN) plus spins from the corners produces a spectral gap far smaller than the order N ^–2 gap believed to hold under the all-plus boundary condition. Our results are valid at all subcritical temperatures.     

Analytic Properties of the Structure Function for the One-Dimensional One-Component Log–Gas

The structure function S(k; ) for the one-dimensional one-component log–gas is the Fourier transform of the charge–charge, or equivalently the density–density, correlation function. We show that for |k|j in the power series expansion of f(k; ) about k=0 is of the form of a polynomial in /2 of degree j divided by (/2)^j. The bulk of the paper is concerned with calculating these polynomials explicitly up to and including those of degree 9. It is remarked that the small k expansion of S(k; ) for the two-dimensional one-component plasma shares some properties in common with those of the one-dimensional one-component log–gas, but these break down at order k⁸.     

Generalized solutions of the radiative transfer equations in a singular case

This paper is devoted to the study of the radiative transfer equations: First, we prove a global existence theorem, which allows a blow-up of the opacity _v() when 0. Thus, it extends Mercier's previous result [13]. This proof relies mainly on a nonlinear version of Hille-Yosida theorem: see Crandall-Ligett [9].Then, we prove the uniqueness of the semigroup solving (TR), and some regularity results (in the class of functions with bounded variation).Finally, we prove the convergence of some splitting algorithms associated to (TR).     

On Existence of Static Metric Extensions in General Relativity

Motivated by problems related to quasi-local mass in general relativity, we study the static metric extension conjecture proposed by R. Bartnik [4]. We show that, for any metric on ¯B ₁ that is close enough to the Euclidean metric and has reflection invariant boundary data, there always exists an asymptotically flat and scalar flat static metric extension in M=³B ₁ such that it satisfies Bartnik's geometric boundary condition [4] on B ₁.     

Attempt of an axiomatic foundation of quantum mechanics and more general theories VI

This contribution continues the series of papers [2, 4, 5, 12] treated by Ludwig and collaborators. It is based on the generalized frame given in [6]; there Ludwig has set up an infinite axiomatic scheme as extension of the finite system [4, 5]. The results of [12] are then proved for a locally finite case; they lead to an extended representation theorem.This paper was supported by the Deutsche Forschungsgemeinschaft.     

A Lipatov bound for Φ 4 4 Euclidean field theory

We bound the large order behavior of these pieces of the renormalized perturbation expansion for ₄ ⁴ which do not contain renormalons [1]. The bound we obtain has the form of the leading asymptotic behavior computed by the Lipatov method, with the exact value of the Lipatov constant. Therefore, this paper is a step towards the rigorous study of the large order behavior of ₄ ⁴ and towards a proof of existence of the first renormalon singularity which should prevent the theory from being Borel summable. Using the results of this paper and the techniques of [15], one can for instance improve [17] the estimate [18] on the finiteness of the radius of convergence of the Borel transform of renormalized ₄ ⁴ and obtain that this radius is at least the exact value conjectured in [1].Supported in part by the National Science Foundation under Grant PHY 85-13554     

Decay of the Bethe–Salpeter Kernel and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We consider lattice classical ferromagnetic spin systems at high temperature (1) with nearest neighbor interactions and even single-spin distributions (ssd). Associated with each system is an imaginary time lattice quantum field theory. It is known that there is a particle of mass m–ln in the energy-momentum spectrum. If s ⁴–3s ²²<0, where s ^k is the kth moment of the ssd, and is sufficiently small, we show that in the two-particle subspace there is no mass spectrum up to 2m. For >0 we show that the only mass spectrum in (m, 2m) is a bound state of mass m _b=2m+ln(1–)+O(), where =(+2s ²²)^–1. A bound on the decay of the kernel of a Bethe–Salpeter equation is obtained and used to prove these results.     

Bianchi type I cosmological models with variableG and Λ: A comment

We treat in an alternate way a problem recently considered by Beesham [1]. We find that anisotropic Bianchi I inflationary cosmologies with variable gravitational and cosmological constants admit de Sitter expansion at least for late times.     

Characterizability of Free Motion in Special Relativity

The concept of forcefree motion is primitive, i.e., unexplained, in special relativity. The paper demonstrates a way to characterize it by more primitive, directly operationally interpreted notions. These are the worldlines of (more or less) pointlike, but non-quantum bodies and of light signals, clock parametrizations of the former kind of worldlines and the direction, in which an observer sees a light signal go out. Already at this general level one can define the radar distance and the radar (initial) velocity of one body with respect to another, and can define in a reasonable manner that two bodies move in opposite directions with respect to an observer. These concepts are then used to formulate a certain criterion for path structures which can experimentally be tested without presupposing inertial frames, atomic clocks, etc. It is demonstrated that the path structure of free motion in gravity-free regions of space-time, i.e., in the domain of validity of special relativity, satisfies that criterion.     

Response functions of free mass gravitational wave antennas

Rainer Weiss and collaborators have from first principles derived the response of a free mass interferometer (or 2-arm gravitational wave antenna) to plane polarized gravitational waves [1]. We here obtain equivalent formulas (generalized slightly to allow for arbitrary elliptical polarization) by a simple differencing of the 3-pulse Doppler response functions of two 1-arm antennas [2]. A 4-pulse response function is found, with quite complicated angular dependences for arbitrary incident polarization. The differencing method can as readily be used to write exact response functions (3n+1 pulse!) for antennas having multiple passes, or having more arms.The research described in this paper was carried out at the Jet Propulsion Laboratory, under contract with the National Aeronautics and Space Administration.     

Near Field Observation of a Refractive Index Grating and a Topographical Grating by an Optically-Trapped Gold Particle

We observed the near field for a refractive index grating fabricated on a planar light waveguide circuit (PLC) by scanning an optically-trapped 100 nm diameter gold particle. We demonstrate that stable trapping and scanning occur with a Gaussian laser beam at the scan velocity of 1.6 m/s and Nd:YAG laser power of 25mW. The scattered Ar laser light from the gold particle is strong at high refractive indexes of the grating with periods of 1.06 m and 0.53 m both by s and p polarized illumination. In addition, we observed the surface profile of the optical disk tracking groove with and without the gold particle. © 2004 The Optical Society of Japan     

The simplified Fermi accelerator in classical and quantum mechanics

We review the simplified classical Fermi acceleration mechanism and construct a quantum counterpart by imposing time-dependent boundary conditions on solutions of the free Schrödinger equation at the unit interval. We find similiar dynamical features in the sense that limiting KAM curves, respectively purely singular quasienergy spectrum, exist(s) for sufficiently smooth wall oscillations (typically ofC ² type). In addition, we investigate quantum analogs to local approximations of the Fermi map both in its quasiperiodic and irregular phase space regions. In particular, we find pure point q.e. spectrum in the former case and conjecture that random boundary conditions are necessary to model a quantum analog to the chaotic regime of the classical accelerator.     

The influence of graphite boat material on the purity of LPE InGaAs

This paper describes the purity of LPE InGaAs layers grown in graphite boats, machined from various graphite materials. The influence of the material is clearly visible if the growth solution is sufficiently pure. Carrier concentrations n<2×l0¹⁵ cm^–3 and mobilities(77 K)> 38000 cm²/Vs are routinely achieved for suitable graphite materials already from the third run of a new large boat applying a prebake of only 15 h. Small boats yield even better results (n=0.5×10¹⁵ cm^–3 and(77 K)=49500 m²/Vs). The sticking of In-rich solutions to the graphite does not depend on the material but is solely dependent on the surface roughness. The problem of graphite particle abrasion is discussed.     

A Model of Subdiffusive Interface Dynamics with a Local Conservation of Minimum Height

We define a new model of interface roughening in one dimension which has the property that the minimum of interface height is conserved locally during the evolution. This model corresponds to the limit q of the q-color dimer deposition-evaporation model introduced by us earlier [Hari Menon and Dhar, J. Phys. A: Math. Gen. 28:6517 (1995)]. We present numerical evidence from Monte Carlo simulations and the exact diagonalization of the evolution operator on finite rings that growth of correlations in this model is subdiffusive with dynamical exponent z2.5. For periodic boundary conditions, the variation of the gap in the relaxation spectrum with system size appears to involve a logarithmic correction term. Some generalizations of the model are briefly discussed.     

Asymptotically abelian systems

We study pairs { , } for which is aC*-algebra and is a homomorphism of a locally compact, non-compact groupG into the group of *-automorphisms of . We examine, especially, those systems { , } which are (weakly) asymptotically abelian with respect to their invariant states (i.e. |A _g (B) — _g (B)A 0 asg for those states such that ( _g (A)) = (A) for allg inG andA in ). For concrete systems (those with -acting on a Hilbert space andg _g implemented by a unitary representationg U _g on this space) we prove, among other results, that the operators commuting with and {U _g } form a commuting family when there is a vector cyclic under and invariant under {U _g }. We characterize the extremal invariant states, in this case, in terms of weak clustering properties and also in terms of factor and irreducibility properties of { ,U _g }. Specializing to amenable groups, we describe operator means arising from invariant group means; and we study systems which are asymptotically abelian in mean. Our interest in these structures resides in their appearance in the infinite system approach to quantum statistical mechanics.     

Polarization of strangeness Arizona muon

The longitudinal polarization of strangeness Arizona muon, namely, the 236 MeV/c ⁺ from the K^{+ +} v decay, has been measured to search for right-handed weak current in the strangeness changing process. The polarization has been determined to be –0.967±0.047.We are grateful to Professors T. Nishikawa, S. Ozaki, A. Kusumegi, and H. Sugawara of KEK for their encouragement and support during the course of this experiment. We are grateful to the operating crew of the KEK proton synchrotron and its experimental facilities for their cooperation during the experiment. This work is partially supported by the Grant-in-Aid of the Ministry of Education, Science and Culture.     

Large scale properties of the Webgraph

In this paper we present an experimental study of the properties of web graphs. We study a large crawl from 2001 of 200M pages and about 1.4 billion edges made available by the WebBase project at Stanford [17]. We report our experimental findings on the topological properties of such graphs, such as the number of bipartite cores and the distribution of degree, PageRank values and strongly connected components.Received: 5 December 2003, Published online: 30 March 2004PACS: 89.20.Hh World Wide Web, Internet - 89.75.Fb Structures and organization in complex systemsPartially supported by the Future and Emerging Technologies programme of the EU under contracts number IST-2001-33555 COSIN Co-evolution and Self-organization in Dynamical Networks and IST-1999-14186 ALCOM-FT Algorithms and Complexity in Future Technologies, and by the Italian research project ALINWEB: Algorithmica per Internet e per il Web, MIUR - Programmi di Ricerca di Rilevante Interesse Nazionale.     

Periodic inverse problem for a new hierarchy of coupled evolution equations

We study the inverse problem with periodic boundary condition for a new class of integrable nonlinear evolution equations. The multiphase periodic solutions for the nonlinear fields (p, q, r) are expressed in terms of the Riemann theta function, which is obtained via the linearization of the flows of the set of auxiliary variables _j on a Riemann surface. An explicit case is evaluated to obtain the form of the algebraic curve on which the variables _j move.