Casimir effect for the sphere revisited

In a recent work Brevik et al. have offered formal proofs of two results which figure prominently in calculations of the Casimir pressure on a sphere. It is shown by means of simple counterexamples that each of those proofs is necessarily incorrect.     

The trousers problem revisited

Anderson and DeWitt considered the quantization of a massless scalar field in a spacetime whose spacelike hypersurfaces change topology and concluded that the topology change gives rise to infinite particle and energy production. We show here that their calculations are insufficient and that their propagation rule is unphysical. However, our results using a more general propagation rule support their conclusion.     

The strong CP problem revisited

The strong CP-violating θ parameter, the problem of strong CP violation and their status are reviewed. Among all possibilities, two natural solutions to the strong CP puzzle are thoroughly discussed and emphasized: the axion-type mechanism for hard CP violation and the non-Peccei-Quinn scheme for spontaneous CP nonconservation. Basic properties of the axion are derived from the modified Peccei-Quinn symmetry. Astrophysical and cosmological constraints are described for two different types of invisible axions. In nonaxion solutions, CP is spontaneously broken at the grand-unification scale and the CP phase is transmitted down to the low energy sector by quantum effects or by fermion mixing effects. As a by-product, the cosmological baryon asymmetry, which is caused by the same source of CP violation ultimately responsible for the kaon ε parameter, is generated adequately at the one-loop level.     

On the Frenkel problem of equivalent steady currents in a sphere

The Frenkel problem of substituting the 3D system of steady currents given in one of two concentric spherical regions by an equivalent system of currents (i.e., by that inducing the same external magnetic field) that is distributed over the surface of the other region is considered. A method of multipole moments providing the direct solution (without calculating the fields) of the problem is described. The case of currents with the density components represented by cubic polynomials of the Cartesian coordinates is considered as an example.     

On the resolvent kernel for the transfer problem in an homogeneous sphere

A scheme for obtaining the resolvent kernel of the integral equation for radiative transfer problems in an isotropically scattering sphere is proposed. Unlike the earlier attempts, the spherical problem is not transformed to its plane-parallel analogue.     

The Method of Images applied to the grounded sphere: The problem of the ground wire

The Method of Images poses an important difficulty when used to solve the problem of a charge in the presence of a grounded conducting sphere. This arises from the fact that the sum of the inducing charge and the image charge is different from zero. As a consequence, there is a monopole field far from the system, and any ground wire physically connected to the sphere will carry an electric current, changing the initial balance of charges until a new equilibrium is reached. The approach taken in this paper assumed an infinite straight wire connecting the sphere to ground. The charge distribution over the surface of the conductors was calculated, and the results analyzed. It was shown that the thinner the wire, the lower will be its total charge, and the closer will be the calculated charge density at the surface of the sphere to the conventional solution by the Method of Images.     

一个简单硬球碰撞问题中的混沌

对于一个在铅垂线上的两个硬球及刚性地面组成的硬球碰撞体系,计算了它的Lyapunov指数．因为该Lyapunov指数的正定性,所以该体系是一个混沌体系．     

On the problem of an inhomogeneous sphere placed in a homogeneous alternating magnetic field

The results of a numerical analysis of the equivalent magnetic moment of a two-layered sphere magnetized by a homogeneous alternating magnetic field are reported. The particular case of a hollow sphere is examined. It is found that for values of the parameter 60, the hollow sphere has the same magnetic moment as a solid sphere.     

Lunar eclipse theory revisited: Scattered sunlight in both the quiescent and the volcanically perturbed atmosphere

The residual brightness of the shadowed Moon during a lunar eclipse is attributed to unscattered sunlight rays refracted in the Earth's atmosphere. The classical theory of lunar eclipses is built on the premise that the sunlight scattered by the gases and particles in the atmosphere contributes negligibly to the brightness of the eclipsed Moon. The current work revisits the lunar eclipse theory, extending it to accommodate spectrally resolved observations and addressing the role of scattered sunlight. Predictions of both direct and diffuse sunlight are produced by integrating the radiative transfer equations over the Earth's disk. The investigation contemplates scenarios of normal aerosol loading as well as conditions representative of the months and years following a major volcanic eruption. It is shown that omitting scattered sunlight is an acceptable approximation for low and moderate aerosol loadings at visible and longer wavelengths. However, towards the ultraviolet, or at times when the atmosphere contains elevated aerosol amounts, the relative significance of direct and diffuse sunlight may reverse. Spectra of the sunlight that reaches the shadowed Moon during the eclipse are presented to illustrate the distinct contributions from both components. It is also shown that lunar eclipse spectra obtained up to 4-5 years after a major volcanic eruption, such as Mt. Pinatubo's in 1991, will reveal that the stratosphere remains perturbed above background aerosol levels.     

The discrete ordinates method for anisotropic scattering in the neutron transport theory: The critical sphere problem

The spherical harmonics method for anisotropic scattering in the neutron transport theory related to the critical sphere problem was investigated by Yildiz [The spherical harmonics method for anisotropic scattering in neutron transport theory: the critical sphere problem. JQSRT 2001;71:25-37]. Some numerical results and figures that they provided are incorrect. The correct numerical results for the critical radius are obtained and tabulated for different scattering parameters by using the discrete ordinates method.     

The low-mass X-ray binary-millisecond radio pulsar birthrate problem revisited

We investigate the birthrate problem for low-mass X-ray binaries (LMXBs) and millisecond radio pulsars (MRPs) in this paper. We consider intermediate-mass and low-mass X-ray binaries (I/LMXBs) to be the progenitors of MRPs, and calculate their evolutionary response to the cosmic star formation rate (SFR) both semi-analytically and numerically. With a typical value (1 Gyr) of the LMXB lifetime, one may expect comparable birthrates of LMXBs and MRPs, but the calculated number of LMXBs is an order of magnitude higher than that observed in the Galaxy. Instead, we suggest that the birthrate problem could be solved if most MRPs have evolved from faint to rather than bright LMXBs. The former may have a population of ∼10⁴ in the Galaxy.

     

On the existence of perturbed robertson-walker universes

Solutions of the full nonlinear field equations of general relativity near the Robertson-Walker universes are examined, together with their relation to linearized perturbations. A method due to Choquet-Bruhat and Deser is used to prove existence theorems for solutions near Robertson-Walker constraint data of the constraint equations on a spacelike hypersurface. These theorems allow one to regard the matter fluctuations as independent quantities, ranging over certain function spaces. In the k = ?1 case the existence theory describes perturbations which may vary within uniform bounds throughout space. When k = +1 a modification of the method leads to a theorem which clarifies some unusual features of these constraint perturbations. The k = 0 existence theorem refers only to perturbations which die away at large distances. The connection between linearized constraint solutions and solutions of the full constraints is discussed. For k = ±1 backgrounds, solutions of the linearized constraints are analyzed using transverse-traceless decompositions of symmetric tensors. Finally the time-evolution of perturbed constraint data and the validity of linearized perturbation theory for Robertson-Walker universes are considered.     

Crystalline order on a sphere and the generalized Thomson problem

We attack the generalized Thomson problem, i.e., determining the ground state energy and configuration of many particles interacting via an arbitrary repulsive pairwise potential on a sphere via a continuum mapping onto a universal long range interaction between angular disclination defects parametrized by the elastic (Young) modulus Y of the underlying lattice and the core energy E(core) of an isolated disclination. Predictions from the continuum theory for the ground state energy agree with numerical simulations of long range power law interactions of the form 1/r(gamma) (0相似文献   

Inverse problem method for the perturbed nonlinear Schrödinger equation

A scattering matrix is defined for eq. (1), and a complete set of equations, governing the time evolution of the scattering parameters, is derived by a general method. These equations form a basis for the perturbation theory.     

The exact solution of an elimination problem in kinetic theory: I. The one-dimensional hard sphere gas

A class of initial value problems for a one-dimensional hard sphere gas is considered where a specified particle has a given distribution f⁽¹⁾(z₁; 0) and the rest are in equilibrium at t=0. An exact expansion is obtained for a certain n-particle reduced distribution function f⁽ⁿ⁾(z₁;…;z_n; t) in terms of the 1-particle reduced distribution function f⁽¹⁾(z₁; t) for the specified particle by starting with separate expressions for these functions in terms of f⁽¹⁾(z₁; 0). Expansions for the corresponding cluster functions are first obtained and then graph theoretic methods applied to obtain a solution.     

Development of instability in the problem of flow around a sphere

Multimoment hydrodynamics equations are used to solve the problem of flow around a quiescent solid sphere. The solutions to the multimoment hydrodynamics equations are found, which enable to interpret of the phenomenon of vortex shedding. The solutions give a pattern of instability development that qualitatively reproduces experimental data over a wide range of Reynolds numbers. The replacement of one unstable flow mode by another unstable mode is governed the tendency of the system to find the fastest way to depart from the state of statistical equilibrium. After stability loss, the system does not reach a new stable state. Such a scenario is at odds with the ideas of classical hydrodynamics, which interprets the development of instability in terms of a bifurcation transition from one stable state to another. This picture presented shows the direction of solving the problems faced by classical hydrodynamics in the interpretation of the phenomenon of vortex shedding.     

An algebraic treatment of the MIC-Kepler problem on S 3 sphere

The quantum-mechanical problem of motion in a dual charged Coulomb field modified by a centrifugal term (MIC-Kepler problem) is considered in a three-dimensional space of constant positive curvature, S ³. Conserved operators are found, and their commutation relations are derived. It is shown that, in the MIC-Kepler problem in S ³ space, conserved operators form a cubic algebra similar to that of the Kepler problem in the same space. This symmetry algebra is used to obtain the energy spectrum of the problem.     

On the spectra of randomly perturbed expanding maps

We consider small random perturbations of expanding and piecewise expanding maps and prove the robustness of their invariant densities and rates of mixing. We do this by proving the robustness of the spectra of their Perron-Frobenius operators.V. Baladi started the present work during a postdoctoral fellowship at IBM, T.J. Watson CenterL.-S. Young is partially supported by the National Science Foundation