A spherically symmetric radiating shell in the presence of a spinless radiating central body

We construct a solution of Einstein's field equations with a possible astrophysical interest by matching a Vaidya solution with another Vaidya solution through a thin spherical shell of radially radiating matter. We study the system of equations for the motion of the shell and the radiation fields in two simple cases. In one of them we consider a dust shell of constant proper mass radiating at constant rate. In the other case we restrict the motion of the shell to a stationary configuration and assume it to be totally opaque. We find that this later solution is unstable under small perturbations in the radius of the shell but there exist stable stationary solutions if the pressure within the shell is different from zero.     

Kinetic theory of hydrodynamic flows. II. The drag on a sphere and on a cylinder

In this paper we continue the study of solutions of the extended Boltzmann equation started previously. In particular, we study an iterated solution of the equation that can be used to describe the flow of a rarefied gas around a macroscopic object. We discuss the rarefied flow and then show how the iterated solution can be extended into the hydrodynamic regime. The results for the drag force and for the distribution function of the gas molecules are shown to be identical to the results obtained in a previous paper by a generalization of the normal solution method. We also discuss the special properties of both rarefied and continuum flows around a cylinder and show that in both regions one must take into account Oseen-like terms which naturally appear in the extended Boltzmann equation. In the hydrodynamic regime we obtain Lamb's formula for the force on the cylinder. By relating the terms in the iterated expression to dynamical events taking place in the fluid, we are able to discuss the dynamical origin of the results obtained here.A preliminary report on the work described here and in Part I was given in Ref. 2.     

Gauge-invariant exact solution of a general separable potential model of a quantum system in a laser field

In this Letter we present the exact stationary solution in the length-gauge of the Schrödinger equation for interaction of a circularly polarized laser field with a quantum system possessing the continuous spectrum and any (finite) number of bound states of arbitrary angular momentum symmetry. This manifestly gauge-invariant solution complements the recently given velocity-gauge solution of the model. We also briefly consider the corresponding model with a quantum field in the number-state representation.     

Observables from a solution of (1+3)-dimensional relativistic hydrodynamics

In this paper we analyze a (1+3)-dimensional solution of relativistic hydrodynamics. We calculate momentum distribution and other observables from the solution and compare them to measurements from the Relativistic Heavy-Ion Collider (RHIC). We find that the solution we analyze is compatible with the data. In the last several years many numerical models were tested, but it is the first time that an exact, parametric, (1+3)-dimensional relativistic solution is compared to data.     

Time dependent compressible flow about a spherically symmetric polymer in solution

We obtain the general solution of the linear Navier-Stokes equation for time dependent compressible viscous flow about a spherically symmetric polymer molecule. The solution is presented in a covariant form valid in a general cartesian coordinate frame. In the course of deriving the solution we obtain a general decomposition of the unperturbed flow in the absence of the polymer. Our solution generalizes the earlier solution derived by Schmitz and Felderhof for the case of creeping flow.     

Curle's equation and acoustic scattering by a sphere

Recent papers have initiated interesting comparisons between aeroacoustic theory and the results of acoustic scattering problems. In this paper, we consider some aspects of these comparisons for acoustic scattering by a sphere. We give a derivation of Curle's equation for a specific class of linear acoustic scattering problems, and, in response to previous claims to the contrary, give an explicit confirmation of Curle's equation for plane wave scattering by a stationary rigid sphere of arbitrary size in an inviscid fluid. We construct the complete solution for scattering by a rigid sphere in a viscous fluid, and show that the neglect of viscous terms in Curie's equation yields an incomplete prediction of the far field dipole pressure. We also consider the null field solution of the sphere scattering problem, and give its extension to the vorticity modes associated with viscosity. Finally, we construct a solution for an elastic sphere in a viscous fluid, and show that the rigid sphere/null field solution is recovered from the limit of infinite longitudinal and shear wave speeds in the elastic solid.     

Created photon distribution in a cavity with a moving wall

In the framework of inverse problems, we present an analytical solution for the problem of photon generation in a cavity with a moving wall. We give a photon distribution. With some discussions on this distribution, we point out that the case when the motion index number is 2 is of particular interest from a physical point of view and we also compute the corresponding spectrum of the created photons.     

Development of a Stokes flow solver robust to large viscosity jumps using a Schur complement approach with mixed precision arithmetic

We develop an iterative solution technique for solving Stokes flow problems with smooth and discontinuous viscosity structures using a three dimensional, staggered grid finite difference discretization. Two preconditioned iterative methodologies are applied to the saddle point arising from the discrete Stokes problem. They consist of a velocity–pressure coupled approach (FC) and a decoupled, Schur complement approach (SC). Within both of these methods, we utilize either the scaled BFBt, or an identity matrix scaled by the local cell viscosity (LV) to define a preconditioner for the Schur complement. Additionally, we propose to use a mixed precision Krylov kernel to improve the convergence by reducing round-off error. In this approach, standard double precision is used during the application of the preconditioner, whilst higher precision arithmetic is used to define the matrix vector product, dot products and norms required by the Krylov method. In our Krylov kernel, we utilize quad precision arithmetic which is emulated via the double–double precision method. We consider several simplified geodynamic problems with a viscosity contrast to demonstrate the robustness and scalability of our solution methods. Through a careful choice of stopping conditions, we are able to quantitatively compare the residuals between the SC and FC approaches. We examine the trade-off relationship between the number of outer iterations required for convergence, and the computational cost per iteration, for the each solution methods. We find that it is advantageous to use the FC approach utilizing relaxed tolerances for solution of the sub-problems, combined with the LV preconditioner. We also observed that in general, the SC approach is more robust than FC and that BFBt is more robust than LV when used in our numerical experimental. In addition, our mixed precision method produces improved convergence rates of Arnoldi type Krylov subspace methods without a drastic increasing the computational time. The usage of a high precision Krylov kernel is found to be useful for the solver associated with the velocity sub-problem.     

Exact solution of a coagulation equation with a product kernel in the multicomponent case

In this paper, we obtain the general solution for the continuous Smoluchowski equation in the multicomponent case with a product kernel as a series expansion. The solution of the problem involves the Laplace transform in several dimensions. We obtain a nonlinear partial differential equation (PDE) of the advective kind generalizing the one previously given by other authors for the mono-component case.As in its relative mono-component case, gelation is produced at some point, the conditions for its occurrence being the same as those for the mono-component case, though substituting a sum of derivatives by a derivative in the Laplace transform field. We demonstrate that for a multicomponent particle size distribution (PSD) of multiplicative form, it is sufficient for one of the marginal PSDs to generate instantaneous gelation for the occurrence of instantaneous gelation in the multicomponent PSD.The general solution is applied to several specific cases, a discrete case that recovers a previously known solution, and another two continuous cases which can be used to check numerical methods designed to directly solve the Smoluchowski equation in more general cases.We have compared the solutions for the multicomponent PSD for constant, additive and product kernels and we conjecture about the relation existing between the functional forms for the solutions both in the mono-component and the multicomponent case.Finally, we have analysed the shape of the solutions for multicomponent PSD for constant, additive and product kernels for very small masses of components, obtaining a qualitatively different behaviour for the product kernel. This has effects in the mixing state of the sol phase as time passes.     

Particle creation if a cosmic string snaps

We calculate the Bogolubov coefficients for aC ⁽⁰⁾ metric which describes the snapping of a cosmic string. In this background, we show that there are noregular solutions with particle interpretation, but we find ageneralized solution with integrable discontinuity, which exhibits particle creation. We also find a regular solution if we allow wave packets.     

Differential Harnack Inequalities Under a Coupled Ricci Flow

In this paper, we prove several differential Harnack inequalities under a coupled Ricci flow. As applications, we get Harnack inequalities for positive solutions of backward heat-type equations with potentials under the coupled Ricci flow. We also derive Perelman??s differential Harnack inequality for fundamental solution of the conjugate heat equation under the Ricci flow.     

Existence and Regularity of a Solution of a Kac Equation Without Cutoff Using the Stochastic Calculus of Variations

We consider a generalized Kac equation without cutoff, with which we associate a non-standard nonlinear stochastic differential equation. We adapt the techniques in Bichteler and Jacod [2] to prove that the law of a solution of the stochastic differential equation has a density, which is a solution of the Kac equation. The initial law is very general: we only assume it has second order moments and is not the Dirac mass at 0. We thus generalize the analytical results of existence of a solution of this equation. If we furthermore assume existence of all moments for the initial law, we obtain as a corollary using the proof in Desvillettes [6] that the density is smooth. We prove a slightly better regularity result under more stringent assumptions using the stochastic calculus of variations, adapting the methods in [1]. Received: 15 July 1998 / Accepted: 4 March 1999     

Conformally invariant thermodynamics of a Maxwell-Dilaton black hole

The thermodynamics of Maxwell-Dilaton black holes has been extensively studied. It has served as a fertile ground to test ideas about temperature through various definitions of surface gravity. In this paper, we make an independent analysis of this black hole solution in both, Einstein and Jordan, frames. We explore a set of definitions for the surface gravity and observe the different predictions they make for the near extremal configuration of this black hole. Finally, motivated by the singularity structure in the interior of the event horizon, we use a holographic argument to remove the micro-states from the disconnected region of this solution. In this manner, we construct a frame independent entropy from which we obtain a temperature which agrees with the standard results in the non-extremal regime, and has a desirable behaviour around the extremal configurations according to the third law of black hole mechanics.     

A nonlinear PDE model for reconstructing a regular surface from sampled data using a level set formulation on triangular meshes

In this paper, we propose a nonlinear PDE model for reconstructing a regular surface from sampled data. At first, we show the existence and the uniqueness of a viscosity solution to this problem. Then we propose a numerical scheme for solving the nonlinear level set equation on unstructured triangulations adapted to the data sample. We show the consistency of this scheme. In addition, we show how to compute nodewise first and second order derivatives. Some application examples of curve or surface construction are provided to illustrate the potential and to demonstrate the accuracy of this method.     

Quantum transport in one-dimensional systems via a master equation approach: Numerics and an exact solution

We discuss recent findings about properties of quantum nonequilibrium steady states. In particular we focus on transport properties. It is shown that the time-dependent density matrix renormalization method can be used successfully to find a stationary solution of Lindblad master equation. Furthermore, for a specific model an exact solution is presented.     

On the analytical solution of viscous fluid flow past a flat plate

In this Letter, we propose a simple approach using HAM to obtain accurate totally analytical solution of viscous fluid flow over a flat plate. First, we show that the solution obtained using HPM is not a reliable one; moreover, we show that HPM is only a special case of HAM and its basic assumptions are restrictive rather than useful. We set ?=−1 for the case of comparison of our results to those obtained using HPM. Afterwards, we introduce an extra auxiliary parameter and a straightforward approach to find best values of this auxiliary parameter which plays a prominent role in the frame of our solution and makes it more convergent in comparison to previous works.     

Can a Circulating Light Beam Produce a Time Machine

In a recent paper, Mallett found a solution of the Einstein equations in which closed timelike curves (CTC’s) are present in the empty space outside an infinitely long cylinder of light moving in circular paths around an axis. Here we show that, for physically realistic energy densities, the CTC’s occur at distances from the axis greater than the radius of the visible universe by an immense factor. We then show that Mallett’s solution has a curvature singularity on the axis, even in the case where the intensity of the light vanishes. Thus it is not the solution one would get by starting with Minkowski space and establishing a cylinder of light.     

Anomalous transport fluctuations in a model of irregular media

We consider a diffusion model with stochastic porosity for which the average solution exhibits an abnormal transport. In this paper we investigate the relation of such an anomalous diffusive property of the mean value with the behavior of the solution corresponding to each realization of the stochastic porosity. Such a solution will correspond to the actual measurements in an experiment made on a particular tube. The most relevant result of our work is that, although the concentration corresponding to each realization diffuses normally for large times, it experiments on large deviations from the mean value during intermediate times.     

A Formalism to Study the Propagation of the Four-Wave Mixing Signal in a Strongly Driven Two-Level System Immersed in a Thermal Reservoir

We analyze two analytical solutions for the study of the propagation of the four-wave mixing (FWM) signal in a strongly driven two-level system, when the stochastic effects of the solvent are explicitly considered. The first solution is valid only for a constant pump intensity, while the second solution considers pump propagation explicitly. In both cases, we were able to derive analytical expressions for the FWM nonlinear intensity signal in terms of the field amplitude and thermal noise parameters. Copyright 2000 Academic Press.     

Frequency Regime of Generation of a Holographic Distributed Feedback Dye Laser

We carried out an experimental investigation of the frequency regime of generation of a holographic distributed feedback (DF) dye laser. We show that the convection induced in liquid by heating-up a solution in the excitation zone ensures self-pumping of the solution through this zone that is sufficient for stable operation of the laser in the regime of frequently repeating pulses without forced circulation of the solution through the cuvette. It is found that the main condition for the operation of a DF-laser in this regime is the sharp focusing of pumping radiation, which ensures transverse dimensions of the generation zone of less than 1 mm. In experiments, we produced stable generation of a holographic DF dye laser in the regime of self-pumping of a solution with a pulse repetition rate of up to 1 kHz with an efficiency of 10% and a spectral line width of 0.01 nm.