The dynamics of a thin spherically-symmetric radiating shell

The conclusions of paper [2] are modified: using the shell formalism, relativistic effect could eventually be detected in X-ray bursters.     

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.     

Interaction of waves with a birefringent medium moving with acceleration

Recent experiments demonstrated that the energy of a neutron traversing an accelerated sample of a refractive medium changes. Later, it was realized that such an accelerated-medium effect (AME) is quite a general phenomenon characteristic of waves and particles of different nature. This paper discusses some special features of the effect for a birefringent medium. In this case, AME shows quite new features. In neutron optics, where birefringence is due to the spin dependence of the refractive index, AME results in a nonstationary state with a precessing spin. In the case of the propagation of a two-flavor neutrino through an accelerated layer of matter, AME affects substantially the ensuing evolution of a neutrino flavor state as it propagates through a free space.     

Nonlinear traveling wave vibration of a circular cylindrical shell subjected to a moving concentrated harmonic force

This is a study of nonlinear traveling wave response of a cantilever circular cylindrical shell subjected to a concentrated harmonic force moving in a concentric circular path at a constant velocity. Donnell's shallow-shell theory is used, so that moderately large vibrations are analyzed. The problem is reduced to a system of ordinary differential equations by means of the Galerkin method. Frequency-responses for six different mode expansions are studied and compared with that for single mode to find the more contracted and accurate mode expansion investigating traveling wave vibration. The method of harmonic balance is applied to study the nonlinear dynamic response in forced oscillations of this system. Results obtained with analytical method are compared with numerical simulation, and the agreement between them bespeaks the validity of the method developed in this paper. The stability of the period solutions is also examined in detail.     

Coupled vibration of a cylindrical shell for radiating high intensity ultrasound

The coupled vibrations of a cylindrical shell were analysed by a new method that we called ‘the apparent-elasticity method’. Several types of radiators using cylindrical shells were designed on the basis of analytical results and several acoustical characteristics were measured. In consequence, the analytical results were in good agreement with the experimental data, and the practicability of high intensity ultrasonic radiators using cylindrical shells was demonstrated.     

Triaxial octupole deformations and shell structure

Manifestations of pronounced shell effects are discovered when non-axial octupole deformations are added to a harmonic oscillator model. The degeneracies of the quantum spectra are in good agreement with the corresponding main periodic orbits and winding number ratios which are found by classical analysis. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 8, 525–530 (25 April 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

惯性系中直线运动的常加速度内禀刚性非惯性系

推导相对惯性系作直线运动的常加速度内禀刚性加速系的坐标变换关系式，并讨论该加速系的主要性质。     

Nonlinear vibrations of electroelastic shells with relatively large shear deformations

A set of two-dimensional nonlinear equations for thin electroelastic shells in vibrations with moderately large thickness-shear deformations are obtained from the variational formulation of the three-dimensional equations of nonlinear electroelasticity by expanding the mechanical displacement vector and the electric potential into power series in the shell thickness coordinate and retaining lower order terms. As an example, the equations are used to study nonlinear thickness-shear vibrations of a circular cylindrical shell driven by an electric voltage. Nonlinear amplitude-frequency behavior of electric current near strong resonance is obtained.     

Dynamic response of a pre-stressed cylindrical shell to a moving load

The work presented in this paper is concerned with the response of a pre-stressed, finite, thin circular cylindrical shell under a moving local load with a constant velocity. An analysis is carried out by a dynamic method, and the solutions which are bounded even at the critical velocity are obtained. The effects of the initial stresses on the dynamic responses of the displacement and the stresses are examined in connection with the velocity of the load.     

Nonlinear molecular deformations and solitons in a nematic liquid crystal

We studied nonlinear molecular deformations in a nematic liquid crystal with homeotropically aligned molecules and hard boundaries. As the basic dynamical equation for the director axis of the liquid crystal resembles the Landau-Lifshitz equation representing spin dynamics in a one dimensional classical continuum isotropic Heisenberg ferromagnetic spin chain, we invoke here the space curve formalism and the stereographic projection technique used in the case of the Heisenberg spin chain. Under space curve mapping, the director dynamics with elastic deformation is found to be governed by a perturbed nonlinear Schrödinger equation. A multiple-scale perturbation analysis brings out perturbed solitons to represent molecular deformations in the nematic liquid crystal. However, when a constant electric field is applied, the director dynamics is expressed under stereographic projection and the molecular deformations are found to be governed by periodic and localized static planar director configurations. A linear stability analysis on the static planar configurations shows that the system exhibits stable deformations.     

Time-average holography of objects vibrating sinusoidally and moving with constant acceleration

The characteristics function of time-average holography is discussed when the object is vibrating sinusoidally and moving with constant acceleration.     

Upon electric charge systems moving without acceleration and associated with charge creation

A discussion is given of certain electromagnetic fields associated with charges moving with zero acceleration. These fields involve zero magnetic field and the creation of charge.     

Collapse of a charged radiating star with shear

The junction conditions for a magnetohydrodynamic fluid sphere undergoing dissipative gravitational collapse in the form of a radial heat flux with shear are obtained. These conditions extend particular results of earlier treatments. We demonstrate that the pressure is proportional to the magnitude of the heat flux as is the case in shear-free models. However in our case the gravitational potentials must be solutions of the Einstein-Maxwell system of equations. The mass function m(v) is increased by a factor related to the charge Q of the radiating star. Physical quantities relating to the local conservation of momentum and surface redshift are obtained.     

On the dynamics of a thin spherically symmetric radiating shell,its classical model,and relativistic effects

A general relativity model of nova and supernova explosions is studied and improved. Its classical limit is found, and the magnitude of the velocity and mass necessary to detect relativistic effects are computed.     

Nonlinear frequency response of a moving grating with an applied field in bismuth silicon oxide

A fully nonlinear frequency response of a moving grating in bismuth silicon oxide, including the effects of an applied electric field, is modeled by solution of the time-dependent Kukhtarev equations for photorefractive materials. The numerical results are used to define fully the nonlinear response function F(m)=a(-1)[1-exp(-am)], where m is the modulation index in the intensity pattern, to yield the unknown quantity a over a broad range of detuning frequencies f . For low f, the response is superlinear with a<0, and for relatively large f it is sublinear with a>0 . In the midrange we predict, for the first time to our knowledge, a characteristic frequency f(l) at which a=0 and the response is linear, that is, F(m) approximately m, despite the presence of nonlinearly generated higher harmonics of the fundamental grating wave number. In view of this linear behavior, writing a hologram at the linear-response frequency f(l) might permit a more faithful reproduction of an object than that which is possible by writing at the frequency of maximum response at the resonance.     

Dynamics of a radiating surface discharge

We have elaborated a code for numerical treatment of two-dimensional problems of the dynamics of a surface discharge with inclusion of radiative energy transfer. The gas dynamic, electric, and radiative properties of a surface discharge in atmospheric air have been studied experimentally for a total energy input of 100 J/cm in the input power range 3–6 MW/cm. A new technique involving a discharge sliding along a conducting surface is applied to initiate an extended surface discharge. The calculations agree satisfactorily with the experiments. The method elaborated here makes it possible to calculate a broad class of linear discharges with an eye to produce a radiation source with problem-oriented spectral power characteristics.