Resonance scattering of sound by spheroidal elastic bodies and shells

The resonances of spheroidal elastic bodies (prolate and oblate) in the form of solid bodies and shells are determined using dynamic elasticity theory and Debye potentials. In addition to analytic solutions, results of computer calculations are presented for the angular characteristics and scattering cross sections of spheroidal elastic bodies.     

Some new radiating Kerr-Newman solutions

Three exact non-static solutions of Einstein-Maxwell equations corresponding to a field of flowing null radiation plus an electromagnetic field are presented. These solutions are non-static generalizations of the well known Kerr-Newman solution. The current vector is null in all the three solutions. These solutions are the electromagnetic generalizations of the three generalized radiating Kerr solutions discussed by Vaidya and Patel. The solutions discussed by us describe the exterior gravitational fields of rotating radiating charged bodies. Many known solutions are derived as particular cases.     

Effect of small total pulse on development of a wake behind the self-propelled bodies

Experimental studies on the wakes behind the self-propelled bodies of revolution have been analysed, and results of stereometric studies on the co-current flows behind autonomous streamlined and bluff bodies of revolution are presented for the times of their development corresponding to the coordinate system of a distant wake of 2400 and 1200 body diameters, correspondingly. Possible modelling of axisymmetric co-currents by the flows generated by a string at its pulse motion along the axis is examined. It is shown that supposed solutions based on the model of interferential development of wakes behind the self-propelled bodies of revolution can approximate both the known results of experimental studies of wakes behind the self-propelled bodies of revolution and the flows generated by corresponding pulse transportation of a string.     

The motion of black holes

The motion of axisymmetric non rotating black holes is discussed using the properties of Weyl solutions. It is shown that there are no such solutions representing more than one black hole or black holes and ordinary massive bodies apart from the exceptional case of a massive body which surrounds or partially surrounds a black hole. A new exact solution is obtained representing a black hole chased by a negative mass particle, both objects being uniformly accelerated and all solutions representing a single black hole tidally distorted by an external static, axisymmetric gravitational field are obtained.     

Variational approach to three-dimensional inverse problems of potential theory

A method of regularization and solving problems of flow around bodies according to a desired distribution of the characteristics of the fields on the surface of the bodies themselves is described. Examples of solutions of such problems for potential flows are given, and a method of reducing inverse problems of the fluid mechanics of an effectively inviscid liquid to potential problems is presented. Zh. Tekh. Fiz. 67, 8–15 (October 1997)     

Nonlinear effects during the tension, bend, and torsion of elastic bodies with distributed dislocations

A series of exact solutions of the problems on large deformations of three-dimensional nonlinearly elastic bodies with distributed dislocations is found. The tension-compression of the prismatic bodies with the distributed straight-linear screw dislocations is investigated. The influence of the distributed screw dislo- cations of the radial direction of the torsion and extension of the circular cylinders under large deformations is investigated. The problem on the strong bend of the rectangular bar containing distributed edge dislocations is solved. It is established that nonuniform rotation fields can occur at zero stresses in a body with continu- ously distributed dislocations.     

Equilibrium Points in the Restricted Four-Body Problem with Radiation Pressure

This paper studies numerically the photogravitational version of the restricted four-body problem, where an infinitesimal particle is moving under the gravitational attraction and radiation pressure of three bodies much bigger than the particle, the primaries. The fourth body does not affect the motion of the three bodies. These bodies are always at the vertices of an equilateral triangle (Lagrange configuration). We consider all the primary bodies (m ₁, m ₂, m ₃) as radiation sources with radiation factors of the two bodies (m ₂ and m ₃) equal. In this paper we suppose the masses of the three primary bodies are equal. It is found that the involved parameters influenced the positions of the equilibrium points. The linear stability of the relative equilibrium solutions is also studied and all these points are unstable.     

Thermo-elastic Greenʼs functions for an infinite bi-material of one-dimensional hexagonal quasi-crystals

This Letter is concerned with thermo-elastic fundamental solutions of an infinite space, which is composed of two half-infinite bodies of different one-dimensional hexagonal quasi-crystals. A point thermal source is embedded in a half-space. The interface can be either perfectly bonded or smoothly contacted. On the basis of the newly developed general solution, the temperature-induced elastic field in full space is explicitly presented in terms of elementary functions. The interactions among the temperature, phonon and phason fields are revealed. The present work can play an important role in constructing farther analytical solutions for crack, inclusion and dislocation problems.     

轴对称体声振耦合的边界子波谱与有限元耦合方法

探讨了子波在Helmholtz积分方程及声振耦合中的应用,在建立了求解轴对称Helmholtz积分方程的子波谱方法的基础上,构造了轴对称子波谱与轴对称有限元的耦合方法,该方法可以处理轴对称问题的任意边界条件.进行了声振耦合问题的模态分析.     

Diffraction of plane waves by the interface between black and soft/hard semi-planes

A theory of scattering, based on the non-perturbation of the incident field, is developed for the black bodies. The method is applied to the diffraction problem of plane waves by an interface between the black and soft/hard half-planes. The solutions are obtained in terms of infinite series and then transformed into Fresnel integrals. The scattered fields are investigated numerically.     

Relativistic Two-Body Problem: Existence and Uniqueness of Two-Sided Solutions to Functional-Differential Equations of Motion

Abstract

We study a class of explicitly Poincare-invariant equations of motion (EMs) of two point bodies with a finite speed of propagation of interactions (combination of retarded and advanced ones) that may be considered as functional-differential equations or differential equations with deviating argument of a neutral type. Under conditions having a clear physical interpretation it is proved that there exist ordinary differential equations with all weakly-relativistic solutions satisfying the initial EMs. The existence and uniqueness of two-sided solutions of initial EMs on the infinite time interval are investigated.     

Ratios of magnetic charge to charge and of magnetic mass to mass

It is shown that, unlike the case of (vacuum) solutions describing isolated bodies, conformal Killing fields are not excluded by the structure of vacuum gravitational magnetic monopoles at null infinity. The resulting dilation must be constant. This brings support to the viewpoint that such solutions might have a role to play in the understanding of gravitational entropy and time's arrow. If, in addition, a Maxwellian magnetic monopole (Dirac string singularity) is available, the ratio of the total magnetic charge (magnetic mass) over the total electric charge (mass) can be identified. This common feature between the gravitational and the electromagnetic interaction finds its origin in the space-time topology.     

Nonlinear dispersion of a pollutant ejected into a channel flow

In this paper, we study the nonlinear coupled boundary value problem arising from the nonlinear dispersion of a pollutant ejected by an external source into a channel flow. We obtain exact solutions for the steady flow for some special cases and an implicit exact solution for the unsteady flow. Additionally, we obtain analytical solutions for the transient flow. From the obtained solutions, we are able to deduce the qualitative influence of the model parameters on the solutions. Furthermore, we are able to give both exact and analytical expressions for the skin friction and wall mass transfer rate as functions of the model parameters. The model considered can be useful for understanding the polluting situations of an improper discharge incident and evaluating the effects of decontaminating measures for the water bodies.     

Low frequency two dimensional flows through a sparse array of bodies

A low frequency and weak interaction theory is developed to study certain types of unsteady two-dimensional flows through an array of bodies. The results, together with the Taylor transformation, provide a simple and systematic yet powerful technique for obtaining solutions for an important, but otherwise extremely difficult, class of problems. The general results are applied to two specific examples in order to illustrate the approach and to produce some interesting results.     

A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities

We introduce a multidimensional peridynamic formulation for transient heat-transfer. The model does not contain spatial derivatives and uses instead an integral over a region around a material point. By construction, the formulation converges to the classical heat transfer equations in the limit of the horizon (the nonlocal region around a point) going to zero. The new model, however, is suitable for modeling, for example, heat flow in bodies with evolving discontinuities such as growing insulated cracks. We introduce the peridynamic heat flux which exists even at sharp corners or when the isotherms are not smooth surfaces. The peridynamic heat flux coincides with the classical one in simple cases and, in general, it converges to it in the limit of the peridynamic horizon going to zero. We solve test problems and compare results with analytical solutions of the classical model or with other numerical solutions. Convergence to the classical solutions is seen in the limit of the horizon going to zero. We then solve the problem of transient heat flow in a plate in which insulated cracks grow and intersect thus changing the heat flow patterns. We also model heat transfer in a fiber-reinforced composite and observe transient but steep thermal gradients at the interfaces between the highly conductive fibers and the low conductivity matrix. Such thermal gradients can lead to delamination cracks in composites from thermal fatigue. The formulation may be used to, for example, evaluate effective thermal conductivities in bodies with an evolving distribution of insulating or permeable, possibly intersecting, cracks of arbitrary shapes.     

Observational manifestations of black holes in the Horndeski gravity model

The geodesic equations for black hole solutions in the scalar–tensor Horndeski gravity model with non-minimal kinetic coupling have been investigated. The ranges of model parameters admitting the existence of bounded orbits have been determined. Constraints on the model parameters providing agreement of the model with the observational data on the accretion and motion of bodies in the Solar system have been obtained.     

Isoholonomic problems and some applications

We study the problem of finding the shortest loops with a given holonomy. We show that the solutions are the trajectories of particles in Yang-Mills potentials (Theorem 4), or, equivalently, the projections of Kaluza-Klein geodesics (Theorem 2). Applications to quantum mechanics (Berry's phase, Sect. 3) and the optimal control of deformable bodies (Sect. 6) are touched upon.     

New solutions for charge distribution on conductor surface

In the paper, a problem of electrostatics for charge distribution on a conductor surface is analytically solved for three new particular cases of conducting surfaces with complicated shape and specified value of electrostatic potential. The exact analytical expressions for surface charge density for the bodies are obtained. All the solutions are represented in a clear view of 3D graphs. It is shown that the proposed method of electrostatic problem for conductors allows to obtain infinitely many numerical solutions for the problem but only several special cases can be solved analytically.     

On the black hole limit of rotating discs and rings

Solutions to Einstein’s field equations describing rotating fluid bodies in equilibrium permit parametric (i.e. quasi-stationary) transitions to the extreme Kerr solution (outside the horizon). This has been shown analytically for discs of dust and numerically for ring solutions with various equations of state. From the exterior point of view, this transition can be interpreted as a (quasi) black hole limit. All gravitational multipole moments assume precisely the values of an extremal Kerr black hole in the limit. In the present paper, the way in which the black hole limit is approached is investigated in more detail by means of a parametric Taylor series expansion of the exact solution describing a rigidly rotating disc of dust. Combined with numerical calculations for ring solutions our results indicate an interesting universal behaviour of the multipole moments near the black hole limit.     

Dependence of irradiation temperature in the response of iron salts

A potential dosimeter based on aqueous frozen solutions and solid-state salt are presented for the evaluation of the energy transferred during the interaction of high-energy radiation with matter at low temperature. The foundation of these dosimeters, both the solid state and the frozen solutions, is based on the measurement of the change of the iron oxidation state. The systems were irradiated with gamma radiation at different doses (up to 10 MGy), and at different temperatures (from 77 to 298 K). The irradiated samples were analysed by UV-spectroscopy and Mössbauer spectroscopy. A theoretical model was developed for the chemical reactions system. This model reproduces the experimental effects produced by the irradiation in aqueous solutions of ferrous salt. The results showed that the response of the dosimeters depends on the irradiation temperature. At low-radiation doses, the response was linear. In particular, this work can be applied to low-temperature dosimetry can be specially applied to simulation experiments of extraterrestrial bodies, as well as in general to space research.