Elastic scattering using an artificial confining potential

The discrete energies of a scattering Hamiltonian calculated under the influence of an artificial confining potential of almost arbitrary functional form can be used to determine its phase shifts. The method exploits the result that two short-range Hamiltonians having the same energy will have the same phase shifts upon removal of the confining potential. An initial verification is performed on a simple model problem. Then the stochastic variational method is used to determine the energies of the confined e(-)-He(2)S(e) system and thus determine the low energy phase shifts.     

Elastic response of an orthogonally reinforced plate

This paper develops a three-dimensional fully elastic analytical model of a solid plate that has two sets of embedded, equally spaced stiffeners that are orthogonal to each other. The dynamics of the solid plate are based on the Navier–Cauchy equations of motion of an elastic body. This equation is solved with unknown wave propagation coefficients at two locations, one solution for the volume above the stiffeners and the second solution for the volume below the stiffeners. The forces that the stiffeners exert on the solid body are derived using beam and bar equations of motion. Stress and continuity equations are then written at the boundaries and these include the stiffener forces acting on the solid. A two-dimensional orthognalization procedure is developed and this produces an infinite number of double indexed algebraic equations. These are all written together as a global system matrix. This matrix can be truncated and solved resulting in a solution to the wave propagation coefficients which allows the systems displacements to be determined. The model is verified by comparison to thin plate theory and finite element analysis. An example problem is formulated. Convergence of the series solution is discussed. The frequency limitations of the model are examined.     

Elastic constants of an aluminum-alumina unidirectional composite

The five independent second-order elastic constants of a transversely isotropic aluminum/alumina fiber composite have been measured for the first time using a resonant ultrasound spectroscopy technique. These data were used to deduce the elastic constants and engineering moduli for off-axis loading conditions.     

Elastic stress field beneath an arbitrary axisymmetric punch

The nanoindentation test is commonly used for the local determination of mechanical properties (hardness, elastic modulus, etc.) and also to study the initial stages of plasticity (dislocation nucleation, dislocation interaction mechanisms) at the nanometre scale. In the latter case, the determination of the elastic stress field beneath the indenter is of primary interest. An analytical expression is derived for the elastic stress and strain fields beneath an axisymmetric punch. Most solutions, in the literature, are given for simple indenter shapes, such as flat, conical or spherical indenters. The complete solution proposed for an arbitrary indenter profile is described by a power law, in which the exponent can be an integer or not. The stress is given as the real part of complex analytical expressions.     

Mathematical Modeling of Nonlinear Waves in an Elastic Cylindrical Shell Surrounded by an Elastic Medium and Containing a Viscous Incompressible Liquid

A mathematical model is proposed for a Kirchhoff–Love-type nonlinear elastic cylindrical shell surrounded by an elastic medium and containing a viscous incompressible liquid. The model is used to analyze wave processes both analytically and numerically. On the basis of the proposed computational algorithm, a software package is developed, which makes it possible to plot diagrams and to obtain numerical solutions to Cauchy problems with initial conditions taken in the form of exact solutions to dynamic equations of shells in the absence of the liquid.     

Elastic scattering of a photon by an atom with an open shell

In the nonrelativistic approximation, the absolute values and the forms of the differential cross sections of the anomalous elastic scattering of a linearly polarized x-ray photon by manganese and copper atoms in the energy region of the ionization threshold of the 1s shell are calculated for the wave functions of one-electron states. We take into account the multiparticle effects of relaxation of atomic shells in the field of core vacancies, multiplet splitting, the configuration interaction, and Auger and radiative decays of vacancies, as well as the processes of double excitation/ionization of the ground state of the atom. The calculation results are in good agreement with the synchrotron experiment.     

Elastic energy of an inhomogeneous solid solution. I

A method of modulated (with respect to the amplitude and wave vector) concentration waves is proposed for determining the elastic energy of an inhomogeneous solid solution in a microscopic approximation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 48–53, September, 1980.     

Elastic energy of an inhomogeneous solid solution. II

The contributions to the elastic energy of an inhomogeneous solid solution due to redistribution of the concentration and the short- and long-range order are considered. The applicability of the continuum approximation is investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 53–57, October, 1980.I am grateful to A. G. Khachaturyan for a discussion that stimulated this work and to B. M. Darinskii for discussions.     

Nonlinear Waves in an Inhomogeneous Fluid Filled Elastic Tube

In a thin-walled, homogeneous, straight, long, circular, and incompressible fluid filled elastic tube, small but finite long wavelength nonlinear waves can be describe by a KdV (Korteweg de Vries) equation, while the carrier wave modulations are described by a nonlinear Schrödinger equation (NLSE). However if the elastic tube is slowly inhomogeneous, then it is found, in this paper, that the carrier wave modulations are described by an NLSE-like equation. There are soliton-like solutions for them, but the stability and instability regions for this soliton-like waves will change, depending on what kind of inhomogeneity the tube has.     

The Four-Pole Transfer Matrices of an Elastic Porous Layer

Acoustical Physics - Relations are proposed for the transfer matrices of linear four-poles that relate the pressure and normal velocity components at free and/or impervious boundaries of a planar...     

Power Flux along a Straight Crack in an Elastic Plate

Propagation of the edge waves along a straight crack in an elastic plate is studied. The power fluxes associated with these waves are calculated, and the modes of vibration are considered.     

Elastic electron scattering in an intense field and two-photon emission

The elastic scattering amplitude, taking into account the mass correction to the propagation function, is found for electrons interacting with an intense electromagnetic field characteristic of non-linear quantum electrodynamics. The probability for two-photon emission e → e2γ, the mass correction to the probability for one-photon emission and the mass correction to the anomalous field-dependent magnetic moment of the electron are found with the aid of the amplitude.     

Elastic response of an acoustic coating on a rib-stiffened plate

This paper develops a three-dimensional analytical model of a fluid-loaded acoustic coating affixed to a rib-stiffened plate. The system is loaded by a plane wave that is harmonic both spatially and temporally. The model begins with Navier-Cauchy equations of motion for an elastic solid, which produces displacement fields that have unknown wave propagation coefficients. These are inserted into stress equations at the boundaries of the plate and the acoustic coating. These stress fields are coupled to the fluid field and the rib stiffeners with force balances. Manipulation of these equations develops an infinite number of indexed equations that are truncated and incorporated into a global matrix equation. This global matrix equation can be solved to determine the wave propagation coefficients. This produces analytical solutions to the systems’ displacements, stresses, and scattered pressure field. This model, unlike previously developed analytical models, has elastic behavior and thus incorporates higher order wave motion that makes it accurate at higher wavenumbers and frequencies. An example problem is investigated for three specific model results: (1) the dynamic response, (2) a sonar array embedded in the acoustic coating, and (3) the scattered pressure field. An expression for the high frequency limitation of the model is derived. It is shown that the ribs can have a significant impact on the structural acoustic response of the system.     

Elastic scattering of an electron by the negative lithium ion

In the framework of the many-body theory, the differential and total cross sections of elastic scattering of slow electrons by the negative lithium ion Li⁻ are obtained. Calculations are performed both in the Hartree-Fock single-particle approximation and with regard to many-electron correlations, which take into account the dynamic polarization of the core. Features observed in the behavior of the phases and cross sections for p and d partial waves are associated with resonance scattering of electron waves. Considering the dynamic polarization of the core by an incident electron heightens the diffraction character of the scattering. The real process is compared with particle scattering in models with a repulsive potential.     

Re-Reflections of an Elastic Precursor of a Shock Wave in Solids

Doklady Physics - By the example of experimental data on the reflection of an elastic–plastic shock wave from a free surface of a steel or aluminum-alloy plate, the conditions and...     

Elastic Interaction between a String of Cells and an Individual Cell

The elastic interaction between a string of cells and an individual cell on an elastic substrate is investigated numerically using the force-dipole model. This interaction is found to be of short range, and the cut-off distance is about 1.4 times of the length of the cell. The energy-minimization distance is about half the cellular length. The specific relationship between the cellular reorientation and the cellular position are obtained quantitatively. A critical distance is found, and the cellular orientation has an abrupt change at this transition point.