Treatment Of Damping Research Articles

Novel simulation model for many-body multipole dispersion interactions

We present a novel simulation technique, within the framework of a molecular dynamics simulation, which accounts for both two- and three-body dispersion interactions, up to the triple-quadrupole interaction. This technique involves a unification of molecular dynamics and quantum-mechanical variational methods, in the spirit of the Car-Parrinello method. The advantage of this new method compared to existing techniques for simulating three-body dispersion forces, is that it allows for a consistent treatment of both dispersion damping and periodic boundary conditions at the pair and three-body level. The latter means that it would be possible, for the first time, to include many-body dispersion effects in the simulation of bulk properties of materials, without making use of effective pair potentials.

Novel simulation model for many-body multipole dispersion interactions

We present a novel simulation technique, within the framework of a molecular dynamics simulation, which accounts for both two- and three-body dispersion interactions, up to the triple-quadrupole interaction. This technique involves a unification of molecular dynamics and quantum-mechanical variational methods, in the spirit of the Car-Parrinello method. The advantage of this new method compared to existing techniques for simulating three-body dispersion forces, is that it allows for a consistent treatment of both dispersion damping and periodic boundary conditions at the pair and three-body level. The latter means that it would be possible, for the first time, to include many-body dispersion effects in the simulation of bulk properties of materials, without making use of effective pair potentials.

A novel simulation model for three-body dispersion interactions

We present a novel molecular dynamics simulation technique, which accounts for both two- and three-body dispersion interactions. This technique is a unified approach of molecular dynamics and quantum mechanical variational methods, in the spirit of the Car - Parrinello method (1985 Phys. Rev. Lett. 55 2471). We use a highly simplified model for the electronic structure of the atoms, which is, nevertheless, sufficient to correctly reproduce the London two-body, and the Axilrod - Teller three-body dispersion forces in an appropriate limit. The advantage of this new method is that it allows for a consistent treatment of both dispersion damping and periodic boundary conditions at the pair and three-body levels.

Self-consistent treatment of the polaron damping in the Holstein model

Using the Holstein model, the damping of the localized polaron state and the small polaron conductivity are represented by the series of contributions from the multiphonon processes in which the polaron damping is taken into account. The self-consistent treatment of the damping shows the enhancement of the small-polaron relaxation rate by the quantum fluctuations of the lattice corresponding to the energy non-conserving phonon processes. The conditions for the polaron localization as well as the dependence of the d.c. conductivity on the electron transfer integral are discussed.

Landau fluid equations for electromagnetic and electrostatic fluctuations

Closure relations are developed to allow approximate treatment of Landau damping and growth using fluid equations for both electrostatic and electromagnetic modes. The coefficients in these closure relations are related to approximations of the plasma dispersion function by ratios of polynomials. Thirteen different numerical sets of coefficients are given and explicitly related to previous fits to the plasma dispersion function. The application of the techniques presented in this paper is illustrated with the specific example of resistive g modes. Comparisons of full kinetic and approximate results are made for the solutions to the dispersion relation, radially resolved modes in sheared magnetic geometry, and the plasma dispersion function itself.

Improvement of Plasma Confinement during RF Current Drive in Tokamaks

It is shown that the E rf × B drift for resonant electrons in tokamaks does not cancel and forms an inward flux during rf heating with a travelling wave type spectrum when Dawson like treatment of Landau damping in the presence of the magnetic field is performed as an initial value problem, where E rf is rf electric field and B is the magnetic field. This effect could be the basis of the phenomenon that the plasma confinement is improved during low density lower-hybrid current drive in tokamaks.

Global wave treatment of mode conversion and wave damping for perpendicular propagation across the electron cyclotron and upper-hybrid resonances

The processes of propagation and absorption of electron cyclotron extraordinary modes in a Tokamak type plasma slab are studied by means of a wave-dynamical system of differential equations in which temperature effects are taken into account. Also the mode conversion of the incoming wave into Bernstein waves is described by the propagation equations and is analysed in the parameter space together with its effects on the global absorption. Similarities and discrepancies between the results of the numerical integration of the full-wave system and those provided by the WKB approximation are discussed as a function of the electron density and temperature.

Radiation damping of degenerate states: I. Theory and application to two-atom systems

Starting from Heitler's theory of radiation damping of discrete states a treatment of the damping of degenerate states is derived. The treatment is used to study the properties of a two-atom system in the dipole approximation using a Hamiltonian which treats atom-atom and atom-photon interactions on an equal footing. The properties calculated to fourth-order terms in the electronic charge include the retarded interaction energy, resonance fluorescence and Rayleigh scattering amplitudes.

Experimental Study of Dilatational vs Distortional Straining Action in Material-Damping Production

Experimental test setups for measuring material damping in structural metals have invariably been limited to producing states of strain wherein the distortional component is dominant. In the case of flexural vibrations of plates and shells, however, this condition is often reversed, sometimes with the elastic energy associated with dilatational straining action exceeding the corresponding distortional component by an order of magnitude. It has, therefore, been conjectured that effects due to dilatational straining, small enough to be masked by experimental scatter in the aforementioned tests, might become significant under conditions of pronounced dilatational straining, viz., plate vibrations. For this purpose, a test machine was designed to measure material damping in thin-walled, cylindrical specimens subject to combined internal pressure and axial cyclic loading. Tests were carried out on a number of manganese-copper alloy specimens for which prior studies, already published, had established damping properties under uniaxial cyclic stress. The new tests extended the ratio of dilatational to distortional strain energies from a fraction up to a factor of 2, the latter limit being determined by possible onset of stress-history effects, which were avoided. The results display a small but definite influence of dilatational straining action in producing additional material damping to that arising from distortional straining action. As a consequence, a modified formula is suggested for the treatment of material damping in plate vibrations.

On the classical theory of radiating electrons

1. In Dirac's classical theory of radiating electrons, the relativistic equations of motion of a point-electron in an electromagnetic field arewhere (x0, x1, x2, x3) denote the electron's coordinates in flat space-time, dots denote differentiation with respect to the proper time , and the external electromagnetic field is described by the usual field quantities Fμν. The units are chosen so that the velocity of light is unity. These equations, which are derived from the principles of conservation of energy and of momentum, are the same as those obtained by Lorentz, when he used the spherical model of the electron and included radiation damping in an approximate way. But Dirac's method of derivation suggests that this treatment of radiation damping, and therefore the resulting scheme of equations, is exact within the limits of the classical theory.

Classical Theory of Point Dipoles

IT is well known that a limit to the validity of quantum mechanics is set by its neglect of the effects of radiation damping, and an indication as to where this limit occurs is given in electron theory by the classical equation of Lorentz, which takes radiation damping into account. Now the interaction of the meson field with a neutron or proton contains an explicit dipole term, and this leads to scattering cross-sections for mesons which increase quadratically with the energy. A classical treatment of radiation damping for a dipole would thus give us the limits of the quantum theory due to neglect of this factor. A non-relativistic attempt has already been made by Heisenberg1 for a dipole of finite extension, but his results even in the limit of a point dipole do not agree with ours. We believe that this is because the usual method of calculation which he follows is inconsistent with the theory of relativity, for whereas the retardation of the field is taken into account, different parts of the dipole are assumed to move instantaneously in phase.