Geodesic Motions in 2 + 1-Dimensional Charged Black Holes

We study the geodesic motions of a test particle around 2 + 1-dimensional charged black holes. We obtain a class of exact geodesic motions for the massless test particle when the ratio of its energy and angular momentum is given by the square root of the cosmological constant. The other geodesic motions for both massless and massive test particles are analyzed using the numerical method.     

Quasi-elastic neutron scattering study of dynamics in condensed matter

Quasi-elastic neutron scattering (QENS) technique, known to study stochastic motions has been successfully used to elucidate the molecular motions and physical properties related to them, in a variety of systems. QENS is a unique technique that provides information on the time-scale of the motion as well as the geometry of the motions. In this paper, results of some of the systems studied using the facility available at Dhruva, Trombay and other mega-facilities are discussed. Emphasis is given on the results obtained from three different systems studied using QENS, namely, (1) alkyl chain motions in monolayer protected metal clusters, (2) molecular motions of propane in Na-Y zeolitic systems and (3) the study of reorientational motions of liquid crystal innO.m series in different mesophases.     

Homothetic transformations with fixed points in spacetime

A study is made of homothetic motions with fixed points in spacetime. Some general properties of such spacetimes are established, and a characterization of generalized plane wave spacetimes is proved. A general discussion of homothetic motions in Einstein's theory is given.This is in the sense that no open subset ofM is flat.     

Tetrad symmetries

It is shown that ifG is a subgroup of the group of motions of a given space-time then a tetrad can be chosen which is symmetric under the subgroup if and only if the rank of the generators ofG is equal to the order ofG. As an example such a tetrad is constructed for the TypeN twisting empty space-time admitting a two-parameter group of motions.     

Estimating the apparent motions of extragalactic radio sources

The apparent motions of 573 extragalactic radio sources are estimated. For this purpose, we analyzed the data that were obtained during 3193 series of observations using very-long baseline radio interferometry (VLBI) from 1984 to 2010. To find a solution, the least-squares method with constraints is applied. It is shown that most radio sources (including defining sources) are characterized by significant apparent motions. Since the stability of the celestial reference system is due to the absence of net rotation (no-net-rotation condition) relative to the defining sources, a change in their coordinates leads to the rotation of the celestial coordinate system (CCS). Owing to this, we believe that the apparent motions of radio sources must be given in catalogs.     

Existence and analytical predictions of periodic motions in a periodically forced,nonlinear friction oscillator

The grazing bifurcation, stick phenomena and periodic motions in a periodically forced, nonlinear friction oscillator are investigated. The nonlinear friction force is approximated by a piecewise linear, kinetic friction model with the static force. The total forces for the input and output flows to the separation boundary are introduced, and the force criteria for the onset and vanishing of stick motions are developed through such input and output flow forces. The periodic motions of such an oscillator are predicted analytically through the corresponding mapping structure. Illustrations of the periodic motions in such a piecewise friction model are given for a better understanding of the stick motion with the static friction. The force responses are presented, which agreed very well with the force criteria. If the fully nonlinear friction force is modeled by several portions of piecewise linear functions, the periodically forced, nonlinear friction oscillator can be predicted more accurately. However, for the fully nonlinear friction force model, only the numerical investigation can be carried out.     

Stationary macroscopic motions of a relativistic gas and its relation to the symmetries of the gravitational field

On the basis of an investigation of the Einstein-Vlasov self-consistent system of equations, a classification is given of the gravitational fields due to a collisionless gravitating gas, using the groups of the motions. It is shown that the time-like Killing vector, directed along the vector of the macroscopic gas velocity, is the center of the group of motions G_r.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 15–20, June, 1979.     

Chaotic dynamics of a whirling pendulum

A physical system is considered consisting of a rigid frame which is free to rotate about a vertical axis and to which is attached a planar simple pendulum. This system has “one and a half” degrees of freedom due to the fact that the frame and pendulum may freely rotate about the vertical axis, i.e., conservation of angular momentum holds for the “ideal”, or unperturbed, system. Using a Hamiltonian formulation we reduce the unperturbed equations of motion to a conservative planar system in which the constant angular momentum plays the role of a parameter. This system is shown to possess one or two sets of homoclinic motions depending on the level of the angular momentum. When this system is perturbed by external excitations and dissipative forces these homoclinic motions can break into homoclinic tangles providing the conditions for chaotic motions of the horseshoe type to exist. The criteria for this to occur can be formulated using a variation of Melnikov's method developed for slowly varying oscillators [1, 2]. For the present problem, the angular momentum becomes a slowly varying parameter upon addition of the disturbances. These ideas are used to rigorously prove the existence of chaotic motions for this system and to compute, to first order, global bifurcation parameter conditions. Since two types of homoclinic motions can occur, two different chaotic modes of motion can result and physical interpretations of these motions are given. In addition, a limiting case is considered in which the system becomes a single degree of freedom oscillator with parametric excitation.     

The apparent motions of extragalactic sources and their angular spectrums

The apparent motions of extragalactic ICRF sources are considered. Computer simulation of apparent motions is carried out assuming that they are stochastic and uncorrelated, while the position angle of the velocity for each source has a uniform distribution. We calculate the vector amplitudes of spherical harmonics and show that the corresponding spectrum has the form of “white noise.” In addition, we discuss observational data and calculate their angular spectra. Preliminary conclusions on the origin of the observed multipolar harmonics in the velocity angular spectrum are given.     

Vacuum spacetimes with a two-dimensional orthogonally transitive group of homothetic motions

Vacuum spacetimes with a two-dimensional orthogonally transitive groupH ₂ of proper homothetic motions acting on nonnull orbits are investigated with the aid of the Geroch-Held-Penrose formalism. It is found that these spacetimes admit in general anH ₃ of homothetic motions containing two commuting and hypersurface orthogonal Killing vector fields. The metric equations are integrated, and the line elements of the spacetimes in question are explicitly given in a diagonal form.     

Gravitational fields,spinor fields,and groups of motions

The problem of finding the most general spinor field possessing the same symmetry as a given gravitational field is solved for every group of motions. Its connection with the resolution of Einstein-Dirac equations is briefly pointed out.Aspirant du Fonds National Belge de la Recherche Scientifique.     

On the rescaling problem of space-times admitting groups of conformal motions

The necessary and sufficient conditions are given that a space-time admitting a group of conformal motions can be mapped conformally on a space-time admitting the same group but of Killing symmetries.     

Time travel in Gödel's space

We present an analysis of the motion of test particles in Gödel's universe. Both geodesical and nongeodesical motions are considered; the accelerations for nongeodesical motions are given. Examples for closed timelike world lines are shown and the dynamical conditions for time travel in Gödel's space-time are discussed. It is shown that these conditions alone do not suffice to exclude time travel in Gödel's space-time.Part of this work was performed while the author was a Research Associate at the Center for Philosophy of Science at the University of Pittsburgh.     

Dynamics of a monolayer of nitrogen physisorbed on graphite

The dynamics of a crystalline monolayer of molecular nitrogen physisorbed on the basal plane of graphite, which was assumed to be rigid, has been studied by means of lattice and molecular dynamics. The study focusses mainly on the registered solid in which the centres of mass adopt the √3 × √3 R30° structure, but some results are also reported for denser monlayers, including one where the centre-of-mass lattice is non-triangular. Harmonic dispersion curves are reported for two models of the N₂-N₂ interaction combined with Steele's representation of the molecule-surface interaction. The one-phonon density of states is given for one of the models. Molecular dynamics results for the same model at two temperatures, 5 and 17 K, are analysed in terms of the dynamical structure factor, and one-phonon approximation to it, and the out-of-plane motions are treated in a manner similar to the one-phonon approximation. In-plane and out-of-plane motions are largely decoupled in all cases studied, and the in-plane motions show evidence of marked anharmonicity. The out-of-plane motions appear to exhibit Fermi-Pasta-Ulam type recurrences, although this is not analysed in detail.     

Probability in Relativistic Bohmian Mechanics of Particles and Strings

Even though the Bohmian trajectories given by integral curves of the conserved Klein-Gordon current may involve motions backwards in time, the natural relativistic probability density of particle positions is well-defined. The Bohmian theory predicts subtle deviations from the statistical predictions of more conventional formulations of quantum theory, but it seems that no present experiment rules this theory out. The generalization to the case of many particles or strings is straightforward, provided that a preferred foliation of spacetime is given.     

原子团簇Ne3的低激发能谱和对称性

采用少体物理方法，计算了惰性元素三原子团Ｎｅ３的低激发能谱，分析量子力学对称性对Ｎｅ３的几何结构和内部运动的影响，给出Ｎｅ３低激发能谱的几条转动带     

Finiteness conditions for plane axisymmetric self-consistent motions of charged plasma electrons in a magnetic field

The plane axisymmetric self-consistent motions of electrons constituting a cylindrical beam is studied. The electrons move under the action of the electric field of uncompensated space self-charge against the background of plasma ions in the presence of a magnetic field. Conditions of electron movement finiteness for the given configuration of the electron beam are found.     

Quantum Bouncer with Dissipation

Effects on the spectra of the quantum bouncer due to dissipation are given when a linear of quadratic dissipation is taken into account. Classical constants of motions and Hamiltonians are deduced for these systems and their quantized eigenvalues are estimated through perturbation theory. Differences were found comparing the eigenvalues of these two quantities.     

Cautionary note regarding the role of dynamic effects in EPR structural analysis

A discussion is presented of possible errors, produced by excitations or atomic motions, in structural analyses carried out using EPR anisotropic parameters. Two examples featuring Ge³⁺ centres in α-quartz are given.     

Schrödinger and Dirac quantum random walks

Quantum random walks, whose amplitude evolutions are given by generalizations of discrete versions of Schrödinger and Dirac equations, are constructed. The results are given in three dimensions and it is shown that they cannot be reduced to stochastically independent one-dimensional motions. Properties of these quantum random walks are analyzed and expressions for their characteristic functions and free propagators are derived.