Geodesic Motions in Euclidean Taub-NUT Spinning Spaces

We investigate the geodesic motions of pseudo-classical spin- \frac12\frac{1}{2} point particles in the Euclidean Taub-NUT space. We derive the constants of motion from the solutions of the generalized Killing equations for spinning spaces and exploiting those the motion of pseudo-classical Dirac fermions are analyzed on a cone and plane.     

Geodesic Motion on Extended Taub-NUT Spinning Space

In this paper we investigate the geodesic motion of the pseudo-classical spinning particle for the extended Taub-NUT metric. The generalized equations for spinning space are investigated and the constants of motion are derived in terms of the solutions of these equations. We find only two types of extended Taub-NUT metrics with Kepler type symmetry admitting Killing-Yano tensors. The solutions for the lowest components of generalized Killing equations are presented for a particular form of extended Taub-NUT metric.     

Invariant solutions of Liouville's equation in Robertson-Walker space-times

We find all solutions of Liouville's equation in Robertson-Walker space-times that are either spatially homogeneous or isotropic or both. Some of these solutions depend on constants of motion that are not generated by Killing vectors. We indicate how these solutions may be used to find Einstein-Liouville solutions.     

Particles with curvature and torsion in three-dimensional pseudo-Riemannian space forms

We consider the motion of relativistic particles described by an action which is a function of the curvature and torsion of the particle path. The Euler–Lagrange equations and the dynamical constants of the motion are expressed in a simple way in terms of a suitable coordinate system. The moduli spaces of solutions in a three-dimensional pseudo-Riemannian space form are completely exhibited.     

Complete integrability of geodesic motion in general higher-dimensional rotating black-hole spacetimes

We explicitly exhibit n-1=[D/2]-1 constants of motion for geodesics in the general D-dimensional Kerr-NUT-AdS rotating black hole spacetime, arising from contractions of even powers of the 2-form obtained by contracting the geodesic velocity with the dual of the contraction of the velocity with the (D-2)-dimensional Killing-Yano tensor. These constants of motion are functionally independent of each other and of the D-n+1 constants of motion that arise from the metric and the D-n=[(D+1)/2] Killing vectors, making a total of D independent constants of motion in all dimensions D. The Poisson brackets of all pairs of these D constants are zero, so geodesic motion in these spacetimes is completely integrable.     

Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure

For quantum systems with semi-simple Lie algebraic structures,the exact solutions of the equations of motion are obtained by means of algebraic dynamics.The Hamiltonian is transformed into a linear function of Cartan operators by a set of gauge transformations. The coefficients of the gauge transformations are determined by a set of ordinary differential equations.From the inverses of these gauge transformations,the solutions of the Schrodinger equation,as well as a set of dynamic constants of motion (dynamic invariant operators) are obtained. An SU(3) model serves as an example.     

Geodesic Motion in Spinning Spaces

In this paper the generalized equations for spinning space are investigated and the constants of motion are derived in terms of the solutions of these equations. We study the geodesic motion of the pseudo-classical spinning particles in the spacetime produced by an idealized cosmic string and the non-extreme stationary axisymmetric black hole spacetime. The bound state orbits in a plane are discussed. We also show, for a conical spacetime and the Kerr spacetime, that the geodesic motion of spinning particles is different.     

Geodesic Motion in Spinning Spaces

In this paper the generalized equations for spinning space are investigated and the constants of motion are derived in terms of the solutions of these equations. We study the geodesic motion of the pseudo-classical spinning particles in the spacetime produced by an idealized cosmic string and the non-extreme stationary axisymmetric black hole spacetime. The bound state orbits in a plane are discussed. We also show, for a conical spacetime and the Kerr spacetime, that the geodesic motion of spinning particles is different.     

Rotational levels of double-minimum potentials: The linear BAB molecule with unequal bond lengths

The rotational constants and energy levels for the linear BAB system are studied under the assumption of unequal AB bond lengths. The quantum mechanical Hamiltonians is derived according to a formalism which allows for a large-amplitude antisymmetric stretching motion. A numberical integration technique is used to obtain solutions of the one-dimensional Schroedinger equation corresponding to a zeroth-order approximation of the Hamiltonian. The behavior of the resulting rotational constants for various heights of the barrier in the double-minimum potential is discussed.     

On the canonical character of the Sawada-Kotera equation

Recursion operators for solutions of two linear equations, associated with the SK equation, are given. A method to construct constants on the motion is described. The hamiltonian structure and the relation with the inverse scattering problem is indicated.     

Bernstein-Greene-Kruskal modes in a three-dimensional plasma

Bernstein-Greene-Kruskal modes in a three-dimensional (3D) unmagnetized plasma are constructed. It is shown that 3D solutions that depend only on energy do not exist. However, 3D solutions that depend on energy and additional constants of motion (such as angular momentum) do exist. Exact analytical as well as numerical solutions are constructed assuming spherical symmetry, and their properties are contrasted with those of 1D solutions. Possible extensions to solutions with cylindrical symmetry with or without a finite magnetic guide field are discussed.     

Radiation impedance of a finite circular piston on a viscoelastic half-space with application to medical diagnosis

In a recent study a new analytical solution was developed and validated experimentally for the problem of surface wave generation on a linear viscoelastic half-space by a rigid circular disk located on the surface and oscillating normal to it. The results of that study suggested that, for the low audible frequency range, some previously reported values of shear viscosity for soft biological tissues may be inaccurate. Those values were determined by matching radiation impedance measurements with theoretical calculations reported previously. In the current study, the sensitivity to shear viscoelastic material constants of theoretical solutions for radiation impedance and surface wave motion are compared. Theoretical solutions are also compared to experimental measurements and numerical results from finite-element analysis. It is found that, while prior theoretical solutions for radiation impedance are accurate, use of such measurements to estimate shear viscoelastic constants is not as precise as the use of surface wave measurements.     

A Solvable N-body Problem of Goldfish Type Featuring N2 Arbitrary Coupling Constants

A N-body problem “of goldfish type” is introduced, the Newtonian (“acceleration equal force”) equations of motion of which describe the motion of N pointlike unit-mass particles moving in the complex z-plane. The model—for arbitrary N—is solvable, namely its configuration (positions and velocities of the N “particles”) at any later time t can be obtained from its configuration at the initial time by algebraic operations. It features specific nonlinear velocity-dependent many-body forces depending on N² arbitrary (complex) coupling constants. Sufficient conditions on these constants are identified which cause the model to be isochronous—so that all its solutions are then periodic with a fixed period independent of the initial data. A variant with twice as many arbitrary coupling constants, or even more, is also identified.     

Composite variational principles,added variables,and constants of motion

It is shown that any second-order differential system admits a variational formulation via the introduction of suitable additional variables. The new variables are related to the existence of invariant 1-forms and to solutions for the adjoint of the equations of variation of the given system. The connections among invariant forms, constants of motion, and infinitesimal invariance transformations are then discussed in some detail.     

Spinning Particles in NUT–Reissner–Nordstrom Space–Time

We study the geodesic motion of pseudo-classical spinning particles in the NUT–Reissner–Nordstrom space–time. We investigate the generalized Killing equations for spinning space and derive the constants of the motion in terms of the solutions of these equations. We give an analysis of the motion on a cone and on a plane.     

Spinning Particles in Reissner-Nordström-de Sitter Spacetime

We study the geodesic motion of pseudo-classical spinning particles in the Reissner-Nordström-de Sitter spacetime. We investigate the generalized Killing equations for spinning space and derive the constants of motion in terms of the solutions of these equations. We discuss bound state orbits in a plane.     

Two particle model for the diffusion of interacting particles in periodic potentials

The random motion of two interacting particles in a periodic potential with a finite number of sites is investigated as a model that may be applied to superionic conductivity. Starting from the Fokker-Planck-equation for the model and using an appropriate series expansion for the probability density, solutions for the frequency dependent conductivity are given. Explicit numerical results are shown for hard-core and Coulomb interaction in the range of intermediate and high friction constants.     

Static and quasistatic solutions of the real Proca field

We consider the theory of the massive real vector field with spin 1 (the real Proca field) and its solutions. First the field equations with dual symmetry [1] are written and the 4-pseudo vector is chosen to be zero. The constants of motion for the real Proca field, the constant “electric” real Proca field, the uniform motion of a point charge in the real Proca field, uniform motions in the “Coulomb” field, dipole and multipole free-momentum, constant “magnetic” field, and the field of a point charge in motion are presented.     

Elastic nonlinearity parameters of tetragonal crystals

The equations of motion for the propagation of finite amplitude elastic waves in crystals of tetragonal symmetry have been derived starting from the expression for the elastic strain energy. The equations have been solved for a finite amplitude sinusoidal wave propagating along the pure mode directions which are [100], [110] and [001] for the tetragonal group TI. The solutions corresponding to longitudinal wave propagation yield expressions for the amplitudes of the fundamental and generated second harmonic for these directions in terms of certain combinations of second and third order elastic constants of the medium. The results will aid the experimenter to determine these constants using ultrasonic harmonic generation technique.     

An approximate global solution of Einstein’s equations for a rotating finite body

We obtain an approximate global stationary and axisymmetric solution of Einstein’s equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using the post-Minkowskian formalism (weak-field approximation) and considering rotation as a perturbation (slow-rotation approximation), we find second-order approximate interior and exterior (asymptotically flat) solutions to this problem in harmonic and quo-harmonic coordinates. In both cases, interior and exterior solutions are matched, in the sense of Lichnerowicz, on the surface of zero pressure to obtain a global solution. The resulting metric depends on three arbitrary constants: mass density, rotational velocity and the star radius at the non-rotation limit. The mass, angular momentum, quadrupole moment and other constants of the exterior metric are determined by these three parameters. It is easy to check that Kerr’s metric cannot be the exterior part of that metric.