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Dynamical Equations (dynamical + equation)

Distribution by Scientific Domains
Physics and Astronomy75%

Selected Abstracts

Time asymmetric quantum theory , I. Modifying an axiom of quantum physics

FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 6 2003
A.R. Bohm
A slight modification of one axiom of quantum theory changes a reversible theory into a time asymmetric theory. Whereas the standard Hilbert space axiom does not distinguish mathematically between the space of states (in-states of scattering theory) and the space of observables (out-"states" of scattering theory) the new axiom associates states and observables to two different Hardy subspaces which are dense in the same Hilbert space and analytic in the lower and upper complex energy plane, respectively. As a consequence of this new axiom the dynamical equations (Schrödinger or Heisenberg) integrate to a semigroup evolution. Extending this new Hardy space axiom to a relativistic theory provides a relativistic theory of resonance scattering and decay with Born probablilities that fulfill Einstein causality and the exponential decay law. [source]

Global lopsided instability in a purely stellar galactic disc

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2007
Kanak Saha
ABSTRACT It is shown that pure exponential discs in spiral galaxies are capable of supporting slowly varying discrete global lopsided modes, which can explain the observed features of lopsidedness in the stellar discs. Using linearized fluid dynamical equations with the softened self-gravity and pressure of the perturbation as the collective effect, we derive self-consistently a quadratic eigenvalue equation for the lopsided perturbation in the galactic disc. On solving this, we find that the ground-state mode shows the observed characteristics of the lopsidedness in a galactic disc, namely the fractional Fourier amplitude A1, increases smoothly with the radius. These lopsided patterns precess in the disc with a very slow pattern speed with no preferred sense of precession. We show that the lopsided modes in the stellar disc are long-lived because of a substantial reduction (approximately a factor of 10 compared to the local free precession rate) in the differential precession. The numerical solution of the equations shows that the ground-state lopsided modes are either very slowly precessing stationary normal mode oscillations of the disc or growing modes with a slow growth rate depending on the relative importance of the collective effect of the self-gravity. N -body simulations are performed to test the spontaneous growth of lopsidedness in a pure stellar disc. Both approaches are then compared and interpreted in terms of long-lived global m= 1 instabilities, with almost zero pattern speed. [source]

Conservative constraint for a quasi-uniform overset grid on the sphere

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 616 2006
Xindong Peng
Abstract A conservative constraint is presented for a new quasi-uniform overset (Yin-Yang) grid on the sphere. The Yin-Yang grid is a newly developed grid system in spherical geometry created by matching two notched latitude,longitude grids which are normal to each other. Global and local conservation is achieved with an interpolation algorithm that exactly guarantees that the fluxes on boundaries of the two grid components are identical. Several numerical experiments are shown to confirm the conservation in passive transport situations and shallow-water dynamical equations. Copyright © 2006 Royal Meteorological Society. [source]

Integrability and the variational formulation of non-conservative mechanical systems

ANNALEN DER PHYSIK, Issue 1 2009
D.H. Delphenich
Abstract It is shown that one can obtain canonically-defined dynamical equations for non-conservative mechanical systems by starting with a first variation functional, instead of an action functional, and finding their zeroes. The kernel of the first variation functional, as an integral functional, is a 1-form on the manifold of kinematical states, which then represents the dynamical state of the system. If the 1-form is exact then the first variation functional is associated with the first variation of an action functional in the usual manner. The dynamical equations then follow from the vanishing of the dual of the Spencer operator that acts on the dynamical state. This operator, in turn, relates to the integrability of the kinematical states. The method is applied to the modeling of damped oscillators. [source]