Interesting inversion problems arise in helioseismology, the seismic study of the interior of the Sun using the frequencies of its global resonant modes of oscillation. In particular, one can use the frequencies to in...
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Interesting inversion problems arise in helioseismology, the seismic study of the interior of the Sun using the frequencies of its global resonant modes of oscillation. In particular, one can use the frequencies to investigate how the rotation of the Sun varies beneath the visible surface. This review concentrates primarily on the methods and tools that have been used in the helioseismic inversion problem. In particular, an analysis of different inversion methods using the spectral properties of a generalized singular-value decomposition has proved useful in helioseismology, and this suggests ways in which the inversion of large datasets can be performed more efficiently.
An approach is developed for the calculation of fluctuations in an ensemble of systems obeying Maxwell-Boltzmann, Fermi-Dirac or Bose-Einstein statistics, and in which a specified set of physical quantities is conserv...
An approach is developed for the calculation of fluctuations in an ensemble of systems obeying Maxwell-Boltzmann, Fermi-Dirac or Bose-Einstein statistics, and in which a specified set of physical quantities is conserved. The technique is applied to two situations of interest: in the first only energy is conserved while in the second both energy and number are conserved.
The charge-drift equations result from charge continuity considerations when viewed from a frame of reference moving with the gaseous ions. They are simple in form and have already been used to good effect for single-...
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The charge-drift equations result from charge continuity considerations when viewed from a frame of reference moving with the gaseous ions. They are simple in form and have already been used to good effect for single-species drift for which references are given in the text. This paper systematically examines the theory for multiple species looking for algebraically expressible solutions, and has met with some success. It has been shown that the charge density of a packet of a particular species of ions can be written in terms of integrals involving the charge densities of other ions that it meets on its way. A power law governing the charge densities has been found for all time-dependent homogeneous ionic movements. Time-independent motions have also been considered and the constant ratios of charge densities and currents confirmed for all points in these flows. Situations with two ionic species are fully investigated, and an analytic solution has been found for homogeneous distributions of positive and negative ions with equal but opposite mobilities. Stable charged clouds with equal but opposite positive and negative ionic distributions are shown to be possible. When disturbed, the variations from equilibrium charge densities within such a cloud are found to be characterized by an exponential law. The destabilizing effect of an externally applied electric field on these clouds is shown to be resisted by the self-field of the resulting ionic displacements. Perturbation solutions and expansions are considered in some detail, and the paper concludes with a section giving explicit solutions for superimposed clouds of ions with either spherical or cylindrical symmetry. Fuller descriptions of the main findings can be found in the conclusions at the end of the text.
Consideration is given to the treatment of the nonlinear partial differential equation describing the diffusion of an assembly of particles which simultaneously coagulate or annihilate. It is shown how a class of solu...
Consideration is given to the treatment of the nonlinear partial differential equation describing the diffusion of an assembly of particles which simultaneously coagulate or annihilate. It is shown how a class of solutions may be obtained in terms of the solutions of an ordinary differential equation and detailed application is made to the case of an initially localized particle distribution.
The Prelle-Singer procedure for determining elementary first integrals of two-dimensional autonomous systems of ordinary differential equations is introduced and how it can be generalized to higher dimensions is discu...
The Prelle-Singer procedure for determining elementary first integrals of two-dimensional autonomous systems of ordinary differential equations is introduced and how it can be generalized to higher dimensions is discussed. The application of this procedure in several dynamical systems is reported.
We present an empirical procedure for determining free-free absorption coefficients of the negative hydrogen ion from phaseshifts for electron-hydrogen scattering, that seems to give results to an accuracy of a few pe...
We present an empirical procedure for determining free-free absorption coefficients of the negative hydrogen ion from phaseshifts for electron-hydrogen scattering, that seems to give results to an accuracy of a few per cent for wavelengths greater than 0.5 mum. Applications of the method to cases not previously considered yield data on the convergence and on the reliability of free-free coefficients. These data support the case that the total absorption coefficient of H- is now known to within an accuracy of one or two per cent or better.
We consider the sensitivity of the dynamical dimensional reduction procedure which arises in the evolution of a homogeneous anisotropic multidimensional cosmological model, when the matter content is described by a pe...
We consider the sensitivity of the dynamical dimensional reduction procedure which arises in the evolution of a homogeneous anisotropic multidimensional cosmological model, when the matter content is described by a perfect fluid with anisotropic pressure satisfying a barotropic equation of state. We study in detail the effects of allowing a non-zero curvature in one of the component spaces. The effects of including the curvature of both components as well as non-zero bulk viscosity are also briefly discussed.
It is pointed out that the equilibrium solutions for pure coagulation and pure fragmentation which Dubovskii et al purport to obtain are in error, and that such solutions do not in fact exist.
It is pointed out that the equilibrium solutions for pure coagulation and pure fragmentation which Dubovskii et al purport to obtain are in error, and that such solutions do not in fact exist.
It is shown that for a particular physical situation the steady state equation describing two-species annihilation possesses a simple analytic solution.
It is shown that for a particular physical situation the steady state equation describing two-species annihilation possesses a simple analytic solution.
By defining an 'energy difference function' a simple picture displaying the states involved in an impact ionizing transition is developed. With this picture it can easily be seen how thresholds and anti-thresh...
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By defining an 'energy difference function' a simple picture displaying the states involved in an impact ionizing transition is developed. With this picture it can easily be seen how thresholds and anti-thresholds arise and how they can be evaluated and identified. In calculating total transition rates only quantum mechanically distinct transitions should be included in the sum and it is discussed how this can be achieved. The thresholds at 300 K for all 21 possible impact ionizing processes in InSb, InAs and Cd(0.8)Hg(0.2)Te are calculated and also the 18 hole-initiated processes in GaAs, InP and In(0.53)Ga(0.47)As using the anisotropic, non-parabolic four-band k . p band structure with higher and lower lying bands taken into account by perturbation theory.
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