The speed of a second-sound wave in liquid helium II is known to depend on amplitude, and thermal shocks may form. Prediction of the shock velocity depends on which conservation laws hold across the discontinuity. Whe...
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The speed of a second-sound wave in liquid helium II is known to depend on amplitude, and thermal shocks may form. Prediction of the shock velocity depends on which conservation laws hold across the discontinuity. When dissipation is taken into account a smooth but rapidly varying wave profile is predicted in place of a discontinuity. It is shown how waves of this kind may be used to resolve an uncertainty surrounding one of the conserved quantities across a shock. A number of wave profiles are also exhibited in the vicinity of a critical equilibrium temperature.
Auger rates, average absorption oscillator strengths (corresponding average wavelengths) and level-to-level dielectronic recombination rate coefficients describing dielectronic recombination for F-like and Ne-like ger...
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Auger rates, average absorption oscillator strengths (corresponding average wavelengths) and level-to-level dielectronic recombination rate coefficients describing dielectronic recombination for F-like and Ne-like germanium ions are explicitly calculated. Our calculations are based on Cowan's non-relativistic multi-configuration Hartree-Fock (HFR) code which includes relativistic mass-velocity and Darwin corrections and successive subroutines for calculating average oscillator strengths and average wavelengths and dielectronic recombination rate coefficients are developed. The dielectronic recombination rate coefficients as the function of temperature of free electrons are given in an analytical form which is very convenient in practice.
In liquid helium II second-sound waves with rectangular profiles degenerate ultimately into triangular form and the speed of the wave front is no longer constant. This effect gives rise to a non-linear dependence of t...
In liquid helium II second-sound waves with rectangular profiles degenerate ultimately into triangular form and the speed of the wave front is no longer constant. This effect gives rise to a non-linear dependence of the shock speed on the initial wave amplitude, but its magnitude is insufficient to account for the experimental results above a certain limited range of amplitudes. However, the degeneration into triangular form is the dominant effect in the dependence of the wave speed on decreasing pulse width, at constant amplitude, and here the authors analysis agrees well with the experimental results.
The evolution of spherical thermal shock waves in helium II is analysed theoretically. At temperatures below 1.88K the wave evolves in a manner similar to that of pressure waves in compressible gases. Between 1.88K an...
The evolution of spherical thermal shock waves in helium II is analysed theoretically. At temperatures below 1.88K the wave evolves in a manner similar to that of pressure waves in compressible gases. Between 1.88K and the lambda -point a new kind of profile emerges. In both cases the predicted forms agree well with those observed in recent experiments.
The energy spectrum and the eigenvectors of a charged particle in a uniform electric field with alternating site energies are studied for infinite systems. For the case of large energy mismatch, exact solutions are pr...
The energy spectrum and the eigenvectors of a charged particle in a uniform electric field with alternating site energies are studied for infinite systems. For the case of large energy mismatch, exact solutions are presented by using perturbation theory, from which it is found that the spectrum is that of two interspaced Stark ladders. The character of these Stark ladders is that the difference of the ratio of the energy and the field between two energies on a same rung is an even number.
The long time behavior of solution for Hirota equation with zero order dissipation is studied. The global weak attractor for this system in Hper^k is constructed. And then by exact analysis of the energy equation, it ...
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The long time behavior of solution for Hirota equation with zero order dissipation is studied. The global weak attractor for this system in Hper^k is constructed. And then by exact analysis of the energy equation, it is shown that the global weak attractor is actually the global strong attractor in Hper^k.
The plane-wave detection problem is: to estimate the incidence angle and waveform of a transient plane traveling wave, from samples recorded at a linear array of receivers. This simple problem shares several important...
The plane-wave detection problem is: to estimate the incidence angle and waveform of a transient plane traveling wave, from samples recorded at a linear array of receivers. This simple problem shares several important math.matical features with other inverse problems of wave propagation, and is of interest in its own rights as a model problem in ocean acoustic signal analysis. Straightforward formulation as a non-linear least-squares problem yields a non-convex objective for which the minima are not stably dependent on the data. In contrast, an infeasible point formulation, in which the signal at each receiver is explained to some extent independently, proves to yield a smooth convex optimization problem with stable optima. Numerical experiments illustrate the theoretical results about the infeasible point approach, differential semblance optimization.
All perfect fluid spacetimes with a purely electric Weyl tensor are shown to have an alignment between the fluid 4-velocity and a canonical null tetrad determined by the Weyl tensor. If, in addition, it is assumed tha...
All perfect fluid spacetimes with a purely electric Weyl tensor are shown to have an alignment between the fluid 4-velocity and a canonical null tetrad determined by the Weyl tensor. If, in addition, it is assumed that the flow is irrotational, the eigenframes of the shear and Weyl tensors coincide. In all but two rather special cases, it is proved that the vectors of this eigenframe are hypersurface orthogonal and consequently that a coordinate system exists in which the metric, shear and Eab(the electric part of the Weyl tensor) are all diagonal. Geodesic Petrov type D spacetimes are shown to be either Bianchi type 1 or to belong to the class of solutions considered by Szekeres (1975) and Szafron (1977). The Allnutt solutions (1982) are shown to be the only purely electric type D fields in which the shear is non-degenerate and in which the acceleration vector lies in the plane spanned by the principal null vectors. The field equations are partially integrated in two classes where no solutions are yet known.
Spacetimes admitting a group of (local) projective collineations are considered. In an n-dimensional proper Einstein space it is shown that any vector field xi(i) generating a proper projective collineation (that is o...
Spacetimes admitting a group of (local) projective collineations are considered. In an n-dimensional proper Einstein space it is shown that any vector field xi(i) generating a proper projective collineation (that is one which is not an affine collineation) is the gradient of a scalar field phi (up to the addition of a Killing vector field). Then a four-dimensional Einstein spacetime admitting a proper projective collineation is shown to have constant curvature. For an n-dimensional space of non-zero constant curvature, the scalar field phi satisfies a system of third-order linear differential equations. The complete solution of this system is found in closed form and depends on (n + 1)(n + 2)/2 arbitrary constants. All gradient vector fields xi(i) generating projective collineations are found explicitly and together with the n(n + 1) /2 killing vector fields generate a Lie algebra of dimension n(n + 2).
An expression for ponderomotive force caused by electromagnetic fields is derived from Valsov-Maxwell equations in a non-stationary, unmagnetized plasma. Comparison between our result and earlier ones is given.
An expression for ponderomotive force caused by electromagnetic fields is derived from Valsov-Maxwell equations in a non-stationary, unmagnetized plasma. Comparison between our result and earlier ones is given.
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