Self-consistent System Of Equations Research Articles

Turbulence in cosmology

Principles of the theory of turbulence in relativistic cosmology are developed. By averaging Einstein's equations over stochastic fields a self-consistent system of equations is obtained which describes statistically: (1) the influence of the turbulence on the ‘basic state of the Universe (the background) on which the turbulence develops; (2) the behaviour of the turbulence on the background ‘distorted’ by it. By means of a qualitative study of exact equations in the region of a strong turbulence at an early stage of cosmological expansion conditions of the absence of singularity are found and the possibility of stationary solutions in the homogeneous, isotropic, on the average, Universe (the cosmological constantA=0) is shown. The rate of cosmological expansion increases if the energy density of the turbulence is positive, and decreases if it is negative. The latter alternative takes place if the absolute value of the energy density of excitations, which will change into potential motions in the future, exceeds the energy density of the remaining part of the turbulence.

Coherent interaction between high-power light pulses and exciton–impurity centers in molecular crystals

A theoretical investigation is made of the coherent interaction between high-power optical radiation and excitons in impurity-doped molecular crystals. A self-consistent system of equations is obtained for the medium and the optical field. It is shown that, under certain conditions, the distances over which coherence effects are observed, decrease sharply. An analysis is made of the specific conditions for the experimental observation of these effects.

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 Gr.

Propagation of high-power light pulses through semiconductors under interband interaction conditions

A theoretical investigation was made of the propagation of a high-power light pulse in a semiconductor under interband absorption conditions. A self-consistent system of equations was obtained for the field and the medium allowing for nonequilibrium particle relaxation processes. Allowance was also made for the influence of a strong pulse field on the intensity of such processes. Analytic and numerical investigation of various interesting cases permit comparison between theory and experiment.

A phenomenological theory of disordered ferromagnetic PdNi-type alloys

An earlier calculation (see ibid., vol.6, p.221 (1976)) based on the generalized Landau theory of phase transitions is extended to ferromagnetic disordered alloys for which the cubic term in the Landau equation is essential. To be tractable the cubic term is linearized and the linearization is tested for an ordered system where numerical solutions of the full cubic equation are available. The Green's function analogy is applied to the linearized equation to derive a general self-consistent system of equations for the susceptibility and magnetization of weakly ferromagnetic disordered alloys. This general system is solved in CPA for PdNi alloys in an applied field and the concentration and field dependences of the susceptibility and magnetization are calculated.

Theory of the propagation of short and ultrashort light pulses in a semiconductor under interband absorption conditions

A self-consistent system of equations is obtained for the field and medium (semiconductor) in the propagation of high-power light pulses under interband absorption conditions. Allowance is made for the relaxation processes. It is shown that a sufficiently strong pulse field may suppress the polarization relaxation processes, increase the coherence time, and thus facilitate the appearance of the self-induced transparency in semiconductors.