Invariant operators of inhomogeneous groups. II. The ISL (n,R)group
Invariant operators of inhomogeneous groups. II. The ISL (n,R)group
A.P. Demichev and N.F. Nelipa
It is shown that the real inhomogeneous unimodular linear group of arbitrary dimensionality ISL(n,R) has one Casimir operator. An explicit form of the invariant operator is obtained in the case of ISL(2,R).
Show AbstractElectron - fhonon interaction in the vicinity of a van-hove singularity
Electron - fhonon interaction in the vicinity of a van-hove singularity
Yu.P. Drozhzhov
The interaction between electrons and acoustic phonons in the vicinity of a Van - Hove singular point is considered. It is shown that even weak interaction leads to a considerable change in the characteristics of the electron gas in the region of the singularity. The electron spectrum changes from quadratic to linear, while the density of states falls off linearly in the neighborhood of the singular point.
Show AbstractThe possibility of amplitude compensation of thermal self-defocusing of a beam of light (a numerical experiment)
The possibility of amplitude compensation of thermal self-defocusing of a beam of light (a numerical experiment)
V.A. Vysloukh, K.D. Egorov and V.P. Kandidov
The possibility of suppressing the effects of self - defocusing by a rational choice of the Initial intensity distribution in the beam channel is investigated. Compensation of the defocusing in a fixed and moving medium is considered, and also when scanning the beam. The method of finite elements is used for the calculation.
Show AbstractTwo problems of nonstationary thermal self-action
Two problems of nonstationary thermal self-action
V.A. Vysloukh and S.S. Chesnokov
Two nonstationary thermal self-action modes are considered: for pulse durations of the order of the transit time of the acoustic wave through the transverse cross section of the beam and of the order of the time taken for a steady temperature to be established in the beam channel. The method of finite elements is used to solve the quasi-optics equation. The equations of hydrodynamics and nonstationary thermal conduction are solved using the Fourier - Bessel transformation. A number of results of a numerical experiment are given for different values of the parameters of the medium in the beam.
Show AbstractThe action of Ƴ-radiation on the electrical characteristics of natural quartz
The action of Ƴ-radiation on the electrical characteristics of natural quartz
V.G. Zubov, A.P. Shtyrkova, Т.M. Glushkova and M.M. Firsova
The temperature - frequency dependences (20-700°C; 0.5-10 kHz) of the dielectric characteristics (ε and tgδ) of natural quartz crystals irradiated with Ƴ-quanta from $^{60}$Со in the dose range 5x10$^5$—2x10$^9$ Rare investigated. It is shown that the maximum loss and the beginning of the rapid increase in ε are shifted due to the irradiation towards higher temperatures, and the shift is greater the higher the radiation dose. It is found that unlike optical properties the radiation change in ε and tgδ does not reach saturation over the whole dose range. A series of successive annealings of the specimens atincreasing temperatures shifts the peak of tg6 and the beginning of the increase in ε in the opposite direction to the temperature, but even annealing at 720°C does not convert the specimen to its initial state. In analyzing the results the applicability of the model of hole Al-centers (used to describe the change in the optical properties due to the action of radiation) to dielectric relaxation processes is discussed.
Show AbstractStability of the flows of an ideal nonuniform liquid
Stability of the flows of an ideal nonuniform liquid
D.M. Alishaev
The stability of two - dimensional stationary flows of an ideal nonuniform liquid with respect to arbitrary three - dimensional infinitely small perturbations is investigated. The time - asymptotic behavior of the solutions of the hydrodynamic equations linearized with respect to the mean state is examined. It is shown that the flow is conditionally stable when Ri > 1/4 everywhere in the flow (the velocities are limited while the vortex increases linearly), and unstable in the regions where Ri < 1/4 (the perturbation energy increases without limit at the expense of the energy of the main flow).
Show AbstractTheory of superradiation in the raman scattering of light
Theory of superradiation in the raman scattering of light
V.I. Emel'yanov and V.N. Seminogov
The process of superradiation (collective spontaneous radiation) in the Raman scattering of an intense electromagnetic wave by an ensemble of molecules is considered. Using the results obtained the mechanism of collisionless excitation of molecules in intense laser fields is discussed.
Show AbstractCollinear acousto-optical filtering in quartz
Collinear acousto-optical filtering in quartz
V.B. Voloshinov, I.V. Nikolaev and V.N. Parygin
The collinear acousto - optical filtering of light in crystalline quartz is investigated. It is shown that when the length of the region of interaction between the light and acoustic beams in increased there is a reduction in the passband of the filter. At the same time the rerquirements imposed on the degree of collimation of the beams are inc reased. At a wavelength of the light of λо= 633 nm apassband of Δλ=0,42 nm is achieved.
Show AbstractMarkovian nonlinear noneqdilibrium thermodynamic relations with external forces
Markovian nonlinear noneqdilibrium thermodynamic relations with external forces
R.L. Stratonovich and A.V. Tolstopyatenko
Исследован вопрос, как по релаксационному уравнению без внешних сил строить релаксационное уравнение с силами. Получены двухиндексные и трехиндексные соответствующие соотношения.
Show AbstractThe cooling of a gas by a resonant electromagnetic field under saturation conditions
The cooling of a gas by a resonant electromagnetic field under saturation conditions
S.N. Luzgin
The cooling of a gas by the field of a standing electromagnetic wave for an arbitrary field amplitude is investigated. In weak fields, when there is no saturation, the rate of cooling is proportional to the incident power, the increase then slows down, and up to the boundary of the region of nonuniform broadening the rate of cooling is proportional to the square root of the radiation power. In the region of uniform broadening(intense field)the increase in the rate of cooling gradually ceases.
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