For the system of equations for surface waves the following problems have been studied: local and global existence of solutions in time, solution breaking during finite time, smoothing of discontinuous initial perturbations in the course of time, construction of generalized solutions, and solution asymptotics for $t \to \infty$. The asymptotic behavior of solutions for $t \to \infty$ is considered for nonlinear equations with dissipation, such as the Kolmogorov-Petrovskii-Piskunov equation, the Whitham equation, the cubic Schr$\stackrel{..}{o}$dinger equation, and the Korteweg-de Vries-Burgers equation.
Show AbstractIn the earlier published papers, when calculating the error in wave energy measurement using Kerr's optical effect it was assumed that the error of measurement of $E^2$ ($E$ is the electric field intensity amplitude) in a nonlinear medium completely determined the error in the wave energy estimation. The fact that during the measurement the wave impedance of the medium became principally indeterminate and the indeterminacy was the greater the higher the accuracy of the $E^2$ measurement was not taken into account. Therefore in such measurements there exists a principal quantum limit of error equal to $(n/(\omega_2\tau))^{1/2}\hbar\omega_1$ (where $n$ is the average number of photons, $\omega_1$ and $\omega_2$ are the wave frequencies before and during the measurement, respectively, and $\tau$ is the measurement duration).
Show AbstractThe concentration dynamics of a solution of an organic dye has been modeled by means of numerical solution of a diffusion type equation with consideration for the effect of the walls of the cell containing the solution under study. The conclusion is drawn that the concentration dynamics should be taken into account when processing experimental data.
Show AbstractThe limiting sensitivity of a test quantum oscillator has been evaluated for the case of tracking of its coordinate during a given limited time. An appropriate procedure of the optimal signal separation from the quantum noise of the coordinate meter has been developed.
Show AbstractA theoretical description is suggested for the ionization of an atom by multiply charged ions, in which, along with the interaction in the terminal state for $Z_1/V_i <1$ (where $Z_1$ is the charge of the incident particle and $V_i$ is the velocity of the colliding particles), allowance is correctly made for the distortion of the initial state of the target atom produced by the incident ion field. It is shown that the effect of the distortion of the initial state on the angular and energy distributions of electrons increases with increasing charge and decreasing ion velocity. The calculation results for collisions of the ions with helium atoms are compared with experimental data.
Show AbstractThe paper considers the possibility of denornmalization of radiation scattered as it passes through a plane chaotic screen and then propagating in the free space. Problems of modeling the initial field distribution on the screen using the experimental data in the observation plane are discussed.
Show AbstractThe number of dislocations has been shown to depend on the perturbation factor of the signal, the construction of the receiving antennas, and on the time of observation of space-time phase differences. The theoretical results are illustrated by experimental data.
Show AbstractIt is shown that during nonresonant excitation of waves of the capillary and gravitational-capillary frequency ranges on a fluid surface, the threshold amplitude of cophased pumping oscillations depends not only on dissipative (viscous) losses but also on radiation losses of the system. An experimental justification of the suggested method for determining the fluid viscosity is given.
Show AbstractUsing the geometro-acoustic approach, it is shown that antisymmetric acoustic oscillations can propagate along the apex of a solid wedge whose local thickness varies quadratically with the height. These oscillations are concentrated near the apex, their phase velocities are characterized by nonmonotonic frequency dependence and can be made arbitrarily small as the wedge truncation height tends to zero.
Show AbstractA new, defect-strain mechanism of subboundary formation during laser-induced recrystallization of semiconductor films is proposed. It underlies the theory yielding an explicit analytic expression for the separation between subboundaries as a function of film thickness and the melt zone velocity. The theoretical results obtained show good agreement with experiment.
Show AbstractThe stationary Schr$\stackrel{..}{o}$dinger equation for an oscillator with perturbation $\lambda x^{-2}$ has been revised. A new choice of even states of the singular oscillator is made based on the automodel requirement for the solution to the Schrodinger equation for a free particle with the same perturbation. In contrast to the orthodox solution, the suggested solution provides alternation of even and odd levels and the stability of the ground state, and consequently, is physically preferable.
Show AbstractA unified model is proposed for describing both the small- and large-angle high-energy scattering. The scattering amplitude for the Jocal potential in a Gaussian form has been computed. The results agree well with the exact scattering amplitude and with the eikonai approximation.
Show AbstractThe natural waves of a periodic waveguide loaded with electron beam have been analyzed by the multimode matrix method. The structure of a field corresponding to "hot" modes of the system has been studied. The beam-field interaction in relativistic Cherenkov oscillators has been shown to be a multiwave process.
Show AbstractA single-mode lumped-parameter dynamic model of a self-contained injection laser is proposed. The model takes into account the effect of carrier diffusion and helps describe the chaotic self-modulation of radiation. The results of a numerical experiment are given.
Show AbstractA cluster model is proposed for the interaction of radiation with nonlinear gyrotropic crystals. The model describes the effects of spatial dispersion within a classical approximation.
Show AbstractThe paper examines the stability of coherent light fields in passive nonlinear ring resonators with respect to time delay of the light wave and to shift disalignment of the resonator mirrors.
Show AbstractA novel control device based on the integrated circuits of Series К155 and KR556 generates commands for starting the carriage driving motor, opening the shutter, and rotating the photographic zenith tube through 180°. The time of commencement of observation cycles and the types of cycles for 256 stars are programmed in the device. The exposure times are set automatically, depending on the type of the cycle. The device simplifies the work of the observer and helps increase the accuracy of determining the latitude and clock correction.
Show AbstractExpressions are derived that allow a theoretical analysis of the effects of the size of a finite source and absorption on the focusing of a spherical X-ray wave upon Bragg diffraction in a bicrystal system composed of crystals bent in mutually perpendicular planes.
Show Abstract
