Classical conservation laws for the elliptic Liouville equation
Classical conservation laws for the elliptic Liouville equation
A.V. Kiselev
Generating sections of conservation laws for the elliptic Liouville equation are constructed. It is shown that a nontrivial conservation law corresponds to any generating section and demonstrated that all classical conservation laws arise from the Lagrangian symmetries. Explicit formulas for the development of a certain conservation law by its generating section are obtained.
Show AbstractStudy of scattering by a nonspherical particle in a layer on a substrate
Study of scattering by a nonspherical particle in a layer on a substrate
E.Yu. Eremina, A.G. Sveshnikov
A mathematical model of the polarized radiation scattering by an axially asymmetric structure placed under a film on a permeable substrate is developed. Results on scattering by variously shaped particles are presented.
Show AbstractThe basis property of root vectors for the radio waveguide
The basis property of root vectors for the radio waveguide
A.N. Bogolyubov, A.L. Delitsyn, M.D. Malykh, A.G. Sveshnikov
The basis property of the system of root vectors for a cylindrical waveguide with a circular cross section and dielectric filling is substantiated. This lays the grounds for applying the normal wave method to the waveguide excitation problem.
Show AbstractThe integral transformation method in the spectral problem for the confining potential
The integral transformation method in the spectral problem for the confining potential
O.S. Pavlova, A.R. Frenkin
An integral transformation method is used to find the energy spectrum of the radial Schr$\stackrel{..}{o}$dinger equation with an infinitely increasing power-law confining potential. The problem is reduced to an approximate solution of an infinite system of linear algebraic equations. Numerical computations are used to determine the $S$-state spectrum of the Schr$\stackrel{..}{o}$dinger equation with a linearly increasing potential.
Show AbstractThe method of integral equations for calculating the dielectric deflector with electrooptical control
The method of integral equations for calculating the dielectric deflector with electrooptical control
N.E. Shapkina
A three-dimensional mathematical model of the dielectric deflector with electrooptical control is considered. A method for calculating the electric field inside the deflector crystal, which adequately takes into account the shape of electrodes, is proposed. The area of application of the earlier developed model is investigated.
Show AbstractMixed problem for the Laplace equation outside the circle arc
Mixed problem for the Laplace equation outside the circle arc
A.I. Sgibnev, P.A. Krutitskii
An explicit solution to the boundary-value problem for a harmonic function outside a cut lying on a circle arc has been constructed. The Dirichlet condition is specified on one bank of the cut, the Neumann condition, on the other bank. The solution of the problem is based on reducing it to the Riemann-Gilbert problem.
Show AbstractA project of investigating the most energetic cosmic rays on the Russian segment of the International Space Station
A project of investigating the most energetic cosmic rays on the Russian segment of the International Space Station
V.V. Aleksandrov$^1$, D.I. Bugrov$^1$, G.K. Garipov$^1$, A. Cordero$^1$, J. Linsley$^1$, H. Salazar$^1$, O.A. Saprykin$^2$, A.A. Silaev$^1$, V.S. Syromyatnikov$^2$, M.I. Panasyuk$^1$, B.A. Khrenov$^1$
An experimental system for studying the most energetic cosmic rays is described, which can be installed on board the Russian segment of the International Space Station.
Show AbstractStrain susceptibilities and elastic-constant anomalies of TmVO$_4$ in magnetic field
Strain susceptibilities and elastic-constant anomalies of TmVO$_4$ in magnetic field
Z.A. Kazei, N.P. Kolmakova, 0.A. Shishkina
Based on the real energy spectrum and wave function of the Tm-ion in the vanadate crystal field, all strain susceptibilities and the $\Delta E$ effect were calculated. A good description of the $C^{\delta}(T)$ and $C^{\gamma}(T)$ experimental elastic constants and their variations in magnetic field in the tetragonal and rhombic phases was obtained. The $B^{\delta}$ and $B^{\gamma}$ magnetoelastic and $K^{\delta}$ and $K^{\gamma}$ pair quadrupole coefficients were determined. The influence of the magnetic field oriented along various symmetrical directions in the crystal on the quadrupole ordering in TmVO$_{4}$ was studied.
Show AbstractThe heat capacity of thin ferroelectric films near the second-order phase transition
The heat capacity of thin ferroelectric films near the second-order phase transition
S.V. Pavlov, O.Yu. Polyakova
Within the framework of the Landau phenomenological model, the temperature and sample-thickness dependences of the heat capacity of thin uniaxial ferroelectric films near the second-order phase transition were studied. The heat capacity jump was found to decrease, diffuse, and shift to lower temperatures as the thickness of thin films decreased. At a certain thin-film thickness, the heat capacity anomaly disappeared (for instance, for triglycine sulfate, at a thickness of several nanometers).
Show AbstractA new approach to space ergodicity in wave propagation through a randomly inhomogeneous refractive medium
A new approach to space ergodicity in wave propagation through a randomly inhomogeneous refractive medium
A.G. Vologdin, V.D. Gusev
A new and simple approach to the space ergodicity problem is suggested. By averaging along an arbitrary horizontal straight line rather than by volume averaging, the spatial statistical characteristics of the phase of a wave normally incident on a randomly inhomogeneous plane-layered medium are obtained. In that case (in contrast to volume averaging), the regular wave properties are not masked. It is demonstrated that the spatial stochastic characteristics can be determined from time-average measurements only when the medium inhomogeneities drift at a constant horizontal velocity.
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