Another method for computing the densities of integrals of motion for the Korteweg-de Vries equation

In the first section of this article a new method for computing the densities of integrals of motion for the KdV equation is given. In the second section the variation with respect to q of the functional ∫ ₀ ^π w (x,t,x,;q)dx (t is fixed) is computed, where W(x, t, s; q) is the Riemann function of the problem $$\begin{gathered} \frac{{\partial ^z u}}{{\partial x^2 }} - q(x)u = \frac{{\partial ^2 u}}{{\partial t^2 }} ( - \infty< x< \infty ), \hfill \\ u|_{t = 0} = f(x), \left. {\frac{{\partial u}}{{\partial t}}} \right|_{t = 0} = 0. \hfill \\ \end{gathered} $$      

Sensitivity enhancement of fiber Bragg gratings to transverse stress by using microstructural fibers

We present simulation and experimental results of fiber Bragg grating responses to transverse stress in microstructure fibers. The grating wavelength shifts and peak splits are studied as a function of external load and fiber orientation. Both simulation and measurement results indicate that the sensitivity of grating sensors to the transverse stress can be enhanced by a factor of eight in a two-hole fiber over that in a standard fiber.     

Friction factor and wall heat transfer for laminar and turbulentflow in a cylindrical duct with a wall-stabilized arc

Friction factor and wall heat-transfer data for axially symmetric flow in a wall-stabilized arc analysis are given. Heat transfer results revealed three significant modes: laminar flow with an unstable arc, laminar flow with a wall-stabilized arc, and turbulent flow with a wall-stabilized arc. It was shown that the critical Reynolds number increases, in comparison with the case of the flow without Joule heating. A friction factor from Reynolds-number dependence peculiarities was not discovered for laminar to turbulent flow transition     

Degeneration of an isotropic random field of electric charge pulsations in electrodynamics

The conditions under which an isotropic field of electric pulsations can exist in an electrically charged medium are indicated, with allowance in Ohm's law for the convection and diffusion of charged particles and their drift in the electric field. Mean parameter distributions are found for isotropic random fields and equations are obtained for correlation moments containing electric pulsations. The equations are analyzed with respect to the two-point correlations between the pulsations in the electric charge densities (the limit of single-point correlations is reached, invariant relations are obtained, and particular solutions are constructed). The degeneration laws of the isotropic fields of the electric parameters as a result of diffusion and drift. processes are found. Field degeneration due only to drift particle motion is studied under arbitrary initial conditions. Such field degeneration if there is no diffusion mechanism is a fundamental feature of turbulent electro-hydrodynamic motions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 38–47, January–February, 1987.The authors thank V. R. Kuznetsov for his useful discussion of the paper.     

Phase-Amplitude Relations for a Particle with a Superposition of Two Energy Levels in a Double Potential Well

We study the connection between the phase and the amplitude of the wave function and the conditions under which this relationship exists. For this we use the model of particle in a box. We have shown that the amplitude can be calculated from the phase and vice versa if the log analytical uncertainty relations are satisfied.