Exact analytical expression for the electromagnetic field in a focused laser beam or pulse

We present a new class of exact nonsingular solutions for the Maxwell equations in vacuum, which describe the electromagnetic field of the counterpropagating focused laser beams and the subperiod focused laser pulse. These solutions are derived by the use of a modification of the "complex source method", investigated and visualized.Comment: 10 pages, 4 figures, an extended version of the talk at the International Conference on Coherent and Nonlinear Optics (ICONO 2007

On the Rate of Convergence for a Characteristic of Multidimensional Birth-Death Process

We consider a multidimensional inhomogeneous birth-death process (BDP) and obtain bounds on the rate of convergence for the corresponding one-dimensional processes

A multi-dimensional numerical scheme for two-fluid Relativistic MHD

The paper describes an explicit multi-dimensional numerical scheme for Special Relativistic Two-Fluid Magnetohydrodynamics of electron-positron plasma and a suit of test problems. The scheme utilizes Cartesian grid and the third order WENO interpolation. The time integration is carried out using the third order TVD method of Runge-Kutta type, thus ensuring overall third order accuracy on smooth solutions. The magnetic field is kept near divergence-free by means of the method of generalized Lagrange multiplier. The test simulations, which include linear and non-linear continuous plasma waves, shock waves, strong explosions and the tearing instability, show that the scheme is sufficiently robust and confirm its accuracy

An improvement of the Berry--Esseen inequality with applications to Poisson and mixed Poisson random sums

By a modification of the method that was applied in (Korolev and Shevtsova, 2009), here the inequalities $$\rho(F_n,\Phi)\le\frac{0.335789(\beta^3+0.425)}{\sqrt{n}}$$ and $$\rho(F_n,\Phi)\le \frac{0.3051(\beta^3+1)}{\sqrt{n}}$$ are proved for the uniform distance $\rho(F_n,\Phi)$ between the standard normal distribution function $\Phi$ and the distribution function $F_n$ of the normalized sum of an arbitrary number $n\ge1$ of independent identically distributed random variables with zero mean, unit variance and finite third absolute moment $\beta^3$. The first of these inequalities sharpens the best known version of the classical Berry--Esseen inequality since $0.335789(\beta^3+0.425)\le0.335789(1+0.425)\beta^3<0.4785\beta^3$ by virtue of the condition $\beta^3\ge1$, and 0.4785 is the best known upper estimate of the absolute constant in the classical Berry--Esseen inequality. The second inequality is applied to lowering the upper estimate of the absolute constant in the analog of the Berry--Esseen inequality for Poisson random sums to 0.3051 which is strictly less than the least possible value of the absolute constant in the classical Berry--Esseen inequality. As a corollary, the estimates of the rate of convergence in limit theorems for compound mixed Poisson distributions are refined.Comment: 33 page

Guided random walk calculation of energies and <\sq {r^2} > values of the 1Σg^1\Sigma_g state of H_2 in a magnetic field

Energies and spatial observables for the $^1\Sigma_g$ state of the hydrogen molecule in magnetic fields parallel to the proton-proton axis are calculated with a guided random walk Feynman-Kac algorithm. We demonstrate that the accuracy of the results and the simplicity of the method may prove it a viable alternative to large basis set expansions for small molecules in applied fields.Comment: 10 pages, no figure

Photon Filamentation in Resonant Media with High Fresnel Numbers

The phenomenon of turbulent photon filamentation occurs in lasers and other active optical media at high Fresnel numbers. A description of this phenomenon is suggested. The solutions to evolution equations are presented in the form of a bunch of filaments chaotically distributed in space and having different radii. The probability distribution of patterns is defined characterizing the probabilistic weight of different filaments. The most probable filament radius and filament number are found, being in good agreement with experiment.Comment: Revtex file, 5 pages. Reference to the English edition of the journal is give

Determination of Ethanol Content in Fuels with Phononic Crystal Sensor

Introduction. In-line analysis of ethanol content in gasoline blends is currently one of the urgent needs of fuel industry. Developing safe and secure approaches is critical for real applications. A phononic crystal sensor have been introduced as an innovative approach to high performance gasoline sensing. Distinguishing feature of proposed sensor is the absence of any electrical contact with analysed gasoline blend, which allows the use of sensors directly in pipelines without the risk of explosion in an emergency.Aim. Investigation of the possibilities of using phononic sensor structures to determine the ethanol content in liquid hydrocarbons.Materials and methods. A theoretical analysis of sensor structure was carried out on the basis of numerical simulation using COMSOL Multiphysics software. For measurement, substances of ordinary gasoline and gasoline 63–80 with ethanol concentrations in the range of 1–10 % by volume in increments of 2 % were prepared. The phononic crystal sensor was designed as a stainless steel plate with cylindrical holes and a resonant cavity, formed as a running across the wave propagation path slit between two lattices.Results. In-line analysis of measuring the concentration of ethanol in alcohol-containing fuels on a phononic crystal structure with a resonant cavity was carried out. Using the Agilent4395A admittance meter, the transmission spectra of longitudinal acoustic waves through the gasoline-filled sensor structure with were obtained. The non-linear correlation between the composition and the speed of sound of the blend is presented in the article is due to the ability to reduce the speed of sound of the mixture with an increase in ethanol concentration in the range of 0–10 % by volume.Conclusion. A measurement structure on the basis of phononic crystal was created. The measurements of various gasoline-ethanol mixtures show that the sensor has significant sensitivity (0.91 kHz/ms−1 ) with quality factor of 200) to distinguish between regular fuels, gasoline based blends and the presence of additives in standard fuels. The sensor has prospects for in-line analyzes the composition of liquid hydrocarbons.Introduction. In-line analysis of ethanol content in gasoline blends is currently one of the urgent needs of fuel industry. Developing safe and secure approaches is critical for real applications. A phononic crystal sensor have been introduced as an innovative approach to high performance gasoline sensing. Distinguishing feature of proposed sensor is the absence of any electrical contact with analysed gasoline blend, which allows the use of sensors directly in pipelines without the risk of explosion in an emergency.Aim. Investigation of the possibilities of using phononic sensor structures to determine the ethanol content in liquid hydrocarbons.Materials and methods. A theoretical analysis of sensor structure was carried out on the basis of numerical simulation using COMSOL Multiphysics software. For measurement, substances of ordinary gasoline and gasoline 63–80 with ethanol concentrations in the range of 1–10 % by volume in increments of 2 % were prepared. The phononic crystal sensor was designed as a stainless steel plate with cylindrical holes and a resonant cavity, formed as a running across the wave propagation path slit between two lattices.Results. In-line analysis of measuring the concentration of ethanol in alcohol-containing fuels on a phononic crystal structure with a resonant cavity was carried out. Using the Agilent4395A admittance meter, the transmission spectra of longitudinal acoustic waves through the gasoline-filled sensor structure with were obtained. The non-linear correlation between the composition and the speed of sound of the blend is presented in the article is due to the ability to reduce the speed of sound of the mixture with an increase in ethanol concentration in the range of 0–10 % by volume.Conclusion. A measurement structure on the basis of phononic crystal was created. The measurements of various gasoline-ethanol mixtures show that the sensor has significant sensitivity (0.91 kHz/ms−1 ) with quality factor of 200) to distinguish between regular fuels, gasoline based blends and the presence of additives in standard fuels. The sensor has prospects for in-line analyzes the composition of liquid hydrocarbons

Determination of the dimensions of the heat-affected zone in welding gas pipeline components

Analytical decisions supported by experimental data were used to determine the dependences for calculating the size of the heat-affected zone (HAZ) in multilayer welding of circumferential joints in transmission gas pipelines. Data on the dimensions of this zone are essential for evaluating the possibility of applying cold cutting in the rejection of elements of gas pipelines because of defects in circumferential welded joints or welded joints in transition rings in the vicinity of circumferential welded joints. © 2013 Copyright Taylor and Francis Group, LLC