A non-uniform basis order for the discontinuous Galerkin method of the acoustic and elastic wave equations

Here, we solve the time-dependent acoustic and elastic wave equations using the discontinuous Galerkin method for spatial discretization and the low-storage Runge-Kutta and Crank-Nicolson methods for time integration. The aim of the present paper is to study how to choose the order of polynomial basis functions for each element in the computational mesh to obtain a predetermined relative error. In this work, the formula 2p+1≈κhk, which connects the polynomial basis order p, mesh parameter h, wave number k, and free parameter κ, is studied. The aim is to obtain a simple selection method for the order of the basis functions so that a relatively constant error level of the solution can be achieved. The method is examined using numerical experiments. The results of the experiments indicate that this method is a promising approach for approximating the degree of the basis functions for an arbitrarily sized element. However, in certain model problems we show the failure of the proposed selection scheme. In such a case, the method provides an initial basis for a more general p-adaptive discontinuous Galerkin method.     

On the stability of the high-order Higdon Absorbing Boundary Conditions

The Higdon sequence of Absorbing Boundary Conditions (ABCs) for the linear wave equation is considered. Building on a previous work of Ha-Duong and Joly, which related to other forms of boundary conditions, the Higdon ABCs are proved to be energy-stable (on the continuous level) up to any order. This type of stability is stronger than the more standard notion of stability of initial boundary value problems in the sense of Kreiss; in particular it leads to stability estimates which are uniform in time. In consequence to the theorem proved here, energy-stability is immediately implied for the high-order Givoli-Neta and Hagstrom-Warburton ABCs, which are reformulations of the Higdon ABCs using auxiliary variables. A weakness of this theory is that it requires sufficiently smooth data, and that the required smoothness level increases with the order of the ABC. This issue and its implications are discussed.     

Equations of anisotropic elastodynamics as a symmetric hyperbolic system: Deriving the time-dependent fundamental solution

The dynamic system of anisotropic elasticity from three second order partial differential equations is written in the form of the time-dependent first order symmetric hyperbolic system with respect to displacement velocity and stress components. A new method of deriving the time-dependent fundamental solution of the obtained system is suggested in this paper. This method consists of the following. The Fourier transform image of the fundamental solution with respect to a space variable is presented as a power series expansion relative to the Fourier parameters. Then explicit formulae for the coefficients of these power series are derived successively. Using these formulae the computer calculation of fundamental solution components (displacement velocity and stress components arising from pulse point forces) has been made for general anisotropic media (orthorhombic and monoclinic) and the simulation of elastic waves has been obtained. These computational examples confirm the robustness of the suggested method.     

The focusing effect on the angular distribution of the Raman antiStokes branch emissions

The angular distributions of the 1st to 3rd antiStokes emissions produced by Nd:YAG pumping a H₂ high pressure Raman cell have been measured and explained as a consequence of the destructive interference of the Stokes-antiStokes interaction.     

Photorefractive “camera obscura”

We demonstrate a novel scheme for lensless image formation which combines the properties of an amplifying dynamic hologram and a pinhole camera. The scheme is realized on the base of a SPS:Sb1% photorefractive crystal working at 633 nm.     

Wave propagation of functionally graded material plates in thermal environments

The wave propagation of an infinite functionally graded plate in thermal environments is studied using the higher-order shear deformation plate theory. The thermal effects and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the plate surface and varied in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Considering the effects of transverse shear deformation and rotary inertia, the governing equations of the wave propagation in the functionally graded plate are derived by using the Hamilton’s principle. The analytic dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. Numerical examples show that the characteristics of wave propagation in the functionally graded plate are relates to the volume fraction index and thermal environment of the functionally graded plate. The influences of the volume fraction distributions and temperature on wave propagation of functionally graded plate are discussed in detail. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.     

New exclusion limits for dark gauge forces from beam-dump data

We re-analyze published proton beam dump data taken at the U70 accelerator at IHEP Serpukhov with the ν-calorimeter I experiment in 1989 to set mass-coupling limits for dark gauge forces. The corresponding data have been used for axion and light Higgs particle searches in Blümlein et al. (1991, 1992) [1] and [2] before. We determine new mass and coupling exclusion bounds for dark gauge bosons.     

General relativity and quantum mechanics in five dimensions

In 5D, I take the metric in canonical form and define causality by null-paths. Then spacetime is modulated by a factor equivalent to the wave function, and the 5D geodesic equation gives the 4D Klein-Gordon equation. These results effectively show how general relativity and quantum mechanics may be unified in 5D.     

Enhanced localization of waves in one-dimensional random media due to nonlinearity: Fixed input case

We study the influence of nonlinearity on wave localization in one-dimensional random media. Using a discrete nonlinear Schrödinger equation with a random on-site energy term, we calculate the localization length in a numerically exact manner. Unlike in many previous works, we fix the intensity of the incident wave and calculate quantities as a function of other parameters. We find that localization is enhanced due to nonlinearity for the focusing and defocusing nonlinearities. For small nonlinearity, the localization length is a decreasing function of nonlinearity. For sufficiently large nonlinearity, however, the localization length is found to approach a saturation value.     

微波增敏方波伏安法测定对乙酰氨基酚

在微波作用下用循环伏安法和方波伏安法研究了对乙酰氨基酚的电化学特性,结果表明微波可以增大氧化峰电流,建立了一种微波增敏作用下检测对乙酰氨基酚的电化学方法.在最佳实验条件下,响应电流与对乙酰氨基酚的浓度在0.2-80μg/mL的浓度范围内呈良好的线性关系(r=0.9966,n=7),回归方程为:ip(μA)=1.92×1...