Extended Group Foliation Method and Functional Separation of Variables to Nonlinear Wave Equations

Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.     

Extension of the Coherent Gradient Sensor (CGS) to the Combined Measurement of In-Plane and Out-of-Plane Displacement Field Gradients

The Coherent Gradient Sensor (CGS) is extended to the optical differentiation of specular, diffracted wave fronts leading to the combined measurement of in- and out-of-plane displacement field gradients. A derivation of the underlying optical interference principles is presented along with an analysis of the effective instrument sensitivity. In order to demonstrate the capabilities of the technique, experimental measurements of crack-tip deformation fields were conducted under various loading conditions corresponding to mode-I, mode-II, and mixed mode near-tip crack fields. The experimental procedures and results of these tests are presented as validation of the technique.     

A compact high‐order HLL solver for nonlinear hyperbolic systems

We present a new finite‐volume method for calculating complex flows on non‐uniform meshes. This method is designed to be highly compact and to accurately capture all discontinuities that may arise within the solution of a nonlinear hyperbolic system. In the first step, we devise a fourth‐degree Hermite polynomial to interpolate the solution. The coefficients defining this polynomial are calculated by using a least‐square method. To introduce monotonicity conditions within the procedure, two constraints are added into the least‐square system. Those constraints are derived by locally matching the high‐order Hermite polynomial with a low‐order TVD polynomial. To emulate these constraints only in regions of discontinuities, data‐depending weights are defined; these weights are based upon normalized indicators of smoothness of the solution and are parameterized by an O(1) quantity. The reconstruction so generated is highly compact and is fifth‐order accurate when the solution is smooth; this reconstruction becomes first order in regions of discontinuities. In the second step, this reconstruction is inserted in an HLL approximate Riemann solver. This solver is designed to correctly capture all discontinuities that may arise into the solution. To this aim, we introduce the contribution of a possible contact discontinuity into the HLL Riemann solver. Thus, a spatially fifth‐order non‐oscillatory method is generated. This method evolves in time the solution and its first derivative. In a one‐dimensional context, a linear spectral analysis and extensive numerical experiments make it possible to assess the robustness and the advantages of the method in computing multi‐scale problems with embedded discontinuities. Copyright © 2008 John Wiley & Sons, Ltd.     

The electrochemical behaviour of the altenuene mycotoxin and its acidic properties

The electrooxidation of altenuene (ALT), one of the mycotoxins of the Alternaria alternata genus, on a glassy carbon disk electrode is studied for the first time by using cyclic and square wave voltammetry. From the electrochemical responses, a complex reaction mechanism could be inferred. Values of 1.06×10⁻⁵ cm² s⁻¹, 1.116 V and 2 were determined for the diffusion coefficient, the apparent formal potential and the electron number, respectively, for the overall electrode process by convolution analysis of linear scan voltammograms. Square wave voltammetry was used to generate I_p versus c_ALT* calibration curves for this fungal metabolite. A detection limit of 4.0×10⁻⁷ M was determined for a 2:1 signal to noise ratio. The acid dissociation constant for ALT was determined from conventional UV–vis spectrophotometric measurements. Experimental variations of absorbance as a function of pH at a given wavelength were fitted by using the exact equation that describes the system. Good agreement between the experimental absorbance versus pH plots and the curves generated by the fitting process was found.     

潮流推算在港口雷达海杂波处理中的应用

利用潮流推算的方法求得海水流速,再利用海水流速得到其所对应的多普勒频率,即海杂波所对应的频率,进而运用多普勒杂波处理的方法对海杂波进行处理。但是这种方法不能将相对于海水流速接近为零的目标检测出来,因此它不能独立地在雷达中完成目标检测的任务,但是却可以作为提高发现概率的有益补充。最后给出了系统框图,并对这种方法进行了评估。     

Travelling wave fronts in a vector disease model with delay

In this paper, we study the diffusive vector disease model with delay. This problem with strong biological background has attracted much research attention. We focus on the existence of traveling wave fronts, and find that there is a moving zone for the transition from the disease-free state to the infective state. To complete the theoretical analysis, we employ the mathematical tools including the monotone iteration technique as well as the upper and lower solution method.     

全反射现象折射波瞬时行为的计算机展示

介绍了借助计算机代数系统Ｍａｐｌｅ实现全反射现象折射波瞬时行为动态展示的做法，讨论它的基础物理教学中的作用。     

Magnetic Properties of Monocrystal 57Fe/V Multilayers Investigated by CEMS,Nuclear Resonance Reflectivity in the Time Domain and Polarized Neutron Scattering

Hyperfine Interactions - We have performed a depth selective investigation of monocrystalline samples with composition [57Fe(10 ML)/V(5 ML)]20 and [57Fe(7 ML)/V(10 ML)]29 by means of synchrotron...     

ORBITAL INSTABILITY OF STANDING WAVES FOR THE COUPLED NONLINEAR KLEIN-GORDON EQUATIONS

This paper deals with a type of standing waves for the coupled nonlinear Klein-Gordon equations in three space dimensions. First we construct a suitable constrained variational problem and obtain the existence of the standing waves with ground state by using variational argument. Then we prove the orbital instability of the standing waves by defining invariant sets and applying some priori estimates.