Fundamental theories of waves and particles formulated without classical mass

Quantum and classical mechanics are two conceptually and mathematically different theories of physics, and yet they do use the same concept of classical mass that was originally introduced by Newton in his formulation of the laws of dynamics. In this paper, physical consequences of using the classical mass by both theories are explored, and a novel approach that allows formulating fundamental (Galilean invariant) theories of waves and particles without formally introducing the classical mass is presented. In this new formulation, the theories depend only on one common parameter called ‘wave mass’, which is deduced from experiments for selected elementary particles and for the classical mass of one kilogram. It is shown that quantum theory with the wave mass is independent of the Planck constant and that higher accuracy of performing calculations can be attained by such theory. Natural units in connection with the presented approach are also discussed and justification beyond dimensional analysis is given for the particular choice of such units.     

Hardy type inequality and application to the stability of degenerate stationary waves

This paper is concerned with the asymptotic stability of degenerate stationary waves for viscous conservation laws in the half space. It is proved that the solution converges to the corresponding degenerate stationary wave at the rate t−α/4 as t→∞, provided that the initial perturbation is in the weighted space for α<αc(q):=3+2/q, where q is the degeneracy exponent. This restriction on α is best possible in the sense that the corresponding linearized operator cannot be dissipative in for α>αc(q). Our stability analysis is based on the space-time weighted energy method combined with a Hardy type inequality with the best possible constant.     

Exact travelling wave solutions of the generalized Bretherton equation

We search for exact travelling wave solutions of the generalized Bretherton equation for integer, greater than one, values of the exponent m of the nonlinear term by two methods: the truncated Painlevé expansion method and an algebraic method. We find periodic solutions for m=2 and m=5, to add to those already known for m=3; in all three cases these solutions exist for finite intervals of the wave velocity. We also find a “kink” shaped solitary wave for m=5 and a family of elementary unbounded solutions for arbitrary m.     

浅水长波近似方程组的拟小波解

以浅水长波近似方程组为例,提出了拟小波方法求解(1 1)维非线性偏微分方程组数值解,该方程用拟小波离散格式离散空间导数,得到关于时间的常微分方程组,用四阶Runge-K utta方法离散时间导数,并将其拟小波解与解析解进行比较和验证.     

Asymptotic and numerical analysis of thermoelastic waves in an isotropic plate

^** Email: n.scott{at}uea.ac.uk This paper considers the propagation of a plane thermoelasticwave in an infinite homogeneous isotropic plate subjected toeither isothermal or thermally insulated traction-free boundaryconditions. The primary concerns are the derivation and numericalexamination of the dispersion relations along with the developmentof asymptotic models for the fundamental branches of the dispersionrelations. Thermal dissipation is also discussed.     

High frequency SAW devices based on third harmonic generation

We demonstrate the third harmonic generation in a ZnO/Si layered structure to obtain high frequency SAW devices. This configuration eliminates the need of high lithography resolution and allows easy integration of such devices and electronics on the same wafer. A theoretical study was carried out for the determination of the phase velocity and the electromechanical coupling coefficient (K²) dispersion curves of the surface acoustic waves. These results are also in agreement with those measured on a SAW filter designed for the third harmonic generation and the operating frequency is up to 2468 MHz.     

Inviscid and viscous stationary waves of gas flow through contracting-expanding nozzles

In this work we study steady states of one-dimensional viscous isentropic compressible flows through a contracting-expanding nozzle. Treating the viscosity coefficient as a singular parameter, the steady-state problem can be viewed as a singularly perturbed system. For a contracting-expanding nozzle, a complete classification of steady states is given and the existence of viscous profiles is established via the geometric singular perturbation theory. Particularly interesting is the existence of a maximal sub-to-super transonic wave and its role in the formation of other complicated transonic waves consisting of a sub-to-super portion.     

Long time approximations for solutions of wave equations associated with the Steklov spectral homogenization problems

The interest in the use of quasimodes, or almost frequencies and almost eigenfunctions, to describe asymptotics for low‐frequency and high‐frequency vibrations in certain singularly perturbed spectral problems, which depend on a small parameter ε, has been recently highlighted in many papers. In this paper we deal with the low frequencies for a Steklov‐type eigenvalue homogenization problem: we consider harmonic functions in a bounded domain of ?², and strongly alternating boundary conditions of the Dirichlet and Steklov type on a part of the boundary. The spectral parameter appears in the boundary condition on small segments T^ε of size O(ε) periodically distributed along the boundary; ε also measures the periodicity of the structure. We consider associated second‐order evolution problems on spaces of traces that depend on ε, and we provide estimates for the time t in which standing waves, constructed from quasimodes, approach their solutions u^ε(t) as ε→0. Copyright © 2009 John Wiley & Sons, Ltd.     

A hyperbolic model for the effects of urbanization on air pollution

A hyperbolic model to study effects of industrialization and urbanization on air pollution propagation is proposed.     

Minimum wave speed for a diffusive competition model with time delay

In this paper we study mono-stable traveling&nbsp;wave solutions for a Lotka-Volterra reaction-diffusion competition model with&nbsp;time delay. By constructing upper and lower solutions, we obtain the precise minimum&nbsp;wave speed of traveling waves under certain conditions. Our results also extend the known results on&nbsp;the minimum wave speed for Lotka-Volterra competition model without delay.