Wave reflection in slightly compressible, finitely deformed elastic media

Summary  In this paper, the reflection of a plane wave at an incrementally traction-free boundary of a half-space composed of nearly incompressible elastic material is considered. It is shown that two distinct cases exist, these being dependent on the underlying primary deformation. In the first case, the appropriate slowness sections are each approximately elliptical, and the corresponding reflection phenomena closely mirrors that associated with the corresponding linear isotropic theory. Specifically, an angular range of direction of incident wave exists, for which both a quasi-longitudinal and quasi-shear wave are reflected, the former being replaced by a surface wave outside this angular range. In the second case, the outer slowness section is re-enrant and, in addition to the scenarios previously mentioned, it is possible for two quasi-shear waves to be reflected. Numerical illustrations of reflection coefficients are presented in respect of a modified Varga material and the case of increasing bulk modulus is investigated. Received 17 January 2000; accepted for publication 22 February 2000     

Phaselock system for millimeter-wave Gunn oscillators used in radio astronomy and laboratory spectroscopy

A frequency-agile heterodyne phaselock loop (PLL) system for millimeter-wave Gunn-effect oscillators between 40 and 110 GHz is described. The Gunn oscillators are phase-locked via the bias in an active second-order servo loop. A facility for fast frequency switching with a maximum rate of 10 kHz and a frequency separation up to 80 MHz is provided. Measurements on the spectral characteristics of a phase-locked Gunn oscillator are presented. The described PLL system is used in radio astronomy and laboratory molecular spectroscopy.     

A hyperbolic reaction–diffusion model for the hantavirus infection

A hyperbolic reaction–diffusion model for the hantavirus infection, generalizing the parabolic set of equations recently derived by Abramson and Kenkre, is proposed within the context of Extended Thermodynamics. The model, as in the parabolic case, captures some of the realistic features of the dynamics of hantavirus in mice population, while it avoids the unphysical features concerning the instantaneous diffusive effects typical of parabolic equations. Traveling wave solutions, related to the spread of the infection in the landscape, are investigated. Both analytical and numerical results obtained herein are discussed and validated from the behavior of the biological system. Copyright © 2007 John Wiley & Sons, Ltd.     

城市交通管理中的出租车规划模型

最佳数量的确定和价格的制定是城市出租车规划中的两个核心问题.对影响出行强度的市区人口和建成区面积分析建立了出行总量预测模型,再通过分析出租车最佳数量与出租车运营里程的关系,得出出租车最佳数量的预测模型.在出租车最佳数量模型的基础上,分析出租车数量的差异和差异产生的原因,给出了出租车定价判断模型,为出租车定价机制的调整指明了方向.最后以长沙市为例进行了实证分析.     

Existence and stability of modulating pulse-solutions in a phenomenological model of nonlinear optics

Modulating pulse-solutions consist of a pulse-like envelope advancing in the laboratory frame and modulating an underlying spatially and temporarily oscillating wave train. Such solutions play a big role in nonlinear optics, where information is transported as pulse-like modulations of an underlying electromagnetic wave. For a phenomenological model we prove criteria for the existence and asymptotic stability of such solutions in terms of the coefficients of the associated equation for the envelope.     

Thermodynamic quantities around a charged dilaton black hole

We use the brick-wall method to investigate the thermodynamic quantities around a charged dilaton black hole. We show that all the thermodynamic quantities contain two terms: the first term has exactly the same form as in a flat space-time, but the second term depends explicitly on the spin of the fields and therefore cannot be neglected. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 1, pp. 154–160, October, 2008.     

Thin viscous fluid film flows over rotating curvilinear surfaces

Thin viscous fluid film flows over rotating curvilinear surfaces are considered. The steady-state flow is studied for large and finite Ekman numbers. The possibility of obtaining a film of given thickness is considered. The wave formation on the surface of an inhomogeneous film and the development of nonlinear waves are also investigated. The film flow parameters in the cases of flow over a plane disk and a curvilinear surface are compared.     

Dynamics of a rotating layer of an ideal electrically conducting incompressible fluid

A system of nonlinear partial differential equations is considered that models perturbations in a layer of an ideal electrically conducting rotating fluid bounded by spatially and temporally varying surfaces with allowance for inertial forces. The system is reduced to a scalar equation. The solvability of initial boundary value problems arising in the theory of waves in conducting rotating fluids can be established by analyzing this equation. Solutions to the scalar equation are constructed that describe small-amplitude wave propagation in an infinite horizontal layer and a long narrow channel.     

Propagation of perturbations in a two-layer stratified fluid with an interface excited by moving sources

Propagation of small perturbations in a two-layer inviscid stratified fluid is studied. It is assumed that the higher density fluid occupies the lower unbounded half-space, while the lower density fluid occupies the upper unbounded half-space. The source of the excitation is a plane wave traveling along the interface of the fluids. An explicit analytical solution to the problem is constructed, and its existence and uniqueness are proved. The long-time wave pattern developing in the fluids is analyzed.