In 1982, the Belgian Pilots' Guild raised the question of what effect exposure to radar radiation--for example, that encountered in passing a pilot launch's radar--might have on the human body. Recapitulating investigations of this question, this article states that in 25 years of experience with radar, there have been no known incidents of pilots being affected by radar waves. In the future, however, involvement by some pilots with Vessel Traffic Service shore-based radar could affect pilots somewhat differently from limited exposure to pilot launch radar. Pilots who find themselves in new working conditions close to an emitting source should exercise care all times.

About heat waves

THE appearance of a treatise in English upon the mathematical theory of elasticity is an event the potential importance of which may be judged by the that the author, in his frequent suggestions for collateral reading, refers to only three such, those of Southwell, Timoshenko, and Love. In spirit and content Sokolnikoff}s book differs greatly from each and all of these. It may be described by a possible sub-title: “A pure mathematician surveys topics related to certain problems in the mathematical theory of elasticity”. It is symptomatic of the change in outlook of American mathematics over the past few decades. Mathematical Theory Of Elasticity Prof. I. S. Sokolnikoff with the collaboration of Asst. Prof. R. D. Speche. Pp. xi + 373. (New York and London: McGraw-Hill Book Co., Inc., 1946.) 22s. 6d.

Mathematical Theory Of Elasticity

A three-phase-lag model of the linearized theory of coupled thermoelasticity is formulated by considering the heat condition law that includes temperature gradient and the thermal displacement gradient among the constitutive variables. The Fourier law is replaced by an approximation to a modification of the Fourier law with three different translations for the heat flux vector, the temperature gradient and also for the thermal displacement gradient. The model formulated is an extension of the thermoelastic models proposed by Lord–Shulman, Green–Naghdi and Tzou.

On A Thermoelastic Three-Phase-Lag Model

T F Torrence (ed) 1982 Edinburgh: Scottish Academic Press xiii + 103 pp price £7.50 In 1865 James Clerk Maxwell published in the Philosophical Transactions a long paper entitled 'A dynamical theory of the electromagnetic field'. In this work, about which he wrote to a relative, 'I have a paper afloat, with an electromagnetic theory of light, which, till I am convinced of the contrary, Ihold to be great guns', he set up the electromagnetic field equations unifying electricity and magnetism, and identified light as 'an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws'.

A Dynamical Theory of the Electromagnetic Field

R Leis 1986 Chichester: John Wiley viii + 266 pp price £2450 ISBN 0 471 90863 0 This book is an account of some recent developments in the theory of partial differential equations for readers thoroughly familiar with functional analysis It deals with various types of problem for the wave equation, Maxwell's equations, Schrodinger's equation, the plate equation etc, but dissipative systems are hardly discussed

https://iopscience.iop.org/article/10.1088/0031-9112/37/10/027/pdf

Initial Boundary Value Problems in Mathematical Physics

The main objective of the present paper is to analyze the effects of phase lags on wave propagation in a two dimensional thick plate due to an axisymmetric temperature distribution. The problem is formulated by employing three recent theories of thermoelasticity in a unified way, namely thermoelasticity of type III (Green and Naghdi in J Therm Stress 15:253–264, 1992), thermoelasticity with dual phase lags (Tzou in ASME J Heat Transf 117:8–16, 1995) and thermoelasticity with three phase lags (Roychoudhuri in J Therm Stress 30:231–238, 2007). The lower and upper surfaces of the plate are assumed to be traction free and subjected to a given axisymmetric temperature distribution. A potential function approach together with the Laplace and Hankel transform method is employed to derive the solution in the transform domain. The Hankel inversion is performed analytically and the solution in the Laplace transform domain is obtained. Detailed analyses on wave propagation and discontinuities of different fields of the medium are presented by using a method due to Boley (Quart Appl Math 19:273–284, 1962). By employing a numerical method for the Laplace inversion the distributions of different fields like temperature, displacement and stresses in the middle plane of the plate have been computed and depicted graphically. Findings are analyzed along with the comparison with the corresponding results obtained in earlier works.

Analysis of phase-lag effects on wave propagation in a thick plate under axisymmetric temperature distribution

Propagation of harmonic plane waves under thermoelasticity with dual-phase-lags

The aim of the present work is to derive the representation of a Galerkin-type solution in the linear theory of generalized thermoelasticity with three phase-lags, recently developed by Roychoudhuri (2007). Firstly, the representation of a Galerkin-type solution of equations of motion is obtained in the form of a theorem. Then, the representation theorem of a Galerkin-type system of equations of steady oscillations is established. Finally, the general solution of the system of homogenous equations of steady oscillation is also presented based on our theorem.

On the representation of solutions for the theory of generalized thermoelasticity with three phase-lags

Thermoelastic damping in micro and nano-mechanical resonators utilizing entropy generation approach and heat conduction model with a single delay term

The present paper is concerned with the theory of two temperature thermoelasticity with two phase-lags in which the theory of heat conduction in deformable bodies depends on two distinct temperatures – the conductive temperature and the thermodynamic temperature. A generalized heat conduction law with dual-phase-lag effects was proposed by Tzou (1995) for the purpose of considering the delayed response in times due to the microstructural interactions in the heat transport mechanism. Recently, Quintanilla (2008) has proposed to combine this constitutive equation with a two temperature heat conduction theory and has proved that a dual-phase-lag theory with two temperatures is a well-posed problem. In the present work we consider the basic equations concerning this dual-phase lag theory of two temperature thermoelasticity and make an attempt to establish some important theorems in this context. A uniqueness theorem has been established for a homogeneous and isotropic body. An alternative characterization of ...

Santwana Mukhopadhyay

Papers

Analysis of phase-lag effects on wave propagation in a thick plate under axisymmetric temperature distribution

Propagation of harmonic plane waves under thermoelasticity with dual-phase-lags

On the representation of solutions for the theory of generalized thermoelasticity with three phase-lags

Thermoelastic damping in micro and nano-mechanical resonators utilizing entropy generation approach and heat conduction model with a single delay term

On the Theory of Two-Temperature Thermoelasticity with Two Phase-Lags