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

\n This work aims to formulate the temperature-rate dependent two-temperature (TRDTT) theory of thermoelasticity. The two-temperature thermoelasticity theory and the temperature-rate dependent thermoelasticity theory are two well-established thermoelasticity theories, which are developed from the generalized thermodynamic principles independently. Although the constitutive equations for TRDTT theory have been introduced, the formulation for the theory from the thermodynamical principles is not yet derived. Therefore, this work is an attempt to establish the theory from the generalized laws of thermodynamics and derive all the governing equations and constitutive relations for the theory. We derive a new and more general two-temperature relation that involves the temperature-rate terms of conductive and thermodynamic temperatures. We observe that this relation is different from the two-temperature relation reported in the literature. Further, we prove the uniqueness of solution for a general mixed initial boundary value problem in the context of linear modified TRDTT thermoelasticity theory for anisotropic medium. To investigate the effect of the present modified TRDTT theory, we solve a one-dimensional half-space problem and highlight the significance of the present theory.

On the Temperature-Rate Dependent Two-Temperature Thermoelasticity Theory

Ultrafast heating has gained serious attention due to technological advancements in recent years. The thermoelastic process accounting for the finite speed of thermal signals is therefore becoming increasingly important. With the help of extended thermodynamics, Yu et al. (Meccanica 53(10):2543–2554, 2018) have established a thermoelastic model by including the strain rate and temperature rate in the constitutive equations. This model is also an attempt to remove the discontinuity in the displacement field under temperature rate-dependent thermoelasticity theory. The present work seeks to derive the representation of a Galerkin-type solution in the context of this recently proposed model in terms of elementary functions. The representation theorem of the Galerkin-type solution of the system of equations for steady oscillation is also proved. In accordance with this theorem, we finally establish a theorem which expresses the general solution of the system of homogeneous equations of steady oscillation in terms of metaharmonic functions.

Galerkin-type solution for the theory of strain and temperature rate-dependent thermoelasticity

The present work is aimed at a mathematical analysis of the newly proposed strain and temperature rate-dependent thermoelasticity theory, also called a modified Green–Lindsay model (MGL) th...

An investigation on strain and temperature rate-dependent thermoelasticity and its infinite speed behavior

The present work is an attempt to derive the representation of a Galerkin-type solution in the linear theory of generalized thermoelastic diffusion. First, the representation of a Galerkin-type solution of equations of motion is obtained in the form of a theorem. Then, the representation theorem of the Galerkin type of system of equations of steady oscillations is established. On the basis of this theorem, we finally establish a theorem which represents the general solution of the system of homogenous equations of steady oscillation in terms of metaharmonic functions.

On the representations of solutions in the theory of generalized thermoelastic diffusion

The aim of the present work is to establish a reciprocal principle of Betti type in the context of linear theory of two-temperature generalized thermoelasticity (Youssef in IMA J Appl Math 71:383–390, 2006; Arch Appl Mech 75:553–565, 2006) for homogeneous and isotropic body. Generalizations of the theorems of Somigliana and Green to two-temperature generalized thermoelasticity are also established on the basis of our reciprocal principle.

Santwana Mukhopadhyay

Papers

On the Temperature-Rate Dependent Two-Temperature Thermoelasticity Theory

Galerkin-type solution for the theory of strain and temperature rate-dependent thermoelasticity

An investigation on strain and temperature rate-dependent thermoelasticity and its infinite speed behavior

On the representations of solutions in the theory of generalized thermoelastic diffusion

Some theorems on two-temperature generalized thermoelasticity