There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

I. Introduction: Transcending Nationalism: The European Community 1958-2000

The Geometry of the Zeros of a Polynomial in a complex variable. By M. Marden. Pp. ix, 183. $5. 1949. Mathematical Surveys, 3. (American Mathematical Society)

Two general models of fractional heat conduction for non-homogeneous anisotropic elastic solids are introduced and the constitutive equations for thermoelasticity theory are obtained, uniqueness an...

On fractional thermoelasticity

https://www.math.uaic.ro/~schirita/Papers/2013JMAA.pdf

On the theory of thermoelasticity with microtemperatures

The present paper describes a method for studying the spatial behaviour of the thermodynamic processes. The method is based on a set of properties for an appropriate time-weighted surface power function associated with the process in question. It allows to obtain a more precisely idea of domain of influence in linear elastodynamics and viscoelastodynamics and, furthermore, to get spatial decay estimates with time-independent decay rate inside of the domain of influence. It also allows to obtain a good description for the spatial behaviour of the thermoelastic processes by means of spatial estimates characterized by independent as well as time-dependent decay and growth rates.

https://www.math.uaic.ro/~schirita/Papers/1999EJMS.pdf

Time-weighted surface power function method for the study of spatial behaviour in dynamics of continua

In this paper we derive necessary and sufficient conditions for strong ellipticity in several classes of anisotropic linearly elastic materials. Our results cover all classes in the rhombic system (nine elasticities), four classes of the tetragonal system (six elasticities) and all classes in the cubic system (three elasticities). As a special case we recover necessary and sufficient conditions for strong ellipticity in transversely isotropic materials. The central result shows that for the rhombic system strong ellipticity restricts some appropriate combinations of elasticities to take values inside a domain whose boundary is the third order algebraic surface defined by x2+y2+z2−2xyz−1=0 situated in the cube $\left\vert x\right\vert <1$, $\left\vert y\right\vert <1$, $ \left\vert z\right\vert <1$. For more symmetric situations, the general analysis restricts combinations of elasticities to range inside either a plane domain (for four classes in the tetragonal system) or in an one-dimensional interval (for the hexagonal systems, transverse isotropy and cubic system). The proof involves only the basic statement of the strong ellipticity condition.

https://www.math.uaic.ro/~schirita/Papers/2007JE.pdf

On the Strong Ellipticity of the Anisotropic Linearly Elastic Materials

This paper studies the time differential dual-phase-lag model of a thermoelastic material, where the elastic deformation is accompanied by thermal effects governed by a time differential equation for the heat flux with dual phase lags. This coupling gives rise to a complex differential system requiring a special treatment. Uniqueness and continuous dependence results are established for the solutions of the mixed initial boundary value problems associated with the model of the linear theory of thermoelasticity with dual-phase-lag for an anisotropic and inhomogeneous material. Two methods are developed in this paper, both being based on an identity of Lagrange type and of a conservation law applied to appropriate initial boundary value problems associated with the model in concern. The uniqueness results are established under mild constitutive hypotheses (right like those in the classical linear thermoelasticity), without any restrictions upon the delay times (excepting the class of thermoelastic materials for which the delay time of phase lag of the conductive temperature gradient is vanishing and the delay time in the phase lag of heat flux vector is strictly positive, when an ill-posed model should be expected). The continuous dependence results are established by using a conservation law and a Gronwall inequality, under certain constitutive restrictions upon the thermoelastic coefficients and the delay times.

Stan Chiriţă

Papers

On the theory of thermoelasticity with microtemperatures

Time-weighted surface power function method for the study of spatial behaviour in dynamics of continua

On the Strong Ellipticity of the Anisotropic Linearly Elastic Materials

On the time differential dual-phase-lag thermoelastic model

On the thermomechanical consistency of the time differential dual-phase-lag models of heat conduction