An eigen theory of electromagnetic waves based on the standard spaces

A thermodynamic theory of localized deformation based on the operator principle

“…Projecting it to the standard space [8][9][10], we get a set of inner scalar variables q * i (i = 1, 2, · · · 6). So, according to the second law of irreversible thermodynamics, the dissipation power of the system can be written as follows…”

“…where * i andX i are the ith stress operator [8][9][10] and dissipation force operator, respectively. Thus, the dissipation force operator of the system can be represented by the stress operator, provided the phenomenological relation of the nonlinear constitutive equation of materials is known.…”

“…In this paper, the fundamental equations of dissipation fields of a continuum are obtained by means of the operator theory of irreversible thermodynamics, which is based on the concepts of elastic operator theory of solid mechanics under standard space [8][9][10]. The equations satisfy the restriction of the second law of irreversible thermodynamics and arrange in states of quantized energy.…”

The Quasi-Static Approximation of Heat Waves in Anisotropic Thermo-Elastic Media

“…The material tensors in Equations (1), (2), (16) There are four independent eigenspaces in a hexagonal (transversely isotropic) crystal [7][8][9][10] (1)…”

“…Although many works have been done for heat or elastic waves in anisotropic media, the explicit uncoupled equations of wave equations in anisotropic media could not be obtained because of the limitations of classical elastic theory [4][5][6]. In this paper, the idea of standard spaces [7][8][9][10] is used to deal with both the equilibrium equation and the heat conduction equation based on the quasi-static approximation of the propagation of heat wave, and by introducing an new thermo-elastic model that obeys the second law of thermo-dynamics, a uncoupled modal equations of heat wave are obtained, which shows that heat wave is of the properties of dissipative waves. Meanwhile the propagation speed, propagation direction and space pattern of heat wave can be completely determined by the modal equations.…”