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Electromagnetism of Continuous Media: Mathematical Modelling and Applications

Mauro Fabrizio, +1 more
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TLDR
In this paper, the authors present a model of a simple electromagnetic field with memory and a finite formulation of electromagnetic functions and problems in non-local electromagnetic fields.
Abstract: 
Preface 1. ELECTROMAGNETIC FIELDS 2. Green's functions and retarded potentials 3. Time-harmonic fields 4. Models of materials with memory 5. THERMODYNAMICS OF SIMPLE ELECTROMAGNETIC SYSTEMS 6. Thermoelectromagnetic systems 7. Existence and uniqueness 8. Wave propagation 9. Extremum principles 10. PROBLEMS IN NONLINEAR ELECTROMAGNETISM 11. Nonlocal electromagnetism and superconductivity 12. Magnetic hysteresis A. SOME PROPERTIES OF BESSEL FUNCTIONS B. Fourier transforms and Sobolev spaces C. Compact operators and eigenfunctions D. Differential operators in curvilinear coordinates E. Finite formulation of electromagnetism

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Thermodynamics of non-local materials: extra fluxes and internal powers

Mauro Fabrizio, +2 more
- 15 Apr 2011 - 
TL;DR: The most usual formulation of the Laws of Thermodynamics turns out to be suitable for local or simple materials, while for non-local systems there are two different ways: either modify this usual formulation by introducing suitable extra fluxes or express the laws of thermodynamics in terms of internal powers directly as mentioned in this paper.

Convergence of the time-domain perfectly matched layer method for acoustic scattering problems

Zhiming Chen
TL;DR: In this article, the authors established the stability and convergence of the time-domain perfectly matched layer (PML) method for solving the acoustic scattering problems with Dirichlet-to-Neumann boundary condition.

On maxwell equations with the transparent boundary condition

Zhiming Chen, +1 more
TL;DR: In this paper, the authors show the well-posedness and stability of the time-harmonic Maxwell scattering problem with complex wave numbers with the transparent boundary condition and show that it is stable with respect to the complex wave number.
Journal ArticleDOI

Thermodynamics of non-local materials: extra fluxes and internal powers

Mauro Fabrizio, +2 more
- 31 Jul 2011 - 
TL;DR: In this article, the authors propose a general formulation of the Laws of Thermodynamics in terms of internal powers, which is a priori defined on the basis of the constitutive equations and allows to highlight the contribution of the internal powers in the variation of the thermodynamic potentials.

On maxwell equations with the transparent boundary condition

Zhiming, +3 more
TL;DR: In this article, the authors discuss well-posedness and well-positioning in a well-posing situation, and propose a method to achieve wellposedness in the environment.