Ebook: Electromagnetic Properties of Multiphase Dielectrics: A Primer on Modeling, Theory and Computation

Recently, several applications, primarily driven
by microtechnology, have emerged where the use of materials with
tailored electromagnetic (dielectric) properties are necessary for a successful overall design. The ``tailored'' aggregate properties are
achieved by combining an easily moldable base matrix with particles
having dielectric properties that are chosen to deliver (desired) effective properties.
In many cases, the analysis of such materials requires the simulation of the macroscopic and microscopic electromagnetic response, as well as its resulting coupled thermal response, which can be important to determine possible failures in ``hot spots.'' This necessitates
a stress analysis. Furthermore, because, oftentimes, such processes initiate degratory chemical processes, it can be necessary to also include models for these processes as well.
A central objective of this work is to provide basic models and numerical solution strategies to analyze the coupled response of
such materials by direct simulation using standard laptop/desktop equipment. Accordingly, this monograph covers:

(1) The foundations of Maxwell's equations,

(2) Basic homogenization theory,

(3) Coupled systems (electromagnetic, thermal, mechanical and chemical),

(4) Numerical methods and

(5) An introduction to select biological problems.

The text can be viewed as a research monograph suitable for use in an upper-division undergraduate or first year graduate course geared towards students in the applied sciences, mechanics and mathematics that have an interest in the analysis of particulate materials.

Recently, several applications, primarily driven
by microtechnology, have emerged where the use of materials with
tailored electromagnetic (dielectric) properties are necessary for a successful overall design. The ``tailored'' aggregate properties are
achieved by combining an easily moldable base matrix with particles
having dielectric properties that are chosen to deliver (desired) effective properties.
In many cases, the analysis of such materials requires the simulation of the macroscopic and microscopic electromagnetic response, as well as its resulting coupled thermal response, which can be important to determine possible failures in ``hot spots.'' This necessitates
a stress analysis. Furthermore, because, oftentimes, such processes initiate degratory chemical processes, it can be necessary to also include models for these processes as well.
A central objective of this work is to provide basic models and numerical solution strategies to analyze the coupled response of
such materials by direct simulation using standard laptop/desktop equipment. Accordingly, this monograph covers:

(1) The foundations of Maxwell's equations,

(2) Basic homogenization theory,

(3) Coupled systems (electromagnetic, thermal, mechanical and chemical),

(4) Numerical methods and

(5) An introduction to select biological problems.

The text can be viewed as a research monograph suitable for use in an upper-division undergraduate or first year graduate course geared towards students in the applied sciences, mechanics and mathematics that have an interest in the analysis of particulate materials.

Recently, several applications, primarily driven
by microtechnology, have emerged where the use of materials with
tailored electromagnetic (dielectric) properties are necessary for a successful overall design. The ``tailored'' aggregate properties are
achieved by combining an easily moldable base matrix with particles
having dielectric properties that are chosen to deliver (desired) effective properties.
In many cases, the analysis of such materials requires the simulation of the macroscopic and microscopic electromagnetic response, as well as its resulting coupled thermal response, which can be important to determine possible failures in ``hot spots.'' This necessitates
a stress analysis. Furthermore, because, oftentimes, such processes initiate degratory chemical processes, it can be necessary to also include models for these processes as well.
A central objective of this work is to provide basic models and numerical solution strategies to analyze the coupled response of
such materials by direct simulation using standard laptop/desktop equipment. Accordingly, this monograph covers:

(1) The foundations of Maxwell's equations,

(2) Basic homogenization theory,

(3) Coupled systems (electromagnetic, thermal, mechanical and chemical),

(4) Numerical methods and

(5) An introduction to select biological problems.

The text can be viewed as a research monograph suitable for use in an upper-division undergraduate or first year graduate course geared towards students in the applied sciences, mechanics and mathematics that have an interest in the analysis of particulate materials.

Content:
Front Matter....Pages 1-17
Multiphase Continua, an Introduction....Pages 1-4
Elementary Notation and Mathematical Operations....Pages 5-11
Governing Electromagnetics: Maxwell’s Equations....Pages 13-37
Classical Linear Constitutive Behavior....Pages 39-43
Extraction of Macroscopic Effective Properties....Pages 45-62
Coupled Effects: Joule-Heating....Pages 63-72
Some Basic Principles of Continuum Mechanics....Pages 73-88
Basic Time-Stepping Schemes....Pages 89-101
A Model Problem: Dielectrics Undergoing Multifield Processes....Pages 103-150
Concluding Remarks and Emerging Applications in the Biological Sciences....Pages 151-166
Back Matter....Pages 0--1

Recently, several applications, primarily driven
by microtechnology, have emerged where the use of materials with
tailored electromagnetic (dielectric) properties are necessary for a successful overall design. The ``tailored'' aggregate properties are
achieved by combining an easily moldable base matrix with particles
having dielectric properties that are chosen to deliver (desired) effective properties.
In many cases, the analysis of such materials requires the simulation of the macroscopic and microscopic electromagnetic response, as well as its resulting coupled thermal response, which can be important to determine possible failures in ``hot spots.'' This necessitates
a stress analysis. Furthermore, because, oftentimes, such processes initiate degratory chemical processes, it can be necessary to also include models for these processes as well.
A central objective of this work is to provide basic models and numerical solution strategies to analyze the coupled response of
such materials by direct simulation using standard laptop/desktop equipment. Accordingly, this monograph covers:

(1) The foundations of Maxwell's equations,

(2) Basic homogenization theory,

(3) Coupled systems (electromagnetic, thermal, mechanical and chemical),

(4) Numerical methods and

(5) An introduction to select biological problems.

The text can be viewed as a research monograph suitable for use in an upper-division undergraduate or first year graduate course geared towards students in the applied sciences, mechanics and mathematics that have an interest in the analysis of particulate materials.

Content:
Front Matter....Pages 1-17
Multiphase Continua, an Introduction....Pages 1-4
Elementary Notation and Mathematical Operations....Pages 5-11
Governing Electromagnetics: Maxwell’s Equations....Pages 13-37
Classical Linear Constitutive Behavior....Pages 39-43
Extraction of Macroscopic Effective Properties....Pages 45-62
Coupled Effects: Joule-Heating....Pages 63-72
Some Basic Principles of Continuum Mechanics....Pages 73-88
Basic Time-Stepping Schemes....Pages 89-101
A Model Problem: Dielectrics Undergoing Multifield Processes....Pages 103-150
Concluding Remarks and Emerging Applications in the Biological Sciences....Pages 151-166
Back Matter....Pages 0--1
....