R. E. Raab and O. L. de Lange
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198567271
- eISBN:
- 9780191717970
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567271.003.0004
- Subject:
- Physics, Atomic, Laser, and Optical Physics
Linear constitutive relations for the response fields D and H in terms of the macroscopic fields E and B of a harmonic plane wave are derived in multipole form up to electric octopole-magnetic ...
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Linear constitutive relations for the response fields D and H in terms of the macroscopic fields E and B of a harmonic plane wave are derived in multipole form up to electric octopole-magnetic quadrupole order. These yield multipole expressions for the permittivity, inverse permeability, and the two magnetoelectric coefficients for both non-magnetic and magnetic media. These four material constants are required to satisfy origin independence, certain symmetries for a non-dissipative medium, and the Post constraint. Derivations of the last two conditions are given. Up to the multipole order considered, all the material constants satisfy the symmetry requirements, but none is origin independent beyond electric dipole order. The Post constraint is involved beyond this order and is not satisfied. These topics are considered further in Chapters 7 and 8.Less
Linear constitutive relations for the response fields D and H in terms of the macroscopic fields E and B of a harmonic plane wave are derived in multipole form up to electric octopole-magnetic quadrupole order. These yield multipole expressions for the permittivity, inverse permeability, and the two magnetoelectric coefficients for both non-magnetic and magnetic media. These four material constants are required to satisfy origin independence, certain symmetries for a non-dissipative medium, and the Post constraint. Derivations of the last two conditions are given. Up to the multipole order considered, all the material constants satisfy the symmetry requirements, but none is origin independent beyond electric dipole order. The Post constraint is involved beyond this order and is not satisfied. These topics are considered further in Chapters 7 and 8.
G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos
- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691142173
- eISBN:
- 9781400842650
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691142173.003.0002
- Subject:
- Mathematics, Applied Mathematics
This chapter first introduces the constitutive relations which are commonly used in electromagnetic theory for the mathematical modelling of complex electromagnetic media. These constitutive ...
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This chapter first introduces the constitutive relations which are commonly used in electromagnetic theory for the mathematical modelling of complex electromagnetic media. These constitutive relations are to be understood as operators connecting the electric flux density and the magnetic flux density with the electric and the magnetic fields. When they are introduced into the Maxwell equations, this chapter obtains differential equations (PDEs) that govern the evolution of the electromagnetic fields. This chapter also seeks to formulate and discuss the scope of the various problems related to the Maxwell equations that will be treated in this volume. It introduces and formulates in terms of differential equations various problems of interest related to the Maxwell equations: time-harmonic problems, scattering problems, time-domain evolution problems, random and stochastic problems, controllability problems, homogenisation problems, and others.Less
This chapter first introduces the constitutive relations which are commonly used in electromagnetic theory for the mathematical modelling of complex electromagnetic media. These constitutive relations are to be understood as operators connecting the electric flux density and the magnetic flux density with the electric and the magnetic fields. When they are introduced into the Maxwell equations, this chapter obtains differential equations (PDEs) that govern the evolution of the electromagnetic fields. This chapter also seeks to formulate and discuss the scope of the various problems related to the Maxwell equations that will be treated in this volume. It introduces and formulates in terms of differential equations various problems of interest related to the Maxwell equations: time-harmonic problems, scattering problems, time-domain evolution problems, random and stochastic problems, controllability problems, homogenisation problems, and others.
Madhucchanda Sen
- Published in print:
- 2015
- Published Online:
- April 2015
- ISBN:
- 9780199453603
- eISBN:
- 9780199084623
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199453603.001.0001
- Subject:
- Philosophy, Philosophy of Mind
A key concern of philosophy is the mind’s relation with the world. The debate between externalism and internalism is not a new one and a great number of thinkers have contributed to it in the recent ...
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A key concern of philosophy is the mind’s relation with the world. The debate between externalism and internalism is not a new one and a great number of thinkers have contributed to it in the recent past. This book explores the inherent contradictions in the traditional line of thought that has shaped this debate so far. The book analyses how an understanding built on compartmentalized categories has stifled the process of philosophical thinking. Despite stating at the outset her inclination towards externalism, the author does not merely take sides in an age-old debate, but rather approaches it from a fresh perspective. By challenging our understanding of what is meant by the external and the internal and by showing how the distinction between them may occasionally blur, the book questions the very existence of the divide that has sustained the debate under discussion. Pointing towards the necessity of a paradigm shift in the way the mind–world relation has been perceived, this work explores the possibility of a dialogue emerging between analytic philosophy, phenomenology, and Navya-Nyāya—an engagement that would cut across the divide between Eastern and Western philosophical traditions.Less
A key concern of philosophy is the mind’s relation with the world. The debate between externalism and internalism is not a new one and a great number of thinkers have contributed to it in the recent past. This book explores the inherent contradictions in the traditional line of thought that has shaped this debate so far. The book analyses how an understanding built on compartmentalized categories has stifled the process of philosophical thinking. Despite stating at the outset her inclination towards externalism, the author does not merely take sides in an age-old debate, but rather approaches it from a fresh perspective. By challenging our understanding of what is meant by the external and the internal and by showing how the distinction between them may occasionally blur, the book questions the very existence of the divide that has sustained the debate under discussion. Pointing towards the necessity of a paradigm shift in the way the mind–world relation has been perceived, this work explores the possibility of a dialogue emerging between analytic philosophy, phenomenology, and Navya-Nyāya—an engagement that would cut across the divide between Eastern and Western philosophical traditions.
Richard M. Christensen
- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199662111
- eISBN:
- 9780191748387
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199662111.003.0015
- Subject:
- Physics, Condensed Matter Physics / Materials
The initial discussion concerns the need for damage characterization for materials. A little more specifically, cumulative damage is the state of damage that grows until it terminates with the ...
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The initial discussion concerns the need for damage characterization for materials. A little more specifically, cumulative damage is the state of damage that grows until it terminates with the materials failure. Damage states are often characterized by inserting into the constitutive relations explicit damage variables with unknown coefficients to be determined. In the present investigation only damage forms with no adjustable parameters are employed. The main approach considered here is that of kinetic crack growth. In this approach, power-law forms are taken for the rate of growth of the idealized crack representing damage. The crack grows until instability causes macroscopic failure. Three other models are compared with the kinetic crack approach: Miner’s rule, the Hashin–Rotem form, and the Broutman–Sahu form. Three methods of testing the four models are utilized: (i) residual strength, (ii) life after damage, or simply life prediction, and (iii) residual life. Only the kinetic-crack method satisfies the consistency tests of all three testing methods.Less
The initial discussion concerns the need for damage characterization for materials. A little more specifically, cumulative damage is the state of damage that grows until it terminates with the materials failure. Damage states are often characterized by inserting into the constitutive relations explicit damage variables with unknown coefficients to be determined. In the present investigation only damage forms with no adjustable parameters are employed. The main approach considered here is that of kinetic crack growth. In this approach, power-law forms are taken for the rate of growth of the idealized crack representing damage. The crack grows until instability causes macroscopic failure. Three other models are compared with the kinetic crack approach: Miner’s rule, the Hashin–Rotem form, and the Broutman–Sahu form. Three methods of testing the four models are utilized: (i) residual strength, (ii) life after damage, or simply life prediction, and (iii) residual life. Only the kinetic-crack method satisfies the consistency tests of all three testing methods.
Richard Freeman, James King, and Gregory Lafyatis
- Published in print:
- 2019
- Published Online:
- February 2019
- ISBN:
- 9780198726500
- eISBN:
- 9780191793325
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198726500.003.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics
A review of the basic elements of electricity and magnetism is presented with an introduction to Maxwell’s equations for steady-state in a vacuum. The modifications to these equations necessary to ...
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A review of the basic elements of electricity and magnetism is presented with an introduction to Maxwell’s equations for steady-state in a vacuum. The modifications to these equations necessary to account for time varying sources are shown to produce to a causal unification of magnetic and electric fields. The application of Maxwell’s equations in the presence of matter leads to the concepts of electric and magnetic polarization of matter. Electromagnetic radiation arises directly from Maxwell’s time-dependent equations and the basic response of materials to this radiation is discussed. Finally, electromagnetic conservation laws are derived, including electromagnetic energy and linear and angular momentum.Less
A review of the basic elements of electricity and magnetism is presented with an introduction to Maxwell’s equations for steady-state in a vacuum. The modifications to these equations necessary to account for time varying sources are shown to produce to a causal unification of magnetic and electric fields. The application of Maxwell’s equations in the presence of matter leads to the concepts of electric and magnetic polarization of matter. Electromagnetic radiation arises directly from Maxwell’s time-dependent equations and the basic response of materials to this radiation is discussed. Finally, electromagnetic conservation laws are derived, including electromagnetic energy and linear and angular momentum.
Bahram Mashhoon
- Published in print:
- 2017
- Published Online:
- July 2017
- ISBN:
- 9780198803805
- eISBN:
- 9780191842313
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198803805.003.0004
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics
Is gravity nonlocal? Einstein interpreted the principle of equivalence of inertial and gravitational masses to mean that there exists a profound relationship between inertia and gravitation. Based on ...
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Is gravity nonlocal? Einstein interpreted the principle of equivalence of inertial and gravitational masses to mean that there exists a profound relationship between inertia and gravitation. Based on Einstein’s fundamental insight, it would seem natural to extend history dependence to the gravitational domain. However, it is not clear how to develop a nonlocal extension of Einstein’s local principle of equivalence. To go forward, we therefore choose an indirect approach based on a certain analogy with electromagnetism. In a material medium, the electromagnetic constitutive relations are nonlocal and this fact leads to the nonlocal electrodynamics of media. It turns out that general relativity can be formulated in a form that resembles the electrodynamics of media. Making the corresponding gravitational constitutive relations nonlocal would then lead to nonlocal GR. This indirect approach is adopted in the rest of this book.Less
Is gravity nonlocal? Einstein interpreted the principle of equivalence of inertial and gravitational masses to mean that there exists a profound relationship between inertia and gravitation. Based on Einstein’s fundamental insight, it would seem natural to extend history dependence to the gravitational domain. However, it is not clear how to develop a nonlocal extension of Einstein’s local principle of equivalence. To go forward, we therefore choose an indirect approach based on a certain analogy with electromagnetism. In a material medium, the electromagnetic constitutive relations are nonlocal and this fact leads to the nonlocal electrodynamics of media. It turns out that general relativity can be formulated in a form that resembles the electrodynamics of media. Making the corresponding gravitational constitutive relations nonlocal would then lead to nonlocal GR. This indirect approach is adopted in the rest of this book.
