Mauro Fabrizio and Angelo Morro
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198527008
- eISBN:
- 9780191713316
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527008.001.0001
- Subject:
- Mathematics, Applied Mathematics
This book is devoted to the mathematical modelling of electromagnetic materials. Electromagnetism in matter is developed with particular emphasis on material effects, which are ascribed to memory in ...
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This book is devoted to the mathematical modelling of electromagnetic materials. Electromagnetism in matter is developed with particular emphasis on material effects, which are ascribed to memory in time and nonlocality. Within the mathematical modelling, thermodynamics of continuous media plays a central role in that it places significant restrictions on the constitutive equations. Further, as shown in connection with uniqueness, existence and stability, variational settings, and wave propagation, a correct formulation of the pertinent problems is based on the knowledge of the thermodynamic restrictions for the material. The book is divided into four parts. Part I (chapters 1 to 4) reviews the basic concepts of electromagnetism, starting from the integral form of Maxwell’s equations and then addressing attention to the physical motivation for materials with memory. Part II (chapers 5 to 9) deals with thermodynamics of systems with memory and applications to evolution and initial/boundary-value problems. It contains developments and results which are unusual in textbooks on electromagnetism and arise from the research literature, mainly post-1960s. Part III (chapters 10 to 12) outlines some topics of materials modelling — nonlinearity, nonlocality, superconductivity, and magnetic hysteresis — which are of great interest both in mathematics and in applications.Less
This book is devoted to the mathematical modelling of electromagnetic materials. Electromagnetism in matter is developed with particular emphasis on material effects, which are ascribed to memory in time and nonlocality. Within the mathematical modelling, thermodynamics of continuous media plays a central role in that it places significant restrictions on the constitutive equations. Further, as shown in connection with uniqueness, existence and stability, variational settings, and wave propagation, a correct formulation of the pertinent problems is based on the knowledge of the thermodynamic restrictions for the material. The book is divided into four parts. Part I (chapters 1 to 4) reviews the basic concepts of electromagnetism, starting from the integral form of Maxwell’s equations and then addressing attention to the physical motivation for materials with memory. Part II (chapers 5 to 9) deals with thermodynamics of systems with memory and applications to evolution and initial/boundary-value problems. It contains developments and results which are unusual in textbooks on electromagnetism and arise from the research literature, mainly post-1960s. Part III (chapters 10 to 12) outlines some topics of materials modelling — nonlinearity, nonlocality, superconductivity, and magnetic hysteresis — which are of great interest both in mathematics and in applications.
Michele Maggiore
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198570745
- eISBN:
- 9780191717666
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570745.003.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter discusses how gravitational waves emerge from general relativity, and what their properties are. The most straightforward approach is ‘linearized theory’, where the Einstein equations ...
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This chapter discusses how gravitational waves emerge from general relativity, and what their properties are. The most straightforward approach is ‘linearized theory’, where the Einstein equations are expanded around the flat Minkowski metric. It is shown how a wave equation emerges and how the solutions can be put in an especially simple form by an appropriate gauge choice. Using standard tools of general relativity such as the geodesic equation and the equation of the geodesic deviation, how these waves interact with a set of test masses is detailed. The energy and momentum carried by GWs are then computed and discussed. This chapter approaches the problem from a geometric point of view, identifying the energy-momentum tensor of GWs from their effect on the background curvature. Finally, GW propagation in curved space is discussed.Less
This chapter discusses how gravitational waves emerge from general relativity, and what their properties are. The most straightforward approach is ‘linearized theory’, where the Einstein equations are expanded around the flat Minkowski metric. It is shown how a wave equation emerges and how the solutions can be put in an especially simple form by an appropriate gauge choice. Using standard tools of general relativity such as the geodesic equation and the equation of the geodesic deviation, how these waves interact with a set of test masses is detailed. The energy and momentum carried by GWs are then computed and discussed. This chapter approaches the problem from a geometric point of view, identifying the energy-momentum tensor of GWs from their effect on the background curvature. Finally, GW propagation in curved space is discussed.
Abraham Bers
- Published in print:
- 2016
- Published Online:
- November 2016
- ISBN:
- 9780199295784
- eISBN:
- 9780191749063
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199295784.003.0013
- Subject:
- Physics, Nuclear and Plasma Physics, Particle Physics / Astrophysics / Cosmology
This chapter completes the task of describing linear natural modes in a homogeneous, drift-free cold-plasma and concludes with a brief look at the nonlinear coupling of linear modes. The linear wave ...
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This chapter completes the task of describing linear natural modes in a homogeneous, drift-free cold-plasma and concludes with a brief look at the nonlinear coupling of linear modes. The linear wave analysis here follows the formulation and developments of the previous two chapters, and highlights the analysis of linear waves at any angle. Waves that propagate at an arbitrary angle are of a very large variety and their detailed description requires approximate analytical approaches for various applications. For propagation in infinitely-extended plasmas, it has been found useful to classify their description in a space of normalized magnetic field and density variables where the cutoff and resonance of the principal waves—this is referred to here as the Clemmow, Mullaly, Allis (CMA) diagram. The chapter also analyses approximate wave propagation treatments that have been found useful in various, more specific, wave applications in magnetized plasmas.Less
This chapter completes the task of describing linear natural modes in a homogeneous, drift-free cold-plasma and concludes with a brief look at the nonlinear coupling of linear modes. The linear wave analysis here follows the formulation and developments of the previous two chapters, and highlights the analysis of linear waves at any angle. Waves that propagate at an arbitrary angle are of a very large variety and their detailed description requires approximate analytical approaches for various applications. For propagation in infinitely-extended plasmas, it has been found useful to classify their description in a space of normalized magnetic field and density variables where the cutoff and resonance of the principal waves—this is referred to here as the Clemmow, Mullaly, Allis (CMA) diagram. The chapter also analyses approximate wave propagation treatments that have been found useful in various, more specific, wave applications in magnetized plasmas.
J. B. Rosenzweig
- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198525547
- eISBN:
- 9780191711725
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525547.003.0007
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter surveys aspects of electromagnetic fields inside of regions bounded by conductors, in scenarios of relevance to accelerator technology. It explains that the discussion was based on ...
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This chapter surveys aspects of electromagnetic fields inside of regions bounded by conductors, in scenarios of relevance to accelerator technology. It explains that the discussion was based on general considerations of electromagnetic wave propagation in vacuum, dielectrics, and conductors. It then builds the discussion of resonant cavity modes upon relevant concepts in waveguide theory. It clarifies the forms of fields in couple cavity linacs, devices that are also profitably viewed as TM waveguides in their own right. It uses the view of rf cavities as generalized oscillators to introduce the Slater perturbation theorem, a powerful tool for tuning and measuring cavity characteristics.Less
This chapter surveys aspects of electromagnetic fields inside of regions bounded by conductors, in scenarios of relevance to accelerator technology. It explains that the discussion was based on general considerations of electromagnetic wave propagation in vacuum, dielectrics, and conductors. It then builds the discussion of resonant cavity modes upon relevant concepts in waveguide theory. It clarifies the forms of fields in couple cavity linacs, devices that are also profitably viewed as TM waveguides in their own right. It uses the view of rf cavities as generalized oscillators to introduce the Slater perturbation theorem, a powerful tool for tuning and measuring cavity characteristics.
Abraham Bers
- Published in print:
- 2016
- Published Online:
- November 2016
- ISBN:
- 9780199295784
- eISBN:
- 9780191749063
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199295784.003.0022
- Subject:
- Physics, Nuclear and Plasma Physics, Particle Physics / Astrophysics / Cosmology
This chapter considers mathematical techniques in the analysis of linear wave propagation and parametric interactions in plasma and beams with spatially-nonuniform (inhomogeneous) equilibria in ...
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This chapter considers mathematical techniques in the analysis of linear wave propagation and parametric interactions in plasma and beams with spatially-nonuniform (inhomogeneous) equilibria in density and confining magnetic fields. These techniques can help in the modeling and analysis of realistic plasma systems. The chapter gives the simplest description of the modifications of collective modes when the plasma equilibrium is no longer homogeneous in space and/or time, but varies sufficiently slowly so that modes maintain their basic character while changing their propagation. This is accomplished by introducing the techniques of geometric optics and ray tracing for a medium with temporal and spatial dispersion such as a plasma. It also describes techniques for analysis of situations in which the basic collective modes are modified and couple to each other due to inhomogeneity in plasma equilibrium, and concludes with a discussion of variational principles which helps in the analysis of bounded plasmas that are also inhomogeneous.Less
This chapter considers mathematical techniques in the analysis of linear wave propagation and parametric interactions in plasma and beams with spatially-nonuniform (inhomogeneous) equilibria in density and confining magnetic fields. These techniques can help in the modeling and analysis of realistic plasma systems. The chapter gives the simplest description of the modifications of collective modes when the plasma equilibrium is no longer homogeneous in space and/or time, but varies sufficiently slowly so that modes maintain their basic character while changing their propagation. This is accomplished by introducing the techniques of geometric optics and ray tracing for a medium with temporal and spatial dispersion such as a plasma. It also describes techniques for analysis of situations in which the basic collective modes are modified and couple to each other due to inhomogeneity in plasma equilibrium, and concludes with a discussion of variational principles which helps in the analysis of bounded plasmas that are also inhomogeneous.
Józef Ignaczak and Martin Ostoja-Starzewski
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199541645
- eISBN:
- 9780191716164
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199541645.001.0001
- Subject:
- Mathematics, Applied Mathematics, Mathematical Physics
Generalized dynamic thermoelasticity is a vital area of research in continuum mechanics, free of the classical paradox of infinite propagation speeds of thermal signals in Fourier‐type heat ...
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Generalized dynamic thermoelasticity is a vital area of research in continuum mechanics, free of the classical paradox of infinite propagation speeds of thermal signals in Fourier‐type heat conduction. Besides that paradox, the classical dynamic thermoelasticity theory offers either unsatisfactory or poor descriptions of a solid's response to a fast transient loading (say, due to short laser pulses) or at low temperatures. Several models were developed and intensively studied over the past four decades, and this book is the first monograph on the subject since the 1970s, aiming to provide a point of reference in the field. It focuses on dynamic thermoelasticity governed by hyperbolic equations, and, in particular, on the two leading theories: that of Lord‐Shulman (with one relaxation time), and that of Green‐Lindsay (with two relaxation times). While the resulting field equations are linear partial differential ones, the complexity of theories is due to the coupling of mechanical with thermal fields. The book is concerned with the mathematical aspects of both theories — existence and uniqueness theorems, domain of influence theorems, convolutional variational principles — as well as with the methods for various initial/boundary value problems. In the latter respect, following the establishment of the central equation of thermoelasticity with finite wave speeds, there are extensive presentations of: the exact, aperiodic‐in‐time solutions of Green‐Lindsay theory; Kirchhoff‐type formulas and integral equations in Green‐Lindsay theory; thermoelastic polynomials; moving discontinuity surfaces; and time‐periodic solutions. This is followed by a chapter on physical aspects of generalized thermoelasticity, with a review of several applications. The book closes with a chapter on a nonlinear hyperbolic theory of a rigid heat conductor for which a number of asymptotic solutions are obtained using a method of weakly nonlinear geometric optics. The book is augmented by an extensive bibliography.Less
Generalized dynamic thermoelasticity is a vital area of research in continuum mechanics, free of the classical paradox of infinite propagation speeds of thermal signals in Fourier‐type heat conduction. Besides that paradox, the classical dynamic thermoelasticity theory offers either unsatisfactory or poor descriptions of a solid's response to a fast transient loading (say, due to short laser pulses) or at low temperatures. Several models were developed and intensively studied over the past four decades, and this book is the first monograph on the subject since the 1970s, aiming to provide a point of reference in the field. It focuses on dynamic thermoelasticity governed by hyperbolic equations, and, in particular, on the two leading theories: that of Lord‐Shulman (with one relaxation time), and that of Green‐Lindsay (with two relaxation times). While the resulting field equations are linear partial differential ones, the complexity of theories is due to the coupling of mechanical with thermal fields. The book is concerned with the mathematical aspects of both theories — existence and uniqueness theorems, domain of influence theorems, convolutional variational principles — as well as with the methods for various initial/boundary value problems. In the latter respect, following the establishment of the central equation of thermoelasticity with finite wave speeds, there are extensive presentations of: the exact, aperiodic‐in‐time solutions of Green‐Lindsay theory; Kirchhoff‐type formulas and integral equations in Green‐Lindsay theory; thermoelastic polynomials; moving discontinuity surfaces; and time‐periodic solutions. This is followed by a chapter on physical aspects of generalized thermoelasticity, with a review of several applications. The book closes with a chapter on a nonlinear hyperbolic theory of a rigid heat conductor for which a number of asymptotic solutions are obtained using a method of weakly nonlinear geometric optics. The book is augmented by an extensive bibliography.
M. E. LINES and A. M. GLASS
- Published in print:
- 2001
- Published Online:
- February 2010
- ISBN:
- 9780198507789
- eISBN:
- 9780191709944
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507789.003.0013
- Subject:
- Physics, Condensed Matter Physics / Materials
A variety of optical phenomena can be classified under the heading of nonlinear optics. Examples are the Kerr and Pockels electro-optic effects, the Zeeman effect, and the photoelastic effect in ...
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A variety of optical phenomena can be classified under the heading of nonlinear optics. Examples are the Kerr and Pockels electro-optic effects, the Zeeman effect, and the photoelastic effect in which a low-frequency electric or magnetic field or mechanical strain is mixed with the optical wave. Another large group of optical nonlinearities involves the scattering of light from atomic or electronic oscillators or other fluctuations within the optical medium. In this category fall, for instance, second- or higher-order Raman scattering from optic phonons in general (including polariton scattering from infrared active phonons), Brillouin scattering from acoustic phonons, and Rayleigh scattering from entropy or orientation fluctuations. This chapter examines the important role played by ferroelectrics in the areas of electro-optics and optical mixing, as well as phenomenological and microscopic theories which relate the acentric nature of the host crystal to the nonlinear optical susceptibilities. Wave propagation in nonlinear dielectrics is discussed, along with phase matching, electro-optics and nonlinear optic coefficients, nonlinear susceptibility, anharmonic oscillator, bond anharmonic polarisability model, polarization potential, and hyper-Rayleigh and hyper-Raman scattering.Less
A variety of optical phenomena can be classified under the heading of nonlinear optics. Examples are the Kerr and Pockels electro-optic effects, the Zeeman effect, and the photoelastic effect in which a low-frequency electric or magnetic field or mechanical strain is mixed with the optical wave. Another large group of optical nonlinearities involves the scattering of light from atomic or electronic oscillators or other fluctuations within the optical medium. In this category fall, for instance, second- or higher-order Raman scattering from optic phonons in general (including polariton scattering from infrared active phonons), Brillouin scattering from acoustic phonons, and Rayleigh scattering from entropy or orientation fluctuations. This chapter examines the important role played by ferroelectrics in the areas of electro-optics and optical mixing, as well as phenomenological and microscopic theories which relate the acentric nature of the host crystal to the nonlinear optical susceptibilities. Wave propagation in nonlinear dielectrics is discussed, along with phase matching, electro-optics and nonlinear optic coefficients, nonlinear susceptibility, anharmonic oscillator, bond anharmonic polarisability model, polarization potential, and hyper-Rayleigh and hyper-Raman scattering.
Yves Frégnac, Pedro V. Carelli, Marc Pananceau, and Cyril Monier
- Published in print:
- 2010
- Published Online:
- August 2013
- ISBN:
- 9780262014717
- eISBN:
- 9780262289818
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262014717.003.0012
- Subject:
- Neuroscience, Research and Theory
This chapter explores dynamic coordination in the primary sensory cortex of mammals during low-level (non-attention-related) perception. It considers the possible existence of subcortical or cortical ...
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This chapter explores dynamic coordination in the primary sensory cortex of mammals during low-level (non-attention-related) perception. It considers the possible existence of subcortical or cortical supervisors in higher mammals and explains how coordination is generated by the sensory drive and amplified by built-in anisotropies in the network connectivity. Drawing on synaptic functional imaging (at the intracellular level) and real-time voltage-sensitive dye network imaging (at the functional map level), it illustrates the role of intracortical depolarizing waves whose functional features support the hypothesis of a dynamic association field. These waves help propagate synaptic modulation in space and time via lateral (and perhaps feedback) connectivity, which explains the emergence of illusions predicted by Gestalt theory. The chapter also explains how lateral propagation waves are reconstructed from synaptic echoes and looks at the propagation of orientation belief.Less
This chapter explores dynamic coordination in the primary sensory cortex of mammals during low-level (non-attention-related) perception. It considers the possible existence of subcortical or cortical supervisors in higher mammals and explains how coordination is generated by the sensory drive and amplified by built-in anisotropies in the network connectivity. Drawing on synaptic functional imaging (at the intracellular level) and real-time voltage-sensitive dye network imaging (at the functional map level), it illustrates the role of intracortical depolarizing waves whose functional features support the hypothesis of a dynamic association field. These waves help propagate synaptic modulation in space and time via lateral (and perhaps feedback) connectivity, which explains the emergence of illusions predicted by Gestalt theory. The chapter also explains how lateral propagation waves are reconstructed from synaptic echoes and looks at the propagation of orientation belief.
Georgios Balasis, Constantinos Papadimitriou, Eftyhia Zesta, and Viacheslav Pilipenko
- Published in print:
- 2016
- Published Online:
- February 2017
- ISBN:
- 9780198705246
- eISBN:
- 9780191774416
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198705246.003.0007
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics
Recent magnetic field missions flying in a low Earth orbit (LEO), like Ørsted, ST5, and CHAMP, have enabled us to study in situ the occurrence of ultra low of frequency (ULF) waves in the topside ...
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Recent magnetic field missions flying in a low Earth orbit (LEO), like Ørsted, ST5, and CHAMP, have enabled us to study in situ the occurrence of ultra low of frequency (ULF) waves in the topside ionosphere. CHAMP satellite has been one of the most successful missions for the study of the Earth’s magnetic field for more than a decade (July 2000–September 2010), allowing for the first time-term statistical studies on the occurrence of ULF wave events in the topside ionosphere. This chapter provides a review of recent studies of ULF waves using spacecraft in low Earth orbit. It combines a topical review of the various subclasses of ULF waves that the amenable to study from LEO with a detailed description of many recent observational studies and of several relevant theoretical efforts. It concludes by focusing on further studies made possible by the Swarm mission (in fruitful combination with other spacecraft and ground data) as well as by recent theoretical developments. The chapter also attempts to point out open questions.Less
Recent magnetic field missions flying in a low Earth orbit (LEO), like Ørsted, ST5, and CHAMP, have enabled us to study in situ the occurrence of ultra low of frequency (ULF) waves in the topside ionosphere. CHAMP satellite has been one of the most successful missions for the study of the Earth’s magnetic field for more than a decade (July 2000–September 2010), allowing for the first time-term statistical studies on the occurrence of ULF wave events in the topside ionosphere. This chapter provides a review of recent studies of ULF waves using spacecraft in low Earth orbit. It combines a topical review of the various subclasses of ULF waves that the amenable to study from LEO with a detailed description of many recent observational studies and of several relevant theoretical efforts. It concludes by focusing on further studies made possible by the Swarm mission (in fruitful combination with other spacecraft and ground data) as well as by recent theoretical developments. The chapter also attempts to point out open questions.
Aitor Anduaga
- Published in print:
- 2016
- Published Online:
- March 2016
- ISBN:
- 9780198755159
- eISBN:
- 9780191816529
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198755159.003.0004
- Subject:
- Physics, History of Physics
Chapter 4 proposes that interactions between radio scientists and commercial companies for elucidating wave propagation in the upper atmosphere was not conspicuously different from those evolved from ...
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Chapter 4 proposes that interactions between radio scientists and commercial companies for elucidating wave propagation in the upper atmosphere was not conspicuously different from those evolved from seismic prospecting of the Earth’s crust in America. It contends that there was a predominant epistemic paradigm in crustal seismology in the interwar period—simplicity—which was altered because of the strong influence of a particular commercial environment, i.e. the oil industry. To this end, several steps are followed. Firstly, it shows how Harold Jeffreys formulated the ‘simplicity postulate’ as the basis for his probabilistic epistemology, embraced by several seismologists who developed crustal models based on mathematical idealizations. Next, it shows that there was a renunciation of simplicity in the 1930s, emerging too quickly to have been the result of new geological evidence. Finally, it demonstrates that the paradigm shift among seismologists was a result of the significant rise in seismic exploration generated by the oil industry.Less
Chapter 4 proposes that interactions between radio scientists and commercial companies for elucidating wave propagation in the upper atmosphere was not conspicuously different from those evolved from seismic prospecting of the Earth’s crust in America. It contends that there was a predominant epistemic paradigm in crustal seismology in the interwar period—simplicity—which was altered because of the strong influence of a particular commercial environment, i.e. the oil industry. To this end, several steps are followed. Firstly, it shows how Harold Jeffreys formulated the ‘simplicity postulate’ as the basis for his probabilistic epistemology, embraced by several seismologists who developed crustal models based on mathematical idealizations. Next, it shows that there was a renunciation of simplicity in the 1930s, emerging too quickly to have been the result of new geological evidence. Finally, it demonstrates that the paradigm shift among seismologists was a result of the significant rise in seismic exploration generated by the oil industry.
John Weiner and Frederico Nunes
- Published in print:
- 2017
- Published Online:
- March 2017
- ISBN:
- 9780198796664
- eISBN:
- 9780191837920
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198796664.003.0002
- Subject:
- Physics, Atomic, Laser, and Optical Physics, Condensed Matter Physics / Materials
Chapter 2 reacquaints the reader with electric and magnetic force fields and their interactions with ponderable media through Maxwell’s equations and the accompanying Lorentz force law. Macroscopic ...
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Chapter 2 reacquaints the reader with electric and magnetic force fields and their interactions with ponderable media through Maxwell’s equations and the accompanying Lorentz force law. Macroscopic quantities of permittivity and permeability are emphasised, and through the constitutive relations, polarisation and magnetisation fields. Dipole radiation, space-propagating and surface-propagating wave solutions to Maxwell’s equations are all fundamental to understanding energy and momentum transport around, and through, atomic scale and nanoscale structured materials. The chapter ends with a development of plane wave propagation, reflection, and transmission in homogenous media and at dielectric and metallic surfaces.Less
Chapter 2 reacquaints the reader with electric and magnetic force fields and their interactions with ponderable media through Maxwell’s equations and the accompanying Lorentz force law. Macroscopic quantities of permittivity and permeability are emphasised, and through the constitutive relations, polarisation and magnetisation fields. Dipole radiation, space-propagating and surface-propagating wave solutions to Maxwell’s equations are all fundamental to understanding energy and momentum transport around, and through, atomic scale and nanoscale structured materials. The chapter ends with a development of plane wave propagation, reflection, and transmission in homogenous media and at dielectric and metallic surfaces.
Heiner Igel
- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780198717409
- eISBN:
- 9780191835070
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198717409.003.0001
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics
The need for numerical approximations of the seismic wave-propaga-tion problem in the field of seismology is motivated by the fact that we have to deal with complex 3D structures. The term ...
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The need for numerical approximations of the seismic wave-propaga-tion problem in the field of seismology is motivated by the fact that we have to deal with complex 3D structures. The term ‘computational seismology’ is defined and contrasted with other more classical approaches such as ray tracing approaches and quasi-analytical solutions such as normal mode techniques and the reflectivity method. The structure of the volume content is illustrated and guidelines are given how to use the content in combination with the supplementary electronic material.Less
The need for numerical approximations of the seismic wave-propaga-tion problem in the field of seismology is motivated by the fact that we have to deal with complex 3D structures. The term ‘computational seismology’ is defined and contrasted with other more classical approaches such as ray tracing approaches and quasi-analytical solutions such as normal mode techniques and the reflectivity method. The structure of the volume content is illustrated and guidelines are given how to use the content in combination with the supplementary electronic material.
Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab
- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691165318
- eISBN:
- 9781400866625
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691165318.003.0001
- Subject:
- Mathematics, Applied Mathematics
This book is about recent mathematical, numerical and statistical approaches for elasticity imaging of inclusions and cracks with waves at zero, single or multiple non-zero frequencies. It considers ...
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This book is about recent mathematical, numerical and statistical approaches for elasticity imaging of inclusions and cracks with waves at zero, single or multiple non-zero frequencies. It considers important developments in asymptotic imaging, stochastic modeling, and analysis of both deterministic and stochastic elastic wave propagation phenomena and puts them together in a coherent way. It gives emphasis on deriving the best possible imaging functionals for small inclusions and cracks in the sense of stability and resolution. For imaging extended elastic inclusions, the book develops accurate optimal control methodologies and examines the effect of uncertainties of the geometric or physical parameters on their stability and resolution properties. It also presents an asymptotic framework for vibration testing and a method for identifying, locating, and estimating inclusions and cracks in elastic structures by measuring their modal characteristics.Less
This book is about recent mathematical, numerical and statistical approaches for elasticity imaging of inclusions and cracks with waves at zero, single or multiple non-zero frequencies. It considers important developments in asymptotic imaging, stochastic modeling, and analysis of both deterministic and stochastic elastic wave propagation phenomena and puts them together in a coherent way. It gives emphasis on deriving the best possible imaging functionals for small inclusions and cracks in the sense of stability and resolution. For imaging extended elastic inclusions, the book develops accurate optimal control methodologies and examines the effect of uncertainties of the geometric or physical parameters on their stability and resolution properties. It also presents an asymptotic framework for vibration testing and a method for identifying, locating, and estimating inclusions and cracks in elastic structures by measuring their modal characteristics.
John A. Adam
- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691148373
- eISBN:
- 9781400885404
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691148373.003.0012
- Subject:
- Mathematics, Applied Mathematics
This chapter deals with the mathematics of ocean acoustics. A number of environmental factors affect the transmission of sound in the ocean, including the depth and configuration of the bottom, the ...
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This chapter deals with the mathematics of ocean acoustics. A number of environmental factors affect the transmission of sound in the ocean, including the depth and configuration of the bottom, the sound velocity structure within the ocean, and the shape of the ocean surface. The depths in the ocean are distributed in a peculiar manner, and the solution of underwater-sound problems may be grouped into two categories that differ mainly in terms of dimension: the average depths of water for deep-water transmission are 10,000 to 20,000 feet, whereas those for shallow-water transmission are less than 300 feet. The chapter first provides an overview of ocean acoustic waveguides before discussing one-dimensional waves in an inhomogeneous medium. It also considers a mathematical model of acoustic wave propagation in a stratified fluid and concludes with an analysis of the one-dimensional time-independent Schrödinger equation for solving the potential well problem.Less
This chapter deals with the mathematics of ocean acoustics. A number of environmental factors affect the transmission of sound in the ocean, including the depth and configuration of the bottom, the sound velocity structure within the ocean, and the shape of the ocean surface. The depths in the ocean are distributed in a peculiar manner, and the solution of underwater-sound problems may be grouped into two categories that differ mainly in terms of dimension: the average depths of water for deep-water transmission are 10,000 to 20,000 feet, whereas those for shallow-water transmission are less than 300 feet. The chapter first provides an overview of ocean acoustic waveguides before discussing one-dimensional waves in an inhomogeneous medium. It also considers a mathematical model of acoustic wave propagation in a stratified fluid and concludes with an analysis of the one-dimensional time-independent Schrödinger equation for solving the potential well problem.
Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab
- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691165318
- eISBN:
- 9781400866625
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691165318.001.0001
- Subject:
- Mathematics, Applied Mathematics
This book comprehensively explores elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave ...
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This book comprehensively explores elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative-based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures.Less
This book comprehensively explores elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative-based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures.
Nathalie Deruelle and Jean-Philippe Uzan
- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198786399
- eISBN:
- 9780191828669
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198786399.003.0017
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter discusses light in Newtonian theory. Astronomy (and physics in general) is certainly not a complete science without a theory of light. However, the nature of light and its kinematical ...
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This chapter discusses light in Newtonian theory. Astronomy (and physics in general) is certainly not a complete science without a theory of light. However, the nature of light and its kinematical properties were not completely understood until the advent of Maxwell’s theory, special and general relativity, and quantum field theory. The answers to these questions provided by Newtonian theory were only partial and sometimes even contradictory. Thus this chapter seeks to present a few aspects of this topic, such as the influences of gravity on light, stellar aberrations, and wave propagation. It also studies the Fizeau and Michelson–Morley experiments.Less
This chapter discusses light in Newtonian theory. Astronomy (and physics in general) is certainly not a complete science without a theory of light. However, the nature of light and its kinematical properties were not completely understood until the advent of Maxwell’s theory, special and general relativity, and quantum field theory. The answers to these questions provided by Newtonian theory were only partial and sometimes even contradictory. Thus this chapter seeks to present a few aspects of this topic, such as the influences of gravity on light, stellar aberrations, and wave propagation. It also studies the Fizeau and Michelson–Morley experiments.
Aitor Anduaga
- Published in print:
- 2016
- Published Online:
- March 2016
- ISBN:
- 9780198755159
- eISBN:
- 9780191816529
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198755159.001.0001
- Subject:
- Physics, History of Physics
Have industry and commerce affected the concepts, values, and epistemic foundations of different sciences? If so, how and to what extent? This book suggests that the most significant influence of ...
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Have industry and commerce affected the concepts, values, and epistemic foundations of different sciences? If so, how and to what extent? This book suggests that the most significant influence of industry on science, in the two case studies treated here, had to do with the issue of realism. These two cases deal with the elucidation of the layers of the upper atmosphere and the Earth’s crust. Using wave propagation as the common thread, this book simultaneously analyses the emergence of realist attitudes towards the entities of the ionosphere and the Earth’s crust. However, what was it that led physicists and engineers to adopt realist attitudes? This book suggests that a new kind of realism—one with social and cultural origins—is the answer: a preliminary, entity realism responding to specific commercial and engineering interests; i.e. a realism that was neither strictly instrumental nor exclusively operational. The book has two parts: while Part I focuses on the study of the ionosphere and how the British radio industry affected ionospheric physics, Part II focuses on the study of the Earth’s crust and how the American oil industry affected crustal seismology.Less
Have industry and commerce affected the concepts, values, and epistemic foundations of different sciences? If so, how and to what extent? This book suggests that the most significant influence of industry on science, in the two case studies treated here, had to do with the issue of realism. These two cases deal with the elucidation of the layers of the upper atmosphere and the Earth’s crust. Using wave propagation as the common thread, this book simultaneously analyses the emergence of realist attitudes towards the entities of the ionosphere and the Earth’s crust. However, what was it that led physicists and engineers to adopt realist attitudes? This book suggests that a new kind of realism—one with social and cultural origins—is the answer: a preliminary, entity realism responding to specific commercial and engineering interests; i.e. a realism that was neither strictly instrumental nor exclusively operational. The book has two parts: while Part I focuses on the study of the ionosphere and how the British radio industry affected ionospheric physics, Part II focuses on the study of the Earth’s crust and how the American oil industry affected crustal seismology.
Dale Chimenti, Stanislav Rokhlin, and Peter Nagy
- Published in print:
- 2011
- Published Online:
- November 2020
- ISBN:
- 9780195079609
- eISBN:
- 9780197560389
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195079609.003.0007
- Subject:
- Chemistry, Industrial Chemistry
Currently, the design of most composite components is based on stiffness, and therefore methods for static measurement of stiffness are in wide use. The disadvantages ...
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Currently, the design of most composite components is based on stiffness, and therefore methods for static measurement of stiffness are in wide use. The disadvantages of these methods lie in their destructive nature (the samples must be cut from parts of different orientations), in the difficulty of measuring shear properties, and in the need for extra care when measuring Young’s modulus in off-axis directions. Ultrasonic methods are more accurate and have higher spatial resolution than static measurements. As we showed in Chapter 2, by measuring ultrasonic velocities in several predefined directions, all elastic constants can be determined. The generic method described there is also destructive, however, requiring cutting numerous samples with appropriate fiber orientation. Specialized nondestructive methods for determining the elastic moduli of composite materials are more powerful and they can be applied to composite coupons before, during, and after strength or fatigue testing. It is important to have a fast and inexpensive technique to estimate input parameters for composite design. It is even more important to have a technique to evaluate composites during service to verify that the manufactured elastic stiffnesses match those assumed in the design. Several methods that utilize bulk ultrasonic waves for measurement of composite elastic constants are considered in this chapter. By bulk wave methods, we mean quasilongitudinal and quasitransverse ultrasonic wave velocity measurement methods that are applicable when the sample thickness h is larger than both the ultrasonic pulse space length τV and the wavelength λ (τ is the ultrasonic pulse length in time, and V is the wave speed). Other methods, which are applicable in the range h < τV and which account for wave interference with the boundaries of the specimen, will be considered in the following chapters. The most promising way to evaluate composite elastic properties nondestructively is to measure ultrasonic velocities in different directions in the composite material and reconstruct the elastic constants from these values using some kind of an inversion technique. One possible method has been suggested by Markham in the 1970s, who used ultrasonic waves obliquely incident from water onto a composite plate to measure ultrasonic velocities in various directions and evaluated the results to determine elastic constants.
Less
Currently, the design of most composite components is based on stiffness, and therefore methods for static measurement of stiffness are in wide use. The disadvantages of these methods lie in their destructive nature (the samples must be cut from parts of different orientations), in the difficulty of measuring shear properties, and in the need for extra care when measuring Young’s modulus in off-axis directions. Ultrasonic methods are more accurate and have higher spatial resolution than static measurements. As we showed in Chapter 2, by measuring ultrasonic velocities in several predefined directions, all elastic constants can be determined. The generic method described there is also destructive, however, requiring cutting numerous samples with appropriate fiber orientation. Specialized nondestructive methods for determining the elastic moduli of composite materials are more powerful and they can be applied to composite coupons before, during, and after strength or fatigue testing. It is important to have a fast and inexpensive technique to estimate input parameters for composite design. It is even more important to have a technique to evaluate composites during service to verify that the manufactured elastic stiffnesses match those assumed in the design. Several methods that utilize bulk ultrasonic waves for measurement of composite elastic constants are considered in this chapter. By bulk wave methods, we mean quasilongitudinal and quasitransverse ultrasonic wave velocity measurement methods that are applicable when the sample thickness h is larger than both the ultrasonic pulse space length τV and the wavelength λ (τ is the ultrasonic pulse length in time, and V is the wave speed). Other methods, which are applicable in the range h < τV and which account for wave interference with the boundaries of the specimen, will be considered in the following chapters. The most promising way to evaluate composite elastic properties nondestructively is to measure ultrasonic velocities in different directions in the composite material and reconstruct the elastic constants from these values using some kind of an inversion technique. One possible method has been suggested by Markham in the 1970s, who used ultrasonic waves obliquely incident from water onto a composite plate to measure ultrasonic velocities in various directions and evaluated the results to determine elastic constants.