Andreas Kirsch and Natalia Grinberg
- Published in print:
- 2007
- Published Online:
- September 2008
- ISBN:
- 9780199213535
- eISBN:
- 9780191707629
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213535.001.0001
- Subject:
- Mathematics, Applied Mathematics
This book is devoted to problems of shape identification in the context of (inverse) scattering problems and problems of impedance tomography. In contrast to traditional methods which are based on ...
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This book is devoted to problems of shape identification in the context of (inverse) scattering problems and problems of impedance tomography. In contrast to traditional methods which are based on iterative schemes of solving sequences of corresponding direct problems, this book presents a completely different method. The Factorization Method avoids the need to solve the (time consuming) direct problems. Furthermore, no a-priori information about the type of scatterer (penetrable or impenetrable), type of boundary condition, or number of components is needed. The Factorization Method can be considered as an example of a Sampling Method. The book aims to construct a binary criterium on the known data to decide whether or not a given point z is inside or outside the unknown domain D. By choosing a grid of sampling points z in a region known to contain D, the characteristic function of D can be computed (in the case of finite data only approximately). The book also introduces some alternative Sampling Methods.Less
This book is devoted to problems of shape identification in the context of (inverse) scattering problems and problems of impedance tomography. In contrast to traditional methods which are based on iterative schemes of solving sequences of corresponding direct problems, this book presents a completely different method. The Factorization Method avoids the need to solve the (time consuming) direct problems. Furthermore, no a-priori information about the type of scatterer (penetrable or impenetrable), type of boundary condition, or number of components is needed. The Factorization Method can be considered as an example of a Sampling Method. The book aims to construct a binary criterium on the known data to decide whether or not a given point z is inside or outside the unknown domain D. By choosing a grid of sampling points z in a region known to contain D, the characteristic function of D can be computed (in the case of finite data only approximately). The book also introduces some alternative Sampling Methods.
Peter Monk
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198508885
- eISBN:
- 9780191708633
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508885.001.0001
- Subject:
- Mathematics, Numerical Analysis
Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell’s equations is now an increasingly important tool in science and ...
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Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell’s equations is now an increasingly important tool in science and engineering. Parallel to the increasing use of numerical methods in computational electromagnetism, there has also been considerable progress in the mathematical understanding of the properties of Maxwell’s equations relevant to numerical analysis. The aim of this book is to provide an up-to-date and sound theoretical foundation for finite element methods in computational electromagnetism. The emphasis is on finite element methods for scattering problems that involve the solution of Maxwell’s equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell’s equations is the main focus of the book. The analysis involves a complete justification of the discrete de Rham diagram and discrete compactness of edge elements. The numerical methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book ends with a short introduction to inverse problems in electromagnetism.Less
Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell’s equations is now an increasingly important tool in science and engineering. Parallel to the increasing use of numerical methods in computational electromagnetism, there has also been considerable progress in the mathematical understanding of the properties of Maxwell’s equations relevant to numerical analysis. The aim of this book is to provide an up-to-date and sound theoretical foundation for finite element methods in computational electromagnetism. The emphasis is on finite element methods for scattering problems that involve the solution of Maxwell’s equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell’s equations is the main focus of the book. The analysis involves a complete justification of the discrete de Rham diagram and discrete compactness of edge elements. The numerical methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book ends with a short introduction to inverse problems in electromagnetism.
Naomi E. Chayen, John R. Helliwell, and Edward H. Snell
- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199213252
- eISBN:
- 9780191707575
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213252.003.0010
- Subject:
- Physics, Crystallography: Physics
Whilst the transition from short‐range order to long‐range order is not a sharp transition, i.e. there is a steady progression, there are metrics to judge the shorter‐range effects. These are ...
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Whilst the transition from short‐range order to long‐range order is not a sharp transition, i.e. there is a steady progression, there are metrics to judge the shorter‐range effects. These are described. Diffuse scattering occurs, from effects associated with both short‐range order and long‐range order. For convenience, and the special nature of the topic, we have kept these two aspects in this chapter. Diffuse scattering as a source of measurement error is described.Less
Whilst the transition from short‐range order to long‐range order is not a sharp transition, i.e. there is a steady progression, there are metrics to judge the shorter‐range effects. These are described. Diffuse scattering occurs, from effects associated with both short‐range order and long‐range order. For convenience, and the special nature of the topic, we have kept these two aspects in this chapter. Diffuse scattering as a source of measurement error is described.
Naomi E. Chayen, John R. Helliwell, and Edward H. Snell
- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199213252
- eISBN:
- 9780191707575
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213252.003.0018
- Subject:
- Physics, Crystallography: Physics
Crystallography is a powerful technique but also one that has limitations. There are a number of complementary techniques that significantly add to the information available crystallographically.
Crystallography is a powerful technique but also one that has limitations. There are a number of complementary techniques that significantly add to the information available crystallographically.
Malcolm Cooper, Peter Mijnarends, Nobuhiro Shiotani, Nobuhiko Sakai, and Arun Bansil
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198501688
- eISBN:
- 9780191718045
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198501688.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This book covers all aspects of the study of ground state electron density in condensed matter through Compton scattering of hard x-rays or gamma rays, i.e., photons with energies between 20 and 500 ...
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This book covers all aspects of the study of ground state electron density in condensed matter through Compton scattering of hard x-rays or gamma rays, i.e., photons with energies between 20 and 500 keV. This inelastic scattering process yields information about the momentum distribution of the electrons: it is complementary to x-ray diffraction studies of the position space electron density. After a brief historical introduction, the scattering cross-section is fully elaborated and the approximations within which the experiments can be interpreted are spelled out. All the experimental methods associated with the study of the electron’s momentum density distribution are described and the interpretative techniques are detailed, including the two methods of reconstructing the three-dimensional distribution from the measurement sets. Particular emphasis is placed on the use of synchrotron radiation as the radiation source, especially the use of circularly polarized synchrotron radiation to study the spin-dependent distribution in ferro-magnets. The book concludes with a comparison between Compton scattering methods and a number of allied techniques.Less
This book covers all aspects of the study of ground state electron density in condensed matter through Compton scattering of hard x-rays or gamma rays, i.e., photons with energies between 20 and 500 keV. This inelastic scattering process yields information about the momentum distribution of the electrons: it is complementary to x-ray diffraction studies of the position space electron density. After a brief historical introduction, the scattering cross-section is fully elaborated and the approximations within which the experiments can be interpreted are spelled out. All the experimental methods associated with the study of the electron’s momentum density distribution are described and the interpretative techniques are detailed, including the two methods of reconstructing the three-dimensional distribution from the measurement sets. Particular emphasis is placed on the use of synchrotron radiation as the radiation source, especially the use of circularly polarized synchrotron radiation to study the spin-dependent distribution in ferro-magnets. The book concludes with a comparison between Compton scattering methods and a number of allied techniques.
Roger E. Raab and Owen L. de Lange
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198567271
- eISBN:
- 9780191717970
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567271.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics
The book opens with a chapter on the classical theory of multipoles in electromagnetism, in which static and dynamic multipole expansions of various physical quantities are derived, including of the ...
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The book opens with a chapter on the classical theory of multipoles in electromagnetism, in which static and dynamic multipole expansions of various physical quantities are derived, including of the Maxwell fields D and H. Chapter 2 presents a semi-classical account of multipole theory, in which the Barron-Gray gauge is used to derive multipole polarizabilities describing the induction of molecular moments by a harmonic plane wave. Aspects of symmetry are treated in Chapter 3 — space-time behaviour of tensors and physical properties of molecules and crystals. In Chapter 4, D(E,B) and H(E,B) are obtained for linear anisotropic media, yielding expressions for the material constants which are required to satisfy origin independence, the Post constraint, and certain symmetries but fail the first two. Despite these difficulties, the standard theory is used in Chapter 5 to derive a wave propagation equation; this is applied to explain various physical effects in transmission, two of which are also described in a scattering theory. Chapter 6 deals with the reflection of electromagnetic waves from an anisotropic medium. The reflected intensities violate origin independence, showing again the unphysical nature of existing multipole theory. In Chapter 7, the fields are transformed while leaving Maxwell's equations unchanged, from which new material constants are derived in Chapter 8 that meet the three requirements in Chapter 4. Chapter 9 applies the transformed expressions to transmission and reflection phenomena, confirming the results of Chapter 5, while yielding reflected intensities that satisfy space and time invariances.Less
The book opens with a chapter on the classical theory of multipoles in electromagnetism, in which static and dynamic multipole expansions of various physical quantities are derived, including of the Maxwell fields D and H. Chapter 2 presents a semi-classical account of multipole theory, in which the Barron-Gray gauge is used to derive multipole polarizabilities describing the induction of molecular moments by a harmonic plane wave. Aspects of symmetry are treated in Chapter 3 — space-time behaviour of tensors and physical properties of molecules and crystals. In Chapter 4, D(E,B) and H(E,B) are obtained for linear anisotropic media, yielding expressions for the material constants which are required to satisfy origin independence, the Post constraint, and certain symmetries but fail the first two. Despite these difficulties, the standard theory is used in Chapter 5 to derive a wave propagation equation; this is applied to explain various physical effects in transmission, two of which are also described in a scattering theory. Chapter 6 deals with the reflection of electromagnetic waves from an anisotropic medium. The reflected intensities violate origin independence, showing again the unphysical nature of existing multipole theory. In Chapter 7, the fields are transformed while leaving Maxwell's equations unchanged, from which new material constants are derived in Chapter 8 that meet the three requirements in Chapter 4. Chapter 9 applies the transformed expressions to transmission and reflection phenomena, confirming the results of Chapter 5, while yielding reflected intensities that satisfy space and time invariances.
Reinhard B. Neder and Thomas Proffen
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199233694
- eISBN:
- 9780191715563
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233694.003.0001
- Subject:
- Physics, Crystallography: Physics
This chapter gives a brief introduction into diffuse scattering and provides a discussion of disordered materials within the scope of this book.
This chapter gives a brief introduction into diffuse scattering and provides a discussion of disordered materials within the scope of this book.
Pier A. Mello and Narendra Kumar
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198525820
- eISBN:
- 9780191712234
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525820.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
This book presents a statistical theory of complex wave scattering and quantum transport in a class of physical systems of current interest having chaotic classical dynamics (e.g., microwave cavities ...
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This book presents a statistical theory of complex wave scattering and quantum transport in a class of physical systems of current interest having chaotic classical dynamics (e.g., microwave cavities and quantum dots) or possessing quenched randomness (e.g., disordered conductors). The emphasis here is on mesoscopic fluctuations of the sample-specific transport. The universal character of the statistical behaviour of these phenomena is revealed in a natural way through a novel maximum-entropy approach (MEA). The latter leads to the most probable distribution for the set of random matrices that describe the ensemble of disordered/chaotic samples, which are macroscopically identical but differ in microscopic details. Here, the Shannon information entropy associated with these random matrices is maximized subject to the symmetries and the constraints which are physically relevant. This non-perturbative information-theoretic approach is reminiscent of, but distinct from, the standard random-matrix theory, and indeed forms the most distinctive feature of the book.Less
This book presents a statistical theory of complex wave scattering and quantum transport in a class of physical systems of current interest having chaotic classical dynamics (e.g., microwave cavities and quantum dots) or possessing quenched randomness (e.g., disordered conductors). The emphasis here is on mesoscopic fluctuations of the sample-specific transport. The universal character of the statistical behaviour of these phenomena is revealed in a natural way through a novel maximum-entropy approach (MEA). The latter leads to the most probable distribution for the set of random matrices that describe the ensemble of disordered/chaotic samples, which are macroscopically identical but differ in microscopic details. Here, the Shannon information entropy associated with these random matrices is maximized subject to the symmetries and the constraints which are physically relevant. This non-perturbative information-theoretic approach is reminiscent of, but distinct from, the standard random-matrix theory, and indeed forms the most distinctive feature of the book.
Sharan Jagpal
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780195371055
- eISBN:
- 9780199870745
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195371055.003.0014
- Subject:
- Business and Management, Marketing
This chapter begins by evaluating methods for determining how productive the firm's aggregate advertising spending is in both the short and long runs. Following this, it analyzes methods for ...
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This chapter begins by evaluating methods for determining how productive the firm's aggregate advertising spending is in both the short and long runs. Following this, it analyzes methods for determining the productivities of different media when the firm uses multiple media (including digital advertising); in particular, it focuses on the effects of measurement error. It shows how marketing-finance fusion allows privately and publicly held firms to allocate their advertising budgets between upfront and scatter advertising, based on their respective risk attitudes. Finally, it analyzes how recent changes in Internet marketing (e.g., the growth of electronic exchanges and the emergence of conquest advertising) are likely to affect the structure of the advertising industry.Less
This chapter begins by evaluating methods for determining how productive the firm's aggregate advertising spending is in both the short and long runs. Following this, it analyzes methods for determining the productivities of different media when the firm uses multiple media (including digital advertising); in particular, it focuses on the effects of measurement error. It shows how marketing-finance fusion allows privately and publicly held firms to allocate their advertising budgets between upfront and scatter advertising, based on their respective risk attitudes. Finally, it analyzes how recent changes in Internet marketing (e.g., the growth of electronic exchanges and the emergence of conquest advertising) are likely to affect the structure of the advertising industry.
Shane Cloude
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199569731
- eISBN:
- 9780191721908
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199569731.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Geophysics, Atmospheric and Environmental Physics
This book is concerned with the exploitation of polarisation effects in electromagnetic wave scattering for applications in remote sensing. It combines, for the first time, the topics of scattering ...
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This book is concerned with the exploitation of polarisation effects in electromagnetic wave scattering for applications in remote sensing. It combines, for the first time, the topics of scattering polarimetry and interferometry, and is written in three main sections. In the first four chapters it provides detailed coverage of all major topics of polarimetry, including its basis in electromagnetic scattering theory, the topic of decomposition theorems, and a detailed analysis of the entropy/alpha approach to characterising polarisation effects. In the next chapter it provides a brief introduction to radar interferometry, before developing in three chapters the important new topic of polarimetric interferometry. In this way it provides a complete treatment of the subject, suitable for those working in interferometry who wish to know about polarimetry, or vice versa, as well as those new to the topic who are seeking a one-stop comprehensive treatment of the subject. The emphasis throughout is on the application of these techniques to remote sensing and the book concludes with a set of practical examples to illustrate the theoretical ideas. Useful appendices on matrix algebra, unitary groups and stochastic signal analysis are provided.Less
This book is concerned with the exploitation of polarisation effects in electromagnetic wave scattering for applications in remote sensing. It combines, for the first time, the topics of scattering polarimetry and interferometry, and is written in three main sections. In the first four chapters it provides detailed coverage of all major topics of polarimetry, including its basis in electromagnetic scattering theory, the topic of decomposition theorems, and a detailed analysis of the entropy/alpha approach to characterising polarisation effects. In the next chapter it provides a brief introduction to radar interferometry, before developing in three chapters the important new topic of polarimetric interferometry. In this way it provides a complete treatment of the subject, suitable for those working in interferometry who wish to know about polarimetry, or vice versa, as well as those new to the topic who are seeking a one-stop comprehensive treatment of the subject. The emphasis throughout is on the application of these techniques to remote sensing and the book concludes with a set of practical examples to illustrate the theoretical ideas. Useful appendices on matrix algebra, unitary groups and stochastic signal analysis are provided.
Andreas Kirsch and Natalia Grinberg
- Published in print:
- 2007
- Published Online:
- September 2008
- ISBN:
- 9780199213535
- eISBN:
- 9780191707629
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213535.003.0004
- Subject:
- Mathematics, Applied Mathematics
This chapter examines the case of a penetrable scatterer with an index of refraction that can be space-dependent and is assumed to be different from the constant background index. The inverse ...
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This chapter examines the case of a penetrable scatterer with an index of refraction that can be space-dependent and is assumed to be different from the constant background index. The inverse scattering problem is to determine the support D of the contrast from far field measurements. The chapter begins with a simple scattering model where the scatterers consists of a finite number of point scatterers. The inverse problem is to determine the locations of these point scatterers from the multistatic response matrix F, which is the discrete analog of the far field operator. In this situation, the Factorization Method is nothing else but the MUSIC-algorithm which is well known in signal processing. The chapter then formulates direct and inverse scattering problem for the scattering by an inhomogeneous medium, reformulates the direct problem as the Lippmann-Schwinger integral equation, and justifies the popular Born approximation. The chapter formulizes the far field operator and proves a characterization of D by the convergence of a Picard series which involves only known data derived from the far field operator. This characterization holds only if the frequency is not an eigenvalue of an unconventional eigenvalue problem of transmission type. The last section shows that there exist at most a quantifiable number of these values.Less
This chapter examines the case of a penetrable scatterer with an index of refraction that can be space-dependent and is assumed to be different from the constant background index. The inverse scattering problem is to determine the support D of the contrast from far field measurements. The chapter begins with a simple scattering model where the scatterers consists of a finite number of point scatterers. The inverse problem is to determine the locations of these point scatterers from the multistatic response matrix F, which is the discrete analog of the far field operator. In this situation, the Factorization Method is nothing else but the MUSIC-algorithm which is well known in signal processing. The chapter then formulates direct and inverse scattering problem for the scattering by an inhomogeneous medium, reformulates the direct problem as the Lippmann-Schwinger integral equation, and justifies the popular Born approximation. The chapter formulizes the far field operator and proves a characterization of D by the convergence of a Picard series which involves only known data derived from the far field operator. This characterization holds only if the frequency is not an eigenvalue of an unconventional eigenvalue problem of transmission type. The last section shows that there exist at most a quantifiable number of these values.
I. M. Vardavas and F. W. Taylor
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199227471
- eISBN:
- 9780191711138
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227471.003.0006
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics
This chapter examines the transfer of solar radiation within the Earth's atmosphere and at the surface. The main processes discussed are molecular absorption in the ultraviolet-visible and ...
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This chapter examines the transfer of solar radiation within the Earth's atmosphere and at the surface. The main processes discussed are molecular absorption in the ultraviolet-visible and near-infrared parts of the spectrum, and how these differ through the atmosphere, especially under cloudy skies. Cloud and aerosol absorption and scattering are developed in terms of the mathematical formulation of Mie theory. Standard radiation transfer techniques, such as the k-distribution and the delta-Eddington methods are presented, including a new technique for the rapid numerical solution for multiple scattering in highly inhomogeneous atmospheric layers.Less
This chapter examines the transfer of solar radiation within the Earth's atmosphere and at the surface. The main processes discussed are molecular absorption in the ultraviolet-visible and near-infrared parts of the spectrum, and how these differ through the atmosphere, especially under cloudy skies. Cloud and aerosol absorption and scattering are developed in terms of the mathematical formulation of Mie theory. Standard radiation transfer techniques, such as the k-distribution and the delta-Eddington methods are presented, including a new technique for the rapid numerical solution for multiple scattering in highly inhomogeneous atmospheric layers.
Sönke Johnsen
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691139906
- eISBN:
- 9781400840663
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691139906.001.0001
- Subject:
- Biology, Evolutionary Biology / Genetics
Optics—a field of physics focusing on the study of light—is also central to many areas of biology, including vision, ecology, botany, animal behavior, neurobiology, and molecular biology. This book ...
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Optics—a field of physics focusing on the study of light—is also central to many areas of biology, including vision, ecology, botany, animal behavior, neurobiology, and molecular biology. This book introduces the fundamentals of optics to biologists and nonphysicists, giving them the tools they need to successfully incorporate optical measurements and principles into their research. The book starts with the basics, describing the properties of light and the units and geometry of measurement. It then explores how light is created and propagates and how it interacts with matter, covering topics such as absorption, scattering, fluorescence, and polarization. The book also provides a tutorial on how to measure light as well as an informative discussion of quantum mechanics. The book features a host of examples drawn from nature and everyday life, and several appendixes that offer further practical guidance for researchers. This concise book uses a minimum of equations and jargon, explaining the basic physics of light in a succinct and lively manner. It is the essential primer for working biologists and for anyone seeking an accessible introduction to optics.Less
Optics—a field of physics focusing on the study of light—is also central to many areas of biology, including vision, ecology, botany, animal behavior, neurobiology, and molecular biology. This book introduces the fundamentals of optics to biologists and nonphysicists, giving them the tools they need to successfully incorporate optical measurements and principles into their research. The book starts with the basics, describing the properties of light and the units and geometry of measurement. It then explores how light is created and propagates and how it interacts with matter, covering topics such as absorption, scattering, fluorescence, and polarization. The book also provides a tutorial on how to measure light as well as an informative discussion of quantum mechanics. The book features a host of examples drawn from nature and everyday life, and several appendixes that offer further practical guidance for researchers. This concise book uses a minimum of equations and jargon, explaining the basic physics of light in a succinct and lively manner. It is the essential primer for working biologists and for anyone seeking an accessible introduction to optics.
Peter Main
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199219469
- eISBN:
- 9780191722516
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199219469.003.0001
- Subject:
- Physics, Crystallography: Physics
This introductory chapter provides information on some fundamental aspects of crystal structures and their diffraction of X-rays as a basis for the rest of the book. It describes electrons, atoms, ...
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This introductory chapter provides information on some fundamental aspects of crystal structures and their diffraction of X-rays as a basis for the rest of the book. It describes electrons, atoms, molecules, and crystals scatter X-rays, leading to the observed diffraction pattern, and introduces concepts such as the reciprocal lattice, structure factors, Fourier transforms, Bragg's law for the geometry of diffraction, the phase problem encountered in crystallography, and the meaning of resolution and how it is related to the extent of the measured diffraction pattern.Less
This introductory chapter provides information on some fundamental aspects of crystal structures and their diffraction of X-rays as a basis for the rest of the book. It describes electrons, atoms, molecules, and crystals scatter X-rays, leading to the observed diffraction pattern, and introduces concepts such as the reciprocal lattice, structure factors, Fourier transforms, Bragg's law for the geometry of diffraction, the phase problem encountered in crystallography, and the meaning of resolution and how it is related to the extent of the measured diffraction pattern.
Robin Devenish and Amanda Cooper-Sarkar
- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198506713
- eISBN:
- 9780191709562
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506713.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
The book provides a self-contained account of deep inelastic scattering (DIS) in high energy physics. It covers the classic results that lead to the quark-parton model of hadrons and the ...
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The book provides a self-contained account of deep inelastic scattering (DIS) in high energy physics. It covers the classic results that lead to the quark-parton model of hadrons and the establishment of quantum chromodynamics (QCD), through to the new vistas in the subject opened up by the electron-proton collider HERA. The extraction of parton momentum distribution functions, a key input for physics at hadron colliders such as the Tevatron and Large Hadron Collider (LHC), is described in detail. The challenges of the HERA data at low-x are described, and possible explanations in terms of gluon dynamics outlined. Other chapters cover: jet production at large momentum transfer and the determination of the strong coupling constant; electroweak probes at very high momentum transfers; the extension of deep inelastic techniques to include hadronic probes; a summary of fully polarised inelastic scattering and the spin structure of the nucleon; and a brief account of methods for searching for signals ‘beyond the standard model’.Less
The book provides a self-contained account of deep inelastic scattering (DIS) in high energy physics. It covers the classic results that lead to the quark-parton model of hadrons and the establishment of quantum chromodynamics (QCD), through to the new vistas in the subject opened up by the electron-proton collider HERA. The extraction of parton momentum distribution functions, a key input for physics at hadron colliders such as the Tevatron and Large Hadron Collider (LHC), is described in detail. The challenges of the HERA data at low-x are described, and possible explanations in terms of gluon dynamics outlined. Other chapters cover: jet production at large momentum transfer and the determination of the strong coupling constant; electroweak probes at very high momentum transfers; the extension of deep inelastic techniques to include hadronic probes; a summary of fully polarised inelastic scattering and the spin structure of the nucleon; and a brief account of methods for searching for signals ‘beyond the standard model’.
Rein Taagepera
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199534661
- eISBN:
- 9780191715921
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534661.003.0012
- Subject:
- Political Science, Comparative Politics, Political Economy
When data are scattered, Ordinary Least-Squares (OLS) regression produces two quite distinct regression lines – one for y versus x and another for x versus y – and both may differ appreciably from ...
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When data are scattered, Ordinary Least-Squares (OLS) regression produces two quite distinct regression lines – one for y versus x and another for x versus y – and both may differ appreciably from what your eyes tell you. If data are scattered, OLS regression of y against x will disconfirm a model that actually fits; thus good statistics can be death of good science. Standard OLS equations cannot form a system of interlocking models, because they are unidirectional and nontransitive. Scale-independent symmetric regression avoids these problems of OLS, offering a single reversible and transitive equation.Less
When data are scattered, Ordinary Least-Squares (OLS) regression produces two quite distinct regression lines – one for y versus x and another for x versus y – and both may differ appreciably from what your eyes tell you. If data are scattered, OLS regression of y against x will disconfirm a model that actually fits; thus good statistics can be death of good science. Standard OLS equations cannot form a system of interlocking models, because they are unidirectional and nontransitive. Scale-independent symmetric regression avoids these problems of OLS, offering a single reversible and transitive equation.
Jean Zinn-Justin
- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics
Path integrals are mathematical objects that can be considered as generalizations to an infinite number of variables, represented by paths, of usual integrals. They share the algebraic properties of ...
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Path integrals are mathematical objects that can be considered as generalizations to an infinite number of variables, represented by paths, of usual integrals. They share the algebraic properties of usual integrals, but have new properties from the viewpoint of analysis. They are powerful tools for the study of quantum mechanics, since they emphasize very explicitly the correspondence between classical and quantum mechanics. Physical quantities are expressed as averages over all possible paths but, in the semi-classical limit, the leading contributions come from paths close to classical paths. Thus, path integrals lead to an intuitive understanding of physical quantities in the semi-classical limit, as well as simple calculations of such quantities. This observation can be illustrated with scattering processes, spectral properties, or barrier penetration effects. Even though the formulation of quantum mechanics based on path integrals seems mathematically more complicated than the usual formulation based on partial differential equations, the path integral formulation is well adapted to systems with many degrees of freedom, where a formalism of Schrödinger type is much less useful. It allows simple construction of a many-body theory both for bosons and fermions.Less
Path integrals are mathematical objects that can be considered as generalizations to an infinite number of variables, represented by paths, of usual integrals. They share the algebraic properties of usual integrals, but have new properties from the viewpoint of analysis. They are powerful tools for the study of quantum mechanics, since they emphasize very explicitly the correspondence between classical and quantum mechanics. Physical quantities are expressed as averages over all possible paths but, in the semi-classical limit, the leading contributions come from paths close to classical paths. Thus, path integrals lead to an intuitive understanding of physical quantities in the semi-classical limit, as well as simple calculations of such quantities. This observation can be illustrated with scattering processes, spectral properties, or barrier penetration effects. Even though the formulation of quantum mechanics based on path integrals seems mathematically more complicated than the usual formulation based on partial differential equations, the path integral formulation is well adapted to systems with many degrees of freedom, where a formalism of Schrödinger type is much less useful. It allows simple construction of a many-body theory both for bosons and fermions.
A.F. Borghesani
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199213603
- eISBN:
- 9780191707421
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213603.003.0005
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter describes the main experimental techniques used to measure the drift velocity in superfluid 4He at low temperature. The experimental results are then presented by showing the ...
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This chapter describes the main experimental techniques used to measure the drift velocity in superfluid 4He at low temperature. The experimental results are then presented by showing the contributions to the ion drag due to the different elementary excitations of the superfluid. The theoretical description of the processes of ion scattering off phonons, rotons, and 3He atomic impurities is also presented, and the theoretical predictions are compared with experimental results. The use of the formalism of the Boltzmann transport equation to predict how the drag force on an ion in the superfluid is determined by the different scattering mechanisms is discussed.Less
This chapter describes the main experimental techniques used to measure the drift velocity in superfluid 4He at low temperature. The experimental results are then presented by showing the contributions to the ion drag due to the different elementary excitations of the superfluid. The theoretical description of the processes of ion scattering off phonons, rotons, and 3He atomic impurities is also presented, and the theoretical predictions are compared with experimental results. The use of the formalism of the Boltzmann transport equation to predict how the drag force on an ion in the superfluid is determined by the different scattering mechanisms is discussed.
Rolf Hempelmann
- Published in print:
- 2000
- Published Online:
- January 2010
- ISBN:
- 9780198517436
- eISBN:
- 9780191706974
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198517436.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
The book provides an account of quasielastic neutron scattering (QENS) which has made many important contributions to the atomistic elucidation of diffusion processes in solids. The unique feature of ...
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The book provides an account of quasielastic neutron scattering (QENS) which has made many important contributions to the atomistic elucidation of diffusion processes in solids. The unique feature of QENS is that it probes the diffusion process on atomistic scales of space and time simultaneously. The aim of this book is to inform of the potential of QENS. Chapters 3-6 present the derivation of all equations in great details. Chapter 2 deals with neutron sources, and Chapter 7 with some experimental details of QENS. The second part addresses the expert and summarizes the scientific applications of quasielastic neutron scattering to special solid state material systems, as for example to diffusion in metals or to diffusion in solid state ionic conductors. By far the most favourable element for QENS is hydrogen: hydrogen is very mobile in metals and ceramics, so the restricted energy/time resolution of QENS is no limitation; hydrogen has a huge scattering cross section, so the limited intensity of existing neutron sources is no limitation; hydrogen leads to almost purely incoherent scattering which facilitates the theoretical treatment and interpretation of neutron scattering events appreciably.Less
The book provides an account of quasielastic neutron scattering (QENS) which has made many important contributions to the atomistic elucidation of diffusion processes in solids. The unique feature of QENS is that it probes the diffusion process on atomistic scales of space and time simultaneously. The aim of this book is to inform of the potential of QENS. Chapters 3-6 present the derivation of all equations in great details. Chapter 2 deals with neutron sources, and Chapter 7 with some experimental details of QENS. The second part addresses the expert and summarizes the scientific applications of quasielastic neutron scattering to special solid state material systems, as for example to diffusion in metals or to diffusion in solid state ionic conductors. By far the most favourable element for QENS is hydrogen: hydrogen is very mobile in metals and ceramics, so the restricted energy/time resolution of QENS is no limitation; hydrogen has a huge scattering cross section, so the limited intensity of existing neutron sources is no limitation; hydrogen leads to almost purely incoherent scattering which facilitates the theoretical treatment and interpretation of neutron scattering events appreciably.
Erich H. Kisi and Christopher J. Howard
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780198515944
- eISBN:
- 9780191705663
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198515944.003.0002
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter presents the properties of thermal neutrons. Their wavelength (from the de Broglie equation) is well suited to the investigation of condensed matter, i.e., to the study of liquids, ...
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This chapter presents the properties of thermal neutrons. Their wavelength (from the de Broglie equation) is well suited to the investigation of condensed matter, i.e., to the study of liquids, glasses (amorphous materials), and crystalline materials with varying degrees of order. That the neutrons carry magnetic moment also makes them well suited to the study of magnetic ordering. The theory of nuclear and magnetic scattering from individual atoms and from assemblies of atoms is presented, this leading to the definition of neutron scattering length and to the concepts of coherent and incoherent scattering. The focus then shifts to the direction and intensity of diffraction from crystalline materials (Bragg's law, structure factors), and to the description of this scattering when samples are presented in polycrystalline or powder form (Debye-Scherrer cones).Less
This chapter presents the properties of thermal neutrons. Their wavelength (from the de Broglie equation) is well suited to the investigation of condensed matter, i.e., to the study of liquids, glasses (amorphous materials), and crystalline materials with varying degrees of order. That the neutrons carry magnetic moment also makes them well suited to the study of magnetic ordering. The theory of nuclear and magnetic scattering from individual atoms and from assemblies of atoms is presented, this leading to the definition of neutron scattering length and to the concepts of coherent and incoherent scattering. The focus then shifts to the direction and intensity of diffraction from crystalline materials (Bragg's law, structure factors), and to the description of this scattering when samples are presented in polycrystalline or powder form (Debye-Scherrer cones).
