Sander van Smaalen
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198570820
- eISBN:
- 9780191718762
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570820.001.0001
- Subject:
- Physics, Crystallography: Physics
Aperiodic crystals are crystalline materials with atomic structures that lack translational symmetry. This book gives a comprehensive account of the superspace theory for the description of the ...
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Aperiodic crystals are crystalline materials with atomic structures that lack translational symmetry. This book gives a comprehensive account of the superspace theory for the description of the crystal structures, and symmetries of incommensurately modulated crystals and composite crystals. It also gives a brief introduction to quasicrystals, thus providing the necessary background for understanding the distinctive features of aperiodic crystals, and it provides the tools for the application of quantitative methods from the realms of crystallography, solid state chemistry, and solid state physics to aperiodic crystal structures. The second half of the book is devoted to crystallographic methods of structural analysis of incommensurate crystals. Thorough accounts are given of the diffraction by incommensurate crystals, the choice of parameters in structure refinements, and the use of superspace in analysing crystal structures. The presentation of methods of structure determination includes direct methods, Fourier methods, Patterson function methods, the maximum entropy method (MEM), and charge flipping. So-called t-plots are introduced as a versatile method for the crystal chemical analysis of incommensurately modulated structures and composite crystals.Less
Aperiodic crystals are crystalline materials with atomic structures that lack translational symmetry. This book gives a comprehensive account of the superspace theory for the description of the crystal structures, and symmetries of incommensurately modulated crystals and composite crystals. It also gives a brief introduction to quasicrystals, thus providing the necessary background for understanding the distinctive features of aperiodic crystals, and it provides the tools for the application of quantitative methods from the realms of crystallography, solid state chemistry, and solid state physics to aperiodic crystal structures. The second half of the book is devoted to crystallographic methods of structural analysis of incommensurate crystals. Thorough accounts are given of the diffraction by incommensurate crystals, the choice of parameters in structure refinements, and the use of superspace in analysing crystal structures. The presentation of methods of structure determination includes direct methods, Fourier methods, Patterson function methods, the maximum entropy method (MEM), and charge flipping. So-called t-plots are introduced as a versatile method for the crystal chemical analysis of incommensurately modulated structures and composite crystals.
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.
Sander Van Smaalen
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198570820
- eISBN:
- 9780191718762
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570820.003.0008
- Subject:
- Physics, Crystallography: Physics
This chapter considers the properties of the generalized electron density as it can be displayed in superspace. Fourier maps and difference Fourier maps allow the visual inspection of various ...
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This chapter considers the properties of the generalized electron density as it can be displayed in superspace. Fourier maps and difference Fourier maps allow the visual inspection of various structural features, including the positions of the atoms, the shapes and amplitudes of modulation functions, and possible advanced properties of the modulations, like modulation of the anisotropic displacement parameters (ADPs) and the presence anharmonic displacements. The maximum entropy method (MEM) is introduced as a model-independent method that provides a more accurate picture of the electron density than is provided by Fourier maps. The MEM can be used to determine the precise shapes of modulation functions and to study the electron density in the chemical bond.Less
This chapter considers the properties of the generalized electron density as it can be displayed in superspace. Fourier maps and difference Fourier maps allow the visual inspection of various structural features, including the positions of the atoms, the shapes and amplitudes of modulation functions, and possible advanced properties of the modulations, like modulation of the anisotropic displacement parameters (ADPs) and the presence anharmonic displacements. The maximum entropy method (MEM) is introduced as a model-independent method that provides a more accurate picture of the electron density than is provided by Fourier maps. The MEM can be used to determine the precise shapes of modulation functions and to study the electron density in the chemical bond.
G. A. D. Briggs and O. V. Kolosov
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199232734
- eISBN:
- 9780191716355
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199232734.003.0008
- Subject:
- Physics, Condensed Matter Physics / Materials
In principle it is possible to reconstruct the reflectance function of a surface from V(z) data. This requires either that V(z) should be measured as a complex‐valued function, or that phase ...
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In principle it is possible to reconstruct the reflectance function of a surface from V(z) data. This requires either that V(z) should be measured as a complex‐valued function, or that phase reconstruction techniques should be used. In practice the highest accuracy is obtained by measuring the period of oscillations in V(z), and using ray analysis. The highest accuracy is obtained from a cylindrical line‐focus‐beam lens, which also gives directionality in anisotropic surfaces. Accuracy better than one part in 104 can be obtained. Stress fields can be imaged and measured. Time‐resolved techniques, enhanced if necessary by a maximum entropy method, give quantitative measurements by separating the echoes from the top and bottom of thin layers.Less
In principle it is possible to reconstruct the reflectance function of a surface from V(z) data. This requires either that V(z) should be measured as a complex‐valued function, or that phase reconstruction techniques should be used. In practice the highest accuracy is obtained by measuring the period of oscillations in V(z), and using ray analysis. The highest accuracy is obtained from a cylindrical line‐focus‐beam lens, which also gives directionality in anisotropic surfaces. Accuracy better than one part in 104 can be obtained. Stress fields can be imaged and measured. Time‐resolved techniques, enhanced if necessary by a maximum entropy method, give quantitative measurements by separating the echoes from the top and bottom of thin layers.
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/9780198515944.003.0012
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter highlights some recent and forthcoming developments that impact on the practice of neutron powder diffraction. New and more powerful neutron sources are now in service or under ...
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This chapter highlights some recent and forthcoming developments that impact on the practice of neutron powder diffraction. New and more powerful neutron sources are now in service or under construction. At the same time, there has been continuing development of critical components, such as neutron guides (supermirrors), compact collimators, focussing monochromators, and fast detection systems. These developments have been incorporated into new neutron powder diffractometers, for high resolution, high intensity, and residual stress applications. Advances in data analysis discussed include an increased focus on the use of group theory, the analysis of the total scattering, e.g., via pair distribution functions, mapping by the maximum entropy method, and rapid handling of extensive data sets. Frontier applications range from fast reaction kinetics (combustion synthesis) to the structure refinement of biological molecules. It is suggested that application of neutron powder diffraction for simultaneous investigation of structure and microstructure will assume increasing importance.Less
This chapter highlights some recent and forthcoming developments that impact on the practice of neutron powder diffraction. New and more powerful neutron sources are now in service or under construction. At the same time, there has been continuing development of critical components, such as neutron guides (supermirrors), compact collimators, focussing monochromators, and fast detection systems. These developments have been incorporated into new neutron powder diffractometers, for high resolution, high intensity, and residual stress applications. Advances in data analysis discussed include an increased focus on the use of group theory, the analysis of the total scattering, e.g., via pair distribution functions, mapping by the maximum entropy method, and rapid handling of extensive data sets. Frontier applications range from fast reaction kinetics (combustion synthesis) to the structure refinement of biological molecules. It is suggested that application of neutron powder diffraction for simultaneous investigation of structure and microstructure will assume increasing importance.
Prasanna Gai
- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199544493
- eISBN:
- 9780191747175
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199544493.003.0007
- Subject:
- Economics and Finance, Financial Economics
This chapter develops a statistical model for assessing financial system resilience that includes fire sale effects, network effects, and the feedback effects to/from the macroeconomy. An important ...
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This chapter develops a statistical model for assessing financial system resilience that includes fire sale effects, network effects, and the feedback effects to/from the macroeconomy. An important innovation is that the model can be calibrated with partially available public data on banking sector exposures. The model presents stylized results largely based on data from the Bank for International Settlements in a set-up that is genuinely international—the financial network comprises domestic banks, foreign banks, and domestic firms. The aggregate system loss distributions that emerge are sensible, despite the crude calibration of the feedback effects from curtailed lending in the macroeconomy. The mode, thus, represents a first step in showing how an integrated model of systemic risk that takes complexity and realistic behavioural responses seriously can begin to be developed.Less
This chapter develops a statistical model for assessing financial system resilience that includes fire sale effects, network effects, and the feedback effects to/from the macroeconomy. An important innovation is that the model can be calibrated with partially available public data on banking sector exposures. The model presents stylized results largely based on data from the Bank for International Settlements in a set-up that is genuinely international—the financial network comprises domestic banks, foreign banks, and domestic firms. The aggregate system loss distributions that emerge are sensible, despite the crude calibration of the feedback effects from curtailed lending in the macroeconomy. The mode, thus, represents a first step in showing how an integrated model of systemic risk that takes complexity and realistic behavioural responses seriously can begin to be developed.