Andrea Braides
- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198507840
- eISBN:
- 9780191709890
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507840.003.0010
- Subject:
- Mathematics, Applied Mathematics
This chapter describes the interaction between homogenization and surface terms using three examples. It shows that in some regimes, there is a separation of scales, while in other regimes the two ...
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This chapter describes the interaction between homogenization and surface terms using three examples. It shows that in some regimes, there is a separation of scales, while in other regimes the two phenomena must be considered together. The first example deals with the interaction between oscillations and phase transitions in producing surface terms. The second exhibits a different scaling of the same problem giving a limit energy finite on piecewise-Sobolev functions through phase accumulation. The third example deals with the homogenization of free-discontinuity problems.Less
This chapter describes the interaction between homogenization and surface terms using three examples. It shows that in some regimes, there is a separation of scales, while in other regimes the two phenomena must be considered together. The first example deals with the interaction between oscillations and phase transitions in producing surface terms. The second exhibits a different scaling of the same problem giving a limit energy finite on piecewise-Sobolev functions through phase accumulation. The third example deals with the homogenization of free-discontinuity problems.
Andrea Braides
- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198507840
- eISBN:
- 9780191709890
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507840.003.0016
- Subject:
- Mathematics, Applied Mathematics
This chapter presents a self-contained account of the slicing method that allows the exhibition of a lower bound for high-dimensional problems through their one-dimensional sections. After computing ...
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This chapter presents a self-contained account of the slicing method that allows the exhibition of a lower bound for high-dimensional problems through their one-dimensional sections. After computing a family of one-dimensional limit problems, an optimization is performed through an argument characterizing the supremum of a family of measures. The upper inequality is obtained by a density argument whenever recovery sequences have a one-dimensional form. This method can be applied to the high-dimensional gradient theory of phase transitions.Less
This chapter presents a self-contained account of the slicing method that allows the exhibition of a lower bound for high-dimensional problems through their one-dimensional sections. After computing a family of one-dimensional limit problems, an optimization is performed through an argument characterizing the supremum of a family of measures. The upper inequality is obtained by a density argument whenever recovery sequences have a one-dimensional form. This method can be applied to the high-dimensional gradient theory of phase transitions.
E. Phoevos Panagiotidis (ed.)
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199584352
- eISBN:
- 9780191594526
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199584352.001.0001
- Subject:
- Linguistics, Semantics and Pragmatics, Syntax and Morphology
This book draws together nine original investigations by leading linguists and promising young scholars on the syntax of complementisers (eg that in She said that she would) and their phrases. The ...
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This book draws together nine original investigations by leading linguists and promising young scholars on the syntax of complementisers (eg that in She said that she would) and their phrases. The chapters are divided into two parts, each of which highlights aspects of the behaviour and function of complementisers. The first part looks at how and when subjects, or parts of subjects, can and cannot move outside their canonical position in a sentence. Each chapter examines and compares the relevance of a number of syntactic factors in languages such as English, Italian, Spanish, Greek, Brazilian Portuguese, and Bavarian. In the second part, the focus turns to the nature and function of complementisers themselves, with discussions drawing on evidence from Italian, Italian dialects, Hebrew, and Dutch.Less
This book draws together nine original investigations by leading linguists and promising young scholars on the syntax of complementisers (eg that in She said that she would) and their phrases. The chapters are divided into two parts, each of which highlights aspects of the behaviour and function of complementisers. The first part looks at how and when subjects, or parts of subjects, can and cannot move outside their canonical position in a sentence. Each chapter examines and compares the relevance of a number of syntactic factors in languages such as English, Italian, Spanish, Greek, Brazilian Portuguese, and Bavarian. In the second part, the focus turns to the nature and function of complementisers themselves, with discussions drawing on evidence from Italian, Italian dialects, Hebrew, and Dutch.
David Paganin
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198567288
- eISBN:
- 9780191717963
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567288.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This book offers a grounding in the field of coherent X-ray optics, which in the closing years of the 20th century experienced something of a renaissance with the availability of third-generation ...
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This book offers a grounding in the field of coherent X-ray optics, which in the closing years of the 20th century experienced something of a renaissance with the availability of third-generation synchrotron sources. It begins with a treatment of the fundamentals of X-ray diffraction for both coherent and partially coherent radiation, together with the interactions of X-rays with matter. X-ray sources, optical elements, and detectors are then discussed, with an emphasis on their role in coherent X-ray optics. Various aspects of coherent X-ray imaging are then considered, including holography, interferometry, self imaging, phase contrast, and phase retrieval. The foundations of the new field of singular X-ray optics are examined, focusing on the topic of X-ray phase vortices. Most topics in the book are developed from first principles using a chain of logic which ultimately derives from the Maxwell equations, with numerous references to the contemporary and historical research literature.Less
This book offers a grounding in the field of coherent X-ray optics, which in the closing years of the 20th century experienced something of a renaissance with the availability of third-generation synchrotron sources. It begins with a treatment of the fundamentals of X-ray diffraction for both coherent and partially coherent radiation, together with the interactions of X-rays with matter. X-ray sources, optical elements, and detectors are then discussed, with an emphasis on their role in coherent X-ray optics. Various aspects of coherent X-ray imaging are then considered, including holography, interferometry, self imaging, phase contrast, and phase retrieval. The foundations of the new field of singular X-ray optics are examined, focusing on the topic of X-ray phase vortices. Most topics in the book are developed from first principles using a chain of logic which ultimately derives from the Maxwell equations, with numerous references to the contemporary and historical research literature.
Douglas L. Dorset
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198529088
- eISBN:
- 9780191712838
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198529088.001.0001
- Subject:
- Physics, Crystallography
This book describes the solid state behaviour of organic materials based the polymethylene chain, i.e., the functional molecular component of polyethylenes, soaps, detergents, edible fats, lipids, ...
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This book describes the solid state behaviour of organic materials based the polymethylene chain, i.e., the functional molecular component of polyethylenes, soaps, detergents, edible fats, lipids, oils, greases, and waxes. Along with chain unsaturation and branching, polydispersity, i.e., the aggregation of several polymethylene chain lengths, is shown to control various physical properties, including the preservation of metastable phases (polymorphic as well as ‘rotator’ forms). Using linear chain waxes as model materials, this book explores how solid solutions are stabilized and what structures are possible. Strictly linear molecules are compared to those functionalized with ‘head-groups’. The onset of fractionation, followed by formation of eutectic phases, is discussed, again describing the structures of favoured molecular assemblies. The rationale for polydisperse aggregation derives from the early work of A. I. Kitaigorodskii, demonstrating how certain homeomorphic parameters such as relative molecular shape and volume, as well as favoured crystalline polymorphs, lead to stable solid solutions. Relevant to high-molecular weight polymers, the influence of chain-folding is also discussed. A comprehensive review of known linear chain single crystal structures, including the alkanes, cycloalkanes, perfluoroalkanes, fatty alcohols, fatty acids, fatty acid esters, and cholesteryl esters, is presented to show how molecular shape, including chain branching, influences layer packing and co-solubility. Finally, a critique of previously suggested models for petroleum and natural wax assemblies is given, based on current crystallographic and spectroscopic information. This includes single crystal structures based on electron diffraction data. Although constrained to single chain molecules in the examples discussed, cited behaviour can be generalized to multiple chain-containing fats and lipids.Less
This book describes the solid state behaviour of organic materials based the polymethylene chain, i.e., the functional molecular component of polyethylenes, soaps, detergents, edible fats, lipids, oils, greases, and waxes. Along with chain unsaturation and branching, polydispersity, i.e., the aggregation of several polymethylene chain lengths, is shown to control various physical properties, including the preservation of metastable phases (polymorphic as well as ‘rotator’ forms). Using linear chain waxes as model materials, this book explores how solid solutions are stabilized and what structures are possible. Strictly linear molecules are compared to those functionalized with ‘head-groups’. The onset of fractionation, followed by formation of eutectic phases, is discussed, again describing the structures of favoured molecular assemblies. The rationale for polydisperse aggregation derives from the early work of A. I. Kitaigorodskii, demonstrating how certain homeomorphic parameters such as relative molecular shape and volume, as well as favoured crystalline polymorphs, lead to stable solid solutions. Relevant to high-molecular weight polymers, the influence of chain-folding is also discussed. A comprehensive review of known linear chain single crystal structures, including the alkanes, cycloalkanes, perfluoroalkanes, fatty alcohols, fatty acids, fatty acid esters, and cholesteryl esters, is presented to show how molecular shape, including chain branching, influences layer packing and co-solubility. Finally, a critique of previously suggested models for petroleum and natural wax assemblies is given, based on current crystallographic and spectroscopic information. This includes single crystal structures based on electron diffraction data. Although constrained to single chain molecules in the examples discussed, cited behaviour can be generalized to multiple chain-containing fats and lipids.
Erich H. Kisi and Christopher J. Howard
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780198515944
- eISBN:
- 9780191705663
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198515944.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
This book covers the theory, practicalities, and the extensive applications of neutron powder diffraction in materials science, physics, chemistry, mineralogy, and engineering. Various highlight ...
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This book covers the theory, practicalities, and the extensive applications of neutron powder diffraction in materials science, physics, chemistry, mineralogy, and engineering. Various highlight applications of neutron powder diffraction are outlined in the introduction, then the theory is developed and instrumentation described sufficient for a return to the applications. The book covers the use of neutron powder diffraction in the solution (hard) and refinement (more straightforward) of crystal and magnetic structures, applications of powder diffraction in quantitative phase analysis, extraction of microstructural information from powder diffraction patterns, and the applications of neutron diffraction in studies of elastic properties and for the measurement of residual stress. Additional theory to underpin these various applications is developed as required.Less
This book covers the theory, practicalities, and the extensive applications of neutron powder diffraction in materials science, physics, chemistry, mineralogy, and engineering. Various highlight applications of neutron powder diffraction are outlined in the introduction, then the theory is developed and instrumentation described sufficient for a return to the applications. The book covers the use of neutron powder diffraction in the solution (hard) and refinement (more straightforward) of crystal and magnetic structures, applications of powder diffraction in quantitative phase analysis, extraction of microstructural information from powder diffraction patterns, and the applications of neutron diffraction in studies of elastic properties and for the measurement of residual stress. Additional theory to underpin these various applications is developed as required.
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/9780199213252.003.0002
- Subject:
- Physics, Crystallography
A basic understanding of crystallization theory exists through the phase‐diagram description. More detailed theories are available but no one theory can currently predict crystallization behaviour. ...
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A basic understanding of crystallization theory exists through the phase‐diagram description. More detailed theories are available but no one theory can currently predict crystallization behaviour. In this chapter we discuss the basic theory and present a typical phase diagram.Less
A basic understanding of crystallization theory exists through the phase‐diagram description. More detailed theories are available but no one theory can currently predict crystallization behaviour. In this chapter we discuss the basic theory and present a typical phase diagram.
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/9780199213252.003.0007
- Subject:
- Physics, Crystallography
The structural studies of membrane proteins lag those of their soluble counterparts. This is mainly due to the difficulty in crystallizing membrane proteins that have large hydrophobic regions that ...
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The structural studies of membrane proteins lag those of their soluble counterparts. This is mainly due to the difficulty in crystallizing membrane proteins that have large hydrophobic regions that are in contact with the alkyl chains of the lipids in the membrane. This chapter describes specific methods for membrane protein crystal growth including screening with detergents, lipidic cubic‐phase crystallization and antibody fragment approaches.Less
The structural studies of membrane proteins lag those of their soluble counterparts. This is mainly due to the difficulty in crystallizing membrane proteins that have large hydrophobic regions that are in contact with the alkyl chains of the lipids in the membrane. This chapter describes specific methods for membrane protein crystal growth including screening with detergents, lipidic cubic‐phase crystallization and antibody fragment approaches.
Arsalan Kahnemuyipour
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199219230
- eISBN:
- 9780191711800
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199219230.001.0001
- Subject:
- Linguistics, Syntax and Morphology, Phonetics / Phonology
This book explores the nature of sentential stress, how it is assigned, and its interaction with information structure. The central thesis is that the position of sentential or nuclear stress — the ...
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This book explores the nature of sentential stress, how it is assigned, and its interaction with information structure. The central thesis is that the position of sentential or nuclear stress — the element with the highest prominence in the sentence — is determined syntactically and that cross-linguistic differences in this respect follow from syntactic variations. In particular, it is proposed that the Sentential Stress Rule applies in a phase-based manner (Chomsky 2000, 2001, and subsequent work) and assigns stress to the highest element in the spelled out constituent. An additional rule, namely the Focus Stress Rule, which also applies in a phase-based manner, is proposed to handle the interaction between sentential structure and information structure. Sentential stress is thus determined in an interplay between two components, the default Sentential Stress Rule and the Focus Stress Rule. The book provides several arguments in favor of this two-component system.Less
This book explores the nature of sentential stress, how it is assigned, and its interaction with information structure. The central thesis is that the position of sentential or nuclear stress — the element with the highest prominence in the sentence — is determined syntactically and that cross-linguistic differences in this respect follow from syntactic variations. In particular, it is proposed that the Sentential Stress Rule applies in a phase-based manner (Chomsky 2000, 2001, and subsequent work) and assigns stress to the highest element in the spelled out constituent. An additional rule, namely the Focus Stress Rule, which also applies in a phase-based manner, is proposed to handle the interaction between sentential structure and information structure. Sentential stress is thus determined in an interplay between two components, the default Sentential Stress Rule and the Focus Stress Rule. The book provides several arguments in favor of this two-component system.
Helmut Hofmann
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198504016
- eISBN:
- 9780191708480
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504016.003.0026
- Subject:
- Physics, Nuclear and Plasma Physics
This chapter elucidates various mathematical formulas. Based on expressions for Gaussian integrals in one and many dimensions, the methods of stationary phase and steepest descent are deduced, ...
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This chapter elucidates various mathematical formulas. Based on expressions for Gaussian integrals in one and many dimensions, the methods of stationary phase and steepest descent are deduced, representations of the delta-function are given and applied to Fourier and Laplace transformations. For quantal operators, the Mori product is introduced and an important formula for the derivative of exponentials is shown. Elementary properties of spin and isospin are discussed; for fermions, the formalism of second quantization is produced.Less
This chapter elucidates various mathematical formulas. Based on expressions for Gaussian integrals in one and many dimensions, the methods of stationary phase and steepest descent are deduced, representations of the delta-function are given and applied to Fourier and Laplace transformations. For quantal operators, the Mori product is introduced and an important formula for the derivative of exponentials is shown. Elementary properties of spin and isospin are discussed; for fermions, the formalism of second quantization is produced.
