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.
Francesco Calogero
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199535286
- eISBN:
- 9780191715853
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199535286.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
In Chapter 8 five directions of future research are tersely mentioned in order of increasing importance. The investigation of Diophantine relations, such as those reported in Appendix C. The ...
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In Chapter 8 five directions of future research are tersely mentioned in order of increasing importance. The investigation of Diophantine relations, such as those reported in Appendix C. The investigation of the behavior in a quantal context of systems described by isochronous Hamiltonians. The investigation of isochronous systems outside the phase space sectors where they behave isochronously. The investigation of the behavior of the isochronous many-body problems treated in Section 5.5, in particular, when the corresponding unmodified system is a realistic molecular dynamics model characterized by a chaotic evolution yielding—in the context of statistical mechanics and thermodynamics—a steadily increasing entropy—which, however, must eventually decrease when the corresponding Ω-modified system returns to its initial state, as entailed by its isochronous character. And, last but by no means least, the investigation of isochronous systems in an applicative context—be it physics, chemistry, biology, medicine, economy, and so on.Less
In Chapter 8 five directions of future research are tersely mentioned in order of increasing importance. The investigation of Diophantine relations, such as those reported in Appendix C. The investigation of the behavior in a quantal context of systems described by isochronous Hamiltonians. The investigation of isochronous systems outside the phase space sectors where they behave isochronously. The investigation of the behavior of the isochronous many-body problems treated in Section 5.5, in particular, when the corresponding unmodified system is a realistic molecular dynamics model characterized by a chaotic evolution yielding—in the context of statistical mechanics and thermodynamics—a steadily increasing entropy—which, however, must eventually decrease when the corresponding Ω-modified system returns to its initial state, as entailed by its isochronous character. And, last but by no means least, the investigation of isochronous systems in an applicative context—be it physics, chemistry, biology, medicine, economy, and so on.
Dennis Sherwood and Jon Cooper
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199559046
- eISBN:
- 9780191595028
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199559046.001.0001
- Subject:
- Physics, Crystallography
This book presents a complete account of the theory of the diffraction of X-rays by crystals with particular reference to the processes of determining the structures of protein molecules. The book ...
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This book presents a complete account of the theory of the diffraction of X-rays by crystals with particular reference to the processes of determining the structures of protein molecules. The book develops from first principles all relevant mathematics, diffraction, and wave theory. The practical aspects of sample preparation and X-ray data collection using both laboratory and synchrotron sources are covered along with data analysis at both the theoretical and practical levels. The important role played by the Patterson function in structure analysis by both molecular replacement and experimental phasing approaches is covered, as are methods for improving the resulting electron density map. The theoretical basis of methods used in refinement of protein crystal structures are then covered in depth along with the crucial task of defining the binding sites of ligands and drug molecules. The complementary roles of other diffraction methods which reveal further detail of great functional importance in a crystal structure are outlined.Less
This book presents a complete account of the theory of the diffraction of X-rays by crystals with particular reference to the processes of determining the structures of protein molecules. The book develops from first principles all relevant mathematics, diffraction, and wave theory. The practical aspects of sample preparation and X-ray data collection using both laboratory and synchrotron sources are covered along with data analysis at both the theoretical and practical levels. The important role played by the Patterson function in structure analysis by both molecular replacement and experimental phasing approaches is covered, as are methods for improving the resulting electron density map. The theoretical basis of methods used in refinement of protein crystal structures are then covered in depth along with the crucial task of defining the binding sites of ligands and drug molecules. The complementary roles of other diffraction methods which reveal further detail of great functional importance in a crystal structure are outlined.
Hidetoshi Nishimori and Gerardo Ortiz
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199577224
- eISBN:
- 9780191722943
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577224.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into ...
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Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.Less
Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.
Antônio M. Figueiredo Neto and Silvio R. A. Salinas
- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198525509
- eISBN:
- 9780191711756
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525509.001.0001
- Subject:
- Physics, Crystallography
Mixtures of surfactant or amphiphilic molecules and solvents are known to display a large number of lyotropic mesophases. Although the physics of thermotropic liquid crystals has been vastly ...
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Mixtures of surfactant or amphiphilic molecules and solvents are known to display a large number of lyotropic mesophases. Although the physics of thermotropic liquid crystals has been vastly discussed in the literature, lyotropic mesophases have been much less explored. This book gives a unifying presentation of the structural and physical properties of lyotropic liquid crystalline systems, including a set of experimental results and a discussion of the characterization of different structures and the corresponding phase transitions. The initial chapters contain a description of the main experimental results and techniques associated with the characterization of lyotropic mixtures, and an overview of some theoretical approaches to account for the phase transitions and phase diagrams of these mesophases. This book includes discussions on periodically organized lyotropic systems, micellar and bicontinuous structures, modulated and cholesteric structures, and a number of related developments (magnetic colloids, microemulsions, films, and lyo-banana mesophases).Less
Mixtures of surfactant or amphiphilic molecules and solvents are known to display a large number of lyotropic mesophases. Although the physics of thermotropic liquid crystals has been vastly discussed in the literature, lyotropic mesophases have been much less explored. This book gives a unifying presentation of the structural and physical properties of lyotropic liquid crystalline systems, including a set of experimental results and a discussion of the characterization of different structures and the corresponding phase transitions. The initial chapters contain a description of the main experimental results and techniques associated with the characterization of lyotropic mixtures, and an overview of some theoretical approaches to account for the phase transitions and phase diagrams of these mesophases. This book includes discussions on periodically organized lyotropic systems, micellar and bicontinuous structures, modulated and cholesteric structures, and a number of related developments (magnetic colloids, microemulsions, films, and lyo-banana mesophases).
Richard Caplan
- Published in print:
- 2005
- Published Online:
- July 2005
- ISBN:
- 9780199263455
- eISBN:
- 9780191602726
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199263450.003.0011
- Subject:
- Political Science, International Relations and Politics
Explores how, and under what circumstances, international authorities should withdraw from the administration of a territory. Whereas elections were once viewed as the capstone of international ...
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Explores how, and under what circumstances, international authorities should withdraw from the administration of a territory. Whereas elections were once viewed as the capstone of international involvement, as in Cambodia, transitional authorities today are focused additionally on the development of institutional safeguards (for minority groups, for instance) that, it is hoped, will endure beyond the transitional period. Other approaches include a phased exit strategy whereby the pace of transfer is commensurate with the demonstrated ability of the local leadership to meet specified benchmarks. Follow-on measures—a role for which regional organizations may be particularly well suited—are also important to reinforce positive results, as are regional stabilization measures, such as the incentive structure represented by the prospect of membership in regional and international organizations.Less
Explores how, and under what circumstances, international authorities should withdraw from the administration of a territory. Whereas elections were once viewed as the capstone of international involvement, as in Cambodia, transitional authorities today are focused additionally on the development of institutional safeguards (for minority groups, for instance) that, it is hoped, will endure beyond the transitional period. Other approaches include a phased exit strategy whereby the pace of transfer is commensurate with the demonstrated ability of the local leadership to meet specified benchmarks. Follow-on measures—a role for which regional organizations may be particularly well suited—are also important to reinforce positive results, as are regional stabilization measures, such as the incentive structure represented by the prospect of membership in regional and international organizations.
Marc Mézard and Andrea Montanari
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780198570837
- eISBN:
- 9780191718755
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570837.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and ...
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This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. The topics which have been selected, including spin glasses, error correcting codes, satisfiability, are central to each field. The approach focuses on the limit of large random instances, adopting a common formulation in terms of graphical models. It presents message passing algorithms like belief propagation and survey propagation, and their use in decoding and constraint satisfaction solving. It also explains analysis techniques like density evolution and the cavity method, and uses them to derive phase diagrams and study phase transitions.Less
This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. The topics which have been selected, including spin glasses, error correcting codes, satisfiability, are central to each field. The approach focuses on the limit of large random instances, adopting a common formulation in terms of graphical models. It presents message passing algorithms like belief propagation and survey propagation, and their use in decoding and constraint satisfaction solving. It also explains analysis techniques like density evolution and the cavity method, and uses them to derive phase diagrams and study phase transitions.
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
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.
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/9780199219469.003.0011
- Subject:
- Physics, Crystallography
Maximum entropy methods are used in crystallography for estimating reflection phases among other applications. This chapter explains the basic concepts behind maximum entropy, including entropy ...
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Maximum entropy methods are used in crystallography for estimating reflection phases among other applications. This chapter explains the basic concepts behind maximum entropy, including entropy itself and its relationship to probability and information. They are illustrated by a simple non-scientific example of estimating missing information based on reasonable assumptions.Less
Maximum entropy methods are used in crystallography for estimating reflection phases among other applications. This chapter explains the basic concepts behind maximum entropy, including entropy itself and its relationship to probability and information. They are illustrated by a simple non-scientific example of estimating missing information based on reasonable assumptions.
John C. H. Spence
- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780199552757
- eISBN:
- 9780191708664
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199552757.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This book covers both practical and theoretical aspects of atomic resolution transmission electron microscopy. The discovery of the carbon nanotube, the three-dimensional imaging of the ribosome, and ...
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This book covers both practical and theoretical aspects of atomic resolution transmission electron microscopy. The discovery of the carbon nanotube, the three-dimensional imaging of the ribosome, and the imaging of a single foreign atom inside a thin crystal by energy-filtered transmission electron microscopy have all demonstrated the immense power of this technique. The recent development of aberration-correction devices has brought the spatial resolution of the method below one Angstrom. The emphasis throughout is on a clear presentation of fundamental concepts, and practical advice. The chapters review simple electron optics, phase contrast theory, coherence theory, and imaging theory for thin crystals. The multiple scattering theory is given in full, and the relationship between the various formulations (Bloch-wave, multislice, scattering matrix, Howie–Whelan equations, phase grating etc) is explained. Applications in biology and materials science are covered, with discussions of radiation damage, sample preparation, image processing and super-resolution, electron holography, and aberration correction. The theory of high-angle annular dark field Z-contrast imaging by scanning transmission electron microscopy is given in full. Additional chapters are devoted to electron sources and detectors, fault diagnosis, experimental methods and associated techniques such as channelling effects in X-ray microanalysis, microdiffraction, cathodoluminescence, environmental microscopy and electron energy-loss spectroscopy.Less
This book covers both practical and theoretical aspects of atomic resolution transmission electron microscopy. The discovery of the carbon nanotube, the three-dimensional imaging of the ribosome, and the imaging of a single foreign atom inside a thin crystal by energy-filtered transmission electron microscopy have all demonstrated the immense power of this technique. The recent development of aberration-correction devices has brought the spatial resolution of the method below one Angstrom. The emphasis throughout is on a clear presentation of fundamental concepts, and practical advice. The chapters review simple electron optics, phase contrast theory, coherence theory, and imaging theory for thin crystals. The multiple scattering theory is given in full, and the relationship between the various formulations (Bloch-wave, multislice, scattering matrix, Howie–Whelan equations, phase grating etc) is explained. Applications in biology and materials science are covered, with discussions of radiation damage, sample preparation, image processing and super-resolution, electron holography, and aberration correction. The theory of high-angle annular dark field Z-contrast imaging by scanning transmission electron microscopy is given in full. Additional chapters are devoted to electron sources and detectors, fault diagnosis, experimental methods and associated techniques such as channelling effects in X-ray microanalysis, microdiffraction, cathodoluminescence, environmental microscopy and electron energy-loss spectroscopy.
Russell L. De Valois and Karen K. De Valois
- Published in print:
- 1991
- Published Online:
- January 2008
- ISBN:
- 9780195066579
- eISBN:
- 9780199872220
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195066579.003.0008
- Subject:
- Psychology, Cognitive Neuroscience
This chapter addresses the general question of how the visual system knows where something is. The visual system is sensitive to the spatial phase of patterns under some conditions, and in many of ...
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This chapter addresses the general question of how the visual system knows where something is. The visual system is sensitive to the spatial phase of patterns under some conditions, and in many of the situations in which spatial frequency channels have been studied, the phase as well as the spatial frequency of the patterns, is critical. Some of the evidence for phase specificity is discussed. It is shown that phase sensitivity does not seem to be present under certain conditions.Less
This chapter addresses the general question of how the visual system knows where something is. The visual system is sensitive to the spatial phase of patterns under some conditions, and in many of the situations in which spatial frequency channels have been studied, the phase as well as the spatial frequency of the patterns, is critical. Some of the evidence for phase specificity is discussed. It is shown that phase sensitivity does not seem to be present under certain conditions.
