## K3 Surfaces

*D. Huybrechts*

### in Fourier-Mukai Transforms in Algebraic Geometry

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199296866
- eISBN:
- 9780191711329
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199296866.003.0010
- Subject:
- Mathematics, Geometry / Topology

After abelian varieties, K3 surfaces are the second most interesting special class of varieties. These have a rich internal geometry and a highly interesting moduli theory. Paralleling the famous ... More

## James’ suspension spring equations

*Robert James Matthys*

### in Accurate Clock Pendulums

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198529712
- eISBN:
- 9780191712791
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198529712.003.0016
- Subject:
- Physics, History of Physics

In 1983, K. James published two useful but rather complicated equations whose purpose was to help design the suspension spring. The equations show the effect that different spring lengths, widths, ... More

## Sasaki–Einstein Geometry

*Charles P. Boyer and Krzysztof Galicki*

### in Sasakian Geometry

- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198564959
- eISBN:
- 9780191713712
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198564959.003.0012
- Subject:
- Mathematics, Geometry / Topology

This chapter is central to the whole book and perhaps the main reason and justification for it. Much of it is based on a new method for proving the existence of Einstein metrics on odd dimensional ... More

## S‐Duality in HyperkäHler Hodge Theory

*TamáS Hausel*

### in The Many Facets of Geometry: A Tribute to Nigel Hitchin

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199534920
- eISBN:
- 9780191716010
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534920.003.0016
- Subject:
- Mathematics, Geometry / Topology

This chapter surveys the motivations, related results, and progress made towards the following problem, raised by Hitchin in 1995: What is the space of L2 harmonic forms on the moduli space of Higgs ... More

## Consistent Orientation of Moduli Spaces

*Daniel S. Freed, Michael J. Hopkins, and Constantin Teleman*

### in The Many Facets of Geometry: A Tribute to Nigel Hitchin

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199534920
- eISBN:
- 9780191716010
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534920.003.0019
- Subject:
- Mathematics, Geometry / Topology

In a series of papers by Freed, Hopkins, and Teleman (2003, 2005, 2007a) the relationship between positive energy representations of the loop group of a compact Lie group G and the twisted ... More

## Smoothness and Asymptotic Smoothness

*Joram Lindenstrauss, David Preiss, and Tiˇser Jaroslav*

### in Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691153551
- eISBN:
- 9781400842698
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153551.003.0008
- Subject:
- Mathematics, Analysis

This chapter describes the modulus of smoothness of a function in the direction of a family of subspaces and the much simpler notion of upper Fréchet differentiability. It also considers the notion ... More

## Fr ´Echet Differentiability of Vector-Valued Functions

*Joram Lindenstrauss, David Preiss, and Tiˇser Jaroslav*

### in Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691153551
- eISBN:
- 9781400842698
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153551.003.0013
- Subject:
- Mathematics, Analysis

This chapter shows that if a Banach space with a Fréchet smooth norm is asymptotically smooth with modulus o(tⁿ logⁿ⁻¹(1/t)) then every Lipschitz map of X to a space of dimension not exceeding n has ... More

## The Mumford-Tate Group of a Variation of Hodge Structure

*Mark Green, Phillip Griffiths, and Matt Kerr*

### in Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691154244
- eISBN:
- 9781400842735
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691154244.003.0004
- Subject:
- Mathematics, Analysis

This chapter deals with the Mumford-Tate group of a variation of Hodge structure (VHS). It begins by presenting a definition of VHS, which consists of a connected complex manifold and a locally ... More

## Extensions of the Mode-Coupling Theory for the Evolution of Glassy Dynamics of Liquids

*Wolfgang Götze*

### in Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199235346
- eISBN:
- 9780191715600
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199235346.003.0005
- Subject:
- Physics, Condensed Matter Physics / Materials

It is demonstrated in this chapter that states of simple systems with density-fluctuation arrest exhibit positive static shear moduli and perfect particle localization. Approaching a generic ... More

## SOLID-SOLUTION STRENGTHENING

*A. S. Argon*

### in Strengthening Mechanisms in Crystal Plasticity

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780198516002
- eISBN:
- 9780191705717
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198516002.003.0005
- Subject:
- Physics, Crystallography

Incorporation of a second constituent into a pure metal offers a very flexible means of strengthening. In this chapter, the interactions of individual solute atoms with dislocations are considered in ... More

## SUSY GAUGE THEORIES

*John Terning*

### in Modern Supersymmetry: Dynamics and Duality

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198567639
- eISBN:
- 9780191718243
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567639.003.0003
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter examines SUSY gauge theories. First, it looks at the role of quantum loop corrections on running couplings and masses. It then studies the space of possible vacua (the moduli space), and ... More

## Arithmetic Compactifications of PEL-Type Shimura Varieties

*Kai-Wen Lan*

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691156545
- eISBN:
- 9781400846016
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691156545.001.0001
- Subject:
- Mathematics, Geometry / Topology

By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical ... More

## A little elementary acoustics

*G. A. D. Briggs and O. V. Kolosov*

### in Acoustic Microscopy: Second Edition

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199232734
- eISBN:
- 9780191716355
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199232734.003.0006
- Subject:
- Physics, Condensed Matter Physics / Materials

Solids support both longitudinal and shear acoustic waves; fluids support only longitudinal waves, with attenuation proportional to the viscosity and to the square of the frequency. The longitudinal ... More

## Solution of Patterson-type syntheses with the Direct methods sum function

*Jordi Rius*

### in Structure Determination from Powder Diffraction Data

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199205530
- eISBN:
- 9780191718076
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199205530.003.0013
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter provides a detailed mathematical definition of the Direct methods modulus sum function and its associated tangent formula (S' – TF). The latter appears to be especially well-suited to ... More

## Geometry and Physics: Volume II: A Festschrift in honour of Nigel Hitchin

*Andrew Dancer, Jørgen Ellegaard Andersen, and Oscar García-Prada (eds)*

- Published in print:
- 2018
- Published Online:
- December 2018
- ISBN:
- 9780198802020
- eISBN:
- 9780191869068
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198802020.001.0001
- Subject:
- Mathematics, Geometry / Topology

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and ... More

## Geometry and Physics: Volume I: A Festschrift in honour of Nigel Hitchin

*Andrew Dancer, Jørgen Ellegaard Andersen, and Oscar García-Prada (eds)*

- Published in print:
- 2018
- Published Online:
- December 2018
- ISBN:
- 9780198802013
- eISBN:
- 9780191840500
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198802013.001.0001
- Subject:
- Mathematics, Geometry / Topology

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and ... More

## Introduction

*C. M. Roland*

### in Viscoelastic Behavior of Rubbery Materials

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199571574
- eISBN:
- 9780191728976
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199571574.003.0001
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter describes the properties arising due to the defining feature of polymers—the enormous size of their constituent molecules. This size and the large aspect ratio of ‘macromolecules’ cause ... More

## Chain dynamics

*C. M. Roland*

### in Viscoelastic Behavior of Rubbery Materials

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199571574
- eISBN:
- 9780191728976
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199571574.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials

The slow dynamics of polymer chains involves extended spatial scales, exceeding many repeat units and making the behavior largely independent of chemical structure. This universality allows modeling ... More

## Soy protein-based polymer nanocomposites

*Jin Huang, Ning Lin, Yun Chen, Peter R. Chang, and Jiahui Yu*

### in Nanocomposites with Biodegradable Polymers: Synthesis, Properties, and Future Perspectives

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199581924
- eISBN:
- 9780191728853
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199581924.003.0011
- Subject:
- Physics, Condensed Matter Physics / Materials

The incorporation of nanofillers into soy protein materials significantly enhances tensile strength and modulus, and in some cases, contributes to a simultaneous increase in strength and elongation. ... More

## Elastic soft matter

*Masao Doi*

### in Soft Matter Physics

- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199652952
- eISBN:
- 9780191774942
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199652952.003.0003
- Subject:
- Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Elastic soft matter typically indicates rubbers and gels, which are made by introducing small amount of cross-links among polymer chains in liquid state (solutions and melts). In elastic materials, ... More