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Harmonic morphisms with one-dimensional fibres

Paul Baird and John C. Wood

in Harmonic Morphisms Between Riemannian Manifolds

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198503620
eISBN:
9780191708435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198503620.003.0012
Subject:
Mathematics, Pure Mathematics

This chapter shows that a harmonic morphism from a manifold of dimension n+1 to a manifold of dimension n is, locally or globally, a principal bundle with a certain metric. When n = 3, in a ... More


Harmonic morphisms defined by polynomials

Paul Baird and John C. Wood

in Harmonic Morphisms Between Riemannian Manifolds

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198503620
eISBN:
9780191708435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198503620.003.0005
Subject:
Mathematics, Pure Mathematics

This chapter establishes the Liouville-type theorem which asserts that any entire (i.e., globally defined) harmonic morphism from a Euclidean space of arbitrary dimension to a Euclidean space of ... More


Relaxor ferroelectrics

Robert Blinc

in Advanced Ferroelectricity

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199570942
eISBN:
9780191728631
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199570942.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

Relaxors are site‐ and charge‐disordered crystals or solid solutions where charge disorder induces random fields. They are characterized by the appearance of polar nanoclusters that are much smaller ... More


Statistical field theory

Hidetoshi Nishimori and Gerardo Ortiz

in Elements of Phase Transitions and Critical Phenomena

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577224
eISBN:
9780191722943
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577224.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Statistical-mechanical systems often involve discrete elementary degrees of freedom such as spins in the Ising model. Field theories, on the other hand, have continuous fields, defined over the whole ... More


Perturbations of weakly expanding critical orbits

Genadi Levin

Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland (eds)

in Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159294
eISBN:
9781400851317
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159294.003.0010
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter studies perturbations of polynomials and rational functions with several (possibly, not all) summable critical points. It proves that there exists an r-dimensional manifold Δ‎ in an ... More


Scaling Analysis of Direct Superconductor-Insulator Transitions in Disordered Ultrathin Films of Metals

A.M. Goldman

in Conductor-Insulator Quantum Phase Transitions

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199592593
eISBN:
9780191741050
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199592593.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Superconductor-insulator (SI) transitions of homogeneously disordered ultrathin quench-condensed films in many instances appear to be direct, without any intervening metallic regime. This is in ... More


Electrocaloric effect in ferroelectrics and ferroelectric thin films

Robert Blinc

in Advanced Ferroelectricity

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199570942
eISBN:
9780191728631
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199570942.003.0008
Subject:
Physics, Condensed Matter Physics / Materials

A theory of the electrocaloric effect is presented. It is shown that the electrocaloric effect in ferroelectrics is maximal at the electric‐field‐induced first‐order phase transition, whereas it is ... More


Penultimate Fate of a Dirty-Fermi Liquid

Alexander Punnoose and Alexander M. Finkel’stein

in Conductor-Insulator Quantum Phase Transitions

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199592593
eISBN:
9780191741050
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199592593.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews here the two-parameter scaling theory of the dirty Fermi-liquid. The chapter shows that this theory captures both quantitatively (for small disorder) and qualitatively (for large ... More


Topological features of DMMs

Massimiliano Di Ventra

in MemComputing: Fundamentals and Applications

Published in print:
2022
Published Online:
March 2022
ISBN:
9780192845320
eISBN:
9780191937521
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192845320.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This Chapter shows that DMMs employ critical points and trajectories between them (instantons) to efficiently solve combinatorial optimization problems. It does so by introducing supersymmetric ... More


Nonlinear and Threshold Effects Related to Neighborhood

George C. Galster

in Making Our Neighborhoods, Making Our Selves

Published in print:
2019
Published Online:
September 2019
ISBN:
9780226599854
eISBN:
9780226599991
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226599991.003.0006
Subject:
Sociology, Social Stratification, Inequality, and Mobility

This chapter demonstrates both in theory and practice that multiple domains related to neighborhoods are characterized by nonlinear or threshold effects that hold powerful implications for both the ... More


The Critical Point in Pure Fluids and Mixtures

Eldred H. Chimowitz

in Introduction to Critical Phenomena in Fluids

Published in print:
2005
Published Online:
November 2020
ISBN:
9780195119305
eISBN:
9780197561249
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195119305.003.0004
Subject:
Chemistry, Physical Chemistry

We showed in chapter 1 that, if the following limit-of-stability condition holds, [math] then the presumption is that the system will be unstable...


Dynamical systems picture of computing

Massimiliano Di Ventra

in MemComputing: Fundamentals and Applications

Published in print:
2022
Published Online:
March 2022
ISBN:
9780192845320
eISBN:
9780191937521
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192845320.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This Chapter introduces the theory of dissipative dynamical systems, the notions of phase space, critical points, attractors, and integrability. It also discusses the advantages of non-quantum ... More


From the Pure to the Concrete: How Mathematics Yields Physical Information

Margaret Morrison

in Reconstructing Reality: Models, Mathematics, and Simulations

Published in print:
2015
Published Online:
January 2015
ISBN:
9780199380275
eISBN:
9780199380299
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199380275.003.0003
Subject:
Philosophy, Philosophy of Science, General

This chapter addresses the question of whether and how mathematics, in and of itself, is capable of providing genuine physical information, where the latter is characterised as information about ... More


In the Vicinity of the Critical Points

Giuseppe Mussardo

in Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics

Published in print:
2020
Published Online:
May 2020
ISBN:
9780198788102
eISBN:
9780191830082
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198788102.003.0015
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 15 introduces the notion of the scaling region near the critical points, identified by the deformations of the critical action by means of the relevant operators. The renormalization group ... More


Arithmetic of Unicritical Polynomial Maps

John Milnor

Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland (eds)

in Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159294
eISBN:
9781400851317
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159294.003.0002
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter studies complex polynomials with only one critical point, relating arithmetic properties of the coefficients to those of periodic orbits and their multipliers and external rays. It first ... More


Heavy fermion superconductors

A.V. Narlikar

in Superconductors

Published in print:
2014
Published Online:
June 2014
ISBN:
9780199584116
eISBN:
9780191747496
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199584116.003.0013
Subject:
Physics, Condensed Matter Physics / Materials

This chapter describes advances made with a variety of heavy fermion (HF) superconducting systems, adding new challenges to the physics of this growing field. Much of the understanding has evolved ... More


Phase Transitions

Robert H. Swendsen

in An Introduction to Statistical Mechanics and Thermodynamics

Published in print:
2019
Published Online:
February 2020
ISBN:
9780198853237
eISBN:
9780191887703
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198853237.003.0017
Subject:
Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

Phase transitions are introduced using the van der Waals gas as an example. The equations of state are derived from the Helmholtz free energy of the ideal gas. The behavior of this model is analyzed, ... More


Extremizers of a Radon Transform Inequality

Michael Christ

Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger (eds)

in Advances in Analysis: The Legacy of Elias M. Stein

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159416
eISBN:
9781400848935
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159416.003.0005
Subject:
Mathematics, Numerical Analysis

This chapter discusses the extremizers of a Radon transform inequality. The model for this analysis is Lieb's characterization of extremizers for the Hardy–Littlewood–Sobolev inequality for certain ... More


Soft matter solutions

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/9780199652952.003.0002
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Soft matter solutions are made of large solute dissolved in small solvent. The contrast in the size of solute and solvent gives special features to soft matter solutions. This chapter discusses these ... More


Spontaneously Broken Symmetries

J. Iliopoulos and T.N. Tomaras

in Elementary Particle Physics: The Standard Theory

Published in print:
2021
Published Online:
December 2021
ISBN:
9780192844200
eISBN:
9780191926983
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192844200.003.0014
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The phenomenon of spontaneous symmetry breaking is a common feature of phase transitions in both classical and quantum physics. In a first part we study this phenomenon for the case of a global ... More


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