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Observer-independent Dynamical Measures of Team Coordination and Performance

Silke M. Dodel, Ajay S. Pillai, Philip W. Fink, Eric R. Muth, Roy Stripling, Dylan D. Schmorrow, Joseph V. Cohn, and Viktor K. Jirsa

in Motor Control: Theories, Experiments, and Applications

Published in print:
2010
Published Online:
January 2011
ISBN:
9780195395273
eISBN:
9780199863518
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195395273.003.0004
Subject:
Neuroscience, Sensory and Motor Systems

Team performance represents an extension of individual performance. It is an outcome of individuals joining together for the purpose of exploiting one another's individual skills to accomplish ... More


A Primer for Dynamical Systems

Kevin S. McCann

in Food Webs (MPB-50)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691134178
eISBN:
9781400840687
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691134178.003.0002
Subject:
Biology, Ecology

This chapter introduces the reader to some of the main conceptual ideas behind dynamical systems theory from the perspective of an experimentalist. It first considers the qualitative approaches used ... More


Hamilton’s Principle

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0006
Subject:
Physics, Atomic, Laser, and Optical Physics

The general calculus of variations discussed in the previous chapter may be used to derive variational principles in mechanics. Two different, but closely related, variational principles are ... More


Collective descriptions of beam distributions

J. B. Rosenzweig

in Fundamentals of Beam Physics

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198525547
eISBN:
9780191711725
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525547.003.0005
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter generalizes the description of charged particle motion from a single particle viewpoint to one concerned with distributions in phase space. It discusses that the first classes of ... More


OUTLOOK

Francesco Calogero

in Isochronous Systems

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 ... More


Coherent states

J. C. Garrison and R. Y. Chiao

in Quantum Optics

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198508861
eISBN:
9780191708640
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508861.003.0006
Subject:
Physics, Atomic, Laser, and Optical Physics

The elementary quantum theory of quasi-classical states for mechanical harmonic oscillators is applied to the radiation oscillators describing light, and thus used to define quasi-classical states of ... More


Bose–Hubbard models: methods of treatment

Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger

in Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199573127
eISBN:
9780191775048
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573127.003.0005
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter reviews various theoretical methods that can be applied to investigate Bose–Hubbard models. In particular, it discusses the Bogolyubov method, strong coupling expansion, the perturbative ... More


Hamiltonian Mechanics with Time as a Coordinate

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0012
Subject:
Physics, Atomic, Laser, and Optical Physics

In the previous chapter, the traditional Lagrange equations were used as the basis for an extended Lagrangian theory in which time is treated as a coordinate. This extended theory combined the ... More


Particle Motion in Curved Spacetime

Valeri P. Frolov and Andrei Zelnikov

in Introduction to Black Hole Physics

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199692293
eISBN:
9780191731860
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199692293.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Particle motion in a curved spacetime is considered. The Lagrangian and Hamiltonian form of the equation of motion of a relativistic particle are described. We discuss here also the Hamilton‐Jacobi ... More


Linear transverse motion

J. B. Rosenzweig

in Fundamentals of Beam Physics

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198525547
eISBN:
9780191711725
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525547.003.0003
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter begins with a discussion that deepened the introductory remarks made on betatron oscillations. It explains that in such a scheme, one can have simultaneous stability in both vertical and ... More


Introduction To Hamiltonian Mechanics

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0004
Subject:
Physics, Atomic, Laser, and Optical Physics

The power of Lagrangian mechanics has caused generations of students to wonder why it is necessary or even desirable, to recast mechanics in Hamiltonian form. The answer is that the Hamiltonian ... More


Path Integrals In Quantum Mechanics: Generalizations

JEAN ZINN-JUSTIN

in Quantum Field Theory and Critical Phenomena

Published in print:
2002
Published Online:
January 2010
ISBN:
9780198509233
eISBN:
9780191708732
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509233.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 2 constructed a path integral representation of the matrix elements of the statistical operator e-βH. This chapter extends the construction to hamiltonians which are general functions of ... More


PATH INTEGRALS IN PHASE SPACE

Jean Zinn-Justin

in Path Integrals in Quantum Mechanics

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198566748
eISBN:
9780191717994
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566748.003.0010
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter contains a few additional results such as a definition of path integrals over phase space trajectories, and the problems generated by the quantization of lagrangians with potentials ... More


Canonical Transformations

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0017
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter considers a broader class of transformations known as canonical transformations, which transform the whole of the extended phase space in a more general way. Each new canonical ... More


ISOCHRONOUS SYSTEMS ARE NOT RARE

Francesco Calogero

in Isochronous Systems

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199535286
eISBN:
9780191715853
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535286.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In Chapter 2 a simple trick—amounting to a change of variables—is introduced that modifies a large class of dynamical systems so that the (autonomous) ω-modified systems thereby obtained are ... More


Circulating beams

E. J. N. Wilson

in An Introduction to Particle Accelerators

Published in print:
2001
Published Online:
January 2010
ISBN:
9780198508298
eISBN:
9780191706363
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508298.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter opens with a discussion of Liouville's theorem—a conservation principle that applies to the area of phase space, usually an ellipse, occupied by a beam. In the transverse phase plane, ... More


Bayesian reconstruction of particle beam phase space

C Nakhleh, D Higdon, C K Allen, and R Ryne

in Bayesian Theory and Applications

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199695607
eISBN:
9780191744167
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199695607.003.0033
Subject:
Mathematics, Probability / Statistics

This chapter discusses the application of Bayesian inversion methodology to reconstruct the initial phase space configuration of charged particle beams using a series of one-dimensional projection ... More


Kinetically constrained models

Juan P. Garrahan, Peter Sollich, and Cristina Toninelli

in Dynamical Heterogeneities in Glasses, Colloids, and Granular Media

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199691470
eISBN:
9780191729799
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199691470.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter summarizes recent developments in the study of kinetically constrained models (KCMs) as models for glass formers. After recalling the definition of the KCMs which are covered in this ... More


Hamilton’s Principle and Noether’s Theorem

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0013
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter presents extended forms of Hamilton’s principle and the phase space Hamilton’s principle based on the extended Lagrangian and Hamiltonian methods developed earlier. It also discusses ... More


Phase Space Reconstruction

Ray Huffaker, Marco Bittelli, and Rodolfo Rosa

in Nonlinear Time Series Analysis with R

Published in print:
2017
Published Online:
February 2018
ISBN:
9780198782933
eISBN:
9780191826153
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198782933.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this chapter we introduce an important concept concerning the study of both discrete and continuous dynamical systems, the concept of phase space or “state space”. It is an abstract mathematical ... More


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