Transport properties in nontwist area-preserving maps

doi:10.1063/1.3247349

Title: Transport properties in nontwist area-preserving maps

Abstract

Nontwist systems, common in the dynamical descriptions of fluids and plasmas, possess a shearless curve with a concomitant transport barrier that eliminates or reduces chaotic transport, even after its breakdown. In order to investigate the transport properties of nontwist systems, we analyze the barrier escape time and barrier transmissivity for the standard nontwist map, a paradigm of such systems. We interpret the sensitive dependence of these quantities upon map parameters by investigating chaotic orbit stickiness and the associated role played by the dominant crossing of stable and unstable manifolds.

Authors:

Szezech Jr., J. D. ^[1]; Caldas, I. L. ^[1]; Lopes, S. R. ^[2]; Viana, R. L. ^[2]; Morrison, P. J. ^[3]

Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo (Brazil)
Departamento de Fisica, Universidade Federal do Parana, Curitiba (Brazil)
Univ. of Texas at Austin (United States)

Publication Date:: 2009-10-23

Research Org.:: Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo (Brazil)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1076438

Grant/Contract Number:: FG03-96ER54346

Resource Type:: Accepted Manuscript

Journal Name:: Chaos: An Interdisciplinary Journal of Nonlinear Science

Additional Journal Information:: Journal Volume: 19; Journal Issue: 4; Journal ID: ISSN 1054-1500

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; Manifolds; Diffusion; Toroidal plasma confinement; Magnetic fields

Citation Formats


                    Szezech Jr., J. D., Caldas, I. L., Lopes, S. R., Viana, R. L., and Morrison, P. J. Transport properties in nontwist area-preserving maps.  United States: N. p., 2009. 
        Web.  doi:10.1063/1.3247349.

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                    Szezech Jr., J. D., Caldas, I. L., Lopes, S. R., Viana, R. L., & Morrison, P. J. Transport properties in nontwist area-preserving maps.  United States.  doi:10.1063/1.3247349.

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                    Szezech Jr., J. D., Caldas, I. L., Lopes, S. R., Viana, R. L., and Morrison, P. J. Fri .  
        "Transport properties in nontwist area-preserving maps".  United States.  doi:10.1063/1.3247349.  https://www.osti.gov/servlets/purl/1076438.

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@article{osti_1076438,

  title        = {Transport properties in nontwist area-preserving maps},

  author       = {Szezech Jr., J. D. and Caldas, I. L. and Lopes, S. R. and Viana, R. L. and Morrison, P. J.},

  abstractNote = {Nontwist systems, common in the dynamical descriptions of fluids and plasmas, possess a shearless curve with a concomitant transport barrier that eliminates or reduces chaotic transport, even after its breakdown. In order to investigate the transport properties of nontwist systems, we analyze the barrier escape time and barrier transmissivity for the standard nontwist map, a paradigm of such systems. We interpret the sensitive dependence of these quantities upon map parameters by investigating chaotic orbit stickiness and the associated role played by the dominant crossing of stable and unstable manifolds.},

  doi          = {10.1063/1.3247349},

  journal      = {Chaos: An Interdisciplinary Journal of Nonlinear Science},

  number       = 4,

  volume       = 19,

  place        = {United States},

  year         = {2009},

  month        = {10}

}

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DOI: 10.1063/1.3247349

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Works referenced in this record:

A universal instability of many-dimensional oscillator systems
journal, May 1979

Chirikov, Boris V.
Physics Reports, Vol. 52, Issue 5
DOI: 10.1016/0370-1573(79)90023-1

Chaotic transport by Rossby waves in shear flow
journal, April 1993

del‐Castillo‐Negrete, Diego; Morrison, P. J.
Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 4
DOI: 10.1063/1.858639

Area preserving nontwist maps: periodic orbits and transition to chaos
journal, March 1996

del-Castillo-Negrete, D.; Greene, J. M.; Morrison, P. J.
Physica D: Nonlinear Phenomena, Vol. 91, Issue 1-2
DOI: 10.1016/0167-2789(95)00257-X

Renormalization and transition to chaos in area preserving nontwist maps
journal, February 1997

del-Castillo-Negrete, D.; Greene, J. M.; Morrison, P. J.
Physica D: Nonlinear Phenomena, Vol. 100, Issue 3-4
DOI: 10.1016/S0167-2789(96)00200-X

Hamiltonian approach to the existence of magnetic surfaces
journal, September 1985

Bernardin, M. P.; Tataronis, J. A.
Journal of Mathematical Physics, Vol. 26, Issue 9
DOI: 10.1063/1.526822

Magnetic field lines, Hamiltonian dynamics, and nontwist systems
journal, June 2000

Morrison, P. J.
Physics of Plasmas, Vol. 7, Issue 6
DOI: 10.1063/1.874062

Turbulent Fluctuations in TFTR Configurations with Reversed Magnetic Shear
journal, October 1996

Mazzucato, E.; Batha, S. H.; Beer, M.
Physical Review Letters, Vol. 77, Issue 15
DOI: 10.1103/PhysRevLett.77.3145

Drift wave test particle transport in reversed shear profile
journal, November 1998

Horton, Wendell; Park, Hyoung-Bin; Kwon, Jae-Min
Physics of Plasmas, Vol. 5, Issue 11
DOI: 10.1063/1.873110

Chaotic transport in zonal flows in analogous geophysical and plasma systems
journal, May 2000

del-Castillo-Negrete, Diego
Physics of Plasmas, Vol. 7, Issue 5
DOI: 10.1063/1.873988

Reduction of chaotic particle transport driven by drift waves in sheared flows
journal, November 2008

Marcus, F. A.; Caldas, I. L.; Guimarães-Filho, Z. O.
Physics of Plasmas, Vol. 15, Issue 11
DOI: 10.1063/1.3009532

Traces of stable and unstable manifolds in heat flux patterns
journal, April 2007

Wingen, A.; Jakubowski, M.; Spatschek, K. H.
Physics of Plasmas, Vol. 14, Issue 4
DOI: 10.1063/1.2715548

Experimental and numerical studies of separatrix splitting and magnetic footprints in DIII-D
journal, June 2007

Evans, T. E.; Joseph, I.; Moyer, R. A.
Journal of Nuclear Materials, Vol. 363-365
DOI: 10.1016/j.jnucmat.2006.12.064

Greene's residue criterion
journal, January 1992

MacKay, R. S.
Nonlinearity, Vol. 5, Issue 1
DOI: 10.1088/0951-7715/5/1/007

KAM Theory and a Partial Justification of Greene's Criterion for Nontwist Maps
journal, January 2000

Delshams, Amadeu; de la Llave, Rafael
SIAM Journal on Mathematical Analysis, Vol. 31, Issue 6
DOI: 10.1137/S003614109834908X

Fractional diffusion in plasma turbulence
journal, August 2004

del-Castillo-Negrete, D.; Carreras, B. A.; Lynch, V. E.
Physics of Plasmas, Vol. 11, Issue 8
DOI: 10.1063/1.1767097

Modeling of stochastic magnetic flux loss from the edge of a poloidally diverted tokamak
journal, December 2002

Evans, T. E.; Moyer, R. A.; Monat, P.
Physics of Plasmas, Vol. 9, Issue 12
DOI: 10.1063/1.1521125

Repellers, semi-attractors, and long-lived chaotic transients
journal, August 1985

Kantz, H.; Grassberger, P.
Physica D: Nonlinear Phenomena, Vol. 17, Issue 1
DOI: 10.1016/0167-2789(85)90135-6

Transport in Hamiltonian systems
journal, August 1984

Mackay, R. S.; Meiss, J. D.; Percival, I. C.
Physica D: Nonlinear Phenomena, Vol. 13, Issue 1-2
DOI: 10.1016/0167-2789(84)90270-7

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Similar Records

Title: Transport properties in nontwist area-preserving maps

Abstract

Citation Formats

A universal instability of many-dimensional oscillator systems journal, May 1979

Chaotic transport by Rossby waves in shear flow journal, April 1993

Area preserving nontwist maps: periodic orbits and transition to chaos journal, March 1996

Renormalization and transition to chaos in area preserving nontwist maps journal, February 1997

Hamiltonian approach to the existence of magnetic surfaces journal, September 1985

Magnetic field lines, Hamiltonian dynamics, and nontwist systems journal, June 2000

Turbulent Fluctuations in TFTR Configurations with Reversed Magnetic Shear journal, October 1996

Drift wave test particle transport in reversed shear profile journal, November 1998

Chaotic transport in zonal flows in analogous geophysical and plasma systems journal, May 2000

Reduction of chaotic particle transport driven by drift waves in sheared flows journal, November 2008

Traces of stable and unstable manifolds in heat flux patterns journal, April 2007

Experimental and numerical studies of separatrix splitting and magnetic footprints in DIII-D journal, June 2007

Greene's residue criterion journal, January 1992

KAM Theory and a Partial Justification of Greene's Criterion for Nontwist Maps journal, January 2000

Fractional diffusion in plasma turbulence journal, August 2004

Modeling of stochastic magnetic flux loss from the edge of a poloidally diverted tokamak journal, December 2002

Repellers, semi-attractors, and long-lived chaotic transients journal, August 1985

Transport in Hamiltonian systems journal, August 1984

A universal instability of many-dimensional oscillator systems
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Chaotic transport by Rossby waves in shear flow
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Area preserving nontwist maps: periodic orbits and transition to chaos
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Renormalization and transition to chaos in area preserving nontwist maps
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Hamiltonian approach to the existence of magnetic surfaces
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Magnetic field lines, Hamiltonian dynamics, and nontwist systems
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Turbulent Fluctuations in TFTR Configurations with Reversed Magnetic Shear
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Drift wave test particle transport in reversed shear profile
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Chaotic transport in zonal flows in analogous geophysical and plasma systems
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Traces of stable and unstable manifolds in heat flux patterns
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