Aging phenomena in the two-dimensional complex Ginzburg-Landau equation

Liu, Weigang; Tauber, Uwe Claus

doi:10.1209/0295-5075/128/30006

Title: Aging phenomena in the two-dimensional complex Ginzburg-Landau equation

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Abstract

The complex Ginzburg-Landau equation with additive noise is a stochastic partial differential equation that describes a remarkably wide range of physical systems which include coupled non-linear oscillators subject to external noise near a Hopf bifurcation instability and spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations or oscillatory chemical reactions. We employ a finite-difference method to numerically solve the noisy complex Ginzburg-Landau equation on a two-dimensional domain with the goal to investigate its non-equilibrium dynamics when the system is quenched into the “defocusing spiral quadrant”. We observe slow coarsening dynamics as oppositely charged topological defects annihilate each other, and characterize the ensuing aging scaling behavior. We conclude that the physical aging features in this system are governed by non-universal aging scaling exponents. We also investigate systems with control parameters residing in the “focusing quadrant”, and identify slow aging kinetics in that regime as well. We provide heuristic criteria for the existence of slow coarsening dynamics and physical aging behavior in the complex Ginzburg-Landau equation.

Authors:

Liu, Weigang ^[1];

^[1]

Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Publication Date:: Fri Jan 24 00:00:00 EST 2020

Research Org.:: Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division

OSTI Identifier:: 1593754

Alternate Identifier(s):: OSTI ID: 1855227

Grant/Contract Number:: SC0002308; FG02-09ER46613

Resource Type:: Accepted Manuscript

Journal Name:: Europhysics Letters (Online)

Additional Journal Information:: Journal Name: Europhysics Letters (Online); Journal Volume: 128; Journal Issue: 3; Journal ID: ISSN 1286-4854

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; pattern formation; complex Ginzburg-Landau equation; aging; dynamic scaling

Citation Formats


                    Liu, Weigang, and Tauber, Uwe Claus. Aging phenomena in the two-dimensional complex Ginzburg-Landau equation.  United States: N. p., 2020. 
Web.  doi:10.1209/0295-5075/128/30006.

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                    Liu, Weigang, & Tauber, Uwe Claus. Aging phenomena in the two-dimensional complex Ginzburg-Landau equation.  United States.  https://doi.org/10.1209/0295-5075/128/30006

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                    Liu, Weigang, and Tauber, Uwe Claus. Fri .  
"Aging phenomena in the two-dimensional complex Ginzburg-Landau equation".  United States.  https://doi.org/10.1209/0295-5075/128/30006.  https://www.osti.gov/servlets/purl/1593754.

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@article{osti_1593754,

  title        = {Aging phenomena in the two-dimensional complex Ginzburg-Landau equation},

  author       = {Liu, Weigang and Tauber, Uwe Claus},

  abstractNote = {The complex Ginzburg-Landau equation with additive noise is a stochastic partial differential equation that describes a remarkably wide range of physical systems which include coupled non-linear oscillators subject to external noise near a Hopf bifurcation instability and spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations or oscillatory chemical reactions. We employ a finite-difference method to numerically solve the noisy complex Ginzburg-Landau equation on a two-dimensional domain with the goal to investigate its non-equilibrium dynamics when the system is quenched into the “defocusing spiral quadrant”. We observe slow coarsening dynamics as oppositely charged topological defects annihilate each other, and characterize the ensuing aging scaling behavior. We conclude that the physical aging features in this system are governed by non-universal aging scaling exponents. We also investigate systems with control parameters residing in the “focusing quadrant”, and identify slow aging kinetics in that regime as well. We provide heuristic criteria for the existence of slow coarsening dynamics and physical aging behavior in the complex Ginzburg-Landau equation.},

  doi          = {10.1209/0295-5075/128/30006},

  journal      = {Europhysics Letters (Online)},

  number       = 3,

  volume       = 128,

  place        = {United States},

  year         = {Fri Jan 24 00:00:00 EST 2020},

  month        = {Fri Jan 24 00:00:00 EST 2020}

}

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