Depinning and flow of a vortex line in an uniaxial random medium

Abstract

We study numerically and analytically the dynamics of a single directed elastic string driven through a 3-dimensional disordered medium. In the quasistatic limit the string is super-rough in the driving direction, with roughness exponent ${\zeta }_{\parallel }=1.25\pm 0.01$, dynamic exponent $z_{\parallel }=1.43\pm 0.01$, correlation-length exponent $\nu =1.33\pm 0.02$, depinning exponent $\beta =0.24\pm 0.01$, and avalanche-size exponent ${\tau }_{\parallel }=1.09\pm 0.03$. In the transverse direction we find ${\zeta }_{\perp }=0.5\pm 0.01$, $z_{\perp }=2.27\pm 0.05$, and ${\tau }_{\perp }=1.17\pm 0.06$. We show that transverse fluctuations do not alter the critical exponents in the driving direction, as predicted by the planar approximation (PA) proposed in 1996 by Ertas and Kardar (EK). We check the PA for the force-force correlator, comparing to the functional renormalization group and simulations. Both Random-Bond (RB) and Random-Field (RF) disorder yield a single universality class, indistinguishable from the one of an elastic string in a 2-dimensional random medium. While $z_{\perp }=z_{\parallel }+1/\nu$ and $\nu =1/(2-{\zeta }_{\parallel })$ of EK are satisfied, the transversal movement is that of a Brownian, with a clock set locally by the forward movement. This implies ${\zeta }_{\perp }=(2-d)/2$, distinct from EK. At small driving velocities the distribution of local parallel displacements has a negative skewness, while in the transverse direction it is a Gaussian. For large scales, the system can be described by anisotropic effective temperatures. In the fast-flow regime the local displacement distributions become Gaussian in both directions and the effective temperatures vanish as $T_{\mathtt{eff}}^{\perp }\sim 1/v$ and $T_{\mathtt{eff}}^{\parallel }\sim 1/v^3$ for RB and as $T_{\mathtt{eff}}^{\perp }\approx T_{\mathtt{eff}}^{\parallel }\sim 1/v$ for RF.

arXiv comment23 pages, 23 figures

References in corpus (60)

• Emergent electrodynamics of skyrmions in a chiral magnet
• Creep and depinning in disordered media
• Collective Transport: From Superconductors to Earthquakes
• Dynamics of a ferromagnetic domain wall: avalanches, depinning transition and the Barkhausen effect
• Vortex-glass phases in type-II superconductors
• The effective temperature
• Renormalization of pinned elastic systems: how does it work beyond one loop ?
• Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition
• 2-loop Functional Renormalization Group Theory of the Depinning Transition
• Nonequilibrium Dynamics of Interfaces and Lines
• Quasi-static crack propagation in heterogeneous media
• Driven Interface Depinning in a Disordered Medium
• Roughness at the depinning threshold for a long-range elastic string
• Interface Depinning in a Disordered Medium - Numerical Results
• Depinning of elastic manifolds
• Avalanche-size distribution at the depinning transition: A numerical test of the theory
• Functional Renormalization Group and the Field Theory of Disordered Elastic Systems
• Driven particle in a random landscape: disorder correlator, avalanche distribution and extreme value statistics of records
• Driven Depinning in Anisotropic Media
• Universality Classes for Interface Growth with Quenched Disorder
• Origin of the roughness exponent in elastic strings at the depinning threshold
• Deformation of crystals: Connections with statistical physics
• Onset of Propagation of Planar Cracks in Heterogeneous Media
• Width distribution of contact lines on a disordered substrate
• Height fluctuations of a contact line: a direct measurement of the renormalized disorder correlator
• Creep dynamics of elastic manifolds via exact transition pathways
• Viscoelastic Effects in Avalanche Dynamics: A Key to Earthquake Statistics
• Statistics of static avalanches in a random pinning landscape
• Numerical Calculation of the Functional renormalization group fixed-point functions at the depinning transition
• Depinning transition and thermal fluctuations in the random-field Ising model
• Non-steady relaxation and critical exponents at the depinning transition
• Anisotropic Scaling in Threshold Critical Dynamics of Driven Directed Lines
• Theory and simulations on strong pinning of vortex lines by nanoparticles
• Universal Statistics of the Critical Depinning Force of Elastic Systems in Random Media
• Quantitative scaling of magnetic avalanches
• Effective temperature in driven vortex lattices with random pinning
• Domain Wall Depinning in Random Media by AC Fields
• Monte Carlo Dynamics of driven Flux Lines in Disordered Media
• Experimental evidence for three universality classes for reaction fronts in disordered flows
• Crack propagation through phase separated glasses: effect of the characteristic size of disorder
• Depinning exponents of the driven long-range elastic string
• The Oslo model, hyperuniformity, and the quenched Edwards-Wilkinson model
• Nonstationary dynamics of the Alessandro-Beatrice-Bertotti-Montorsi model
• Targeted evolution of pinning landscapes for large superconducting critical currents
• Functional renormalization group for anisotropic depinning and relation to branching processes
• Crossover behavior in interface depinning
• Statics and dynamics of elastic manifolds in media with long-range correlated disorder
• Intermittent collective dynamics of domain walls in the creep regime
• Random-Manifold to Random-Periodic Depinning of an Elastic Interface
• Universal distribution of threshold forces at the depinning transition
• Vortex dynamics in type II superconductors under strong pinning conditions
• Localization of soft modes at the depinning transition
• Sinai model in presence of dilute absorbers
• Universal Critical Exponents of the Magnetic Domain Wall Depinning Transition
• Distribution of velocities and acceleration for a particle in Brownian correlated disorder: inertial case
• Universal energy distribution for interfaces in a random field environment
• Mean-Field Theories for Depinning and their Experimental Signatures
• Roughness of a Tilted Anharmonic String at Depinning
• Depinning of stiff directed lines in random media
• Pinning Induced Fluctuations on Driven Vortices

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