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Inferring the nature of disorder in the media where elastic objects are nucleated is of crucial importance for many applications but remains a challenging basic-science problem. Here we propose a method to discern whether weak-point or strong-correlated disorder dominates based on characterizing the distribution of the interaction forces between objects mapped in large fields-of-view. We illustrate our proposal with the case-study system of vortex structures nucleated in type-II superconductors with different pinning landscapes. Interaction force distributions are computed from individual vortex positions imaged in thousands-vortices fields-of-view in a two-orders-of-magnitude-wide vortex-density range. Vortex structures nucleated in point-disordered media present Gaussian distributions of the interaction force components. In contrast, if the media have dilute and randomly-distributed correlated disorder, these distributions present non-Gaussian algebraically-decaying tails for large force magnitudes. We propose that detecting this deviation from the Gaussian behavior is a fingerprint of strong disorder, in our case originated from a dilute distribution of correlated pinning centers.
RESUMO
We consider a massive particle driven with a constant force in a periodic potential and subjected to a dissipative friction. As a function of the drive and damping, the phase diagram of this paradigmatic model is well known to present a pinned, a sliding, and a bistable regime separated by three distinct bifurcation lines. In physical terms, the average velocity v of the particle is nonzero only if either (i) the driving force is large enough to remove any stable point, forcing the particle to slide or (ii) there are local minima but the damping is small enough, below a critical damping, for the inertia to allow the particle to cross barriers and follow a limit cycle; this regime is bistable and whether v>0 or v=0 depends on the initial state. In this paper, we focus on the asymptotes of the critical line separating the bistable and the pinned regimes. First, we study its behavior near the "triple point" where the pinned, the bistable, and the sliding dynamical regimes meet. Just below the critical damping we uncover a critical regime, where the line approaches the triple point following a power-law behavior. We show that its exponent is controlled by the normal form of the tilted potential close to its critical force. Second, in the opposite regime of very low damping, we revisit existing results by providing a simple method to determine analytically the exact behavior of the line in the case of a generic potential. The analytical estimates, accurately confirmed numerically, are obtained by exploiting exact soliton solutions describing the orbit in a modified tilted potential which can be mapped to the original tilted washboard potential. Our methods and results are particularly useful for an accurate description of underdamped nonuniform oscillators driven near their triple point.
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Magnetic domain wall motion is at the heart of new magnetoelectronic technologies and hence the need for a deeper understanding of domain wall dynamics in magnetic systems. In this context, numerical simulations using simple models can capture the main ingredients responsible for the complex observed domain wall behavior. We present a scalar field model for the magnetization dynamics of quasi-two-dimensional systems with a perpendicular easy axis of magnetization which allows a direct comparison with typical experimental protocols, used in polar magneto-optical Kerr effect microscopy experiments. We show that the thermally activated creep and depinning regimes of domain wall motion can be reached and the effect of different quenched disorder implementations can be assessed with the model. In particular, we show that the depinning field increases with the mean grain size of a Voronoi tessellation model for the disorder.
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Any decomposition of the total trajectory entropy production for Markovian systems has a joint probability distribution satisfying a generalized detailed fluctuation theorem, when all the contributing terms are odd with respect to time reversal. The expression of the result does not bring into play dual probability distributions, hence easing potential applications. We show that several fluctuation theorems for perturbed nonequilibrium steady states are unified and arise as particular cases of this general result. In particular, we show that the joint probability distribution of the system and reservoir trajectory entropies satisfy a detailed fluctuation theorem valid for all times.
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We study the nonstationary dynamics of an elastic interface in a disordered medium at the depinning transition. We compute the two-time response and correlation functions, found to be universal and characterized by two independent critical exponents. We find a good agreement between two-loop functional renormalization group calculations and molecular dynamics simulations for the scaling forms, and for the response aging exponent theta_{R}. We also describe a dynamical dimensional crossover, observed at long times in the relaxation of a finite system. Our results are relevant for the nonsteady driven dynamics of domain walls in ferromagnetic films and contact lines in wetting.
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We study numerically correlation and response functions in nonequilibrium driven vortex lattices with random pinning. From a generalized fluctuation-dissipation relation, we calculate an effective transverse temperature in the fluid moving phase. We find that the effective temperature decreases with increasing driving force and becomes equal to the equilibrium melting temperature when the dynamic transverse freezing occurs. We also discuss how the effective temperature can be measured experimentally from a generalized Kubo formula.