Collective dynamics in a model of sliding charge-density waves. I. Critical behavior

Scale-free Spatio-temporal Correlations in Conformational Fluctuations of Intrinsically Disordered Proteins

The self-assembly of intrinsically disordered proteins (IDPs) into condensed phases and the formation of membrane-less organelles (MLOs) can be considered as the phenomenon of collective behavior. The conformational dynamics of IDPs are essential for their interactions and the formation of a condensed phase. From a physical perspective, collective behavior and the emergence of phase are associated with long-range correlations. Here the conformational dynamics of IDPs and the correlations therein are analyzed, using µs-scale atomistic molecular dynamics (MD) simulations and single-molecule Förster resonance energy transfer (smFRET) experiments. The existence of typical scale-free spatio-temporal correlations in IDP conformational fluctuations is demonstrated. Their conformational evolutions exhibit "1/f noise" power spectra and are accompanied by the appearance of residue domains following a power-law size distribution. Additionally, the motions of residues present scale-free behavioral correlation. These scale-free correlations resemble those in physical systems near critical points, suggesting that IDPs are poised at a critical state. Therefore, IDPs can effectively respond to finite differences in sequence compositions and engender considerable structural heterogeneity which is beneficial for IDP interactions and phase formation.

Realizing avalanche criticality in neuromorphic networks on a 2D hBN platform

Networks and systems which exhibit brain-like behavior can analyze information from intrinsically noisy and unstructured data with very low power consumption. Such characteristics arise due to the critical nature and complex interconnectivity of the brain and its neuronal network. We demonstrate a system comprising of multilayer hexagonal boron nitride (hBN) films contacted with silver (Ag), which can uniquely host two different self-assembled networks, which are self-organized at criticality (SOC). This system shows bipolar resistive switching between the high resistance state (HRS) and the low resistance state (LRS). In the HRS, Ag clusters (nodes) intercalate in the van der Waals gaps of hBN forming a network of tunnel junctions, whereas the LRS contains a network of Ag filaments. The temporal avalanche dynamics in both these states exhibit power-law scaling, long-range temporal correlation, and SOC. These networks can be tuned from one to another with voltage as a control parameter. For the first time, two different neural networks are realized in a single CMOS compatible, 2D material platform.

Detecting depinning and nonequilibrium transitions with unsupervised machine learning

Using numerical simulations of a model disk system, we demonstrate that a machine learning generated order-parameter-like measure can detect depinning transitions and different dynamic flow phases in systems driven far from equilibrium. We specifically consider monodisperse passive disks with short range interactions undergoing a depinning phase transition when driven over quenched disorder. The machine learning derived order-parameter-like measure identifies the depinning transition as well as different dynamical regimes, such as the transition from a flowing liquid to a phase separated liquid-solid state that is not readily distinguished with traditional measures such as velocity-force curves or Voronoi tessellation. The order-parameter-like measure also shows markedly distinct behavior in the limit of high density where jamming effects occur. Our results should be general to the broad class of particle-based systems that exhibit depinning transitions and nonequilibrium phase transitions.

Avalanches and scaling collapse in the large-N Kuramoto model

We study avalanches in the Kuramoto model, defined as excursions of the order parameter due to ephemeral episodes of synchronization. We present scaling collapses of the avalanche sizes, durations, heights, and temporal profiles, extracting scaling exponents, exponent relations, and scaling functions that are shown to be consistent with the scaling behavior of the power spectrum, a quantity independent of our particular definition of an avalanche. A comprehensive scaling picture of the noise in the subcritical finite-N Kuramoto model is developed, linking this undriven system to a larger class of driven avalanching systems.

Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: a review

We review the depinning and nonequilibrium phases of collectively interacting particle systems driven over random or periodic substrates. This type of system is relevant to vortices in type-II superconductors, sliding charge density waves, electron crystals, colloids, stripe and pattern forming systems, and skyrmions, and could also have connections to jamming, glassy behaviors, and active matter. These systems are also ideal for exploring the broader issues of characterizing transient and steady state nonequilibrium flow phases as well as nonequilibrium phase transitions between distinct dynamical phases, analogous to phase transitions between different equilibrium states. We discuss the differences between elastic and plastic depinning on random substrates and the different types of nonequilibrium phases which are associated with specific features in the velocity-force curves, fluctuation spectra, scaling relations, and local or global particle ordering. We describe how these quantities can change depending on the dimension, anisotropy, disorder strength, and the presence of hysteresis. Within the moving phase we discuss how there can be a transition from a liquid-like state to dynamically ordered moving crystal, smectic, or nematic states. Systems with periodic or quasiperiodic substrates can have multiple nonequilibrium second or first order transitions in the moving state between chaotic and coherent phases, and can exhibit hysteresis. We also discuss systems with competing repulsive and attractive interactions, which undergo dynamical transitions into stripes and other complex morphologies when driven over random substrates. Throughout this work we highlight open issues and future directions such as absorbing phase transitions, nonequilibrium work relations, inertia, the role of non-dissipative dynamics such as Magnus effects, and how these results could be extended to the broader issues of plasticity in crystals, amorphous solids, and jamming phenomena.

Scaling ansatz for the jamming transition

We propose a Widom-like scaling ansatz for the critical jamming transition. Our ansatz for the elastic energy shows that the scaling of the energy, compressive strain, shear strain, system size, pressure, shear stress, bulk modulus, and shear modulus are all related to each other via scaling relations, with only three independent scaling exponents. We extract the values of these exponents from already known numerical or theoretical results, and we numerically verify the resulting predictions of the scaling theory for the energy and residual shear stress. We also derive a scaling relation between pressure and residual shear stress that yields insight into why the shear and bulk moduli scale differently. Our theory shows that the jamming transition exhibits an emergent scale invariance, setting the stage for the potential development of a renormalization group theory for jamming.

Pinning Susceptibility: The Effect of Dilute, Quenched Disorder on Jamming

We study the effect of dilute pinning on the jamming transition. Pinning reduces the average contact number needed to jam unpinned particles and shifts the jamming threshold to lower densities, leading to a pinning susceptibility, χ_{p}. Our main results are that this susceptibility obeys scaling form and diverges in the thermodynamic limit as χ_{p}∝|ϕ-ϕ_{c}^{∞}|^{-γ_{p}} where ϕ_{c}^{∞} is the jamming threshold in the absence of pins. Finite-size scaling arguments yield these values with associated statistical (systematic) errors γ_{p}=1.018±0.026(0.291) in d=2 and γ_{p}=1.534±0.120(0.822) in d=3. Logarithmic corrections raise the exponent in d=2 to close to the d=3 value, although the systematic errors are very large.

Effect of inertia on sheared disordered solids: critical scaling of avalanches in two and three dimensions

Molecular dynamics simulations with varying damping are used to examine the effects of inertia and spatial dimension on sheared disordered solids in the athermal quasistatic limit. In all cases the distribution of avalanche sizes follows a power law over at least three orders of magnitude in dissipated energy or stress drop. Scaling exponents are determined using finite-size scaling for systems with 10(3)-10(6) particles. Three distinct universality classes are identified corresponding to overdamped and underdamped limits, as well as a crossover damping that separates the two regimes. For each universality class, the exponent describing the avalanche distributions is the same in two and three dimensions. The spatial extent of plastic deformation is proportional to the energy dissipated in an avalanche. Both rise much more rapidly with system size in the underdamped limit where inertia is important. Inertia also lowers the mean energy of configurations sampled by the system and leads to an excess of large events like that seen in earthquake distributions for individual faults. The distribution of stress values during shear narrows to zero with increasing system size and may provide useful information about the size of elemental events in experimental systems. For overdamped and crossover systems the stress variation scales inversely with the square root of the system size. For underdamped systems the variation is determined by the size of the largest events.

Nonlinear driven response of a phase-field crystal in a periodic pinning potential

We study numerically the phase diagram and the response under a driving force of the phase field crystal model for pinned lattice systems introduced recently for both one- and two-dimensional systems. The model describes the lattice system as a continuous density field in the presence of a periodic pinning potential, allowing for both elastic and plastic deformations of the lattice. We first present results for phase diagrams of the model in the absence of a driving force. The nonlinear response to a driving force on an initially pinned commensurate phase is then studied via overdamped dynamic equations of motion for different values of mismatch and pinning strengths. For large pinning strength the driven depinning transitions are continuous, and the sliding velocity varies with the force from the threshold with power-law exponents in agreement with analytical predictions. Transverse depinning transitions in the moving state are also found in two dimensions. Surprisingly, for sufficiently weak pinning potential we find a discontinuous depinning transition with hysteresis even in one dimension under overdamped dynamics. We also characterize structural changes of the system in some detail close to the depinning transition.

93Nb NMR spin echo spectroscopy in single crystal NbSe3

We report electric field induced phase displacements of the charge density wave (CDW) in a single crystal of NbSe3 using 93Nb NMR spin-echo spectroscopy. CDW polarizations in the pinned state induced by unipolar and bipolar pulses are linear and reversible up to at least E = (0.96)ET. The polarizations have a broad distribution extending up to phase angles of order 60 degrees for electric fields close to threshold. No evidence for polarizations in excess of a CDW wavelength or for a divergence in polarization near ET are observed. The results are consistent with elastic depinning models, provided that the critical regime expected in large systems is not observable.

Phase diagram and commensurate-incommensurate transitions in the phase field crystal model with an external pinning potential

We study the phase diagram and the commensurate-incommensurate transitions in a phase field model of a two-dimensional crystal lattice in the presence of an external pinning potential. The model allows for both elastic and plastic deformations and provides a continuum description of lattice systems, such as for adsorbed atomic layers or two-dimensional vortex lattices. Analytically, a mode expansion analysis is used to determine the ground states and the commensurate-incommensurate transitions in the model as a function of the strength of the pinning potential and the lattice mismatch parameter. Numerical minimization of the corresponding free energy shows reasonable agreement with the analytical predictions and provides details on the topological defects in the transition region. We find that for small mismatch the transition is of first order, and it remains so for the largest values of mismatch studied here. Our results are consistent with results of simulations for atomistic models of adsorbed overlayers.

Critical exponents of the driven elastic string in a disordered medium

We analyze the harmonic elastic string driven through a continuous random potential above the depinning threshold. The velocity exponent beta = 0.33(2) is calculated. We observe a crossover in the roughness exponent zeta from the critical value 1.26 to the asymptotic (large force) value of 0.5. We calculate directly the velocity correlation function and the corresponding correlation length exponent nu = 1.29(5), which obeys the scaling relation nu = 1/(2 - zeta), and agrees with nu(FS), the finite-size-scaling exponent of fluctuations in the critical force. Surprisingly, the velocity correlation function is nonuniversal at short distances.

Dynamics of two-dimensional colloids on a disordered substrate

Using Langevin simulations, we numerically study the dynamics of two-dimensional colloids on a disordered substrate. With a decreasing strength of the interaction between colloids, we find a crossover from elastic to plastic depinnings, where a substantial increase in the depinning force is observed. Furthermore, we find a dynamical phase transition from the moving liquid to the moving smectic at high driving forces by decreasing the temperature. Peak effect occurs in the dynamical critical driving force across the transition, accompanied by a clear crossing of velocity-force dependence curves.

Colloidal dynamics on disordered substrates

Using Langevin simulations, we examine driven colloids interacting with quenched disorder. For weak substrates the colloids form an ordered state and depin elastically. For increasing substrate strength, we find a sharp crossover to inhomogeneous depinning and a substantial increase in the depinning force, analogous to the peak effect in superconductors. The velocity versus driving force curve shows criticality at depinning, with a change in scaling exponent occurring at the order to disorder crossover. Upon application of a sudden pulse of driving force, pronounced transients appear in the disordered regime which are due to the formation of long-lived colloidal flow channels.

Crackling noise

Crackling noise arises when a system responds to changing external conditions through discrete, impulsive events spanning a broad range of sizes. A wide variety of physical systems exhibiting crackling noise have been studied, from earthquakes on faults to paper crumpling. Because these systems exhibit regular behaviour over a huge range of sizes, their behaviour is likely to be independent of microscopic and macroscopic details, and progress can be made by the use of simple models. The fact that these models and real systems can share the same behaviour on many scales is called universality. We illustrate these ideas by using results for our model of crackling noise in magnets, explaining the use of the renormalization group and scaling collapses, and we highlight some continuing challenges in this still-evolving field.

Self-organized criticality: sandpiles, singularities, and scaling

We present an overview of the statistical mechanics of self-organized criticality. We focus on the successes and failures of hydrodynamic description of transport, which consists of singular diffusion equations. When this description applies, it can predict the scaling features associated with these systems. We also identify a hard driving regime where singular diffusion hydrodynamics fails due to fluctuations and give an explicit criterion for when this failure occurs.