Mean-field Predictions Research Articles

Graph neural network modeling of grain-scale anisotropic elastic behavior using simulated and measured microscale data

Here we assess the applicability of graph neural networks (GNNs) for predicting the grain-scale elastic response of polycrystalline metallic alloys. Using GNN surrogate models, grain-averaged stresses during uniaxial elastic tension in low solvus high-refractory (LSHR) Ni Superalloy and Ti 7 wt%Al (Ti-7Al) are predicted as example face-centered cubic and hexagonal closed packed alloys, respectively. A transfer learning approach is taken in which GNN surrogate models are trained using crystal elasticity finite element method (CEFEM) simulations and then the trained surrogate models are used to predict the mechanical response of microstructures measured using high-energy X-ray diffraction microscopy (HEDM). The performance of using various microstructural and micromechanical descriptors for input nodal features to the GNNs is explored through comparisons to traditional mean-field theory predictions, reserved full-field CEFEM data, and measured far-field HEDM data. The effects of elastic anisotropy on GNN model performance and outlooks for the extension of the framework are discussed.

Hard-sphere jamming through the lens of linear optimization.

The jamming transition is ubiquitous. It is present in granular matter, foams, colloids, structural glasses, and many other systems. Yet, it defines a critical point whose properties still need to be fully understood. Recently, a major breakthrough came about when the replica formalism was extended to build a mean-field theory that provides an exact description of the jamming transition of spherical particles in the infinite-dimensional limit. While such theory explains the jamming critical behavior of both soft and hard spheres, investigating the transition in finite-dimensional systems poses very difficult and different problems, in particular from the numerical point of view. Soft particles are modeled by continuous potentials; thus, their jamming point can be reached through efficient energy minimization algorithms. In contrast, the latter methods are inapplicable to hard-sphere (HS) systems since the interaction energy among the particles is always zero by construction. To overcome these difficulties, here we recast the jamming of hard spheres as a constrained optimization problem and introduce the CALiPPSO algorithm, capable of readily producing jammed HS packings without including any effective potential. This algorithm brings a HS configuration of arbitrary dimensions to its jamming point by solving a chain of linear optimization problems. We show that there is a strict correspondence between the force balance conditions of jammed packings and the properties of the optimal solutions of CALiPPSO, whence we prove analytically that our packings are always isostatic and in mechanical equilibrium. Furthermore, using extensive numerical simulations, we show that our algorithm is able to probe the complex structure of the free-energy landscape, finding qualitative agreement with mean-field predictions. We also characterize the algorithmic complexity of CALiPPSO and provide an open-source implementation of it.

Core-Shell Gyroid in ABC Bottlebrush Block Terpolymers.

Block polymer self-assembly provides a versatile platform for creating useful materials endowed with three-dimensional periodic network morphologies that support orthogonal physical properties such as high ionic conductivity and a high elastic modulus. However, coil configurations limit conventional linear block polymers to finite ordered network dimensions, which are further restricted by slow self-assembly kinetics at high molecular weights. A bottlebrush architecture can circumvent both shortcomings owing to extended backbone configurations due to side chain crowding and molecular dynamics substantially free of chain entanglements. However, until now, network morphologies have not been reported in AB bottlebrush block copolymers, notwithstanding favorable mean-field predictions. We explored the phase behavior by small-angle X-ray scattering of 133 poly(ethylene-alt-propylene)-b-polystyrene (PEP-PS) diblock and PEP-PS-PEO triblock bottlebrush copolymers prepared by ring-opening metathesis polymerization (ROMP) of norbornene-functionalized poly(ethylene-alt-propylene) (PEP), poly(styrene) (PS), and poly(ethylene oxide) (PEO) macromonomers with total backbone degrees of polymerization Nbb between 20 and 40. The PEP-PS diblocks exhibited only cylindrical and lamellar morphologies over the composition range of ca. 30-70%. However, addition of variable-length bottlebrush PEO blocks to diblocks containing 30-50% PS led to the formation of a substantial core-shell double gyroid (GYR) phase window containing 20 bottlebrush triblock specimens, which is the focus of this report. Encouragingly, the GYR unit cell dimensions increased as d ∼ Nbb0.92, portending the ability to access larger network dimensions than previously obtained with linear AB or ABC block polymers. This work highlights extraordinary opportunities associated with applying facile ROMP chemistry to multiblock bottlebrush polymers.

Condensation temperature of strongly interacting 39K condensates in the mean-field and semi-classical approximations

We consider the effect of inter-atom interactions on the condensation temperature Tc of an atomic Bose-Einstein condensate. We find an analytic expression of the shift in Tc induced by interactions with respect the ideal non-interacting case, in the mean-field and semi-classical approximations. Such a shift is expressed in terms of the ratio a/λTc between the s-wave scattering length a and the thermal wavelength λTc. This result is used to discuss the tension between mean-field predictions and observations in strongly interacting K39 condensates. It is shown that such a tension is solved taking into account the details of the Feshbach resonance used to tune a in the experiments.

Collective dynamics of capacity-constrained ride-pooling fleets

Ride-pooling (or ride-sharing) services combine trips of multiple customers along similar routes into a single vehicle. The collective dynamics of the fleet of ride-pooling vehicles fundamentally underlies the efficiency of these services. In simplified models, the common features of these dynamics give rise to scaling laws of the efficiency that are valid across a wide range of street networks and demand settings. However, it is unclear how constraints of the vehicle fleet impact such scaling laws. Here, we map the collective dynamics of capacity-constrained ride-pooling fleets to services with unlimited passenger capacity and identify an effective fleet size of available vehicles as the relevant scaling parameter characterizing the dynamics. Exploiting this mapping, we generalize the scaling laws of ride-pooling efficiency to capacity-constrained fleets. We approximate the scaling function with a queueing theoretical analysis of the dynamics in a minimal model system, thereby enabling mean-field predictions of required fleet sizes in more complex settings. These results may help to transfer insights from existing ride-pooling services to new settings or service locations.

Nuclear-spin polaron formation: Anisotropy effects and quantum phase transition

We study theoretically the formation of the nuclear-spin polaron state in semiconductor nanosystems within the Lindblad equation approach. To this end, we derive a general Lindblad equation for the density operator that complies with the symmetry of the system Hamiltonian and address the nuclear-spin polaron formation for localized charge carriers subject to an arbitrarily anisotropic hyperfine interaction when optically cooling the nuclei. The steady-state solution of the density matrix for an anisotropic central spin model is presented as a function of the electron and nuclear spin bath temperature. Results for the electron-nuclear spin correlator as well as data for the nuclear spin distribution function serve as a measure of spin-entanglement. The features in both of them clearly indicate the formation of the nuclear polaron state at low temperatures where the crossover regime coincides with an enhancement of quantum fluctuations and agrees with the mean-field prediction of the critical temperature line. We can identify two distinct polaron states dependent upon the hyperfine anisotropy which are separated by a quantum phase transition at the isotropic point. These states are reflected in the temporal spin auto-correlation functions accessible in experiment via spin-noise measurements.

Casimir Contribution to the Interfacial Hamiltonian for 3D Wetting.

Previous treatments of three-dimensional (3D) short-ranged wetting transitions have missed an entropic or low-temperature Casimir contribution to the binding potential describing the interaction between the unbinding interface and wall. This we determine by exactly deriving the interfacial model for 3D wetting from a more microscopic Landau-Ginzburg-Wilson Hamiltonian. The Casimir term changes the interpretation of fluctuation effects occurring at wetting transitions so that, for example, mean-field predictions are no longer obtained when interfacial fluctuations are ignored. While the Casimir contribution does not alter the surface phase diagram, it significantly increases the adsorption near a first-order wetting transition and changes completely the predicted critical singularities of tricritical wetting, including the nonuniversality occurring in 3D arising from interfacial fluctuations. Using the numerical renormalization group, we show that, for critical wetting, the asymptotic regime is extremely narrow with the growth of the parallel correlation length characterized by an effective exponent in quantitative agreement with Ising model simulations, resolving a long-standing controversy.

Frame-guided assembly from a theoretical perspective.

The molecular self-assembly of various structures such as micelles and vesicles has been the subject of comprehensive studies. Recently, a new approach to design these structures, the frame-guided assembly, has been developed to progress toward fabrics of predefined shape and size, following an initially provided frame of guiding elements. Here, we study the frame-guided assembly in a two-dimensional membrane via computer simulations based on a single-bead coarse grained surfactant model in continuous space. In agreement with the experiment, the assembly process already starts for surfactant concentrations below the critical micelle concentration. Furthermore, upon increasing temperature, the formation process gets more delocalized. Additionally, the assembly process of the resulting membrane plane is modeled by a lattice gas model. It displays a similar phenomenology but additionally allows for the derivation of analytical mean-field predictions. In this way, a fundamental understanding of frame-guided assembly can be gained.

Coordination and equilibrium selection in games: the role of local effects

We study the role of local effects and finite size effects in reaching coordination and in equilibrium selection in two-player coordination games. We investigate three update rules — the replicator dynamics (RD), the best response (BR), and the unconditional imitation (UI). For the pure coordination game with two equivalent strategies we find a transition from a disordered state to coordination for a critical value of connectivity. The transition is system-size-independent for the BR and RD update rules. For the IU it is system-size-dependent, but coordination can always be reached below the connectivity of a complete graph. We also consider the general coordination game which covers a range of games, such as the stag hunt. For these games there is a payoff-dominant strategy and a risk-dominant strategy with associated states of equilibrium coordination. We analyse equilibrium selection analytically and numerically. For the RD and BR update rules mean-field predictions agree with simulations and the risk-dominant strategy is evolutionary favoured independently of local effects. When players use the unconditional imitation, however, we observe coordination in the payoff-dominant strategy. Surprisingly, the selection of pay-off dominant equilibrium only occurs below a critical value of the network connectivity and disappears in complete graphs. As we show, it is a combination of local effects and update rule that allows for coordination on the payoff-dominant strategy.

Observation of chiral solitons in LiCuVO4

Quantum spin liquids represent a magnetic ground state arising in the presence of strong quantum fluctuations that preclude ordering down to zero temperature and leave clear fingerprints in the excitation spectra. While theory bears a variety of possible quantum spin liquid phases their experimental realization is still scarce. Here, we report experimental evidence for chiral solitons in the S = 1/2 spin chain compound LiCuVO4 from measurements of the complex permittivity ε* in the GHz range. In zero magnetic field our results show short-lived thermally activated chiral fluctuations above the multiferroic phase transition at TN = 2.4 K. In ε* these fluctuations are seen as the slowing down of a relaxation with a critical dynamical exponent νξz ≈ 1.3 in agreement with mean-field predictions. When using a magnetic field to suppress TN towards 0 K the influence of quantum fluctuations increases until the thermally activated fluctuations vanish and only an excitation can be observed in the dielectric response in close proximity to the phase transition below 400 mK. From direct measurements we find this excitation’s energy gap as ESE ≈ 14.1 μeV, which is in agreement with a nearly gapless chiral soliton that has been proposed for LiCuVO4 based on quantum spin liquid theory.

Experimental Observation of Phase Transitions in Spatial Photonic Ising Machine.

Statistical spin dynamics plays a key role in understanding the working principle for novel optical Ising machines. Here, we propose the gauge transformation for a spatial photonic Ising machine, where a single spatial phase modulator simultaneously encodes spin configurations and programs interaction strengths. Using gauge transformation, we experimentally evaluate the phase diagram of a high-dimensional spin-glass equilibrium system with 100 fully connected spins. We observe the presence of paramagnetic, ferromagnetic, and spin-glass phases and determine the critical temperature T_{c} and the critical probability p_{c} of the phase transitions, which agree well with the mean-field theory predictions. Thus, the approximation of the mean-field model is experimentally verified in the spatial photonic Ising machine. Furthermore, we discuss the phase transition in parallel with solving combinatorial optimization problems during the cooling process and identify that the spatial photonic Ising machine is robust with sufficient many-spin interactions even when the system is associated with optical aberrations and measurement uncertainty.

Finite-size effects in the microscopic critical properties of jammed configurations: A comprehensive study of the effects of different types of disorder.

Jamming criticality defines a universality class that includes systems as diverse as glasses, colloids, foams, amorphous solids, constraint satisfaction problems, neural networks, etc. A particularly interesting feature of this class is that small interparticle forces (f) and gaps (h) are distributed according to nontrivial power laws. A recently developed mean-field (MF) theory predicts the characteristic exponents of these distributions in the limit of very high spatial dimension, d→∞ and, remarkably, their values seemingly agree with numerical estimates in physically relevant dimensions, d=2 and 3. These exponents are further connected through a pair of inequalities derived from stability conditions, and both theoretical predictions and previous numerical investigations suggest that these inequalities are saturated. Systems at the jamming point are thus only marginally stable. Despite the key physical role played by these exponents, their systematic evaluation has yet to be attempted. Here, we carefully test their value by analyzing the finite-size scaling of the distributions of f and h for various particle-based models for jamming. Both dimension and the direction of approach to the jamming point are also considered. We show that, in all models, finite-size effects are much more pronounced in the distribution of h than in that of f. We thus conclude that gaps are correlated over considerably longer scales than forces. Additionally, remarkable agreement with MF predictions is obtained in all but one model, namely near-crystalline packings. Our results thus help to better delineate the domain of the jamming universality class. We furthermore uncover a secondary linear regime in the distribution tails of both f and h. This surprisingly robust feature is understood to follow from the (near) isostaticity of our configurations.

Cracking of human teeth: An avalanche and acoustic emission study

Teeth are the hardest part of the human body. Cracking of human teeth under compression progresses by avalanches emitting acoustic noise. Acoustic emission (AE) spectroscopy reveals that tooth avalanches are statistically fully compatible with predictions of mean field (MF) theory. Avalanche energies collapse into a power law distributed which is stable over more than five decades with an energy exponent ε = 1.4. Acoustic amplitudes (exponent ~τ), durations (~α), correlations between amplitudes and energies (~x), and correlations between amplitude and duration (~χ) follow equally power laws with MF values of all exponents. The exponents correlation: τ-1 = x(ε-1) = (α-1)/χ is confirmed. Crack propagation bifurcates and shows the hallmarks of avalanches where main cracks nucleate secondary cracks.

Chiral edge modes in Helmholtz-Onsager vortex systems

Vortices play a fundamental role in the physics of two-dimensional (2D) fluids across a range of length scales, from quantum superfluids to geophysical flows. Despite a history dating back to Helmholtz, point vortices in a 2D fluid continue to pose interesting theoretical problems, owing to their unusual statistical mechanics. Here we show that the strongly interacting Helmholtz-Onsager vortex systems can form statistical edge modes at low energies, extending a previously identified analogy between vortex matter and quantum Hall systems. Through dynamical simulations, Monte-Carlo sampling, and mean-field theory, we demonstrate that these edge modes are associated with the formation of dipoles of real and image vortices at boundaries. The edge modes are robust, persisting in nonconvex domains, and are in quantitative agreement with the mean-field predictions.1 MoreReceived 1 March 2021Accepted 11 June 2021DOI:https://doi.org/10.1103/PhysRevFluids.6.064702©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasVortex flowsVortices in superfluidsPhysical SystemsClassical fluidsHamiltonian systemsQuantum fluids & solidsFluid DynamicsStatistical Physics

Quantum Monte Carlo simulations of two-dimensional repulsive Fermi gases with population imbalance

The ground-state properties of two-component repulsive Fermi gases in two dimensions are investigated by means of fixed-node diffusion Monte Carlo simulations. The energy per particle is determined as a function of the intercomponent interaction strength and of the population imbalance. The regime of universality in terms of the s-wave scattering length is identified by comparing results for hard-disk and for soft-disk potentials. In the large imbalance regime, the equation of state turns out to be well described by a Landau-Pomeranchuk functional for two-dimensional polarons. To fully characterize this expansion, we determine the polarons' effective mass and their coupling parameter, complementing previous studies on their chemical potential. Furthermore, we extract the magnetic susceptibility from low-imbalance data, finding only small deviations from the mean-field prediction. While the mean-field theory predicts a direct transition from a paramagnetic to a fully ferromagnetic phase, our diffusion Monte Carlo results suggest that the partially ferromagnetic phase is stable in a narrow interval of the interaction parameter. This finding calls for further analyses on the effects due to the fixed-node constraint.

Filament-motor protein system under loading: instability and limit cycle oscillations

ABSTRACT We consider the dynamics of a rigid filament in a motor protein assay under external loading. The motor proteins are modeled as active harmonic linkers with tail ends immobilized on a substrate. Their heads attach to the filament stochastically to extend along with it, resulting in a force on the filament, before detaching. The rate of extension and detachment are load-dependent. Here we formulate and characterize the governing dynamics in the mean field approximation using linear stability analysis, and direct numerical simulations of the motor proteins and filament. Under constant loading, the system shows transition from a stable configuration to instability toward detachment of the filament from motor proteins. Under elastic loading, we find emergence of stable limit cycle oscillations via a supercritical Hopf bifurcation with change in activity and the number of motor proteins. The number of motor proteins required at the onset of limit cycle oscillations increases with the increasing stiffness of the elastic loading. Numerical simulations of the system for large number of motor proteins show good agreement with the mean field predictions.

The role of friction in statistics and scaling laws of avalanches.

We investigate statistics and scaling laws of avalanches in two-dimensional frictional particles by numerical simulations. We find that the critical exponent for avalanche size distributions is governed by microscopic friction between the particles in contact, where the exponent is larger and closer to mean-field predictions if the friction coefficient is finite. We reveal that microscopic "slips" between frictional particles induce numerous small avalanches which increase the slope, as well as the power-law exponent, of avalanche size distributions. We also analyze statistics and scaling laws of the avalanche duration and maximum stress drop rates, and examine power spectra of stress drop rates. Our numerical results suggest that the microscopic friction is a key ingredient of mean-field descriptions and plays a crucial role in avalanches observed in real materials.

Critical charge fluctuations and emergent coherence in a strongly correlated excitonic insulator

Excitonic insulator is a coherent electronic phase that results from the formation of a macroscopic population of bound particle-hole pairs—excitons. With only a few candidate materials known, the collective excitonic behavior is challenging to observe, being obscured by crystalline lattice effects. Here we use polarization-resolved Raman spectroscopy to reveal the quadrupolar excitonic mode in the candidate zero-gap semiconductor Ta2NiSe5 disentangling it from the lattice phonons. The excitonic mode pronouncedly softens close to the phase transition, showing its electronic character, while its coupling to noncritical lattice modes is shown to enhance the transition temperature. On cooling, we observe the gradual emergence of coherent superpositions of band states at the correlated insulator gap edge, with strong departures from mean-field theory predictions. Our results demonstrate the realization of a strongly correlated excitonic state in an equilibrium bulk material.

A direct link between active matter and sheared granular systems

The similarity in mechanical properties of dense active matter and sheared amorphous solids has been noted in recent years without a rigorous examination of the underlying mechanism. We develop a mean-field model that predicts that their critical behavior-as measured by their avalanche statistics-should be equivalent in infinite dimensions up to a rescaling factor that depends on the correlation length of the applied field. We test these predictions in two dimensions using a numerical protocol, termed "athermal quasistatic random displacement," and find that these mean-field predictions are surprisingly accurate in low dimensions. We identify a general class of perturbations that smoothly interpolates between the uncorrelated localized forces that occur in the high-persistence limit of dense active matter and system-spanning correlated displacements that occur under applied shear. These results suggest a universal framework for predicting flow, deformation, and failure in active and sheared disordered materials.

Finite-size scaling analysis of localization transitions in the disordered two-dimensional Bose-Hubbard model within the fluctuation operator expansion method

The disordered Bose-Hubbard model in two dimensions at non-integer filling admits a superfluid to Bose-glass transition at weak disorder. Less understood are the properties of this system at strong disorder and energy densities corresponding to excited states. In this work we study the Bose-glass transition of the ground state and the related finite energy localization transition, the mobility edge of the quasiparticle spectrum, a critical energy separating extended from localized quasiparticle excitations. To study these the fluctuation operator expansion is used. The level spacing statistics of the quasiparticle excitations, the fractal dimension and decay of the corresponding wave functions are consistent with a many-body mobility edge. The finite-size scaling of the lowest gaps yields a correction to the mean-field prediction of the superfluid to Bose-glass transition. In its vicinity we discuss spectral properties of the ground state in terms of the dynamic structure factor and the spectral function which also shows distinct behavior above and below the mobility edge.