When a densely packed monolayer of macroscopic spheres floats on chaotic capillary Faraday waves, a coexistence of large scale convective motion and caging dynamics typical for glassy systems is observed. We subtract the convective mean flow using a coarse graining (homogenization) method and reveal subdiffusion for the caging time scales followed by a diffusive regime at later times. We apply the methods developed to study dynamic heterogeneity and show that the typical time and length scales of the fluctuations due to rearrangements of observed particle groups significantly increase when the system approaches its largest experimentally accessible packing concentration. To connect the system to the dynamic criticality literature, we fit power laws to our results. The resultant critical exponents are consistent with those found in densely packed suspensions of colloids.

The efficient evaluation of tensor expressions involving sums over multiple indices is of significant importance to many fields of research, including quantum many-body physics, loop quantum gravity, and quantum chemistry. The computational cost of evaluating an expression may depend strongly on the order in which the index sums are evaluated, and determination of the operation-minimizing contraction sequence for a single tensor network (single term, in quantum chemistry) is known to be NP-hard. The current preferred solution is an exhaustive search, using either an iterative depth-first approach with pruning or dynamic programming and memoization, but these approaches are impractical for many of the larger tensor network ansätze encountered in quantum many-body physics. We present a modified search algorithm with enhanced pruning which exhibits a performance increase of several orders of magnitude while still guaranteeing identification of an optimal operation-minimizing contraction sequence for a single tensor network. A reference implementation for matlab, compatible with the $\mathsf{ncon()}$ and $\mathsf{multienv()}$ network contractors of arXiv:1402.0939 and Evenbly and Pfeifer, Phys. Rev. B 89, 245118 (2014), respectively, is supplied.

In the sequence of quenches to either nontopological phases or other topological phases, we study the stability of Majorana fermions at the edges of a two-dimensional topological superconductor with spin-orbit coupling and in the presence of a Zeeman term. Both instantaneous and slow quenches are considered. In the case of instantaneous quenches, the Majorana modes generally decay, but for a finite system there is a revival time that scales to infinity as the system size grows. Exceptions to this decaying behavior are found in some cases due to the presence of edge states with the same momentum in the final state. Quenches to a topological $Z_2$ phase reveal some robustness of the Majorana fermions in the sense that even though the survival probability of the Majorana state is small, it does not vanish. If the pairing is not aligned with the spin-orbit Rashba coupling, it is found that the Majorana fermions are fairly robust with a finite survival probability. It is also shown that the Chern number remains invariant after the quench, until the propagation of the mode along the transverse direction reaches the middle point, beyond which the Chern number fluctuates between increasing values. The effect of varying the rate of change in slow quenches is also analyzed. It is found that the defect production is nonuniversal and does not follow the Kibble-Zurek scaling with the quench rate, as obtained before for other systems with topological edge states.

We investigate the large order aspects of the $\delta$ expansion under the estimation procession of the critical quantities. As illustrative examples, we revisit the one-dimensional Ising model for the analytic study and the two-dimensional square Ising model in the high-temperature phase for the numerical experiment to large orders. In both models, the proposed fundamental base on which the estimation protocol should be constructed is investigated in detail and confirmed to be valid. In the square lattice model, we present a new protocol for the estimation of critical exponents and temperature.

We use a computationally efficient graph-cut method (GCM) to obtain the ground-state morphologies (at zero temperature) of the random-field Ising model in $d=2,3$. The GCM enables us to obtain comprehensive numerical results on large-scale systems. We analyze the morphologies by computing correlation functions and structure factors. These quantities enable us to precisely evaluate characteristic properties, e.g., domain sizes, scaling functions, roughness exponents, fractal dimensions, etc.

A quantitative measure of convergence to effective ergodicity, the Thirumalai-Mountain (TM) metric, is applied to Metropolis and Glauber single-spin-flip dynamics. In computing this measure, finite lattice ensemble averages are obtained using the exact solution for a one dimensional Ising model, whereas the time averages are computed with Monte Carlo simulations. The time evolution of the effective ergodic convergence of Ising magnetization is monitored. By this approach, diffusion regimes of the effective ergodic convergence of magnetization are identified for different lattice sizes, nonzero temperature, and nonzero external field values. Results show that caution should be taken when using the TM metric at system parameters that give rise to strong correlations.

Uniform planar impact on a two-dimensional square packing of spheres with intruders at interstitial locations is investigated. An equivalent one-dimensional granular chain model is proposed with appropriate scaling and is verified numerically. Numerical observations demonstrate the existence of a new family of plane solitary waves with different profiles at unique combinations of material properties. In particular, a special case of a solitary wave whose profile is similar to that of the homogeneous chains is also reported. Material combinations that cause solitary waves are systematically extracted for a wide range of material properties. For the solitary wave similar to that of a homogeneous chain, a quasicontinuum approximation is employed to predict the shape and width of the solitary wave, showing good agreement with the numerical results. Finally, an asymptotic analysis is conducted to predict the solitary wave solutions.

We perform molecular dynamics simulations to compress binary hard spheres into jammed packings as a function of the compression rate $R$, size ratio $\alpha$, and number fraction $x_S$ of small particles to determine the connection between the glass-forming ability (GFA) and packing efficiency in bulk metallic glasses (BMGs). We define the GFA by measuring the critical compression rate $R_c$, below which jammed hard-sphere packings begin to form “random crystal” structures with defects. We find that for systems with $\alpha \gtrsim 0.8$ that do not demix, $R_c$ decreases strongly with $\Delta {\varphi }_J$, as $R_c\sim exp(-1/\Delta {\varphi }_J^2)$, where $\Delta {\varphi }_J$ is the difference between the average packing fraction of the amorphous packings and random crystal structures at $R_c$. Systems with $\alpha \lesssim 0.8$ partially demix, which promotes crystallization, but we still find a strong correlation between $R_c$ and $\Delta {\varphi }_J$. We show that known metal-metal BMGs occur in the regions of the $\alpha$ and $x_S$ parameter space with the lowest values of $R_c$ for binary hard spheres. Our results emphasize that maximizing GFA in binary systems involves two competing effects: minimizing $\alpha$ to increase packing efficiency, while maximizing $\alpha$ to prevent demixing.

Minimal fragmentation models intend to unveil the statistical properties of large ensembles of identical objects, each one segmented in two parts only. Contrary to what happens in the multifragmentation of a single body, minimally fragmented ensembles are often amenable to analytical treatments, while keeping key features of multifragmentation. In this work we present a study on the minimal fragmentation of regular polygonal plates with up to 100 sides. We observe in our model the typical statistical behavior of a solid torn apart by a strong impact, for example. We obtain a robust power law, valid for several decades, in the small mass limit. In the present case we were able to analytically determine the exponent of the cumulative probability distribution to be $½$. Less usual, but also reported in a number of experimental and numerical references on impact fragmentation, is the presence of a sharp crossover to a second power-law regime, whose exponent we found to be between $⅓$ and 1 depending on the way anisotropy is introduced in the model.

In order to obtain a better understanding of short-range (SR) and long-range (LR) nanoparticle (NP) interactions during the self-assembly of dodecanethiol-coated Au NPs in toluene via drop drying, we have investigated the dependence of the island density, scaled island-size distribution (ISD), and scaled capture-zone distribution (CZD) on coverage, deposition flux, and NP size. Our results indicate that, while the critical island size is larger than 1 for all NP sizes studied, due to the increase in the strength of the SR attraction between NPs with increasing NP size, both the exponent describing the dependence of the island density on deposition flux and the critical island-size decrease with increasing NP size. We also find that, despite the existence of significant cluster diffusion and coalescence, the ISD is sharply peaked as in epitaxial growth. In particular, for large NP size, we find good agreement between the scaled ISD and epitaxial growth models as well as good agreement between the scaled CZD and scaled ISD. However, for smaller NPs the scaled ISD is less sharply peaked despite the fact that the critical island size is larger. This latter result suggests that in this case additional effects such as enhanced island coalescence or NP detachment from large islands may play an important role. Results for the ordering of NP islands are also presented which indicate the existence of LR repulsive interactions. One possible mechanism for such an interaction is the existence of a small dipole moment on each NP which arises as a result of an asymmetry, driven by surface tension, in the thiol distribution for NPs adsorbed at the toluene-air interface. Consistent with this mechanism, we find good agreement between experimental results for the nearest-neighbor island-distance distribution and simulations which include dipole repulsion.

Two-dimensional (2D) nuclear magnetic resonance (NMR) experiments involve a sequence of longitudinal $\left(T_1\right)$ and transverse $\left(T_2\right)$ measurements. When such experiments are applied to porous media, they are believed to provide new and important information regarding diffusive coupling between distinct pore subpopulations. However, we show in this paper that, in many cases of interest, this is simply not true. One often encounters systems in which the one-dimensional (1D) $T_1$ and $T_2$ processes are each controlled by just two distinct decay modes. If these modes form a complete set, then one can derive analytic formulas that describe, exactly, the 2D NMR measurements. Therefore, for such systems, the 2D measurements bring no additional information over that which is already present in the 1D results. Our predictions agree quite well with numerical results based on the microporous grain-consolidation $\left(\mu -\mathrm{GC}\right)$ model.

A bimesogen, BR1, composed of a bent-core and calamitic unit, linked laterally via a flexible spacer is investigated by dielectric and electro-optic techniques. X-ray results show the presence of clusters in the nematic phase, and the cluster size is of the order of the thickness of a single layer. The splitting of the small-angle scattering $\Delta \chi /2$ is about 50°, which indicates SmC like clusters with a significant tilt of the molecules in the quasilayers. The sign reversal of the dielectric anisotropy Δε′ is observed as a function of frequency; the behavior is rather similar to that exhibited by the conventional dual frequency nematics, composed of a calamitic mesogen, with the exception that it occurs at much lower frequencies in this material. Interestingly, as the bimesogen enters its nematic phase, the average permittivity decreases as the temperature is lowered. This indicates the onset of antiparallel association of some of the dipoles in the system, and this type of association is much more prominent in BR1 in comparison to other bent-core liquid crystalline systems composed of the same bisbenzoate core unit. The analysis of the dielectric spectra using the Maier-Meier model confirms the onset of an antiparallel correlation of dipoles occurring at the isotropic to nematic phase transition temperature. Additionally these results support a model of the cluster where the transverse dipole moments in the neighboring layers are antiparalleled to each other.

We identify problems with the standard complex order parameter formalism for smectic-A (SmA) liquid crystals and discuss possible alternative descriptions of smectic order. In particular, we suggest an approach based on the real smectic density variation rather than a complex order parameter. This approach gives reasonable numerical results for the smectic layer configuration and director field in sample geometries and can be used to model smectic liquid crystals under nanoscale confinement for technological applications.

We generalize the theory of $k\text{−}\mathrm{core}$ percolation on complex networks to $\mathbf{k}\text{−}\mathrm{core}$ percolation on multiplex networks, where $\mathbf{k}\equiv (k_1,k_2,...,k_M)$. Multiplex networks can be defined as networks with vertices of one kind but $M$ different types of edges, representing different types of interactions. For such networks, the $\mathbf{k}\text{−}\mathrm{core}$ is defined as the largest subgraph in which each vertex has at least $k_i$ edges of each type, $i=1,2,...,M$. We derive self-consistency equations to obtain the birth points of the $\mathbf{k}\text{−}\mathrm{cores}$ and their relative sizes for uncorrelated multiplex networks with an arbitrary degree distribution. To clarify our general results, we consider in detail multiplex networks with edges of two types and solve the equations in the particular case of Erdős-Rényi and scale-free multiplex networks. We find hybrid phase transitions at the emergence points of $\mathbf{k}\text{−}\mathrm{cores}$ except the $(1,1)$-core for which the transition is continuous. We apply the $\mathbf{k}\text{−}\mathrm{core}$ decomposition algorithm to air-transportation multiplex networks, composed of two layers, and obtain the size of $(k_1,k_2)$-cores.

We examine a weighted-network multiagent model with preferential selection such that agents choose partners with probability $p\left(w\right)$, where $w$ is the number of their past selections. When $p\left(w\right)$ increases sublinearly with the number of past selections $[p\left(w\right)\sim w^{\alpha },\alpha <1]$, agents develop a uniform preference for all other agents. At $\alpha =1$, this state loses stability and more complex structures form. For a superlinear increase $(\alpha >1)$, strong heterogeneities emerge and agents make selections mainly within small and sometimes asymmetric clusters. Even in a few-agent case, the formation of such clusters resembles phase transitions with spontaneous symmetry breaking.

We considered a clustered network of bursting neurons described by the Huber-Braun model. In the upper level of the network we used the connectivity matrix of the cat cerebral cortex network, and in the lower level each cortex area (or cluster) is modelled as a small-world network. There are two different coupling strengths related to inter- and intracluster dynamics. Each bursting cycle is composed of a quiescent period followed by a rapid chaotic sequence of spikes, and we defined a geometric phase which enables us to investigate the onset of synchronized bursting, as the state in which the neuron start bursting at the same time, whereas their spikes may remain uncorrelated. The bursting synchronization of a clustered network has been investigated using an order parameter and the average field of the network in order to identify regimes in which each cluster may display synchronized behavior, whereas the overall network does not. We introduce quantifiers to evaluate the relative contribution of each cluster in the partial synchronized behavior of the whole network. Our main finding is that we typically observe in the clustered network not a complete phase synchronized regime but instead a complex pattern of partial phase synchronization in which different cortical areas may be internally synchronized at distinct phase values, hence they are not externally synchronized, unless the coupling strengths are too large.

In stochastic block models, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A recent extension by Karrer and Newman [Karrer and Newman, Phys. Rev. E 83, 016107 (2011)] incorporates a node degree correction to model degree heterogeneity within each group. Although this demonstrably leads to better performance on several networks, it is not obvious whether modeling node degree is always appropriate or necessary. We formulate the degree corrected stochastic block model as a nonparametric Bayesian model, incorporating a parameter to control the amount of degree correction that can then be inferred from data. Additionally, our formulation yields principled ways of inferring the number of groups as well as predicting missing links in the network that can be used to quantify the model's predictive performance. On synthetic data we demonstrate that including the degree correction yields better performance on both recovering the true group structure and predicting missing links when degree heterogeneity is present, whereas performance is on par for data with no degree heterogeneity within clusters. On seven real networks (with no ground truth group structure available) we show that predictive performance is about equal whether or not degree correction is included; however, for some networks significantly fewer clusters are discovered when correcting for degree, indicating that the data can be more compactly explained by clusters of heterogenous degree nodes.

It has been commonly recognized that heterogeneously connected networks are robust against random decays but vulnerable to malicious attacks. However, little is known about measures of heterogeneity geared towards robustness of complex networks. Here, we propose two types of percolation on general networks triggered by random-link errors, where occupied links support the nodes to be alive. Rich resilience behaviors are observed in terms of the percolation threshold and the (integrated) fraction of giant cluster. The discrepancy unraveled between the two models allows us to dynamically define compact measures that have acute discrimination in gauging network heterogeneity. The results provide a connection between network performance, structure, and dynamics.

We investigate the statistical properties of the Barkhausen noise in amorphous ferromagnetic films with thicknesses in the range between 100 and 1000 nm. From Barkhausen noise time series measured with the traditional inductive technique, we perform a wide statistical analysis and establish the scaling exponents $\tau ,\alpha ,1/\sigma \nu z$, and $\vartheta$. We also focus on the average shape of the avalanches, which gives further indications on the domain-wall dynamics. Based on experimental results, we group the amorphous films in a single universality class, characterized by scaling exponents $\tau =1.28\pm 0.02,\alpha =1.52\pm 0.3$, and $1/\sigma \nu z=\vartheta =1.83\pm 0.03$, values compatible with that obtained for several bulk amorphous magnetic materials. Besides, we verify that the avalanche shape depends on the universality class. By considering the theoretical models for the dynamics of a ferromagnetic domain wall driven by an external magnetic field through a disordered medium found in literature, we interpret the results and identify an experimental evidence that these amorphous films, within this thickness range, present a typical three-dimensional magnetic behavior with predominant short-range elastic interactions governing the domain-wall dynamics. Moreover, we provide experimental support for the validity of a general scaling form for the average avalanche shape for non-mean-field systems.

We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone input. The nodes may have either a discrete or continuous set of states and there is no limit on the complexity of the network. The results provide both an efficient numerical method and the potential for accurate analytic approximation of the dynamics on such networks. As illustrative applications, we introduce a quasistatic mechanical model with objects interacting via frictional forces and a financial market model with avalanches and critical behavior that are generated by momentum trading strategies.