We investigate the flat phase of quantum polymerized phantom membranes by means of a nonperturbative renormalization group approach. We first implement this formalism for general quantum polymerized membranes and derive the flow equations that encompass both quantum and thermal fluctuations. We then deduce and analyze the flow equations relevant to study the flat phase and discuss their salient features: quantum to classical crossover and, in each of these regimes, strong to weak coupling crossover. We finally illustrate these features in the context of free-standing graphene physics.

Properties of the fiber bundle model have been studied using equal load-sharing dynamics where each fiber obeys a nonlinear stress ($s$)-strain ($x$) characteristic function $s=\mathcal{G}\left(x\right)$ till its breaking threshold. In particular, four different functional forms have been studied: $\mathcal{G}\left(x\right)=e^{\alpha x}, 1+x^{\alpha }, x^{\alpha }$, and $x{e}^{\alpha x}$ where $\alpha$ is a continuously tunable parameter of the model in all cases. Analytical studies, supported by extensive numerical calculations of this model, exhibit a brittle to quasibrittle phase transition at a critical value of ${\alpha }_c$ only in the first two cases. This transition is characterized by the weak power law modulated logarithmic (brittle) and logarithmic (quasibrittle) dependence of the relaxation time on the two sides of the critical point. Moreover, the critical load ${\sigma }_c\left(\alpha \right)$ for the global failure of the bundle depends explicitly on $\alpha$ in all cases. In addition, four more cases have also been studied, where either the nonlinear functional form or the probability distribution of breaking thresholds has been suitably modified. In all these cases similar brittle to quasibrittle transitions have been observed.

The efficiency of routing traffic through a network, comprising nodes connected by links whose cost of traversal is either fixed or varies in proportion to volume of usage, can be measured by the “price of anarchy.” This is the ratio of the cost incurred by agents who act to minimize their individual expenditure to the optimal cost borne by the entire system. As the total traffic load and the network variability—parameterized by the proportion of variable-cost links in the network—changes, the behaviors that the system presents can be understood with the introduction of a network of simpler structure. This is constructed from classes of nonoverlapping paths connecting source to destination nodes that are characterized by the number of variable-cost edges they contain. It is shown that localized peaks in the price of anarchy occur at critical traffic volumes at which it becomes beneficial to exploit ostensibly more expensive paths as the network becomes more congested. Simulation results verifying these findings are presented for the variation of the price of anarchy with the network's size, aspect ratio, variability, and traffic load.

Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated with a delayed process but instead use an estimated average delay time. In an effort to examine the validity of this approach, we study systems with significant delays by explicitly incorporating intermediate steps. We show that such explicit models often yield significantly different equilibrium distributions and transition times as compared to DDEs with deterministic delay values. Additionally, different explicit models with qualitatively different dynamics can give rise to the same DDEs revealing important ambiguities. We also show that DDE-based predictions of oscillatory behavior may fail for the corresponding explicit model.

The onset of irreversible deformation in low-temperature amorphous solids is due to the accumulation of elementary events, consisting of spatially and temporally localized atomic rearrangements involving only a few tens of atoms. Recently, numerical and experimental work addressed the issue of spatiotemporal correlations between these plastic events. Here, we provide further insight into these correlations by investigating, via molecular dynamics (MD) simulations, the plastic response of a two-dimensional amorphous solid to artificially triggered local shear transformations. We show that while the plastic response is virtually absent in as-quenched configurations, it becomes apparent if a shear strain was previously imposed on the system. Plastic response has a fourfold symmetry, which is characteristic of the shear stress redistribution following the local transformation. At high shear rate we report evidence for a fluctuation-dissipation relation, connecting plastic response and correlation, which seems to break down if lower shear rates are considered.

The self-propulsion of a three-dimensional flapping flexible plate near the ground is studied using an immersed boundary-lattice Boltzmann method for fluid flow and a finite-element method for plate motion. When the leading edge of the flexible plate is forced into a vertical oscillation near the ground, the entire plate moves freely due to the fluid-structure interaction. The mechanisms underlying the dynamics of the plate near the ground are elucidated. Based on the propulsive behaviors of the flapping plate, three distinct regimes due to the ground effect can be qualitatively identified. These regimes can be described briefly as the expensive, benefited, and uninfluenced propulsion regimes. The analysis of unsteady dynamics and plate deformation indicates that the ground effect becomes weaker for a more flexible plate. We have found that a suitable degree of flexibility can improve propulsion near the ground. The vortical structure around the plate and the pressure distribution on the plate are analyzed to understand propulsive behaviors. The results obtained in this study can provide some physical insights into the propulsive mechanisms of a flapping flexible plate near the ground.

Radially polarized intense terahertz (THz) radiation behind a thin foil irradiated by ultrahigh-contrast ultrashort relativistic laser pulse is recorded by a single-shot THz time-domain spectroscopy system. As the thickness of the target is reduced from 30 to 2 µm, the duration of the THz emission increases from 5 to over 20 ps and the radiation energy increases dramatically, reaching $\sim 10.5\mathrm{mJ}$ per pulse, corresponding to a laser-to-THz radiation energy conversion efficiency of $1.7\%$. The efficient THz emission can be attributed to reflection (deceleration and acceleration) of the laser-driven hot electrons by the target-rear sheath electric field. The experimental results are consistent with that of a simple model as well as particle-in-cell simulation.

Continuum percolation of randomly orientated congruent overlapping spherocylinders (composed of cylinder of height $H$ with semispheres of diameter $D$ at the ends) with aspect ratio $\alpha =H/D$ in $[0,\infty )$ is studied. The percolation threshold ${\varphi }_c$, percolation transition width Δ, and correlation-length critical exponent $\nu$ for spherocylinders with $\alpha$ in [0, 200] are determined with a high degree of accuracy via extensive finite-size scaling analysis. A generalized excluded-volume approximation for percolation threshold with an exponent explicitly depending on both aspect ratio and excluded volume for arbitrary $\alpha$ values in $[0,\infty )$ is proposed and shown to yield accurate predictions of ${\varphi }_c$ for an extremely wide range of $\alpha$ in [0, 2000] based on available numerical and experimental data. We find ${\varphi }_c$ is a universal monotonic decreasing function of $\alpha$ and is independent of the effective particle size. Our study has implications in percolation theory for nonspherical particles and composite material design.

We study the evolution of binary mixtures far from equilibrium, and show that the interplay between phase separation and hydrodynamic instability can arrest the Ostwald ripening process characteristic of nonflowing mixtures. We describe a model binary system in a Hele-Shaw cell using a phase-field approach with explicit dependence of both phase fraction and mass concentration. When the viscosity contrast between phases is large (as is the case for gas and liquid phases), an imposed background flow leads to viscous fingering, phase branching, and pinch off. This dynamic flow disorder limits phase growth and arrests thermodynamic coarsening. As a result, the system reaches a regime of statistical steady state in which the binary mixture is permanently driven away from equilibrium.

While there are intensive studies on the coalescence of sessile macroscale droplets, there is little study on the coalescence of sessile microdroplets. In this paper, the coalescence process of two sessile microdroplets is studied by using a many-body dissipative particle dynamics numerical method. A comprehensive parametric study is conducted to investigate the effects on the coalescence process from the wettability gradient, hydrophilicity of the solid surface, and symmetric or asymmetric configurations. A water bridge is formed after two microdroplets contact. The temporal evolution of the coalescence process is characterized by the water bridge's radii parallel to the solid surface $\left(W_m\right)$ and perpendicular to the solid surface $\left(H_m\right)$. It is found that the changes of both $H_m$ and $W_m$ with time follow a power law; i.e., $H_m={\beta }_1{\tau }^{\beta }$ and $W_m={\alpha }_1{\tau }^{\alpha }$. The growth of $H_m$ and $W_m$ depends on the hydrophilicity of the substrate. $W_m$ grows faster than $H_m$ on a hydrophilic surface, and $H_m$ grows faster than $W_m$ on a hydrophobic surface. This is due to the strong competition between capillary forces induced by the water-bridge curvature and the solid substrate hydrophobicity. Also, flow structure analysis shows that regardless of the coalescence type once the liquid bridge is formed the liquid flow direction inside the capillary bridge is to expand the bridge radius. Finally, we do not observe oscillation of the merged droplet during the coalescence process, possibly due to the significant effects of the viscous forces.

The target Lagrangian kinematic simulation method was motivated as a stochastic Lagrangian particle model that better synthesizes turbulence structure, relative to stochastic separated flow models. By this method, the trajectories of particles are constructed according to synthetic turbulent-like fields, which conform to a target Lagrangian integral timescale. In addition to recovering the expected Lagrangian properties of fluid tracers, this method is shown to reproduce the crossing trajectories and continuity effects, in agreement with an experimental benchmark.

The chiral spin-glass Potts system with $q=3$ states is studied in $d=2$ and 3 spatial dimensions by renormalization-group theory and the global phase diagrams are calculated in temperature, chirality concentration $p$, and chirality-breaking concentration $c$, with determination of phase chaos and phase-boundary chaos. In $d=3$, the system has ferromagnetic, left-chiral, right-chiral, chiral spin-glass, and disordered phases. The phase boundaries to the ferromagnetic, left- and right-chiral phases show, differently, an unusual, fibrous patchwork (microreentrances) of all four (ferromagnetic, left-chiral, right-chiral, chiral spin-glass) ordered phases, especially in the multicritical region. The chaotic behavior of the interactions, under scale change, are determined in the chiral spin-glass phase and on the boundary between the chiral spin-glass and disordered phases, showing Lyapunov exponents in magnitudes reversed from the usual ferromagnetic-antiferromagnetic spin-glass systems. At low temperatures, the boundaries of the left- and right-chiral phases become thresholded in $p$ and $c$. In $d=2$, the chiral spin-glass Potts system does not have a spin-glass phase, consistently with the lower-critical dimension of ferromagnetic-antiferromagnetic spin glasses. The left- and right-chirally ordered phases show reentrance in chirality concentration $p$.

We analyze the dynamics of a large network of coupled quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The network is heterogeneous in that it includes both inherently spiking and excitable neurons. The coupling is global via synapses that take into account the finite width of synaptic pulses. Using a recently developed reduction method based on the Lorentzian ansatz, we derive a closed system of equations for the neuron's firing rate and the mean membrane potential, which are exact in the infinite-size limit. The bifurcation analysis of the reduced equations reveals a rich scenario of asymptotic behavior, the most interesting of which is the macroscopic limit-cycle oscillations. It is shown that the finite width of synaptic pulses is a necessary condition for the existence of such oscillations. The robustness of the oscillations against aging damage, which transforms spiking neurons into nonspiking neurons, is analyzed. The validity of the reduced equations is confirmed by comparing their solutions with the solutions of microscopic equations for the finite-size networks.

In recent years, many variants of percolation have been used to study network structure and the behavior of processes spreading on networks. These include bond percolation, site percolation, $k$-core percolation, bootstrap percolation, the generalized epidemic process, and the Watts threshold model (WTM). We show that—except for bond percolation—each of these processes arises as a special case of the WTM, and bond percolation arises from a small modification. In fact “heterogeneous $k$-core percolation,” a corresponding “heterogeneous bootstrap percolation” model, and the generalized epidemic process are completely equivalent to one another and the WTM. We further show that a natural generalization of the WTM in which individuals “transmit” or “send a message” to their neighbors with some probability less than 1 can be reformulated in terms of the WTM, and so this apparent generalization is in fact not more general. Finally, we show that in bond percolation, finding the set of nodes in the component containing a given node is equivalent to finding the set of nodes activated if that node is initially activated and the node thresholds are chosen from the appropriate distribution. A consequence of these results is that mathematical techniques developed for the WTM apply to these other models as well, and techniques that were developed for some particular case may in fact apply much more generally.

In this work, we aim to contribute to the understanding of human prosocial behavior by studying the influence that a particular form of social pressure, “being watched,” has on the evolution of cooperative behavior. We study how cooperation emerges in multiplex complex topologies by analyzing a particular bidirectionally coupled dynamics on top of a two-layer multiplex network (duplex). The coupled dynamics appears between the prisoner's dilemma game in a network and a threshold cascade model in the other. The threshold model is intended to abstract the behavior of a network of vigilant nodes that impose the pressure of being observed altering hence the temptation to defect of the dilemma. Cooperation or defection in the game also affects the state of a node of being vigilant. We analyze these processes on different duplex networks structures and assess the influence of the topology, average degree and correlated multiplexity, on the outcome of cooperation. Interestingly, we find that the social pressure of vigilance may impact cooperation positively or negatively, depending on the duplex structure, specifically the degree correlations between layers is determinant. Our results give further quantitative insights in the promotion of cooperation under social pressure.

A commonly used assumption in evolutionary game theory is that natural selection acts on individuals in the same time scale; e.g., players use the same frequency to update their strategies. Variation in learning rates within populations suggests that evolutionary game theory may not necessarily be restricted to uniform time scales associated with the game interaction and strategy adaption evolution. In this study, we remove this restricting assumption by dividing the population into fast and slow groups according to the players' strategy updating frequencies and investigate how different strategy compositions of one group influence the evolutionary outcome of the other's fixation probabilities of strategies within its own group. Analytical analysis and numerical calculations are performed to study the evolutionary dynamics of strategies in typical classes of two-player games (prisoner's dilemma game, snowdrift game, and stag-hunt game). The introduction of the heterogeneity in strategy-update time scales leads to substantial changes in the evolution dynamics of strategies. We provide an approximation formula for the fixation probability of mutant types in finite populations and study the outcome of strategy evolution under the weak selection. We find that although heterogeneity in time scales makes the collective evolutionary dynamics more complicated, the possible long-run evolutionary outcome can be effectively predicted under technical assumptions when knowing the population composition and payoff parameters.

Fluctuation-induced interactions are an important organizing principle in a variety of soft matter systems. We investigate the role of fluctuation-based or thermal Casimir interactions between cross linkers in a semiflexible network. One finds that, by integrating out the polymer degrees of freedom, there is an attractive logarithmic potential between nearest-neighbor cross linkers in a bundle, with a significantly weaker next-nearest-neighbor interaction. Here we show that a one-dimensional gas of these strongly interacting linkers in equilibrium with a source of unbound ones admits a discontinuous phase transition between a sparsely and a densely bound bundle. This discontinuous transition induced by the long-ranged nature of the Casimir interaction allows for a similarly abrupt structural transition in semiflexible filament networks between a low cross linker density isotropic phase and a higher cross link density bundle network. We support these calculations with the results of finite element Brownian dynamics simulations of semiflexible filaments and transient cross linkers.

We present large-scale molecular dynamics simulations to study the free evolution of granular gases. Initially, the density of particles is homogeneous and the velocity follows a Maxwell-Boltzmann (MB) distribution. The system cools down due to solid friction between the granular particles. The density remains homogeneous, and the velocity distribution remains MB at early times, while the kinetic energy of the system decays with time. However, fluctuations in the density and velocity fields grow, and the system evolves via formation of clusters in the density field and the local ordering of velocity field, consistent with the onset of plug flow. This is accompanied by a transition of the velocity distribution function from MB to non-MB behavior. We used equal-time correlation functions and structure factors of the density and velocity fields to study the morphology of clustering. From the correlation functions, we obtain the cluster size, $L$, as a function of time, $t$. We show that it exhibits power law growth with $L\left(t\right)\sim t^{1/3}$.

We are inspired by the tensile buckling of a thin sheet with a slit to create a foldable planar metamaterial. The buckled shape comprises two pairs of identical e-cones connected to the slit, which we refer to as a k-cone. We approximate this shape as discrete vertices that can be folded out of plane as the slit is pulled apart. We determine their kinematics and we calculate generic shape properties using a simple elastic model of the folded shape. We then show how the folded sheet may be tessellated as a unit cell within a larger sheet, which may be constructed a priori by cutting and folding the latter in a regular way, in order to form a planar kirigami structure with a single degree of freedom.

The structural properties of liquid silica at high pressure and moderate temperature conditions, also referred to as the warm dense matter regime, were investigated using time-resolved $K$-edge x-ray absorption spectroscopy and ab initio calculations. We used a nanosecond laser beam to compress uniformly a solid $\mathrm{Si}{\mathrm{O}}_2$ target and a picosecond laser beam to generate a broadband x-ray source. We obtained x-ray absorption spectra at the Si $K$ edge over a large pressure-temperature domain to probe the liquid phase up to 3.6 times the normal solid density. Using ab initio simulations, we are able to interpret the changes in the x-ray absorption near-edge structure with increasing densities as an increase in the coordination number of silicon by oxygen atoms from 4 to 9. This indicates that, up to significant temperatures, the liquid structure becomes akin to what is found in the solid $\mathrm{Si}{\mathrm{O}}_2$ phases.