We introduce a family of complex networks that interpolates between the Apollonian network and its binary version, recently introduced in E. M. K. Souza et al. [Phys. Rev. E 107, 024305 (2023)], via random removal of nodes. The dilution process allows the clustering coefficient to vary from $C=0.828$ to $C=0$ while maintaining the behavior of average path length and other relevant quantities as in the deterministic Apollonian network. Robustness against the random deletion of nodes is also reported on spectral quantities such as the ground-state localization degree and its energy gap to the first excited state. The loss of the $2\pi /3$ rotation symmetry as a treelike network emerges is investigated in the light of the hub wavefunction amplitude. Our findings expose the interplay between the small-world property and other distinctive traits exhibited by Apollonian networks, as well as their resilience against random attacks.

Optically responsive liquid crystal elastomer (LCE) devices have thriving potential to flourish in soft robots and microdrives, owing to their advantages of remote controllability, structural simplicity, and no power supply. In terms of illumination-driven modes, most research has focused on the dynamic response of LCE devices under continuous and periodic illumination, while the theoretical study of the dynamic response under moving illumination is limited. In this paper, based on the coupling of LCE and mechanical deformation under moving illumination, the dynamic model of a LCE simply supported beam is built to investigate its dynamic response under moving illumination. The analytical solution of the dynamic response of the LCE beam under moving illumination is derived through the modal superposition method and the Duhamel integration, and the solution is programed and analyzed with matlab software. By numerical calculations, the influence of the internal and driving parameters of the structure on the dynamic response of the LCE simply supported beam can be analyzed. The results show that when the moving speed of illumination reaches the first-order critical frequency, the maximum amplitude of the dynamic response at the beam mid-span will reach a peak. Meanwhile, the dynamic response of beam can be improved by increasing the illumination width, increasing the light intensity, increasing the shrinkage coefficient, and reducing the damping coefficient. This work provides theoretical guidance for applying the dynamic response of LCE devices under moving illumination in soft robots, microactuators, energy harvesters, sensors, etc.

The mechanical behavior of granular materials results from interparticle interactions, which are predominantly frictional. With the presence of even very small amounts of cohesion this frictional interparticle behavior significantly changes. In this study, we introduce trace amounts of cohesive binder between the intergranular contacts in a sample of quartz particles and apply one-dimensional (1D) compression loading. X-ray computed tomography is performed in situ during 1D compression. We make observations at three different length scales. At the macroscopic or ensemble scale, we track the evolution of the porosity, particle size and the stress-strain response during this compression. At the microstructure or interparticle scale, we compute the directional distribution of contacts and the particles. We also track the evolution of the fabric chains with continued compression. We also evaluate particle rotations, displacements, contact twist, rotation, and sliding. We show through our experiments that even a small amount of cohesion (as low as 1% by weight) significantly changes the response at multiple length scales. This interparticle cohesion suppresses the fragmentation of grains, alters force transmission and changes the structure of the ensemble.

Many fibrous materials are modeled as elastic networks featuring a substantial separation between the stiffness scales that characterize different microscopic deformation modes of the network's constituents. This scale separation has been shown to give rise to emergent complexity in these systems' linear and nonlinear mechanical response. Here we study numerically a simple model featuring said stiffness scale separation in two-dimensions and show that its mechanical response is governed by the competition between the characteristic stiffness of collective nonphononic soft modes of the stiff subsystem, and the characteristic stiffness of the soft interactions. We present and rationalize the behavior of the shear modulus of our complex networks across the unjamming transition at which the stiff subsystem alone loses its macroscopic mechanical rigidity. We further establish a relation in the soft-interaction-dominated regime between the shear modulus, the characteristic frequency of nonphononic vibrational modes, and the mesoscopic correlation length that marks the crossover from a disorder-dominated response to local mechanical perturbations in the near field, to a linear, continuumlike response in the far field. The effects of spatial dimension on the observed scaling behavior are discussed, in addition to the interplay between stiffness scales in strain-stiffened networks, which is relevant to understanding the nonlinear mechanics of non-Brownian fibrous biomatter.

A wide variety of engineered and natural systems are modeled as networks of coupled nonlinear oscillators. In nature, the intrinsic frequencies of these oscillators are not constant in time. Here, we probe the effect of such a temporal heterogeneity on coupled oscillator networks through the lens of the Kuramoto model. To do this, we shuffle repeatedly the intrinsic frequencies among the oscillators at either random or regular time intervals. What emerges is the remarkable effect that frequent shuffling induces earlier onset (i.e., at a lower coupling) of synchrony among the oscillator phases. Our study provides a novel strategy to induce and control synchrony under resource constraints. We demonstrate our results analytically and in experiments with a network of Wien Bridge oscillators with internal frequencies being shuffled in time.

We investigate the effect of a finite particle number $N$ on the violent relaxation leading to the quasistationary state (QSS) in a one-dimensional self-gravitating system. From the theoretical point of view, we demonstrate that the local Poissonian fluctuations embedded in the initial state give rise to an additional term proportional to $1/N$ in the Vlasov equation. This term designates the strength of the local mean-field variations by fluctuations. Because it is of the mean-field origin, we interpret it differently from the known collision term in the way that it effects the violent relaxation stage. Its role is to deviate the distribution function from the Vlasov limit, in the collisionless manner, at a rate proportional to $1/N$ while the violent relaxation is progressing. This hypothesis is tested by inspecting the QSSs in simulations of various $N$. We observe that the core phase-space density can exceed the limiting density deduced from the Vlasov equation and its deviation degree is in accordance with the $1/N$ estimate. This indicates the deviation from the standard mean-field approximation of the violent relaxation process by that $1/N$ term. In conclusion, the finite-$N$ effect has a significant contribution to the QSS apart from that it plays a role in the collisional stage that takes place long after. The conventional collisionless Vlasov equation might not be able to describe the violent relaxation of a system of particles properly without the correction term of the local finite-$N$ fluctuations.

Hard-sphere (HS) shear, longitudinal, cross, and bulk viscosities and the thermal conductivity are obtained by molecular dynamics (MD) simulations, covering the entire density range from the dilute fluid to the solid crystal near close-packing. The transport coefficient data for the HS crystal are largely new and display, unlike for the fluid, a surprisingly simple behavior in that they can be represented well by a simple function of the density compressibility factor. In contrast to the other four transport coefficients (which diverge), the bulk viscosity in the solid is quite small and decreases rapidly with increasing density, tending to zero in the close-packed limit. The so-called cross viscosity exhibits a different behavior to the other viscosities, in being negative over the entire solid range, and changes sign from negative to positive on increasing the density in the fluid phase. The extent to which the viscosity tensor and thermal conductivity of the HS crystal can be represented by revised Enskog theory (RET) is investigated. The RET expressions are sums of an instantaneous $\left(I\right)$, a kinetic $\left(K\right)$, and a so-called $\alpha$ part. The $I$ part of the transport coefficients evaluated directly by MD are statistically indistinguishable from those of the corresponding kinetic theory (Enskog and RET) expressions. For the $K$ part the integral over the spatial two-particle distribution function at contact was determined and the $\alpha$ part was estimated using the direct correlation function and density functional theory approximations. All three parts were determined in this work which allowed the accuracy of RET for solid systems to be assessed rigorously. It is found that in the case of the thermal conductivity the predictions of RET are in excellent agreement with the MD results. Also, for the shear viscosity the agreement over the entire solid phase is quite good but is considerably worse for the three remaining viscosities in the solid phase.

The complexity of quantum evolutions can be understood by examining their spread in a chosen basis. Recent research has stressed the fact that the Krylov basis is particularly adept at minimizing this spread [Balasubramanian et al., Phys. Rev. D 106, 046007 (2022)]. This property assigns a central role to the Krylov basis in the investigation of quantum chaos. Here, we delve into the transition from integrability to chaos using the Krylov approach, employing an Ising spin chain and a banded random matrix model as our testing models. Our findings indicate that both the saturation of Krylov complexity and the spread of the Lanczos coefficients can exhibit a significant dependence on the initial condition. However, both quantities can gauge dynamical quantum chaos with a proper choice of the initial state.

The propagation of wave trains resulting from a local external trigger inside a network described by a metric graph is analyzed using quantum graph theory. The external trigger is a finite-time perturbation imposed at one vertex of the graph, leading to a consecutive wave train into the network, supposedly at rest before the applied external perturbation. A complete analytical solution for the induced wave train is found having a specific spectrum as well as mode's amplitudes. Furthermore the precise condition by which the external trigger can transfer a maximal energy to any specific natural mode of the quantum graph is derived. Finally, the wave damping associated with boundary-layer dissipation is computed within a multiple time-scale asymptotic analysis. Exponential damping rates are explicitly found related to their corresponding mode's eigenvalue. Each mode energy is then obtained, as well as their exponential damping rate. The relevance of these results to the physics of waves within networks are discussed.

Recent findings suggest that shell protein distribution and the morphology of bacterial microcompartments regulate the chemical fluxes facilitating reactions which dictate their biological function. We explore how the morphology and component patterning are coupled through the competition of mean and gaussian bending energies in multicomponent elastic shells that form three-component irregular polyhedra. We observe two softer components with lower bending rigidities allocated on the edges and vertices while the harder component occupies the faces. When subjected to a nonzero interfacial line tension, the two softer components further separate and pattern into subdomains that are mediated by the gaussian curvature. We find that this degree of fractionation is maximized when there is a weaker line tension and when the ratio of bending rigidities between the two softer domains $\approx 2$. Our results reveal a patterning mechanism in multicomponent shells that can capture the observed morphologies of bacterial microcompartments, and moreover, can be realized in synthetic vesicles.

One of the key hallmarks of dense active matter in the liquid, supercooled, and solid phases is the so-called equal-time velocity correlations. Crucially, these correlations can emerge spontaneously, i.e., they require no explicit alignment interactions, and therefore represent a generic feature of dense active matter. This indicates that for a meaningful comparison or possible mapping between active and passive liquids one not only needs to understand their structural properties, but also the impact of these velocity correlations. This has already prompted several simulation and theoretical studies, though they are mostly focused on athermal systems and thus overlook the effect of translational diffusion. Here, we present a fully microscopic method to calculate nonequilibrium correlations in two-dimensional systems of thermal active Brownian particles (ABPs). We use the integration through transients formalism together with (active) mode-coupling theory and analytically calculate qualitatively consistent static structure factors and active velocity correlations. We complement our theoretical results with simulations of both thermal and athermal ABPs which exemplify the disruptive role that thermal noise has on velocity correlations.

Holevo introduced a fidelity between quantum states that is symmetric and as effective as the trace distance in evaluating their similarity. This fidelity is bounded by a function of the trace distance, a relationship to which we will refer as Holevo's inequality. More broadly, Holevo's fidelity is part of a one-parameter family of symmetric Petz-Rényi relative entropies, which in turn satisfy a Pinsker's-like inequality with respect to the trace distance. Although Holevo's inequality is tight, Pinsker's inequality is loose for this family. We show that the symmetric Petz-Rényi relative entropies satisfy a tight inequality with respect to the trace distance, improving Pinsker's and reproducing Holevo's as a specific case. Additionally, we show how this result emerges from a symmetric Petz-Rényi uncertainty relation, a result that encompasses several relations in quantum and stochastic thermodynamics.

Driven classical self-sustained oscillators have been studied extensively in the context of synchronization. Using the master equation, this work considers the classically driven generalized quantum Rayleigh–van der Pol oscillator, which is characterized by linear dissipative gain and loss terms as well as three nonlinear dissipative terms. Since two of the nonlinear terms break the rotational phase space symmetry, the Wigner distribution of the quantum mechanical limit cycle state of the undriven system is, in general, not rotationally symmetric. The impact of the symmetry-breaking dissipators on the long-time dynamics of the driven system are analyzed as functions of the drive strength and detuning, covering the deep quantum to near-classical regimes. Phase localization and frequency entrainment, which are required for synchronization, are discussed in detail. We identify a large parameter space where the oscillators exhibit appreciable phase localization but only weak or no entrainment, indicating the absence of synchronization. Several observables are found to exhibit the analog of the celebrated classical Arnold tongue; in some cases, the Arnold tongue is found to be asymmetric with respect to vanishing detuning between the external drive and the natural oscillator frequency.

Cells that collide with each other repolarize away from contact, in a process called contact inhibition of locomotion (CIL), which is necessary for correct development of the embryo. CIL can occur even when cells make a micron-scale contact with a neighbor—much smaller than their size. How precisely can a cell sense cell-cell contact and repolarize in the correct direction? What factors control whether a cell recognizes it has contacted a neighbor? We propose a theoretical model for the limits of CIL where cells recognize the presence of another cell by binding the protein ephrin with the Eph receptor. This recognition is made difficult by the presence of interfering ligands that bind nonspecifically. Both theoretical predictions and simulation results show that it becomes more difficult to sense cell-cell contact when it is difficult to distinguish ephrin from the interfering ligands, or when there are more interfering ligands, or when the contact width decreases. However, the error of estimating contact position remains almost constant when the contact width changes. This happens because the cell gains spatial information largely from the boundaries of cell-cell contact. We study using statistical decision theory the likelihood of a false-positive CIL event in the absence of cell-cell contact, and the likelihood of a false negative where CIL does not occur when another cell is present. Our results suggest that the cell is more likely to make incorrect decisions when the contact width is very small or so large that it nears the cell's perimeter. However, in general, we find that cells have the ability to make reasonably reliable CIL decisions even for very narrow (micron-scale) contacts, even if the concentration of interfering ligands is ten times that of the correct ligands.

Optimization of the mean completion time of random processes by restart is a subject of active theoretical research in statistical physics and has long found practical application in computer science. Meanwhile, one of the key issues remains largely unsolved: how to construct a restart strategy for a process whose detailed statistics are unknown to ensure that the expected completion time will reduce? Addressing this query here we propose several constructive criteria for the effectiveness of various protocols of noninstantaneous restart in the mean completion time problem and in the success probability problem. Being expressed in terms of a small number of easily estimated statistical characteristics of the original process (MAD, median completion time, low-order statistical moments of completion time), these criteria allow informed restart decision based on partial information.

We study the transition to synchronization in an ensemble of chaotic oscillators that are interacting on a star network. These oscillators possess an invariant symmetry and we study emergent behavior by introducing the timescale variations in the dynamics of the nodes and the hub. If the coupling preserves the symmetry, the ensemble exhibits consecutive explosive transitions, each one associated with a hysteresis. The first transition is the explosive synchronization from a desynchronized state to a synchronized state which occurs discontinuously with the formation of intermediate clusters. These clusters appear because of the driving-induced multistability and the resulting attractors exhibit intermittent synchrony (antisynchrony). The second transition is the explosive death that occurs as a result of stabilization of the stable fixed points. However, if the symmetry is not preserved, the system again makes a first-order transition from an oscillatory state to death, namely, an explosive death. These transitions are studied with the help of the master stability functions, Lyapunov exponents, and the stability analysis.

Rayleigh-Taylor instability (RTI) is observed in soft materials that have significant resistance to yield. Estimating the instability threshold is critical to several engineering applications and has been the topic of several studies in past decades. However, limited attention has been given to the elastic-to-plastic (EP) transition threshold, where material properties vary significantly. This study explores the phase transition between the pure elastic and stable plastic regimes in RTI in a soft solid (mayonnaise) using a rotating wheel experimental setup with a time-varying acceleration profile. The material properties of the soft solid are characterized using rheological techniques. Different initial perturbation wavelength and amplitude combinations are used to analyze their role in the EP transition threshold and the subsequent maximum fully recoverable elastic strain. The effects of the initial perturbation dimensions, the steepness of the perturbation, and the mass of the perturbation on the stability of the samples, the EP transition thresholds, and the maximum fully recoverable elastic strains are analyzed. The samples with the largest full elastic recovery potentials and the parameters governing this phenomenon are identified, and the physics behind it is discussed. It is observed that increasing the initial perturbation wavelength decreases the required phase transition acceleration while increasing the maximum fully recoverable elastic strain. Finally, nondimensional parameters that involve the perturbation dimensions, as well as the mechanical properties of the material, are introduced to provide a generalized approach to the problem.

A coarse-grained molecular Monte Carlo simulation of the barocaloric effect in a model Gay-Berne liquid crystal is presented, following the so-called indirect approach wherein the caloric response is obtained from thermodynamic arguments applied to the simulated equilibrium relation between pressure, density, and temperature. From simulation, the magnitude of the effect across the isotropic-nematic and nematic-smectic phase transitions is estimated, together with the heat exchanged outside these transitions, in order to assess its potential for novel cooling and heat pumping applications. Under adiabatic conditions, pressure-induced phase transitions are predicted to result in a temperature variation of a few degrees Kelvin. As a by-product of the simulation, an approximate partial phase diagram of the Gay-Berne fluid under study is also obtained.

We consider the persistent voter model (PVM), a variant of the voter model (VM) that includes transient, dynamically induced zealots. Due to peer reinforcement, the internal confidence ${\eta }_i$ of a normal voter increases in steps of size $\mathrm{\Delta }\eta$. Once it surpasses a given threshold, it becomes a zealot. Its opinion remains frozen until enough interactions with the opposing opinion occur, resetting its confidence. No longer a zealot, the regular voter may change opinion once again. This mechanism of opinion inertia, though simplified, is responsible for an effective surface tension, and the PVM exhibits a crossover from a fluctuation-driven dynamics, as in the VM, to a curvature-driven one, akin to the Ising model at low temperature. The average time $\tau$ to attain consensus is nonmonotonic with respect to $\mathrm{\Delta }\eta$ and reaches a minimum at $\mathrm{\Delta }{\eta }_{min}$. In this paper we elucidate the mechanisms that accelerate the system towards consensus close to $\mathrm{\Delta }{\eta }_{min}$. Near the crossover at $\mathrm{\Delta }{\eta }_{min}$, the intermediate region around the domains where the regular voters accumulate (the active region, AR) is large. The surface tension, albeit small, is sufficient to maintain the shape and reduce the domain fragmentation. The large size of the AR in the region of $\mathrm{\Delta }{\eta }_{min}$ has two important effects that accelerate the dynamics. First, it dislodges the zealots within the bulk of the domains. Secondly, it maximally suppresses the formation of slowly evolving stripes typical in Ising-like models. This suggests the importance of understanding the role of the AR, where opinion changes are facilitated, and the interplay between regular voters and zealots in disrupting polarized states.