Identifying and extracting topological characteristics are essential for understanding associated structures and organizational principles of complex networks. For temporal networks where the network topology varies with time, beyond the classical patterns such as small-worldness and scale-freeness extracted from the perspective of traditional aggregated static networks, the temporality and simultaneity of time-varying interactions should also be included. Here we extend the traditional analysis on the local clustering coefficient $C$ in static networks and study the dynamical local clustering coefficient of temporal networks. We demonstrate that the temporal local clustering coefficient $TC$ conveys the hidden information of nodes' neighboring connectance when interactions occur at various rhythms. By systematically analyzing various empirical datasets, we find that $TC$ uncovers different interaction patterns in different types of temporal networks. Specifically, we show that $TC$ has a strong positive correlation with $C$ in efficiency-related networks, whereas they are uncorrelated in social activity-related networks. Moreover, $TC$ helps to exclude interference from accidental interactions and reflect the actual clustering properties of network nodes. Our results shed light on the importance of digging into dynamical characteristics to fundamentally understand the underlying temporal structures of real complex systems.

Polymer dispersed liquid crystal (PDLC) films are formed of droplets of liquid crystal (LC) held in a polymer matrix. Similar to aligned LC films, PDLCs exhibit the acousto-optic (AO) effect when excited by acoustic waves of sufficient amplitude, whereby the PDLC film becomes transparent in the excited regions (acoustic clearing). Despite decades of research there is still debate over the mechanisms of the AO effect for the case of LC films, with several competing theories, and AO effects in PDLC have not been studied theoretically. This paper explores the AO effect in PDLC both experimentally and theoretically, and attempts a theoretical description of the observed phenomena based on the theoretical approach by Selinger et al. for aligned LC films. The acousto-optic effect in PDLC is shown to be due to direct interaction of acoustic waves with LC droplets, rather than due to compression of the droplet itself. Polarizing microscopy revealed changes in droplet shape at excited points. This is consistent with reorientation as a contributing factor, possibly coexisting with flows at higher excitation powers. In previous experimental studies PDLC films were prepared with cover slides, in the same way as LC AO cells, significantly limiting applications by adding complexity to the design. Also, to exhibit AO clearing it was considered that the PDLC needed to be prepared with high LC concentrations (over 75% by weight). We demonstrate that no cover slide is necessary, and that PDLC coatings without a cover have improved sensitivity to acoustic waves. We demonstrate the AO effect for LC concentrations as low as 40% by weight. The ability to use standard composition PDLC, with no top cover, is paving the way to paint-on visual ultrasound sensors.

We reveal and analyze an efficient magnetic dynamo action due to precession-driven hydrodynamic turbulence in the local model of a precessional flow, focusing on the kinematic stage of this dynamo. The growth rate of the magnetic field monotonically increases with the Poincaré number $\mathrm{Po}$, characterizing precession strength, and the magnetic Prandtl number $\mathrm{Pm}$, equal to the ratio of viscosity to resistivity, for the considered ranges of these parameters. The critical ${\mathrm{Po}}_c$ for the dynamo onset decreases with increasing $\mathrm{Pm}$. To understand the scale-by-scale evolution (growth) of the precession dynamo and its driving processes, we perform spectral analysis by calculating the spectra of magnetic energy and of different terms in the induction equation in Fourier space. To this end, we decompose the velocity field of precession-driven turbulence into two-dimensional (2D) vortical and three-dimensional (3D) inertial wave modes. It is shown that the dynamo operates across a broad range of scales and exhibits a remarkable transition from a primarily vortex-driven regime at lower $\mathrm{Po}$ to a more complex regime at higher $\mathrm{Po}$ where it is driven jointly by vortices, inertial waves, and the shear of the background precessional flow. Vortices and shear drive the dynamo mostly at large scales comparable to the flow system size, and at intermediate scales, while at smaller scales it is mainly driven by inertial waves. This study can be important not only for understanding the magnetic dynamo action in precession-driven flows, but also in a general context of flows where vortices emerge and govern the flow dynamics and evolution.

We use analytical methods and particle-in-cell simulation to investigate the origin of electrons accelerated by the process of direct laser acceleration driven by high-power laser pulses in preformed narrow cylindrical plasma channels. The simulation shows that the majority of accelerated electrons are originally located along the interface between the channel wall and the channel interior. The analytical model based on the electron hydrodynamics illustrates the underlying physical mechanism of the release of electrons from the channel wall when irradiated by an intense laser, the subsequent electron dynamics, and the corresponding evolution of the channel density profile. The quantitative predictions of the total charge of released electrons and the average electron density inside the channel are validated by comparison with the simulation results.

Emergent nonreciprocal interactions violating Newton's third law are widespread in out-of-equilibrium systems. Phase separating mixtures with such interactions exhibit traveling states with no equilibrium counterpart. Using extensive Brownian dynamics simulations, we investigate the existence and stability of such traveling states in a generic nonreciprocal particle system. By varying a broad range of parameters including aggregate state of mixture components, diffusivity, degree of nonreciprocity, effective spatial dimension and density, we determine that traveling states do exist below the predator-prey regime, but nonetheless are only found in a narrow region of the parameter space. Our work also sheds light on the physical mechanisms for the disappearance of traveling states when relevant parameters are being varied, and has implications for a range of nonequilibrium systems including nonreciprocal phase separating mixtures, nonequilibrium pattern formation and predator-prey models.

Studying the implications and characterizations of the excited-state quantum phase transitions (ESQPTs) would enable us to understand various phenomena observed in quantum many-body systems. In this work, we delve into the affects and characterizations of the ESQPTs in the anharmonic Lipkin-Meshkov-Glick (LMG) model by means of the entropy of the quantum work distribution. The entropy of the work distribution measures the complexity of the work distribution and behaves as a valuable tool for analyzing nonequilibrium work statistics. We show that the entropy of the work distribution captures salient signatures of the underlying ESQPTs in the model. In particular, a detailed analysis of the scaling behavior of the entropy verifies that it not only acts as a witness of the ESQPTs but also reveals the difference between different types of ESQPTs. We further demonstrate that the work distribution entropy also behaves as a powerful tool for understanding the features and differences of ESQPTs in the energy space. Our results provide further evidence of the usefulness of the entropy of the work distribution for investigating various phase transitions in quantum many-body systems and open up a promising way for experimentally exploring the signatures of ESQPTs.

The detailed fluctuation theorem implies symmetry in the generating function of entropy production probability. The integral fluctuation theorem directly follows from this symmetry and the normalization of the probability. In this paper, we rewrite the generating function by integrating measurements and evolution into a constructed mapping. This mapping is completely positive, and the original integral fluctuation theorem is determined by the trace-preserving property of these constructed maps. We illustrate the convenience of this method by discussing the eigenstate fluctuation theorem and heat exchange between two baths. This set of methods is also applicable to the generating functions of quasiprobability, where we observe the Petz recovery map arising naturally from this approach.

A central concern across the natural sciences is a quantitative understanding of the mechanism governing rare transitions between two metastable states. Recent research has uncovered a fundamental equality between the time-reversal asymmetry of the ensemble of such transition paths and the informativeness of system dynamics about the reactivity of a given trajectory, immediately leading to quantitative criteria for judging the importance of distinct system coordinates for the transition. Here we generalize this framework to multiple mesostates. We find that the main system-wide and coordinate-specific results generalize intuitively, while the combinatorial diversity of pairwise transitions raises new questions and points to new concepts. This work increases the previous framework's generality and applicability and forges connections to enhanced-sampling and coarse-grained dynamical approaches such as milestoning and Markov-state models.

Other than the fully synchronized state, a twisted state can also be an equilibrium solution in the Kuramoto model and its variations. In the present work, we explore the stability of the twisted state in Kuramoto oscillators put on a rim of a planar circle in the two-dimensional space in the presence of power-law decaying interaction strength ($\sim r^{-\alpha }$ with the distance $r$) and time delays due to a finite speed of information transfer. For example, our model can phenomenologically mimic a large sports stadium where many people try to sing or clap their hands in unison; the sound intensity decays with the distance and there can exist a time delay proportional to the distance due to the finiteness of sound speed. We first consider the case without the time delay effect and numerically find that stable twisted states emerge when the exponent $\alpha$ exceeds a critical value of ${\alpha }_c\approx 2$. In other words, for $\alpha <{\alpha }_c$, the fully synchronized state, not the twisted state, is the only stable fixed point of the dynamics. In our analytic approach, we also derive an equation for ${\alpha }_c$ and discuss its solutions. In the presence of time delay, we find that it is possible that the synchronized state becomes unstable while twisted states are stable.

The interaction between two large spherical particles, called intruders, in a dry granular flow down an incline is brought to light and studied experimentally and numerically. Several parameters are varied, namely, the size ratio between the intruders and the small flowing particles, the thickness of the granular flow, the incline slope and roughness, and the densities of the intruders with respect to the small-particle density. In all cases, intruders get aligned with the flow. A thorough parametric study shows that a transition occurs between attractive and repulsive regimes of interaction: at steady state, intruders either flow at a defined longitudinal distance, which may be zero with intruders in contact, or stand as far apart as possible. The mean longitudinal and vertical distances between the intruders are found to be tightly linked, with all points plotting the pairs on a single, master curve. The wake and shear effects are shown to control the relative position of the intruders. They may be modulated due to the weight and buoyancy of the intruders, and to local modifications of the collisions between intruders and small flowing particles because of the proximity of the incline bottom or the flow surface.

Magnetohydrodynamic (MHD) simulations of electrically exploded aluminum and copper rods demonstrate a technique to validate equations of state (EOS) for rapidly Joule-heated conductors. The balance of internal and magnetic forces at the conductor-insulator interface drives the metal there along the vaporization phase boundary. Variations between critical points and vaporization curves in existing models predict differing densities and temperatures in MHD simulations for these models. The inclusion of Maxwell constructs in the liquid-vapor biphase region of the EOS caused the rod surface to vaporize earlier in time than unmodified tables with van der Waals loops. Velocimetry of recent experiments is used to validate the location of the vaporization curve in existing EOS models and differentiate between the vapor dome treatments. Dielectric coatings applied to the metal surface restricted the conductor's expansion and diverted the metal into the warm dense matter regime.

Crystal defects crucially influence the properties of crystalline materials and have been extensively studied. Even for the simplest type of defect—the point defect—however, basic properties such as their diffusive behavior, and their interactions, remain elusive on the atomic scale. Here, we demonstrate in situ control over the creation of isolated point defects in a three-dimensional (3D) colloidal crystal allowing insight on a single-particle level. Our system consists of thermoresponsive microgel particles embedded in a crystal of nonresponsive colloids. Heating this mixed-particle system triggers the shrinking of the embedded microgels, which then vacate their lattice positions, creating vacancy-interstitial pairs. We use temperature-controlled confocal laser scanning microscopy to verify and visualize the formation of the point defects. In addition, by reswelling the microgels we quantify the local lattice distortion around an interstitial defect. Our experimental model system provides a unique opportunity to shed light on the interplay between point defects, on the mechanisms of their diffusion, on their interactions, and on collective dynamics.

We develop a comprehensive framework for analyzing full-record statistics, covering record counts $M\left(t_1\right),M\left(t_2\right),...$, their corresponding attainment times $T_{M\left(t_1\right)},T_{M\left(t_2\right)},...$, and the intervals until the next record. From this multiple-time distribution, we derive general expressions for various observables related to record dynamics, including the conditional number of records given the number observed at a previous time and the conditional time required to reach the current record given the occurrence time of the previous one. Our formalism is exemplified by a variety of stochastic processes, including biased nearest-neighbor random walks, asymmetric run-and-tumble dynamics, and random walks with stochastic resetting.

We present a theory characterizing the phases emerging as a consequence of continuous symmetry-breaking in quantum and classical systems. In symmetry-breaking phases, dynamics is restricted due to the existence of a set of conserved charges derived from the order parameter of the phase transition. Their expectation values are determined by the privileged direction appearing in the ordered phase as a consequence of symmetry breaking, and thus they can be used to determine whether this direction is well defined or has quantum fluctuations. Our theory is numerically exemplified via the two-dimensional limit of the vibron model, a fully connected system invariant under a rotation operator which generates the continuous symmetry-breaking.

In this study, we investigate the effectiveness of entropic uncertainty relations (EURs) in discerning the energy variation in quantum batteries (QBs) modelled by battery-charger field in the presence of bosonic and fermionic reservoirs. Our results suggest that the extractable works (exergy and ergotropy) have versatile characteristics in different scenarios, resulting in a complex relationship between tightness and extractable work. It is worth noting that the tightness of the lower bound of entropic uncertainty can be a good indicator for energy conversion efficiency in charging QBs. Furthermore, we disclose how the EUR including uncertainty and lower bound contributes to energy conversion efficiency in the QB system. It is believed that these findings will be beneficial for better understanding the role of quantum uncertainty in evaluating quantum battery performance.

In percolation of patchy disks on lattices, each site is occupied by a disk, and neighboring disks are regarded as connected when their patches contact. Clusters of connected disks become larger as the patchy coverage of each disk $\chi$ increases. At the percolation threshold ${\chi }_c$, an incipient cluster begins to span the whole lattice. For systems of disks with $n$ symmetric patches on Archimedean lattices, a recent work [Wang et al., Phys. Rev. E 105, 034118 (2022)] found symmetric properties of ${\chi }_c\left(n\right)$, which are due to the coupling of the patches' symmetry and the lattice geometry. How does ${\chi }_c$ behave with increasing $n$ if the patches are randomly distributed on the disks? We consider two typical random distributions of the patches, i.e., the equilibrium distribution and a distribution from random sequential adsorption. Combining Monte Carlo simulations and the critical polynomial method, we numerically determine ${\chi }_c$ for 106 models of different $n$ on the square, honeycomb, triangular, and kagome lattices. The rules governing ${\chi }_c\left(n\right)$ are investigated in detail. They are quite different from those for disks with symmetric patches and could be useful for understanding similar systems.

Developing an equilibrium solution for a pairwise spin-glass with a quenched random infinite range shows a continuous phase transition. Models with $p$-spin interactions have been studied and the exact solution was provided that shows a continuous phase transition for $p=2$ and a first-order one for $p>2$. Although the $p$-spin interactions were studied individually without considering lower-order interactions, is it always feasible to ignore the lower ones? Here, we are interested in finding an analytical solution for considering a triadic interaction as a perturbation in the background of a pairwise interaction in the Sherrington-Kirkpatrick spin-glass model. Our results indicate a sudden phase transition as a consequence of considering triadic interactions that signal a switch from a continuous to an explosive phase transition.

We formulate a short-time expansion for one-dimensional Fokker-Planck equations with spatially dependent diffusion coefficients, derived from stochastic processes with Gaussian white noise, for general values of the discretization parameter $0\le \alpha \le 1$ of the stochastic integral. The kernel of the Fokker-Planck equation (the propagator) can be expressed as a product of a singular and a regular term. While the singular term can be given in closed form, the regular term can be computed from a Taylor expansion whose coefficients obey simple ordinary differential equations. We illustrate the application of our approach with examples taken from statistical physics and biophysics. Furthermore, we show how our formalism allows us to define a class of stochastic equations which can be treated exactly. The convergence of the expansion cannot be guaranteed independently from the discretization parameter $\alpha$.

We study the out-of-equilibrium behavior of statistical systems along critical relaxational flows arising from instantaneous quenches of the temperature $T$ to the critical point $T_c$, starting from equilibrium conditions at time $t=0$. In the case of soft quenches, i.e., when the initial temperature $T$ is assumed sufficiently close to $T_c$ (to keep the system within the critical regime), the critical modes develop an out-of-equilibrium finite-size-scaling (FSS) behavior in terms of the rescaled time variable $\mathrm{\Theta }=t/L^z$, where $t$ is the time interval after quenching, $L$ is the size of the system, and $z$ is the dynamic exponent associated with the dynamics. However, the realization of this picture is less clear when considering the energy density, whose equilibrium scaling behavior (corresponding to the starting point of the relaxational flow) is generally dominated by a temperature-dependent regular background term or mixing with the identity operator. These issues are investigated by numerical analyses within the three-dimensional lattice $N$-vector models, for $N=3$ and 4, which provide examples of critical behaviors with negative values of the specific-heat critical exponent $\alpha$, implying that also the critical behavior of the specific heat gets hidden by the background term. The results show that, after subtraction of its asymptotic critical value at $T_c$, the energy density develops an asymptotic out-of-equilibrium FSS in terms of $\mathrm{\Theta }$ as well, whose scaling function appears singular in the small-$\mathrm{\Theta }$ limit.

Hyperuniform point patterns can be classified by the hyperuniformity scaling exponent $\alpha >0$, that characterizes the power-law scaling behavior of the structure factor $S\left(\mathbf{k}\right)$ as a function of wave number $k\equiv \left|\mathbf{k}\right|$ in the vicinity of the origin, e.g., $S\left(\mathbf{k}\right)\sim {\left|\mathbf{k}\right|}^{\alpha }$ in cases where $S\left(\mathbf{k}\right)$ varies continuously with $k$ as $k\to 0$. In this paper, we show that the spreadability is an effective method for determining $\alpha$ for quasiperiodic systems where $S\left(\mathbf{k}\right)$ is discontinuous and consists of a dense set of Bragg peaks. It has been shown in [Phys. Rev. E 104, 054102 (2021)] that, for media with finite $\alpha$, the long-time behavior of the excess spreadability $\mathcal{S}\left(\infty \right)-\mathcal{S}\left(t\right)$ can be fit to a power law of the form $t^{-(d-\alpha )/2}$, where $d$ is the space dimension, to accurately extract $\alpha$ for the continuous case. We first transform quasiperiodic and limit-periodic point patterns into two-phase media by mapping them onto packings of identical nonoverlapping disks, where space interior to the disks represents one phase and the space in exterior to them represents the second phase. We then compute the spectral density ${\tilde{\chi }}_{{}_V}\left(k\right)$ of the packings, and finally compute and fit the long-time behavior of their excess spreadabilities. Specifically, we show that the excess spreadability can be used to accurately extract $\alpha$ for the one-dimensional (1D) limit-periodic period-doubling chain ($\alpha =1$) and the 1D quasicrystalline Fibonacci chain ($\alpha =3$) to within $0.02\%$ of the analytically known exact results. Moreover, we obtain a value of $\alpha =5.97\pm 0.06$ for the two-dimensional Penrose tiling and present plausible theoretical arguments strongly suggesting that $\alpha$ is exactly equal to six. We also show that, due to the self-similarity of the structures examined here, one can truncate the small-$k$ region of the scattering information used to compute the spreadability and obtain an accurate value of $\alpha$, with a small deviation from the untruncated case that decreases as the system size increases. This strongly suggests that one can obtain a good estimate of $\alpha$ for an infinite self-similar quasicrystal from a modestly sized finite sample. The methods described here offer a simple and general procedure to characterize accurately the large-scale translational order present in quasicrystalline and limit-periodic media in any space dimension that are self-similar. Moreover, the scattering information extracted from these two-phase media encoded in ${\tilde{\chi }}_{{}_V}\left(k\right)$, can be used to estimate their physical properties, such as their effective dynamic dielectric constants, effective dynamic elastic constants, and fluid permeabilities.