We investigate the dynamical fixed points of the zero temperature Glauber dynamics in Ising-like models. The stability analysis of the fixed points in the mean field calculation shows the existence of an exponent that depends on the coordination number $z$ in the Ising model. For the generalized voter model, a phase diagram is obtained based on this study. Numerical results for the Ising model for both the mean field case and short ranged models on lattices with different values of $z$ are also obtained. A related study is the behavior of the exit probability $E\left(x_0\right)$, defined as the probability that a configuration ends up with all spins up starting with $x_0$ fraction of up spins. An interesting result is $E\left(x_0\right)=x_0$ in the mean field approximation when $z=2$, which is consistent with the conserved magnetization in the system. For larger values of $z, E\left(x_0\right)$ shows the usual finite size dependent nonlinear behavior both in the mean field model and in the Ising model with nearest neighbor interaction on different two dimensional lattices. For such a behavior, a data collapse of $E\left(x_0\right)$ is obtained using $y=\frac{(x_0-x_c)}{x_c}{L}^{1/\nu }$ as the scaling variable and $f\left(y\right)=\frac{1+tanh\left(\lambda y\right)}{2}$ appears as the scaling function. The universality of the exponent and the scaling factor is investigated.

The study of spreading phenomena in networks, in particular the spread of disease, has attracted considerable interest in the network science research community. In this paper, we show that the outbreak of an epidemic can be effectively contained and suppressed in a small subnetwork by a combination of antidote distribution and partial quarantine. We improve over existing antidote distribution schemes based on personalized PageRank in two ways. First, we replace the constraint on the topology of this subnetwork described by Chung et al. [Internet Math. 6, 237 (2009)] that a large fraction of the value of the personalized PageRank vector must be contained in the local cluster, with a partial quarantine scheme. Second, we derive a different lower bound on the amount of antidote. We show that, under our antidote distribution scheme, the probability of the infection spreading to the whole network is bounded, and the infection inside the subnetwork will disappear after a period that is proportional to the logarithm of the number of initially infected nodes. We demonstrate the effectiveness of our strategy with numerical simulations of epidemics on benchmark networks. We also test our strategy on two examples of epidemics in real-world networks. Our strategy is dependent only on the rate of infection, the rate of recovery, and the topology around the initially infected nodes, and is independent of the rest of the network.

We study the shear flow of active filaments confined in a thin channel for extensile and contractile fibers. We apply the Ericksen-Leslie equations of liquid crystal flow with an activity source term. The dimensionless form of this system includes the Ericksen, activity, and Reynolds numbers, together with the aspect ratio of the channel, as the main driving parameters. We perform a normal mode stability analysis of the base shear flow. For both types of fibers, we arrive at a comprehensive description of the stability properties and their dependence on the parameters of the system. The transition to unstable frequencies in extensile fibers occurs at a positive threshold value of the activity parameter, whereas for contractile ones a complex behavior is found at low absolute value of the activity number. The latter might be an indication of the biologically relevant plasticity and phase transition issues. In contrast with extensile fibers, flows of contractile ones are also found to be highly sensitive to the Reynolds number. The work on extensile fibers is guided by experiments on active filaments in confined channels and aims at quantifying their findings in the prechaotic regime.

Interactions between large-amplitude laser light and strongly magnetized dense plasma have been investigated by one- and two-dimensional electromagnetic particle-in-cell simulations. Since whistler waves have no critical density, they can propagate through plasmas beyond the critical density in principle. However, we have found the propagation of whistler waves is restricted significantly by the stimulated Brillouin scattering. It is confirmed that the period during which the whistler wave can propagate in overcritical plasmas is proportional to the growth time of the ion-acoustic wave via the Brillouin instability. The allowable pulse duration of the whistler wave has a power-law dependence on the amplitude of the whistler wave and the external magnetic field.

Laser experiments are becoming established as tools for astronomical research that complement observations and theoretical modeling. Localized strong magnetic fields have been observed at a shock front of supernova explosions. Experimental confirmation and identification of the physical mechanism for this observation are of great importance in understanding the evolution of the interstellar medium. However, it has been challenging to treat the interaction between hydrodynamic instabilities and an ambient magnetic field in the laboratory. Here, we developed an experimental platform to examine magnetized Richtmyer-Meshkov instability (RMI). The measured growth velocity was consistent with the linear theory, and the magnetic-field amplification was correlated with RMI growth. Our experiment validated the turbulent amplification of magnetic fields associated with the shock-induced interfacial instability in astrophysical conditions. Experimental elucidation of fundamental processes in magnetized plasmas is generally essential in various situations such as fusion plasmas and planetary sciences.

Based on the phase-field theory, a multiple-relaxation-time (MRT) lattice Boltzmann model is proposed for the immiscible multiphase fluids. In this model, the local Allen-Chan equation is chosen as the target equation to capture the phase interface. Unlike previous MRT schemes, an off-diagonal relaxation matrix is adopted in the present model so that the target phase-field equation can be recovered exactly without any artificial terms. To check the necessity of removing those artificial terms, comparative studies were carried out among different MRT schemes with or without correction. Results show that the artificial terms can be neglected at low March number but will cause unphysical diffusion or interface undulation instability for the relatively large March number cases. The present modified model shows superiority in reducing numerical errors by adjusting the free parameters. As the interface transport coupled to the fluid flow, a pressure-evolution lattice Boltzmann equation is adopted for hydrodynamic properties. Several benchmark cases for multiphase flow were conducted to test the validity of the present model, including the static drop test, Rayleigh-Taylor instability, and single rising bubble test. For the rising bubble simulation at high density ratios, bubble dynamics obtained by the present modified MRT lattice Boltzmann model agree well with those obtained by the FEM-based level set and FEM-based phase-field models.

Pressure plays a vital role in changing the transport properties of matter. To understand this phenomenon at a microscopic level, we here focus on a more fundamental problem, i.e., how pressure affects the thermalization properties of solids. As illustrating examples, we study the thermalization behavior of the monatomic chain and the mass-disordered chain of Fermi-Pasta-Ulam-Tsingou-$\beta$ under different strains in the thermodynamic limit. It is found that the pressure-induced change in integrability results in qualitatively different thermalization processes for the two kinds of chains. However, for both cases, the thermalization time follows the same law—it is inversely proportional to the square of the nonintegrability strength. This result suggests that pressure can significantly change the integrability of a system, which provides a new perspective for understanding the pressure-dependent thermal transport behavior.

Using the harmonic approximation and Green's function technique, we investigate the contribution of phonons to heat transport across a narrow vacuum gap by an extended mass-spring chain model. We base the investigation on the van Beest–Kramer–van Santen potential that applies to two cases of simple and alternating mass systems at a finite temperature. Employing this model, we show that in specific values of interaction strengths, incoming phonon frequency, and gap distance, the phonon transmission across the vacuum gap can be improved. Finally, the thermal conductance of the system is computed as a function of interaction strength, gap distance, and temperature. These calculations reveal a suitable fitting function that can provide valuable insight into determining the internal interaction strengths from this quantity or controlling it by variation of the gap distance.

We investigate the statistics of selected rare events in a $(1+1)$-dimensional (classical) stochastic growth model which describes the evolution of (quantum) random unitary circuits. In such classical formulation, particles are created and/or annihilated at each step of the evolution process, according to rules which generally favor a growing cluster size. We apply a large-deviation approach based on biased Monte Carlo simulations, with suitable adaptations, to evaluate (a) the probability of ending up with a single particle at a specified final time $t_f$ and (b) the probability of having particles outside the light cone, defined by a “butterfly velocity” $v_B$, at $t_f$. Morphological features of single-particle final configurations are discussed, in connection with whether the location of such particle is inside or outside the light cone; we find that joint occurrence of both events of types (a) and (b) drives significant changes to such features, signaling a second-order phase transition.

A fundamental paradigm in polymer physics is that macromolecular conformations in equilibrium can be described by universal scaling laws, being key for structure, dynamics, and function of soft (biological) matter and in the materials sciences. Here we reveal that during diffusion-influenced, nonequilibrium chain-growth polymerization, scaling laws change qualitatively, in particular, the growing polymers exhibit a surprising self-avoiding walk behavior in poor and $\theta$ solvents. Our analysis, based on monomer-resolved, off-lattice reaction-diffusion computer simulations, demonstrates that this phenomenon is a result of (i) nonequilibrium monomer density depletion correlations around the active polymerization site, leading to a locally directed and self-avoiding growth, in conjunction with (ii) chain (Rouse) relaxation times larger than the competing polymerization reaction time. These intrinsic nonequilibrium mechanisms are facilitated by fast and persistent reaction-driven diffusion (“sprints”) of the active site, with analogies to pseudochemotactic active Brownian particles. Our findings have implications for time-controlled structure formation in polymer processing, as in, e.g., reactive self-assembly, photocrosslinking, and three-dimensional printing.

Using the Husimi quasiprobability distribution, we investigate the phase space signatures of excited-state quantum phase transitions (ESQPTs) in the Lipkin-Meshkov-Glick and coupled top models. We show that the ESQPT is evinced by the dynamics of the Husimi function, that exhibits a distinct time dependence in the different ESQPT phases. We also discuss how to identify the ESQPT signatures from the long-time averaged Husimi function and its associated marginal distributions. Moreover, from the calculated second moment and Wherl entropy of the long-time averaged Husimi function, we estimate the critical points of the ESQPT in both models, obtaining a good agreement with analytical (mean field) results. We provide a firm evidence that phase space methods are both a new probe for the detection and a valuable tool for the study of ESQPTs.

Out-of-time-order correlators (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalization in interacting quantum many-body systems. It was recently argued that the expected exponential growth of the OTOC is connected to the existence of correlations beyond those encoded in the standard Eigenstate Thermalization Hypothesis (ETH). We show explicitly, by an extensive numerical analysis of the statistics of operator matrix elements in conjunction with a detailed study of OTOC dynamics, that the OTOC is indeed a precise tool to explore the fine details of the ETH. In particular, while short-time dynamics is dominated by correlations, the long-time saturation behavior gives clear indications of an operator-dependent energy scale ${\omega }_{\text{GOE}}$ associated to the emergence of an effective Gaussian random matrix theory. We provide an estimation of the finite-size scaling of ${\omega }_{\text{GOE}}$ for the general class of observables composed of sums of local operators in the infinite-temperature regime and found linear behavior for the models considered.

We address the old and widely debated question of the spectrum statistics of integrable quantum systems, through the analysis of the paradigmatic Lieb-Liniger model. This quantum many-body model of one-dimensional interacting bosons allows for the rigorous determination of energy spectra via the Bethe ansatz approach and our interest is to reveal the characteristic properties of energy levels in dependence of the model parameters. Using both analytical and numerical studies we show that the properties of spectra strongly depend on whether the analysis is done for a full energy spectrum or for a single subset with fixed total momentum. We show that the Poisson distribution of spacing between nearest-neighbor energies can occur only for a set of energy levels with fixed total momentum, for neither too large nor too weak interaction strength, and for sufficiently high energy. By studying long-range correlations between energy levels, we found strong deviations from the predictions based on the assumption of pseudorandom character of the distribution of energy levels.

Solitary waves interacting with random Rayleigh-Jeans distributed waves of a nonintegrable and noncollapsing nonlinear Schrödinger equation are studied. Two opposing types of dynamics are identified: First, the random thermal waves can erode the solitary wave; second, this structure can grow as a result of this interaction. These two types of behavior depend on a dynamical property of the solitary wave (its angular frequency), and on a statistical property of the thermal waves (the chemical potential). These two quantities are equal at a saddle point of the entropy that marks a transition between the two types of dynamics: high-amplitude coherent structures whose frequency exceeds the chemical potential grow and smaller structures with a lower frequency decay. Either process leads to an increase of the wave entropy. We show this using a thermodynamic model of two coupled subsystems, one representing the solitary wave and one for the thermal waves. Numerical simulations verify our results.

Higher-order interactions are increasingly recognized as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraphs as well as simplicial complexes capture the higher-order interactions of complex systems and allow us to investigate the relation between their higher-order structure and their function. Here we establish a general framework for assessing hypergraph robustness and we characterize the critical properties of simple and higher-order percolation processes. This general framework builds on the formulation of the random multiplex hypergraph ensemble where each layer is characterized by hyperedges of given cardinality. We observe that in presence of the structural cutoff the ensemble of multiplex hypergraphs can be mapped to an ensemble of multiplex bipartite networks. We reveal the relation between higher-order percolation processes in random multiplex hypergraphs, interdependent percolation of multiplex networks, and $K$-core percolation. The structural correlations of the random multiplex hypergraphs are shown to have a significant effect on their percolation properties. The wide range of critical behaviors observed for higher-order percolation processes on multiplex hypergraphs elucidates the mechanisms responsible for the emergence of discontinuous transition and uncovers interesting critical properties which can be applied to the study of epidemic spreading and contagion processes on higher-order networks.

Piezo ion channels underlie many forms of mechanosensation in vertebrates and have been found to bend the membrane into strongly curved dome shapes. We develop a methodology describing the self-assembly of lipids and Piezo proteins into polyhedral bilayer vesicles. We validate this methodology for bilayer vesicles formed from bacterial mechanosensitive channels of small conductance, for which experiments found a polyhedral arrangement of proteins with snub cube symmetry and a well-defined characteristic vesicle size. On this basis, we calculate the self-assembly diagram for polyhedral bilayer vesicles formed from Piezo proteins. We find that the radius of curvature of the Piezo dome provides a critical control parameter for the self-assembly of Piezo vesicles, with high abundances of Piezo vesicles with octahedral, icosahedral, and snub cube symmetry with increasing Piezo dome radius of curvature.

It is well known that liquid and saturated vapor, separated by a flat interface in an unbounded space, are in equilibrium. One would similarly expect a liquid drop, sitting on a flat substrate, to be in equilibrium with the vapor surrounding it. Yet, it is not: as shown in this work, the drop evaporates. Mathematically, this conclusion is deduced using the diffuse-interface model, but it is also reformulated in terms of the maximum-entropy principle, suggesting model independence. Physically, evaporation of drops is due to the so-called Kelvin effect, which gives rise to a liquid-to-vapor mass flux if the boundary of the liquid phase is convex.

Continuous-time Markovian evolution appears to be manifestly different in classical and quantum worlds. We consider ensembles of random generators of $N$-dimensional Markovian evolution, quantum and classical ones, and evaluate their universal spectral properties. We then show how the two types of generators can be related by superdecoherence. In analogy with the mechanism of decoherence, which transforms a quantum state into a classical one, superdecoherence can be used to transform a Lindblad operator (generator of quantum evolution) into a Kolmogorov operator (generator of classical evolution). We inspect spectra of random Lindblad operators undergoing superdecoherence and demonstrate that, in the limit of complete superdecoherence, the resulting operators exhibit spectral density typical to random Kolmogorov operators. By gradually increasing strength of superdecoherence, we observe a sharp quantum-to-classical transition. Furthermore, we define an inverse procedure of supercoherification that is a generalization of the scheme used to construct a quantum state out of a classical one. Finally, we study microscopic correlation between neighboring eigenvalues through the complex spacing ratios and observe the horseshoe distribution, emblematic of the Ginibre universality class, for both types of random generators. Remarkably, it survives both superdecoherence and supercoherification.

With the development of probing and computing technology, the study of complex systems has become a necessity in various science and engineering problems, which may be treated efficiently with Koopman operator theory based on observed time series. In the current paper, combined with a singular value decomposition (SVD) of the constructed Hankel matrix, Koopman analysis is applied to a system of coupled oscillators. The spectral properties of the operator and the Koopman modes of a typical orbit reveal interesting invariant structures with periodic, quasiperiodic, or chaotic motion. By checking the amplitude of the principal modes along a straight line in the phase space, cusps of different sizes on the magnitude profiles are identified whenever a qualitative change of dynamics takes place. There seems to be no obstacle to extend the current analysis to high-dimensional nonlinear systems with intricate orbit structures.