In this article, a correlation metric ${\kappa }_c$ is proposed for the inference of the dynamical state of neuronal networks. ${\kappa }_C$ is computed from the scaling of the correlation length with the size of the observation region, which shows qualitatively different behavior near and away from the critical point of a continuous phase transition. The implementation is first studied on a neuronal network model, where the results of this new metric coincide with those obtained from neuronal avalanche analysis, thus well characterizing the critical state of the network. The approach is further tested with brain optogenetic recordings in behaving mice from a publicly available database. Potential applications and limitations for its use with currently available optical imaging techniques are discussed.

Percolation models have long served as a paradigm for unraveling the structure and resilience of complex systems comprising interconnected nodes. In many real networks, nodes are identified by not only their connections but nontopological metadata such as age and gender in social systems, geographical location in infrastructure networks, and component contents in biochemical networks. However, there is little known regarding how the nontopological features influence network structures under percolation processes. In this paper we introduce a feature-enriched core percolation framework using a generic multiplex network approach. We thereby analytically determine the corona cluster, size, and number of edges of the feature-enriched cores. We find a hybrid percolation transition combining a jump and a square root singularity at the critical points in both the network connectivity and the feature space. Integrating the degree-feature distribution with the Farlie-Gumbel-Morgenstern copula, we show the existence of continuous and discrete percolation transitions for feature-enriched cores at critical correlation levels. The inner and outer cores are found to undergo distinct phase transitions under the feature-enriched percolation, all limited by a characteristic curve of the feature distribution.

Vortex motion in coupled phase oscillator lattices is analogous to the dislocation motion in crystals. A single vortex exhibits a glide motion by force at the boundaries. Thermal fluctuations induce the glide motion even below the critical point corresponding to the Peierls stress. The random drift motion is approximated as a random walk in a tilted potential. If the temperature is high, vortices are spontaneously generated. A nonlinear response where the frequency profile is relatively flat in the central region and changes sharply near the boundaries is observed when the vortex density becomes large and nonuniform.

We investigate the synchronization behavior of a generalized useful mode of the emergent collective behavior in sets of interacting dynamic elements. The network-frustrated Kuramoto model with interaction-repulsion frequency characteristics is presented, and its structural features are crucial to capture the correct physical behavior, such as describing steady states and phase transitions. Quantifying the effect of small-world phenomena on the global synchronization of the given network, the impact of the random phase-shift and their mutual behavior shows particular challenges. In this paper, we derive the phase-locked states and identify the significant synchronization transition points analytically with exact boundary conditions for the correlated and uncorrelated degree-frequency distributions and their full stability analysis. We find that a supercritical to subcritical bifurcation transition occurs depending on the synchronic transition points, characterized by the power scale of the network for the correlated degree frequency and the largest eigenvalue of the network in the uncorrelated case. Furthermore, our frustrated degree-frequency distribution brings us to the classical Kuramoto model with all-to-all coupling, with $\beta =1/2$ for the correlated case and ${\lambda }_N=1$ for the uncorrelated distribution. In addition, the interplay between the network topology and the frustration forms a powerful alliance, where they control the synchronization ability of the generalized model without affecting its stability.

Using demographic data of high spatial resolution for a region in the south of Europe, we study the population over fixed-size spatial cells. We find that, counterintuitively, the distribution of the number of inhabitants per cell increases its variability when the size of the cells is increased. Nevertheless, the shape of the distributions is kept constant, which allows us to introduce a scaling law, analogous to finite-size scaling, with a scaling function reasonably well fitted by a gamma distribution. This means that the distribution of the number of inhabitants per cell is stable or invariant under addition with neighboring cells (plus rescaling), defying the central-limit theorem, due to the obvious dependence of the random variables. The finite-size scaling implies a power-law relations between the moments of the distribution and its scale parameter, which are found to be related with the fractal properties of the spatial pattern formed by the population. The match between theoretical predictions and empirical results is reasonably good.

We investigate the nonequilibrium dynamics of a three-state kinetic exchange model of opinion formation, where switches between extreme states are possible, depending on the value of a parameter $q$. The mean field dynamical equations are derived and analyzed for any $q$. The fate of the system under the evolutionary rules used in S. Biswas et al. [Physica A 391, 3257 (2012)] shows that it is dependent on the value of $q$ and the initial state in general. For $q=1$, which allows the extreme switches maximally, a quasiconservation in the dynamics is obtained which renders it equivalent to the voter model. For general $q$ values, a “frozen” disordered fixed point is obtained which acts as an attractor for all initially disordered states. For other initial states, the order parameter grows with time $t$ as $exp\left[\alpha \right(q\left)t\right]$ where $\alpha =\frac{1-q}{3-q}$ for $q\ne 1$ and follows a power law behavior for $q=1$. Numerical simulations using a fully connected agent-based model provide additional results like the system size dependence of the exit probability and consensus times that further accentuate the different behavior of the model for $q=1$ and $q\ne 1$. The results are compared with the nonequilibrium phenomena in other well-known dynamical systems.

In the study of dynamics on networks, moment closure is a commonly used method to obtain low-dimensional evolution equations amenable to analysis. The variables in the evolution equations are mean counts of subgraph states and are referred to as moments. Due to interaction between neighbors, each moment equation is a function of higher-order moments, such that an infinite hierarchy of equations arises. Hence, the derivation requires truncation at a given order and an approximation of the highest-order moments in terms of lower-order ones, known as a closure formula. Recent systematic approximations have either restricted focus to closed moment equations for SIR epidemic spreading or to unclosed moment equations for arbitrary dynamics. In this paper, we develop a general procedure that automates both derivation and closure of arbitrary order moment equations for dynamics with nearest-neighbor interactions on undirected networks. Automation of the closure step was made possible by our generalized closure scheme, which systematically decomposes the largest subgraphs into their smaller components. We show that this decomposition is exact if these components form a tree, there is independence at distances beyond their graph diameter, and there is spatial homogeneity. Testing our method for SIS epidemic spreading on lattices and random networks confirms that biases are larger for networks with many short cycles in regimes with long-range dependence. A Mathematica package that automates the moment closure is available for download.

Complex spatial systems can experience critical transitions or tippings on crossing a threshold value in their response to stochastic perturbations. While previous studies have well characterized the impact of white noise on tipping, the effect of correlated noise in spatial ecosystems remains largely unexplored. Here, we investigate the effect of both multiplicative and additive Ornstein-Uhlenbeck (OU) correlated noise on the occurrence of critical transitions in spatial ecosystems. We find that decreasing the noise correlation time of OU (exponentially correlated) noise aggravates the chance of critical transitions in spatiotemporal ecological systems. Our results hold good and are supported by the analysis of three well-studied spatial ecological models of varying nonlinearity. We also compute spatial early warning indicators (e.g., spatial variance, spatial skewness, and spatial correlation) to determine their reliability in anticipating tipping points with variations in noise correlation. The indicators of critical transitions exhibit mixed success in forewarning the occurrence of a tipping point, as indicated by the distribution of Kendall's rank correlation.

It is well known that granular mixtures that differ in size or shape segregate when sheared. In the past, two mechanisms have been proposed to describe this effect, and it is unclear if both exist. To settle this question, we consider a bidisperse mixture of spheroids of equal volume in a rotating drum, where the two mechanisms are predicted to act in opposite directions. We present evidence that there are two distinct segregation mechanisms driven by relative overstress. Additionally, we showed that, for nonspherical particles, these two mechanisms (kinetic and gravity) can act in different directions leading to a competition between the effects of the two. As a result, the segregation intensity varies nonmonotonically as a function of aspect ratio (AR), and, at specific points, the segregation direction changes for both prolate and oblate spheroids, explaining the surprising segregation reversal previously reported. Consistent with previous results, we found that the kinetic mechanism is dominant for (almost) spherical particles. Furthermore, for moderate aspect ratios, the kinetic mechanism is responsible for the spherical particles' segregation to the periphery of the drum, and the gravity mechanism plays only a minor role. Whereas, at the extreme values of AR, the gravity mechanism notably increases and overtakes its kinetic counterpart.

Although it has been known for half a century that the physical aging of glasses in experiments is described well by a linear thermal-history convolution integral over the so-called material time, the microscopic definition and interpretation of the material time remains a mystery. We propose that the material-time increase over a given time interval reflects the distance traveled by the system's particles. Different possible distance measures are discussed, starting from the standard mean-square displacement and its inherent-state version that excludes the vibrational contribution. The viewpoint adopted, which is inspired by and closely related to pioneering works of Cugliandolo and Kurchan from the 1990s, implies a “geometric reversibility” and a “unique-triangle property” characterizing the system's path in configuration space during aging. Both of these properties are inherited from equilibrium, and they are here confirmed by computer simulations of an aging binary Lennard-Jones system. Our simulations moreover show that the slow particles control the material time. This motivates a “dynamic-rigidity-percolation” picture of physical aging. The numerical data show that the material time is dominated by the slowest particles' inherent mean-square displacement, which is conveniently quantified by the inherent harmonic mean-square displacement. This distance measure collapses data for potential-energy aging well in the sense that the normalized relaxation functions following different temperature jumps are almost the same function of the material time. Finally, the standard Tool-Narayanaswamy linear material-time convolution-integral description of physical aging is derived from the assumption that when time is replaced by distance in the above sense, an aging system is described by the same expression as that of linear-response theory.

Using numerical simulations, we study the failure of an amorphous solid under athermal quasistatic expansion starting from a homogeneous high-density state. During the expansion process, plastic instabilities occur, manifested via sudden jumps in pressure and energy, with the largest event happening via cavitation leading to the material's yielding. We demonstrate that all these plastic events are characterized by saddle-node bifurcation, during which the smallest nonzero eigenvalue of the Hessian matrix vanishes via a square-root singularity. We find that after yielding and prior to complete fracture, the statistics of pressure or energy jumps corresponding to the plastic events show subextensive system-size scaling, similar to the case of simple shear but with different exponents. Thus, overall, our paper reveals universal features in the fundamental characteristics during mechanical failure in amorphous solids under any quasistatic deformation protocol.

Developing adhesives whose bond strength can be externally manipulated is a topic of considerable interest for practical and scientific purposes. In this work, we propose a method of controlling the adhesion force of a regular fluid, such as water and/or glycerol, confined between two parallel plates by applying an external electric field. Our results show the possibility of enhancing or diminishing the bond strength of the liquid sample by appropriately tuning the intensity and direction of the electric current generated by the applied electric field. Furthermore, we verify that, for a given direction of the electric current, the adhesion force can be reduced enough for the fluid to lose its adhesive properties and begin exerting a force to move apart the confining plates. In these circumstances, we obtain an analytical expression for the minimum electric current required to detach the plates without requiring the action of an external force.

High magnetic fields at the kilotesla scale have been experimentally generated and finding methods to fully embed such fields into high-density plasma is interesting for magnetically assisted a fast ignition scheme of inertial confinement fusion, laboratory astrophysics, and magnetically guided fast electron beam for broad applications. We investigate diffusion and embedment of an external magnetic field inwards a high-density plasma by analysis and simulation. By introducing the magnetic Péclet number, dimensional analysis indicates that the magnetizing process is sensitive to the jet velocity, temperature, and size of the plasma and gives a phenomenological scaling law of the magnetic field embedment time with an arbitrary jet velocity. The analytical results are verified by magnetic field simulation and applied in $100\text{−}\mathrm{g}/{\mathrm{cm}}^3, 100\text{−}\mathrm{\mu }\mathrm{m}$-radius plasmas with a jet velocity of 0–400 km/s and a temperature of 50–500 eV, typically adopted in experiments. Attributed to an effective electric field from frame transformation, the magnetic field embedment time can be significantly reduced by one order of magnitude when a jetting plasma is adopted with a velocity of hundreds of kilometers per second, e.g., from 5.5 ns in a static plasma to a 0.5 ns timescale in a jetting plasma of 200 km/s. The promoted embedment process favors for various applications mentioned above.

Especially small values of the static structure factor $S\left(k\right)$ at long wavelengths, i.e., small $k$, were obtained in an analysis of experimental data, for a two-dimensional dusty plasma in its liquid state. For comparison, an analysis of $S\left(k\right)$ data was carried out for many previously published experiments with other liquids. The latter analysis indicates that the magnitude of $S\left(k\right)$ at small $k$ is typically in a range 0.02–0.13. In contrast, the corresponding value for a dusty plasma liquid was found to be as small as 0.0139. Another basic finding for the dusty plasma liquid is that $S\left(k\right)$ at small $k$ generally increases with temperature, with its lowest value, noted above, occurring near the melting point. Simulations were carried out for the dusty plasma liquid, and their results are generally consistent with the experiment. Since a dusty plasma has a soft interparticle interaction, our findings support earlier theoretical suggestions that a useful design strategy for creating materials having exceptionally low values of $S\left(0\right)$, so-called hyperuniform materials, is the use of a condensed material composed of particles that interact softly at their periphery.

The generation of terahertz (THz) radiation under the effect of a femtosecond laser pulse on a transparent semibounded plasma in a constant magnetic field is studied. It is shown how the generation patterns of THz radiation depend on the laser pulse duration and the ratio between the cyclotron and plasma frequencies of electrons. In each of the modes considered, the total energy per unit area, spectral composition, and pulse shape of the generated THz radiation are found. It has been established that optimal generation conditions are realized at laser pulse duration comparable to the reciprocal frequency of plasma oscillations and at electron cyclotron frequency lower than plasma frequency. When cyclotron frequency exceeds plasma frequency, the possibility of increasing the generation frequency up to frequencies comparable to the cyclotron frequency is revealed.

A series of two-dimensional particle-in-cell simulations with speckled laser drivers was carried out to study hot electron generation in direct-drive inertial confinement fusion on OMEGA. Scaling laws were obtained for hot electron fraction and temperature as functions of laser/plasma conditions in the quarter-critical region. Using these scalings and conditions from hydro simulations, the temporal history of hot electron generation can be predicted. The scalings can be further improved to predict hard x-rays for a collection of OMEGA warm target implosions within experimental error bars. These scalings can be readily implemented into inertial confinement fusion design codes.

We derive exact results for the fluctuations in energy produced by microscopic disorder in near-crystalline athermal systems. Our formalism captures the heterogeneity in the elastic energy of polydisperse soft disks in energy-minimized configurations. We use this to predict the distribution of interaction energy between two defects in a disordered background. We show that this interaction energy displays a disorder-averaged power-law behavior $\langle \delta E\rangle \sim {\mathrm{\Delta }}^{-4}$ at large distances $\mathrm{\Delta }$ between the defects. These interactions upon disorder average also display the sixfold symmetry of the underlying reference crystal. Additionally, we show that the fluctuations in the interaction energy encode the athermal correlations introduced by the disordered background. We verify our predictions with energy-minimized configurations of polydisperse soft disks in two dimensions.

Natural processes occur in a finite amount of time and dissipate energy, entropy, and matter. Near equilibrium, thermodynamic intuition suggests that fast irreversible processes will dissipate more energy and entropy than slow quasistatic processes connecting the same initial and final states. For small systems, recently discovered thermodynamic speed limits suggest that faster processes will dissipate more than slower processes. Here, we test the hypothesis that this relationship between speed and dissipation holds for stochastic paths far from equilibrium. To analyze stochastic paths on finite timescales, we derive an exact expression for the path probabilities of continuous-time Markov chains from the path summation solution to the master equation. We present a minimal model for a driven system in which relative energies of the initial and target states control the speed, and the nonequilibrium currents of a cycle control the dissipation. Although the hypothesis holds near equilibrium, we find that faster processes can dissipate less under far-from-equilibrium conditions because of strong currents. This model serves as a minimal prototype for designing kinetics to sculpt the nonequilibrium path space so that faster paths produce less dissipation.

Using the age-structure formalism, we definitely establish connections between semi-Markov processes and the dynamics of open quantum systems that satisfy the Markov quantum master equations. A generalized Feynman-Kac formula of the semi-Markov processes is also proposed. In addition to inheriting all statistical properties possessed by the piecewise deterministic processes of wave functions, the semi-Markov processes show their unique advantages in quantum counting statistics. Compared with the conventional method of the tilted quantum master equation, they can be applied to more general counting quantities. In particular, the terms involved in the method have precise probability meanings. We use a driven two-level quantum system to exemplify these results.

Explicit simulations of fluid mixtures of highly size-dispersed particles are constrained by numerical challenges associated with identifying pair-interaction neighbors. Recent algorithmic developments have ameliorated these difficulties to an extent, permitting more efficient simulations of systems with many large and small particles of disperse sizes. We leverage these capabilities to perform molecular dynamics simulations of binary sphere mixtures with elastically stiff particles approaching the hard sphere limit and particle size ratios of up to 50, approaching the colloidal limit. The systems considered consist of 500 large particles and up to nearly $3.6\times {10}^6$ small particles with total particle volume fractions up to 0.51. Our simulations confirm qualitative predictions for correlations between large particles previously obtained analytically and for simulations employing effective depletion interactions, but also reveal additional insights into the near-contact structure that result from the explicit treatment of the small particle solvent. No spontaneous crystal nucleation was observed during the simulations, suggesting that nucleation rates in the fluid-solid coexistence region are too small to observe crystal nucleation for feasible simulation system sizes and timescales.