A classical $\alpha -\mathit{XY}$ inertial model, consisting of $N$ two-component rotators and characterized by interactions decaying with the distance $r_{ij}$ as $1/r_{ij}^{\alpha }$ ($\alpha \ge 0$) is studied through first-principle molecular-dynamics simulations on $d$-dimensional lattices of linear size $L$ ($N\equiv L^d$ and $d=1,2,3$). The limits $\alpha =0$ and $\alpha \to \infty$ correspond to infinite-range and nearest-neighbor interactions, respectively, whereas the ratio $\alpha /d>1$ ($0\le \alpha /d\le 1$) is associated with short-range (long-range) interactions. By analyzing the time evolution of the kinetic temperature $T\left(t\right)$ in the long-range-interaction regime, one finds a quasi-stationary state (QSS) characterized by a temperature $T_{\text{QSS}}$; for fixed $N$ and after a sufficiently long time, a crossover to a second plateau occurs, corresponding to the Boltzmann-Gibbs temperature $T_{\text{BG}}$ (as predicted within the BG theory), with $T_{\text{BG}}>T_{\text{QSS}}$. It is shown that the QSS duration ($t_{\text{QSS}}$) depends on $N, \alpha$, and $d$, although the dependence on $\alpha$ appears only through the ratio $\alpha /d$; in fact, $t_{\text{QSS}}$ decreases with $\alpha /d$ and increases with both $N$ and $d$. Considering a fixed energy value, a scaling for $t_{\text{QSS}}$ is proposed, namely, $t_{\text{QSS}}\propto N^{A(\alpha /d)}{e}^{-B\left(N\right){(\alpha /d)}^2}$, analogous to a recent analysis carried out for the classical $\alpha$-Heisenberg inertial model. It is shown that the exponent $A(\alpha /d)$ and the coefficient $B\left(N\right)$ present universal behavior (within error bars), comparing the $XY$ and Heisenberg cases. The present results should be useful for other long-range systems, very common in nature, like those characterized by gravitational and Coulomb forces.

In systems with dynamical transitions, criticality is usually defined by the behavior of suitable individual variables of the system. In the case of time series, the usual procedure involves the analysis of the statistical properties of the selected variable as a function of a control parameter in both the time and frequency domains. An interesting question, however, is how to identify criticality when multiple simultaneous signals are required to provide a reliable representation of the system, especially when the signals exhibit different dynamics and do not individually display the characteristic signs of criticality. In that situation, a technique that analyzes the collective behavior of the signals is necessary. In this work we show that the eigenvalues and eigenvectors obtained from principal components analysis (PCA) can be used as a way to identify collective criticality. To do this, we construct a multilayer Ising model comprised of coupled two-dimensional Ising lattices that have distinct critical temperatures when isolated. We apply PCA to the collection of magnetization signals for a range of global temperatures and study the resulting eigenvalues. We find that there exists a single global temperature at which the eigenvalue spectrum follows a power law, and identify this as an indicator of “multicriticality” for the system. We then apply the technique to electroencephalographic recordings of brain activity, as this is a prime example of multiple signals with distinct individual dynamics. The analysis reveals a power-law eigenspectrum, adding further evidence to the brain criticality hypothesis. We also show that the eigenvectors can be used to distinguish the recordings in the resting state from those during a cognitive task, and that there is important information contained in all eigenvectors, not just the first few dominant ones, establishing that PCA has great utility beyond dimensionality reduction.

The planted $p$-spin interaction model is a paradigm of random-graph systems possessing both a ferromagnetic phase and a disordered phase with the latter splitting into many spin-glass states at low temperatures. Conventional simulated annealing dynamics is easily blocked by these low-energy spin-glass states. Here we demonstrate that actually this planted system is exponentially dominated by a microcanonical polarized phase at intermediate energy densities. There is a discontinuous microcanonical spontaneous symmetry breaking transition from the paramagnetic phase to the microcanonical polarized phase. This transition can serve as a mechanism to avoid all the spin-glass traps, and it is accelerated by the restart strategy of microcanonical random walk. We also propose an unsupervised learning problem on microcanonically sampled configurations for inferring the planted ground state.

Connectedness percolation phenomena in the two-dimensional packing of elongated particles (discorectangles) were studied numerically. The packings were produced using random sequential adsorption off-lattice models with preferential orientations of the particles along a given direction. The partial ordering was characterized by the order parameter $S$, with $S=0$ for completely disordered films (random orientation of particles) and $S=1$ for completely aligned particles along the horizontal direction $x$. The aspect ratio (length-to-width ratio) of the particles was varied within the range $\varepsilon \in [1;100]$. Analysis of connectivity was performed assuming a core-shell structure of the particles. The value of $S$ affected the structure of the packings, the formation of long-range connectivity, and the behavior of the electrical conductivity. The effects can be explained by taking accounting of the competition between the particles' orientational degrees of freedom and excluded volume effects. For aligned deposition, anisotropy in the electrical conductivity was observed with the values along the alignment direction ${\sigma }_x$ being larger than the values in the perpendicular direction ${\sigma }_y$. Anisotropy in the localization of the percolation threshold was also observed in finite-sized packings, but it disappeared in the limit of infinitely large systems.

Local anaxonic neurons with graded potential release are important ingredients of nervous systems, present in the olfactory bulb system of mammalians and in the human visual system, as well as in arthropods and nematodes. We develop a neuronal network model including both axonic and anaxonic neurons and monitor the activity tuned by the following parameters: the decay length of the graded potential in local neurons, the fraction of local neurons, the largest eigenvalue of the adjacency matrix, and the range of connections of the local neurons. Tuning the fraction of local neurons, we derive the phase diagram including two transition lines: a critical line separating subcritical and supercritical regions, characterized by power-law distributions of avalanche sizes and durations, and a bifurcation line. We find that the overall behavior of the system is controlled by a parameter tuning the relevance of local neuron transmission with respect to the axonal one. The statistical properties of spontaneous activity are affected by local neurons at large fractions and on the condition that the graded potential transmission dominates the axonal one. In this case the scaling properties of spontaneous activity exhibit continuously varying exponents, rather than the mean-field branching model universality class.

Using lattice Boltzmann simulations we investigate the impact of the amplitude of concentration fluctuations in binary fluid mixtures prior to demixing when in contact with a surface that is preferentially wet by one of the components. We find a bicontinuous structure near the surface for an initial, prequench state of the mixture close to the critical point where the amplitude of concentration fluctuations is large. In contrast, if the initial state of the mixture is not near the critical point and concentration fluctuations are relatively weak, then the morphology is not bicontinuous but remains layered until the very late stages of coarsening. In both cases, it is the morphology of a depletion layer rich in the nonpreferred component that dictates the growth exponent of the thickness of the fluid layer that is in direct contact with the substrate. In the early stages of demixing, we find a growth exponent consistent with a value of $1/4$ for a prequench state away from the critical point, which is different from the usual diffusive scaling exponent of $1/3$ that we recover for a prequench state close to the critical point. We attribute this to the structure of a depletion layer that is penetrated by tubes of the preferred fluid, connecting the wetting layer to the bulk fluid even in the early stages if the initial state is characterized by concentration fluctuations that are large in amplitude. Furthermore, we find that in the late stages of demixing the flow through these tubes results in significant in-plane concentration variations near the substrate, leading to dropletlike structures with a concentration lower than the average concentration in the wetting layer. This causes a deceleration in the growth of the wetting layer in the very late stages of the demixing. Irrespective of the prequench state of the mixture, the late stages of the demixing process produce the same growth law for the layer thickness, with a scaling exponent of unity usually associated with the impact of hydrodynamic flow fields.

Among various algorithms of multifractal analysis (MFA) for complex networks, the sandbox MFA algorithm behaves with the best computational efficiency. However, the existing sandbox algorithm is still computationally expensive for MFA of large-scale networks with tens of millions of nodes. It is also not clear whether MFA results can be improved by a largely increased size of a theoretical network. To tackle these challenges, a computationally efficient sandbox algorithm (CESA) is presented in this paper for MFA of large-scale networks. Distinct from the existing sandbox algorithm that uses the shortest-path distance matrix to obtain the required information for MFA of networks, our CESA employs the compressed sparse row format of the adjacency matrix and the breadth-first search technique to directly search the neighbor nodes of each layer of center nodes, and then to retrieve the required information. A theoretical analysis reveals that the CESA reduces the time complexity of the existing sandbox algorithm from cubic to quadratic, and also improves the space complexity from quadratic to linear. Then the CESA is demonstrated to be effective, efficient, and feasible through the MFA results of ($u,v$)-flower model networks from the fifth to the 12th generations. It enables us to study the multifractality of networks of the size of about 11 million nodes with a normal desktop computer. Furthermore, we have also found that increasing the size of ($u,v$)-flower model network does improve the accuracy of MFA results. Finally, our CESA is applied to a few typical real-world networks of large scale.

We show that the Brownian motion of a nanoparticle (NP) can reach a ballistic limit when intensely heated to form supercavitation. As the NP temperature increases, its Brownian motion displays a sharp transition from normal to ballistic diffusion upon the formation of a vapor bubble to encapsulate the NP. Intense heating allows the NP to instantaneously extend the bubble boundary via evaporation, so the NP moves in a low-friction gaseous environment. We find the dynamics of the supercavitating NP is largely determined by the near field effect, i.e., highly localized vapor phase property in the vicinity of the NP.

Considering an entropy-based division of energy transferred into heat and work, we develop an alternative theoretical framework for the thermodynamic analysis of two-level systems. When comparing these results with those obtained using the standard definitions of these quantities, we observe the appearance of a different term of work, which represents the energy cost of rotating the Bloch vector in the presence of the external field that defines the local Hamiltonian. Additionally, we obtain explicit expressions for the temperature, the heat capacity, and the internal entropy production of the system in both paradigms. In order to illustrate our findings we study, from both perspectives, matter-radiation interaction processes for two different systems.

Self-organized criticality in the Hwa-Kardar model of a “running sandpile” [Phys. Rev. Lett. 62, 1813 (1989); Phys. Rev. A 45, 7002 (1992)] with a turbulent motion of the environment taken into account is studied with the field theoretic renormalization group (RG). The turbulent flow is modeled by the synthetic $d$-dimensional generalization of the anisotropic Gaussian velocity ensemble with finite correlation time, introduced by Avellaneda and Majda [Commun. Math. Phys. 131, 381 (1990); Commun. Math. Phys. 146, 139 (1992)]. The Hwa-Kardar model with time-independent (spatially quenched) random noise is considered alongside the original model with white noise. The aim of the present paper is to explore fixed points of the RG equations which determine the possible types of universality classes (regimes of critical behavior of the system) and critical dimensions of the measurable quantities. Our calculations demonstrate that influence of the type of random noise is extremely large: in contrast to the case of white noise where the system possesses three fixed points, the case of spatially quenched noise involves four fixed points with overlapping stability regions. This means that in the latter case the critical behavior of the system depends not only on the global parameters of the system, which is the usual case, but also on the initial values of the charges (coupling constants) of the system. These initial conditions determine the specific fixed point which will be reached by the RG flow. Since now the critical properties of the system are not defined strictly by its parameters, the situation may be interpreted as a universality violation. Such systems are not forbidden, but they are rather rare. It is especially interesting that the same model without turbulent motion of the environment does not predict this nonuniversal behavior and demonstrates the usual one with prescribed universality classes instead [J. Stat. Phys. 178, 392 (2020)].

We calculate exactly cumulant generating functions (full counting statistics) for the transverse, staggered magnetization, and the domain walls at zero temperature for a finite interval of the $XY$ spin chain. In particular, we also derive a universal interpolation formula in the scaling limit for the full counting statistics of the transverse magnetization and the domain walls which is based on the solution of a Painlevé V equation. By further determining subleading corrections in a large interval asymptotics, we are able to test the applicability of conformal field theory predictions at criticality. As a by-product, we also obtain exact results for the probability of formation of ferromagnetic and antiferromagnetic domains in both the ${\sigma }^z$ and ${\sigma }^x$ basis in the ground state. The analysis hinges upon asymptotic expansions of block Toeplitz determinants, for which we formulate and check numerically a different conjecture.

According to the eigenstate thermalization hypothesis (ETH), the eigenstate-to-eigenstate fluctuations of expectation values of local observables should decrease with increasing system size. In approaching the thermodynamic limit—the number of sites and the particle number increasing at the same rate—the fluctuations should scale as $\sim D^{-1/2}$ with the Hilbert space dimension $D$. Here, we study a different limit—the classical or semiclassical limit—by increasing the particle number in fixed lattice topologies. We focus on the paradigmatic Bose-Hubbard system, which is quantum-chaotic for large lattices and shows mixed behavior for small lattices. We derive expressions for the expected scaling, assuming ideal eigenstates having Gaussian-distributed random components. We show numerically that, for larger lattices, ETH scaling of physical midspectrum eigenstates follows the ideal (Gaussian) expectation, but for smaller lattices, the scaling occurs via a different exponent. We examine several plausible mechanisms for this anomalous scaling.

In this work, we show how “chimera states,” namely, the dynamical situation when synchronized and desynchronized domains coexist in an oscillator ensemble, can be controlled through a linear augmentation (LA) technique. Specifically, in the networks of coupled chaotic oscillators, we obtain chimera states through induced multistability and demonstrate how LA can be used to control the size and spatial location of the incoherent and coherent populations in the ensemble. We examine basins of attraction of the system to analyze the effects of LA on its multistable behavior and thus on chimera states. Stability of the synchronized dynamics is analyzed through a master stability function. We find that these results are independent of a system's initial conditions and the strategy is applicable to the networks of globally, locally as well as nonlocally coupled oscillators. Our results suggest that LA control can be an effective method to control chimera states and to realize a desired collective dynamics in such ensembles.

We refine a recently proposed class of local entropic loss functions by restricting the smoothening regularization to only a subset of weights. The new loss functions are referred to as partial local entropies. They can adapt to the weight-space anisotropy, thus outperforming their isotropic counterparts. We support the theoretical analysis with experiments on image classification tasks performed with multilayer, fully connected, and convolutional neural networks. The present study suggests how to better exploit the anisotropic nature of deep landscapes, and it provides direct probes of the shape of the minima encountered by stochastic gradient descent algorithms. As a byproduct, we observe an asymptotic dynamical regime at late training times where the temperature of all the layers obeys a common cooling behavior.

Evaluation of systemic risk in networks of financial institutions in general requires information of interinstitution financial exposures. In the framework of the DebtRank algorithm, we introduce an approximate method of systemic risk evaluation which requires only node properties, such as total assets and liabilities, as inputs. We demonstrate that this approximation captures a large portion of systemic risk measured by DebtRank. Furthermore, using Monte Carlo simulations, we investigate network structures that can amplify systemic risk. Indeed, while no topology in general sense is a priori more stable if the market is liquid (i.e., the price of transaction creation is small) [T. Roukny et al., Sci. Rep. 3, 2759 (2013)], a larger complexity is detrimental for the overall stability [M. Bardoscia et al., Nat. Commun. 8, 14416 (2017)]. Here we find that the measure of scalar assortativity correlates well with level of systemic risk. In particular, network structures with high systemic risk are scalar assortative, meaning that risky banks are mostly exposed to other risky banks. Network structures with low systemic risk are scalar disassortative, with interactions of risky banks with stable banks.

Many self-propelled objects are large enough to exhibit inertial effects but still suffer from environmental fluctuations. The corresponding basic equations of motion are governed by active Langevin dynamics, which involve inertia, friction, and stochastic noise for both the translational and orientational degrees of freedom coupled via the self-propulsion along the particle orientation. In this paper, we generalize the active Langevin model to time-dependent parameters and explicitly discuss the effect of time-dependent inertia for achiral and chiral particles. Realizations of this situation are manifold, ranging from minirockets (which are self-propelled by burning their own mass), to dust particles in plasma (which lose mass by evaporating material), to walkers with expiring activity. Here we present analytical solutions for several dynamical correlation functions, such as mean-square displacement and orientational and velocity autocorrelation functions. If the parameters exhibit a slow power law in time, we obtain anomalous superdiffusion with a nontrivial dynamical exponent. Finally, we constitute the “Langevin rocket” model by including orientational fluctuations in the traditional Tsiolkovsky rocket equation. We calculate the mean reach of the Langevin rocket and discuss different mass ejection strategies to maximize it. Our results can be tested in experiments on macroscopic robotic or living particles or in self-propelled mesoscopic objects moving in media of low viscosity, such as complex plasma.

Intense laser-plasma interactions are an essential tool for the laboratory study of ion acceleration at a collisionless shock. With two-dimensional particle-in-cell calculations of a multicomponent plasma we observe two electrostatic collisionless shocks at two distinct longitudinal positions when driven with a linearly polarized laser at normalized laser vector potential $a_0$ that exceeds 10. Moreover, these shocks, associated with protons and carbon ions, show a power-law dependence on $a_0$ and accelerate ions to different velocities in an expanding upstream with higher flux than in a single-component hydrogen or carbon plasma. This results from an electrostatic ion two-stream instability caused by differences in the charge-to-mass ratio of different ions. Particle acceleration in collisionless shocks in multicomponent plasma are ubiquitous in space and astrophysics, and these calculations identify the possibility for studying these complex processes in the laboratory.

This work discusses the development of a sharp interface immersed boundary (IB) method for viscous compressible flows and its assessment for accurate computations of wall shear and heat fluxes in hypersonic flows. The IB method is implemented in an unstructured Cartesian finite-volume (FV) framework and resolves the geometric interface sharply on the nonconformal mesh through direct imposition of boundary conditions employing a local reconstruction approach. The efficacy of the IB-FV solver is investigated for canonical high-speed viscous flows over a range of Mach numbers. The numerical results indicate that the surface pressure and shear stress distributions are computed with reasonable accuracy, whereas surface heat fluxes for aerodynamically blunt configurations are underpredicted. Employing a set of carefully designed experiments and simple diagnostic tools, we probe the possible causes for the underprediction in heat flux. We show that there exist two sources of error—one due to grid resolution and the other due to solution reconstruction, with the latter being more prominent and responsible for the observed underprediction in heat fluxes. Studies reveal that the heat flux estimates are sensitive to the choice of temperature reconstruction and linear interpolations could lead to poor estimates of heat flux. Our investigations conclusively point out the fact that existing polynomial-based reconstruction approaches for sharp interface IB techniques are not necessarily adequate for heat transfer predictions in high Reynolds number hypersonic flows.

Alternans of cardiac action potential duration represent critical precursors for the development of life-threatening arrhythmias and sudden cardiac death. The system's thermal state affects these electrical disorders requiring additional theoretical and experimental efforts to improve a patient-specific clinical understanding. In such a scenario, we generalize a recent work from Loppini et al. [Phys. Rev. E 100, 020201(R) (2019)] by performing an extended spatiotemporal correlation study. We consider high-resolution optical mapping recordings of canine ventricular wedges' electrical activity at different temperatures and pacing frequencies. We aim to recommend the extracted characteristic length as a potential predictive index of cardiac alternans onset and evolution within a wide range of system states. In particular, we show that a reduction of temperature results in a drop of the characteristic length, confirming the impact of thermal instabilities on cardiac dynamics. Moreover, we theoretically investigate the use of such an index to identify and predict different alternans regimes. Finally, we propose a constitutive phenomenological law linking conduction velocity, characteristic length, and temperature in view of future numerical investigations.