When a plane electromagnetic wave impinges on a diffraction grating or other periodic structures, reflected and transmitted waves propagate away from the structure in different radiation channels. A diffraction anomaly occurs when the outgoing waves in one or more radiation channels vanish. Zero reflection, zero transmission, and perfect absorption are important examples of diffraction anomalies, and they are useful for manipulating electromagnetic waves and light. Since diffraction anomalies appear only at specific frequencies and/or wave vectors, and may require the tuning of structural or material parameters, they are relatively difficult to find by standard numerical methods. Iterative methods may be used, but good initial guesses are required. To determine all diffraction anomalies in a given frequency interval, it is necessary to repeatedly solve the diffraction problem for many frequencies. In this paper, an efficient numerical method is developed for computing diffraction anomalies. The method relies on nonlinear eigenvalue formulations for scattering anomalies and solves the nonlinear eigenvalue problems by a contour-integral method. Numerical examples involving periodic arrays of cylinders are presented to illustrate the new method.

Thermodynamics strongly restricts the direction of heat flow in static macroscopic thermal diffusive systems. To overcome this constraint, spatiotemporal modulated systems are used instead. Here, we unveil the underlying geometric heat pump effect in macroscopic driven thermal diffusion, which is crucial for achieving thermal nonreciprocity. We obtain a geometric expression to formulate the nontrivial current in a driven system, manifesting as an extra pumped heat ably diffusing from cold to hot that has no analogy in static setups. Moreover, we analyze the underlying geometric curvature of driven diffusive systems and derive no-pumping restriction theorems that constrain the thermal action under modulations and guide the optimization of driving protocols. Following the restrictions from geometry, we finally implement a minimum experiment and observe the predicted pumped heat in the absence of thermal bias at every instant, which is independent of the driving speed in the adiabatic limit, clearly validating the geometric theory. An extension of the geometric pump effect and no-pumping restrictions to macroscopic mass diffusion governed by Fick's law is also discussed. These results pave the way for designing and implementing nonreciprocal and topological diffusive systems under spatiotemporal modulations.

Bistable biological regulatory systems need to cope with stochastic noise to fine tune their function close to bifurcation points. Here, we study stability properties of this regime in generic systems to demonstrate that cooperative interactions buffer system variability, hampering noise-induced regime shifts. Our analysis also shows that, in the considered cooperativity range, impending regime shifts can be generically detected by statistical early warning signals from distributional data. Our generic framework, based on minimal models, can be used to extract robustness and variability properties of more complex models and empirical data close to criticality.

Dynamical simulation of the cascade failures on the Europe and United States (U.S.) high-voltage power grids has been done via solving the second-order Kuramoto equation. We show that synchronization transition happens by increasing the global coupling parameter $K$ with metasatble states depending on the initial conditions so that hysteresis loops occur. We provide analytic results for the time dependence of frequency spread in the large-$K$ approximation and by comparing it with numerics of $d=2,3$ lattices, we find agreement in the case of ordered initial conditions. However, different power-law (PL) tails occur, when the fluctuations are strong. After thermalizing the systems we allow a single line cut failure and follow the subsequent overloads with respect to threshold values $T$. The PDFs $p\left(N_f\right)$ of the cascade failures exhibit PL tails near the synchronization transition point $K_c$. Near $K_c$ the exponents of the PLs for the U.S. power grid vary with $T$ as $1.4\le \tau \le 2.1$, in agreement with the empirical blackout statistics, while on the Europe power grid we find somewhat steeper PLs characterized by $1.4\le \tau \le 2.4$. Below $K_c$, we find signatures of $T$-dependent PLs, caused by frustrated synchronization, reminiscent of Griffiths effects. Here we also observe stability growth following the blackout cascades, similar to intentional islanding, but for $K>K_c$ this does not happen. For $T<T_c$, bumps appear in the PDFs with large mean values, known as “dragon king” blackout events. We also analyze the delaying or stabilizing effects of instantaneous feedback or increased dissipation and show how local synchronization behaves on geographic maps.

Centrality measures quantify the importance of a node in a network based on different geometric or diffusive properties, and focus on different scales. Here, we adopt a geometrical viewpoint to define a multiscale centrality in networks. Given a metric distance between the nodes, we measure the centrality of a node by its tendency to be close to geodesics between nodes in its neighborhood, via the concept of triangle inequality excess. Depending on the size of the neighborhood, the resulting Gromov centrality defines the importance of a node at different scales in the graph, and it recovers as limits well-known concepts such as the clustering coefficient and closeness centrality. We argue that Gromov centrality is affected by the geometric and boundary constraints of the network, and illustrate how it can help distinguish different types of nodes in random geometric graphs and empirical transportation networks.

Extracting environmental forces from noisy data is a common yet challenging task in complex physical systems. Machine learning (ML) represents a robust approach to this problem, yet is mostly tested on simulated data with known parameters. Here we use supervised ML to extract the electrostatic, dissipative, and stochastic forces acting on micron-sized charged particles levitated in an argon plasma (dusty plasma). By tracking the subpixel motion of particles in subsequent images, we successfully estimated these forces from their random motion. The experiments contained important sources of non-Gaussian noise, such as drift and pixel locking, representing a data mismatch from methods used to analyze simulated data with purely Gaussian noise. Our model was trained on simulated particle trajectories that included all of these artifacts, and used more than 100 dynamical and statistical features, resulting in a prediction with 50% better accuracy than conventional methods. Finally, in systems with two interacting particles, the model provided noncontact measurements of the particle charge and Debye length in the plasma environment.

Extracting physical parameters that cannot be directly measured from an observed data set remains a great challenge in several fields of science and physics. In many of these problems, the construction of a physical model from waveforms is hampered by the phase ambiguity of the recorded wave fronts. In this work, we present an approach for mitigating the effect of phase ambiguity in waveform-driven issues. Our proposal combines the optimal transport theory with the $\kappa$-statistical thermodynamics approach. We construct an energy function from the most probable state of a system described by a finite-variance $\kappa$-Gaussian distribution to introduce an optimal transport metric. We demonstrate that our proposal outperforms the classical frameworks by considering a nonlinear geophysical data-driven problem based on a wave equation numerical solution. The $\kappa$-generalized optimal transport metric is easily adapted to various inverse problems, from estimating power-law exponents to machine learning approaches in quantum mechanics.

We apply Selberg's trace formula to solve problems in hyperbolic band theory, a recently developed extension of Bloch theory to model band structures on experimentally realized hyperbolic lattices. For this purpose we incorporate the higher-dimensional crystal momentum into the trace formula and evaluate the summation for periodic orbits on the Bolza surface of genus two. We apply the technique to compute partition functions on the Bolza surface and propose an approximate relation between the lowest bands on the Bolza surface and on the $\{8,3\}$ hyperbolic lattice. We discuss the role of automorphism symmetry and its manifestation in the trace formula.

We have developed an analytical theory for a simple model of liquid water. We apply Wertheim's thermodynamic perturbation theory (TPT) and integral equation theory (IET) for associative liquids to the rose model, which is among the simplest models of water. The particles interact through rose potentials for orientation dependent pairwise interactions. Modifying both the shape and range of a three-petal rose function, we construct an efficient and dynamical mimic of the two-dimensional (2D) Mercedes-Benz (MB) water model. The particles in 2D MB are 2D Lennard–Jones disks with three hydrogen bonding arms arranged symmetrically, resembling the Mercedes-Benz logo. Both models qualitatively predict both the anomalous properties of pure water and the anomalous solvation thermodynamics of nonpolar molecules. The IET is based on the orientationally averaged version of the Ornstein-Zernike equation. This is one of the main approximations in the present work. IET correctly predicts the pair correlation functions at high temperatures. Both TPT and IET are in semi-quantitative agreement with the Monte Carlo values of the molar volume, isothermal compressibility, thermal expansion coefficient, and heat capacity. A major advantage of these theories is that they require orders of magnitude less computer time than the Monte Carlo simulations.

The lack of signed random networks in standard balance studies has prompted us to extend the Hamiltonian of the standard balance model. Random networks with tunable parameters are suitable for better understanding the behavior of standard balance as an underlying dynamics. Moreover, the standard balance model in its original form does not allow preserving tensed triads in the network. Therefore, the thermal behavior of the balance model has been investigated on a fully connected signed network recently. It has been shown that the model undergoes an abrupt phase transition with temperature. Considering these two issues, we examine the thermal behavior of the structural balance model defined on Erdös-Rényi random networks within the range of their connected regime. We provide a mean-field solution for the model. We observe a first-order phase transition with temperature for a wide range of connection probabilities. We detect two transition temperatures, $T_{\mathrm{cold}}$ and $T_{\mathrm{hot}}$, characterizing a hysteresis loop. We find that with decreasing the connection probability, both $T_{\mathrm{cold}}$ and $T_{\mathrm{hot}}$ decrease. However, the slope of decreasing $T_{\mathrm{hot}}$ with decreasing connection probability is larger than the slope of decreasing $T_{\mathrm{cold}}$. Hence, the hysteresis region gets narrower until it disappears in a certain connection probability. We provide a phase diagram in the temperature-tie density plane to accurately observe the metastable or coexistence region behavior. Then we justify our mean-field results with a series of Monte Carlo simulations.

We propose a new centrality incorporating two classical node-level centralities, the degree centrality and the information centrality, which are considered as local and global centralities, respectively. These two centralities have expressions in terms of the graph Laplacian $L$, which motivates us to exploit its fractional analog $L^{\gamma }$ with a fractional parameter $\gamma$. As $\gamma$ varies from 0 to 1, the proposed fractional version of the information centrality makes intriguing changes in the node centrality rankings. These changes could not be generated by the fractional degree centrality since it is mostly influenced by the local aspect. We prove that these two fractional centralities behave similarly when $\gamma$ is close to 0. This result provides its complete understanding of the boundary of the interval in which $\gamma$ lies since the fractional information centrality with $\gamma =1$ is the usual information centrality. Moreover, our computation for the correlation coefficients between the fractional information centrality and the degree centrality reveals that the fractional information centrality is transformed from a local centrality into being a global one as $\gamma$ changes from 0 to 1.

We characterize a system of hard spheres with a simple collision rule that breaks time-reversal symmetry but conserves energy. The collisions lead to an achiral, isotropic, and homogeneous stationary state whose properties are determined in simulations and compared to an approximate theory originally developed for elastic hard spheres. In the nonequilibrium fluid state, velocities are correlated, a phenomenon known from other nonequilibrium stationary states. The correlations are long-ranged decaying like $1/r^D$ in $D$ dimensions. Such correlations are expected on general grounds far from equilibrium and had previously been observed in driven or nonstationary systems.

The motility-induced phase separation exhibited by active particles with repulsive interactions is well known. We show that the interaction softness of active particles destabilizes the highly ordered dense phase, leading to the formation of a porous cluster which spans the system. This soft limit can also be achieved if the particle motility is increased beyond a critical value, at which the system clearly exhibits all the characteristics of a standard percolation transition. We also show that in the athermal limit, active particles exhibit similar transitions even at low motility. With these additional new phases, the phase diagram of repulsive active particles is revealed to be richer than what was previously conceived.

We derive the coarse-graining (CG) equations of incompressible Hall magnetohydrodynamic (HMHD) turbulence to investigate the local (in space) energy transfer rate as a function of the filtering scale $\ell$. First, the CG equations are space averaged to obtain the analytical expression of the mean cascade rate. Its application to three-dimensional simulations of (weakly compressible) HMHD shows a cascade rate consistent with the value of the mean dissipation rate in the simulations and with the classical estimates based on the “third-order” law. Furthermore, we developed an anisotropic version of CG that allows us to study the magnitude of the cascade rate along different directions with respect to the mean magnetic field. Its implementation on the numerical data with moderate background magnetic field shows a weaker cascade along the magnetic field than in the perpendicular plane, while an isotropic cascade is recovered in the absence of a background field. The strength of the CG approach is further revealed when considering the local-in-space energy transfer, which is shown theoretically and numerically to match at a given position $\mathit{x}$, when locally averaged over a neighboring region, the (quasi-)local dissipation. Prospects of exploiting this model to investigate local dissipation in spacecraft data are discussed.

We discuss a field-theoretical approach to liquids, solids, and glasses, published recently [Phys. Rev. E 105, 034108 (2022)], which aims to describe these materials in a common formalism. We argue that such a formalism contradicts the known hydrodynamic theory of classical liquids. In particular, the authors miss the important particle-number conservation law and the density fluctuations as a hydrodynamic slow variable. This results in an exotic mechanism of hydrodynamic sound instead of the standard hydrodynamic one due to combined particle-number and momentum conservation, a fact well documented in fluid-mechanics textbooks.

We reply to the Comment by Bryk et al. [Phys Rev. E 106, 036601 (2022)] on our paper [Phys. Rev. E 105, 024602 (2022)].

One-dimensional particle chains are fundamental models to explain anomalous thermal conduction in low-dimensional solids such as nanotubes and nanowires. In these systems the thermal energy is carried by phonons, i.e., propagating lattice oscillations that interact via nonlinear resonance. The average energy transfer between the phonons can be described by the wave kinetic equation, derived directly from the microscopic dynamics. Here we use the spatially nonhomogeneous wave kinetic equation of the prototypical $\beta$-Fermi-Pasta-Ulam-Tsingou model, to study thermal conduction in one-dimensional particle chains on a mesoscale description. By means of numerical simulations, we study two complementary aspects of thermal conduction: in the presence of thermostats setting different temperatures at the two ends and propagation of a temperature perturbation over an equilibrium background. Our main findings are as follows. (i) The anomalous scaling of the conductivity with the system size, in close agreement with the known results from the microscopic dynamics, is due to a nontrivial interplay between high and low wave numbers. (ii) The high-wave-number phonons relax to local thermodynamic equilibrium transporting energy diffusively, in the manner of Fourier. (iii) The low-wave-number phonons are nearly noninteracting and transfer energy ballistically. These results present perspectives for the applicability of the full nonhomogeneous wave kinetic equation to study thermal propagation.

We introduce an alternative way to understand the decomposition of a quantum system into interacting parts and show that it is natural in several physical models. This enables us to define a reduced density operator for a working system interacting with a thermal bath that is consistent with the inclusion of the interaction Hamiltonian within the working system's energy. We subsequently provide a self-consistent formulation of quantum thermodynamics that incurs nontrivial physical corrections to thermodynamic relations and quantities previously defined within the literature.

Landauer's principle imposes a fundamental limit on the energy cost to perfectly initialize a classical bit, which is only reached under the ideal operation with infinitely long time. The question on the cost in the practical operation for a bit has been raised under the constraint by the finiteness of operation time. We discover a raise-up of energy cost by ${\mathcal{L}}^2\left(\epsilon \right)/\tau$ from the Landaeur's limit ($k_{B}Tln2$) for a finite-time $\tau$ initialization of a bit with an error probability $\epsilon$. The thermodynamic length $\mathcal{L}\left(\epsilon \right)$ between the states before and after initializing in the parametric space increases monotonously as the error decreases. For example, in the constant dissipation coefficient (${\gamma }_0$) case, the minimal additional cost is $0.997k_{B}T/\left({\gamma }_0\tau \right)$ for $\epsilon =1\%$ and $1.288k_{B}T/\left({\gamma }_0\tau \right)$ for $\epsilon =0.1\%$. Furthermore, the optimal protocol to reach the bound of minimal energy cost is proposed for the bit initialization realized via a finite-time isothermal process.

Networks and graphs provide a simple but effective model to a vast set of systems in which building blocks interact throughout pairwise interactions. Unfortunately, such models fail to describe all those systems in which building blocks interact at a higher order. Higher-order graphs provide us the right tools for the task, but introduce a higher computing complexity due to the interaction order. In this paper we analyze the interplay between the structure of a directed hypergraph and a linear dynamical system, a random walk, defined on it. How can one extend network measures, such as centrality or modularity, to this framework? Instead of redefining network measures through the hypergraph framework, with the consequent complexity boost, we will measure the dynamical system associated to it. This approach let us apply known measures to pairwise structures, such as the transition matrix, and determine a family of measures that are amenable to such a procedure.