In the present work, the orientation of two-dimensional square crystals is studied using the radial distribution function (RDF) defined with the Chebyshev distance. Traditional RDF methods, based on the Euclidean metric, fail to detect changes in crystal orientation due to their isotropic nature. To overcome this limitation, we introduce a modification of the RDF employing the Chebyshev metric, which adds sensitivity to directional changes within square lattices. This approach expands the information conventionally obtained from the RDF by incorporating not only translational properties but also orientational information. The study provides a mathematical analysis of the peak distribution in this enhanced RDF approach when applied to square crystals rotated through various orientations. We found that the orientation of square crystals can be efficiently determined by calculating the abscissa of the first peak in the Chebyshev RDF, which reduces computational times, even for fine numerical resolutions of differential annular widths as small as ${10}^{-3}$ or less. This approach can be applied to any two-dimensional (2D) Bravais lattice structure, with potential modifications based on lattice parameters and is robust for analyzing imperfect lattices with noise and vacancies. In this study, we demonstrate its application on rotated 2D Bravais square lattices, laying the groundwork for future studies on other 2D lattice structures. Additionally, we explore the use of this method to characterize jamming in 2D granular cubic systems, focusing on the orientation of oblique square grains in tilted vibrated layers under cyclic shear.

Metasurfaces, artificial materials with unique electromagnetic (EM) properties arising from electron oscillations in highly conductive metals, often utilize split-ring resonators (SRRs) as key components for nonlinear effects. In this paper, we investigate the nonlinear phenomena caused by charge carrier motion at the gap of a single SRR operating in the terahertz (THz) frequency range. Unlike previous approaches, our model incorporates an additional controlled field to adjust the loss parameter, providing a more generalized framework for understanding nonlinear behavior in SRRs. The nonlinear dynamics are revealed by the two-parameter space diagrams, which allow us to identify periodic and chaotic oscillations for different parameter sets of the nonlinear SRR material. In order to explore the multifunctionality of the material, we construct two-dimensional diagrams by sweeping each parameter in two directions for the same initial values and we find a plethora of hysteresis regions, demonstrating the interesting phenomenon of multistability. Our results show that this behavior occurs in extremely large dynamic regions for all cases studied, favoring the coexistence of up to three different signals/attractors. The different types of multistable patterns are studied in the cross-section of the demarcation region and presented as the coexistence of chaotic with periodic states, and the coexistence of only periodic states. We analyze the parallel branches in hysteresis regions, and we identify a parallel branch in some range where the bifurcation presents a jump. According to our results, the parallel branch has a key impact on multistability, since it increases the number of coexisting states. However, it appears in a very tiny range of parameters and annihilates after a collision crisis. Finally, we analyze the influence of the loss parameter on nonlinear material dynamics using two-parameter spatial diagrams, demonstrating that control of the loss parameter can gradually eliminate the presence of chaotic behavior, thus serving as a pivotal control mechanism for future applications.

We investigate quench dynamics in a one-dimensional spin model, comparing both quantum and classical descriptions. Our primary focus is on the different timescales involved in the evolution of the observables as they approach statistical relaxation. Numerical simulations, supported by semianalytical analysis, reveal that the relaxation of single-particle energies (global quantity) and on-site magnetization (local observable) occurs on a timescale independent of the system size $L$. This relaxation process is equally well-described by classical equations of motion and quantum solutions, demonstrating excellent quantum-classical correspondence, provided the system is strongly chaotic. The correspondence persists even for small quantum spin values ($S=1$), where a semiclassical approximation is not applicable. Conversely, for the participation ratio, which characterizes the initial state spread in the many-body Hilbert space and which lacks a classical analog, the relaxation timescale is system-size dependent.

Many dynamic processes on complex networks, from disease outbreaks to cascading failures, can rapidly accelerate once a critical threshold is exceeded, potentially leading to severe social and economic costs. Therefore, in order to develop effective mitigation strategies, it is essential to understand how these catastrophic events occur. In this work, we investigate the dynamic of disease propagation on networks with fully connected subgraphs (or cliques) using a susceptible-infected-quarantined (SIQ) model, and considering a scenario in which only a proportion $f$ of the population has access to testing. For this model, we derive the time-evolution equations governing the spread of epidemics, and we show that the final proportion of infected individuals undergoes a sudden transition at a critical threshold $f_c$. Moreover, close to this transition point, our results on the time evolution of the SIQ model reveal that the number of new cases can exhibit a faster-than-exponential growth. This accelerated spread dynamics is more likely to occur in networks with larger cliques.

An example system of collective behavior in the presence of active agents is the structural maintenance of chromosome (SMC) protein complexes within the nucleus that create an architecture to facilitate the organization and proper function of the genome. Of the diverse functions these SMC proteins are capable of producing, we focus on the creation of localized clusters of chromatin in the nucleolus through transient cross-links. Large-scale simulations revealed three different dynamic behaviors as a function of timescale: slow cross-linking leads to no clusters, fast cross-linking produces rigid slowly changing clusters, while intermediate timescales produce flexible clusters that mediate gene interaction. By mathematically analyzing different relative scalings of the two sources of stochasticity, thermal fluctuations, and the force induced by the transient cross-links, we predict these three distinct regimes of cluster behavior. Standard time averaging that takes the fluctuations of the transient cross-link force to zero predicts the existence of rigid clusters. Accounting for the interaction of both fluctuations from the cross-links and thermal noise with an effective energy landscape predicts the timescale-dependent lifetimes of flexible clusters. No clusters are predicted when the fluctuations of the transient cross-link force are taken to be large relative to thermal fluctuations. This mathematical perturbation analysis illuminates the importance of accounting for stochasticity in local incoherent transient forces to predict emergent complex biological behavior.

In this work, we analyze the performance of different topological metrics to characterize the three-dimensional structure of a granular sample. In particular, we investigate the problem of granular tapping as it has been shown that different tapping intensities may drive the system to configurations that, sharing the same global packing fraction, are slightly different; hence supposing a challenge in terms of differentiation using only geometrical features. Provided that persistent homology was shown to be a convenient tool to distinguish among two-dimensional deposits in the same scenario, we further extend this machinery to evaluate its performance in 3D cases. We find that, generically, two-dimensional topological features are more appropriate to distinguishing among different states than one-dimensional ones.

Micelles, liposomes, microgels, dendrimers, macrocyclic host molecules, and nanoparticles represent nanocarriers used to transfer cargo, such as drug molecules, among each other and to target sites. We calculate the kinetics of collision-mediated transfer of cargo within ensembles of chemically distinct mobile nanocarriers that each hosts noninteracting cargo items on discrete and identical sites. Rate equations for collision-mediated transfer of cargo are expressed in the Gaussian limit as a set of Fokker-Planck equations and solved in the limit of low occupation. The results are analytic expressions for the detailed cargo distributions of each carrier type as a function of time, from an arbitrary initial apportionment to a set of Gaussians in equilibrium.

Granular flows can occur under low inertia conditions, called the quasi-static regime, and extend to highly inertial systems, called the inertial regime. In the latter, granular flows, particularly those having a variety of grain sizes—property known as polydispersity—have not been extensively studied. Existing rheological laws for monodisperse flows effectively capture volume and friction variations across inertial ranges, assuming the grains diameter as the flow characteristic length. For polydisperse materials, this assumption is less intuitive, and rheological laws cannot be extended straightforwardly. In this work, we employed the Discrete Element Method to study granular flows across varying inertial levels, aiming to identify a physically based length scale that represents the grain scale for polydisperse flows. We show that the average branch length (i.e., distance between the centers of contacting grains) is a representative value of the material's grain size distribution, remaining nearly constant across the explored range of inertia. Moreover, we show that monodisperse and polydisperse flows follow common inertial volume and friction laws when the average branch length is considered as the characteristic length. The findings of this work propose a new perspective for understanding the characteristic length of granular flows, providing a comprehensive interpretation based on the grains contacts. They also permit to extend rheological laws, initially proposed for monodisperse flows, to polydisperse flows by considering the characteristic length scale as the average branch length. Finally, Our results are useful for choosing the characteristic length that controls large-scale flows where polydispersity plays an important role.

We study the problem of a resetting random walk on a lattice in the presence of impurities, and, as has been previously shown with a single impurity, the walker undergoes a transition from a localized to delocalized state. We study the nature of the localized states and transition to delocalized state in the presence of two impurities. We find that when the separation between impurities exceeds a characteristic length, the stronger impurity determines the transition threshold and the walker becomes localized on the stronger impurity. Deviation from the single-impurity phase diagram occurs when the impurities are close to each other and have almost the same strength, and the transition threshold is less than the threshold of each of impurities. In other words, two impurities enhance the localization.

We study the collective charging of a quantum battery (QB) consisting of a one-dimensional molecular aggregate and a coupled single-mode cavity, to which we refer to as an “organic quantum battery” since the battery part is an organic material. The organic QB can be viewed as an extension of the so-called Dicke QB [D. Ferraro et al., Phys. Rev. Lett. 120, 117702 (2018)] by including finite exciton hopping and exciton-exciton interaction within the battery. We consider two types of normalizations of the exciton-cavity coupling when the size of the aggregate $N$ is increased: (I) the cavity length also increases to keep the density of monomers constant, and (II) the cavity length does not change. Our main findings are the following. (i) For fixed $N$ and exciton-cavity coupling, there exist optimal exciton-exciton interactions at which the maximum stored energy density and the maximum charging power density reach their respective maxima that both increase with increasing exciton-cavity coupling. The existence of such maxima for weak exciton-cavity coupling is argued to be due to the nonmonotonic behavior of the one-exciton to two-exciton transition probability in the framework of second-order time-dependent perturbation theory. (ii) Under normalization I, no quantum advantage is observed in the scaling of the two quantities with varying $N$. Under normalization II, it is found that both the maximum stored energy density and the maximum charging power density exhibit quantum advantages compared with the Dicke QB.

Ultrashort pulsed lasers can produce thin columns of plasma in the air via femtosecond filamentation, and these plasmas have been found to generate broadband terahertz and radio frequency (RF) radiation. A recent theory argues that the currents driven at the boundary of the plasma excite a surface plasmon polariton (SPP) surface wave (in particular, a Sommerfeld-Goubau wave given the cylindrical symmetry), which proceeds to detach from the end of the plasma to become the RF pulse. We have performed near-field measurements of these plasmas with a D-dot probe, and find an excellent agreement with this theory. The radial field dependence is precisely fit by a Hankel function, with an outer length scale in agreement with plasma conductivity and radius, and a measured longitudinal drift in frequency maxima closely matches both SPP simulations and analytic expectations.

The dynamical interplay between turbulent particle transport $\left(\mathrm{\Gamma }\right)$ and Reynolds stress $\left(\Re \right)$ at the edge of toroidal magnetically confined plasmas is experimentally investigated on the basis of the cross-coupling between density and potential fluctuations in drift-wave turbulence. Both $\mathrm{\Gamma }$ and $\Re$ are found to be temporally anticorrelated, with a dynamical coupling of the density and potential fluctuations as an agent in their interplay. The density-potential coupling is shown for the first time to be dynamically related to the Reynolds stress in agreement with the $E\times B$ vortex-tilting mechanism. Consistently, a temporal deterioration of the coupling links the evolution of particle transport to the drop in the Reynolds stress. Small-scale contributions $(k_{\theta }{\rho }_s>0.6)$ are shown to play a key role via a mutual stabilization-destabilization process.

Generative modeling aims to produce new data points whose statistical properties resemble those in a training dataset. In recent years, there has been a burst of machine learning techniques and settings that can achieve this goal with remarkable performances. In most of these settings, one uses the training dataset in conjunction with noise, which is added as a source of statistical variability and is essential for the generative task. Here, we explore the idea of using internal chaotic dynamics in high-dimensional chaotic systems as a way to generate new data points from a training dataset. We show that simple learning rules can achieve this goal within a set of vanilla architectures and characterize the quality of the generated data points through standard accuracy measures.

Quantum computing has made tremendous progress in recent years, providing potentialities for breaking the bottleneck of computing power in the field of scientific computing, like computational fluid dynamics. To reduce computational costs and achieve an acceleration, we propose an ancilla-free quantum lattice Boltzmann method for advection-diffusion equations that fully leverages the parallelism of quantum computing. More significantly, there is no need to perform quantum state tomography in each previous loop, if the macroscopic variables for a certain loop is needed. The nonunitary collision operators are replaced by the unique local unitary operations, and the removal of ancilla qubit greatly diminishes the complexity of the quantum circuit. The numerical simulations of the $D_1{Q}_3$ and $D_2{Q}_5$ models have confirmed the feasibility of the proposed algorithm.

Graph neural networks can accurately predict the chemical properties of many molecular systems, but their suitability for large, macromolecular assemblies such as gels is unknown. Here, graph neural networks were trained and optimized for two large-scale classification problems: the rigidity of a molecular network, and the connectivity percolation status, which is nontrivial to determine for systems with periodic boundaries. Models trained on lattice systems were found to achieve accuracies $>95\%$ for rigidity classification, with slightly lower scores for connectivity percolation due to the inherent class imbalance in the data. Dynamically generated off-lattice networks achieved consistently lower accuracies overall due to the correlated nature of the network geometry that was absent in the lattices. An open source tool is provided allowing usage of the highest-scoring trained models, and directions for future improved tools to surmount the challenges limiting accuracy in certain situations are discussed.

We investigate the steady-state organization of active particles residing on an interface. Particle activity induces interface deformations, while the local shape of the interface guides particle movement. We consider multiple species of particles which can locally pull on the interface or push it. This coupled system exhibits a wide variety of behaviors, including clustering, anticlustering, diffusion, mixing, demixing, and localization. Our findings suggest that one can control surface properties by strategically adding or removing specific particle types. Furthermore, by adjusting particle activity levels, we can selectively disperse particle types, enabling precise manipulation of surface movement and geometry.

We apply evolutionary reinforcement learning to a simulation model to identify efficient time-dependent erasure protocols for a physical realization of a 1-bit memory using an underdamped mechanical cantilever. We show that these protocols, when applied to the cantilever in the laboratory, are considerably more efficient than our best hand-designed protocols. The learned protocols allow reliable high-speed erasure by minimizing the heating of the memory during its operation. More generally, the combination of methods used here opens the door to the rational design of efficient protocols for various physics applications.

Homogenization of random media is a practical approach to efficiently simulate stochastic radiative transfer, which requires establishing a reliable effective opacity model. In this work, a new effective opacity model is developed by considering the two-point spatial correlations of the opacity fluctuation, which is further simplified by introducing the analytically empirical function of the optical depth. Our new model has been extensively verified by comparing with direct numerical simulations (DNSs) of stochastic radiative transfer in participating random media in two dimensions. A systematic comparison with existing effective opacity models in the literature is made. For more than 50 different sets of physical parameters of random media, including constant and temperature-dependent opacities, it shows that our new model is the most accurate, which can reproduce the DNS transport results within a relative error of 5% in most cases. In contrast, the performance of existing models is problem-dependent, and it yields considerable errors spanning over three orders of magnitude. The reasons why the newly developed model works well and why existing models fail are also discussed. For more realistic problems, radiative transfer in the aluminum-foam mixture is investigated, where our new model shows the best performance among analytical effective opacity models. In addition, the newly developed model's limitations are briefly analyzed.

The most important characteristics of the Knudsen layer are the temperature jump $\mathrm{\Delta }T$ between the liquid and vapor and the probability ${\theta }_K$ that a molecule, emitted by the liquid into the vapor, reaches infinity (as opposed to bouncing back due to collisions). In the present paper, the linearized Bhatnagar-Gross-Krook model is used to calculate $\mathrm{\Delta }T$ and ${\theta }_K$ and show that, in the absence of macroscopic gradients of temperature and density, ${\theta }_K\approx 96.3\%$. It is then examined how $\mathrm{\Delta }T$ and ${\theta }_K$ are affected by a combination of a temperature gradient (heat flux) and the matching density gradient, such that the resulting pressure field is uniform.

In distributed systems, knowledge of the network structure of the connections among the unitary components is often a requirement for an accurate prediction of the emerging collective dynamics. However, in many real-world situations, one has, at best, access to partial connectivity data, and therefore the entire graph structure needs to be reconstructed from a limited number of observations of the dynamical processes that take place on it. While existing studies predominantly focused on reconstructing traditional pairwise networks, higher-order interactions remain largely unexplored. Here we introduce three methods to reconstruct a simplicial complex structure of connection from observations of evolutionary games that take place on it and demonstrate their high accuracy and excellent overall performance in synthetic and empirical complexes. The methods have different requirements and different complexity, thereby constituting a series of approaches from which one can pick the most appropriate one given the specific circumstances of the application under study.