Random assemblies of magnetic nanowires represent a unique class of materials with promising applications in spintronics and information storage. These assemblies exhibit complex behavior due to the combination of magnetic dipolar interactions between the nanowires and electronic transport properties governed by tunneling barriers at magnetic tunnel junctions (MTJs). The intricate interplay of these phenomena makes the study of magnetic nanowire networks a rich area of research. In this study, we develop a theoretical framework to analyze the resistive behavior of random magnetic nanowire networks. By employing a combination of graph theoretical approaches and mean-field theory, we derive an effective resistance model that encapsulates the contributions of magnetic interactions between the nanowires. Our findings show the importance of considering both the magnetic and electrical properties of nanowire networks in the design and optimization of amorphous resistive devices.

Stress-stress correlations in crystalline solids with long-range order can be straightforwardly derived using elasticity theory (ET). In contrast, the emergent elasticity of amorphous solids, rigid materials characterized by an underlying disordered structure, defies direct explanation within traditional theoretical frameworks. To address this challenge, tensor gauge theories have been recently proposed as a promising approach to describe the emergent elasticity of disordered solids and predict their stress-stress correlations. In this work, we revisit this problem in two-dimensional (2D) amorphous and crystalline solids by employing a canonical ET approach, supported by experimental and simulation data. We demonstrate that, with respect to static stress-stress correlations, the response of a 2D disordered solid is indistinguishable from that of a 2D isotropic crystalline solid, and it is well predicted by vanilla ET. Moreover, we show that the presence of pinch-point singularities in the stress response is not an exclusive feature of amorphous solids. Our results confirm previous observations about the universal character of static stress-stress correlations in crystalline and amorphous packings.

The transformed mean height profile (TMHP) technique, recently proposed in the context of interface analysis, smooths local fluctuations that give rise to intrinsic roughness in stochastic surfaces formed during nonequilibrium growth, by averaging the height field over bins of a specified size. In this work, we present an analytical proof that TMHP minimizes such intrinsic roughness, which in turn reduces spatial scaling corrections, thereby enabling more accurate characterization of both global and local roughness. Compared to recent existing methods, TMHP more effectively suppresses short-wavelength fluctuations while preserving intermediate- and long-wavelength features of the interface. We validate these findings using the ballistic deposition (BD) model on a substrate with dimension $d=2$, a case in which the consistent determination of the local roughness exponent had remained unresolved. By applying TMHP with an optimal bin size, we recover a local roughness exponent consistent with the most accurate numerical estimates of the global roughness exponent in the Kardar-Parisi-Zhang universality class for $d=2$, thereby resolving a longstanding gap in the scaling analysis of the BD model.

In this paper, we introduce a new stochastic process of $N$ interacting particles on the line that evolve via Dyson Brownian motion (DBM) with Dyson's index $\beta >0$ and undergo simultaneous resetting to their initial positions at a constant rate $r$. We call this process the resetting Dyson Brownian motion (RDBM) with a parameter $\beta >0$, in short the $\beta$-RDBM process. For $\beta =1,2,4$, the positions of the particles in the RDBM can be interpreted as the eigenvalues of a new random matrix ensemble where the entries of an $N\times N$ Gaussian matrix evolve as simultaneously resetting Brownian motions (with rate $r$) in the presence or absence of a harmonic trap. For $r=0$ and in the presence of a harmonic trap, this system reaches an equilibrium Gibbs-Boltzmann state of the so called Dyson log-gas. However, the stochastic resetting drives the system at long time to a nonequilibrium stationary state (NESS). We compute exactly the joint distribution of the positions of the particles in this NESS for all $\beta >0$ and calculate several macroscopic and microscopic observables in the large $N$ limit. These include the average density profile of the gas, the extreme value statistics, the spacing between two consecutive particles and the full counting statistics, i.e., the distribution of the number of particles in an interval $[-L,L]$. We show that a nonzero resetting rate $r>0$ drastically changes the nature of the fluctuations in the stationary state: while the log-gas ($r=0$) is rather rigid, the $\beta$-RDBM in its NESS becomes fluffy, i.e., the fluctuations of different observables are of the same order as their mean. In the absence of a harmonic trap, our results for the $\beta =2$ RDBM can be related to nonintersecting Brownian motions (vicious walkers) in the presence of resetting. Our model demonstrates interesting effects arising from the interplay between the eigenvalue repulsion and the all-to-all attraction (generated by stochastic resetting) in an interacting particle system. Numerical simulations are in excellent agreement with our analytical results.

Quasiparticles in semiconductors reveal different regimes of propagation. Here we theoretically analyze phonon-assisted transport of excited quasiparticles in two-dimensional systems by means of a quasi-classical kinetic equation in the presence of relaxation and local uniform force field in the vicinity of the one-dimensional interface formed by two different atomically flat materials stitched together. We analyze the dynamics of excitons and focus on the situation when initial exciton density distribution is optically excited directly at the interface of two atomically flat materials. We considered both homogeneous and inhomogeneous cases, when identical and different diffusion coefficients for materials are present. The appearance of negative diffusivity was revealed in both cases. Moreover, mean-squared displacement was studied for various system parameters, and different behavior was observed in short- and long-time domains.

We studied the statistical properties of a quantum system in the pseudointegrable regime through the gap ratios between consecutive energy levels of the scattering spectra. A two-dimensional quantum billiard containing a point-like (zero-range) perturbation was experimentally simulated using a flat rectangular resonator with wire antennas. We show that the system exhibits semi-Poisson behavior in the frequency range $8<\nu <16\mathrm{GHz}$. The probability distribution $P\left(r\right)$ of the studied system is characterized by the parameter $\xi =0.97\pm 0.03$, with the expected value $\xi =1$ for the short-range plasma model. Furthermore, we provide a theoretical expression for the higher-order nonoverlapping probability distribution $P_{\mathrm{sP}}^k\left(r\right)$, $k\ge 1$ in the semi-Poisson regime, incorporating long-range spectral correlations between levels. The experimental and numerical results confirm the pseudointegrability of the studied system. The semi-Poisson ensemble for $k=2$ approaches the Gaussian orthogonal ensemble distribution. In addition, the uncorrelated Poisson statistics mimic Random Matrix Theory ensembles at certain $k$ values, $k=4$ for the Gaussian unitary ensemble and $k=7$ for the Gaussian symplectic ensemble. This unexpected scale-dependent convergence shows how spectral statistics can exhibit chaos-like features even in nonchaotic systems, suggesting that scale-dependent analysis bridges integrable and chaotic regimes.

We present a study of the theoretical Brusselator model with time-delayed self-feedback, demonstrating its ability to induce extreme events when delays in reaction processes significantly influence subsequent dynamics, with and without diffusion. Stability analyses reveal the mechanisms driving this behavior with respect to the delay time. The occurrence of extreme events is validated using various numerical and statistical tools, including phase portraits, time series, probability distribution functions, return periods, and spatiotemporal evolution. A comprehensive two-parameter scan delineates the parameter regimes where the extreme events emerge, alongside the identification of transient chaos within specific regions of the parameter space. To confirm these numerical findings, we constructed an analog electronic circuit that emulates the model, providing experimental validation of the predicted dynamics.

Natural systems are modeled by networks with nodes and links. Often, the nodes are segregated into communities with different connectivity patterns. Node heterogeneity such as political affiliation in social networks or biological function in gene networks is highlighted as a key factor driving the segregation of nodes into communities. Here, by means of numerical simulations, I show that node heterogeneity is not a necessary requirement. To this end I introduce the Ramsey community number $r_{\kappa }$, the minimum graph size that guarentees the emergence of network communities with almost certainty. Using the stochastic block model and Infomap methods for community detection, I show that networks generated by local rules have finite $r_{\kappa }$ values, while their randomized versions do not have emergent communities. I conjecture that network communities are an emergent property of networks evolving with local rules.

A critical question in epidemic control concerns the minimal requirements for a vaccination campaign to effectively halt a contagion process. However, control measures can inadvertently trigger resurgence dynamics, driven by a reservoir of susceptible individuals left unexposed in the controlled wave. This phenomenon, known as the “rebound effect,” is often preceded by a temporary drop in cases, usually termed as the “honeymoon period.” In this study, we examine the fundamental conditions for rebound dynamics within a metapopulation network framework. By elucidating the mechanisms underlying rebound events, we derive a rigorous mathematical criterion that identifies, based solely on the metapopulation network structure, the specific vaccination strategies likely to precipitate a rebound. Additionally, we propose an alternative vaccination protocol designed to eliminate rebound dynamics entirely. This approach is analytically validated and offers a robust pathway toward sustainable epidemic control.

A modification of the original Enskog equation, which is different from the so-called modified (or revised) Enskog equation, is proposed. The modification changes the correlation factor from a function of density to a functional of density in a simple form without series structure. The present modification is semiphenomenological but is generic to be adapted to a given equation of state for nonideal gases. It is shown that the H theorem can be established for the Enskog and the Enskog-Vlasov equation with the proposed modification.

We address the longstanding challenge in quantum many-body theory of reconciling unitary dynamics with irreversible relaxation. In classical chaos, the unitary evolution operator develops Ruelle-Pollicott (RP) resonances inside the unit circle in the continuum limit, leading to mixing. In the semiclassical limit, chaotic single-particle quantum systems relax with the same RP resonances. In contrast, the theory of quantum many-body RP resonances and their link to irreversibility remain underdeveloped. Here, we relate the spectral form factor to the sum of autocorrelation functions and, in generic many-body lattice systems without conservation laws, we argue that all quantum many-body RP resonances converge inside the unit disk, highlighting the role of nonunitary and the thermodynamic limit. While we conjecture this picture to be general, we analytically prove the emergence of irreversibility in the random phase model (RPM), a paradigmatic Floquet quantum circuit model, in the limit of large local Hilbert space dimension. To this end, we couple it to local environments and compute the exact time evolution of autocorrelation functions, the dissipative form factor, and out-of-time-order correlation functions (OTOCs). Although valid for any dissipation strength, we then focus on weak dissipation to clarify the origin of irreversibility in unitary systems. When the dissipationless limit is taken after the thermodynamic limit, the unitary quantum map develops an infinite tower of decaying RP resonances—chaotic systems display so-called anomalous relaxation. We identify the exact RP resonances in the RPM and prove that the same RP resonances are obtained from operator truncation. We also show that the OTOC in the RPM can undergo a two-stage relaxation, and that during the second stage, the approach to the stationary value is again controlled by the leading RP resonance. Finally, we demonstrate how conservation laws, many-body localization, and nonlocal interactions merge the leading RP resonance into the unit circle, thereby suppressing anomalous relaxation. Our findings clarify the microscopic origin of macroscopic relaxation in quantum systems and emphasize the role of RP resonances as a largely unexplored signature of many-body quantum chaos.

Real-world networks are often characterized by simultaneous interactions between multiple agents that adapt themselves due to feedback from the environment. In this article, we investigate the dynamics of an adaptive multilayer network of Kuramoto oscillators with higher-order interactions. The dynamics of the nodes within the layers are adaptively controlled through the global synchronization order parameter with the adaptations present alongside both pairwise and higher-order interactions. We first explore the dynamics with a linear form of the adaptation function and discover a tiered transition to synchronization, along with continuous and abrupt routes to synchronization. Multiple routes to synchronization are also observed due to the presence of multiple stable states. We investigate the bifurcations behind these routes and illustrate the basin of attraction to attain a deeper understanding of the multistability that is born as a consequence of the adaptive interactions. When nonlinear adaptation is infused in the system, we observe three different kinds of tiered transition to synchronization, viz., continuous tiered, discontinuous tiered, and tiered transition with a hysteretic region. Our study provides an overview of how inducting order parameter adaptations in higher-order multilayer networks can influence dynamics and alter the route to synchronization in dynamical systems.

Neuronal hyperexcitability is a key feature in the early stages of Alzheimer's disease (AD). However, the underlying mechanisms have not been fully elucidated, particularly the impact of amyloid β-peptide (Aβ)-mediated astrocyte dysfunction on neuronal hyperexcitability. Building upon recent experiments demonstrating that Aβ induces neuronal hyperexcitability by reducing glutamate uptake and increasing glutamate release in astrocytes, we have developed here a neurocomputational model of the Aβ-mediated astrocyte-neuron tripartite synapse. This model included a presynaptic neuron, a postsynaptic neuron, and an astrocyte, with information exchange between the neurons and the astrocyte facilitated by glutamate. The astrocytic glutamate pathways depended on synapse-cleft-oriented glutamate transporters (GLT-syn) and extra-synapse-oriented glutamate transporters (GLT-ess), metabotropic glutamate receptors (mGluR), and glutamate gliotransmitter release (Glio-Rel). Our numerical simulations have indicated that Aβ-induced down-regulation of astrocytic glutamate transporters and increased glutamate gliotransmitter release result in neuronal hyperexcitability, characterized by increased neuronal firing rate, enhanced presynaptic neuronal glutamate release intensity, and elevated postsynaptic neuron calcium concentration, which are in good agreement with previous experimental findings. Furthermore, our study has revealed that Aβ primarily induces hyperexcitation of presynaptic neurons through the Glio-Rel and GLT-ess pathways and hyperexcitation of postsynaptic neurons through the GLT-syn, Glio-Rel, and GLT-ess pathways. Additionally, we have found a strong, monotonically increasing correlation between the average firing rate of neurons and the average amplitude (or frequency) of astrocyte calcium oscillations, suggesting a close relationship between neuronal hyperexcitability and astrocyte calcium dysfunction. In conclusion, these results not only support experimental observations but also provide crucial insights into understanding neuronal hyperexcitation in AD.

Discovering the governing equations of physical systems from data is crucial for our deep understanding and effective modeling of such systems. In this paper, we propose a framework that integrates physics-informed neural networks (PINNs) with sparse regression to discover partial differential control equations from scarce and noisy data. Specifically, the framework effectively reduces the size of the candidate function library through dimensional verification while leveraging the powerful nonlinear fitting capabilities and automatic differentiation features of deep neural networks to model physical systems and compute candidate functions. We investigate and validate the effectiveness and robustness of the proposed method in discovering equations from data using three examples: the Burgers equation, the heat equation, and the Navier-Stokes vorticity equation. Comparisons with other methods that combine PINNs with sparse regression based on overcomplete libraries demonstrate that our approach achieves better discovery accuracy and smaller prediction errors. Additionally, we discuss various details of the framework, such as the process of discovering equations and the influence of measurement points and residual points on the results.

A class of type-2 Schloegl models is considered for particles on a square lattice with variable-range cooperativity. These models involve: (i) spontaneous particle annihilation at rate $p$; (ii) autocatalytic particle creation at unoccupied sites (i, j) with $n\ge 2$ particles within a specified neighborhood, ${\mathrm{\Omega }}_N(\mathrm{i},\mathrm{j})$, of $N$ sites at rate $k_n=\frac{\left(\genfrac{}{}{0pt}{}{n}{2}\right)}{\left(\genfrac{}{}{0pt}{}{N}{2}\right)}=\frac{n\left(n-1\right)}{N\left(N-1\right)}$; and (iii) possible spontaneous particle creation at unoccupied sites at “small” rate $\varepsilon \ge 0$. In some cases, ${\mathrm{\Omega }}_N$ just includes all symmetry-equivalent sites at a single specific distance $d$ (in units of lattice constants) from the unoccupied site, e.g., $d=1$ (nearest-neighbor sites) where $N=4$, or $d=\surd 5$ (or $\surd 13$ or…) where $N=8$. In other cases, ${\mathrm{\Omega }}_N$ includes sites multiple distances from the unoccupied site, e.g., $d=\{1,\surd 2\}$, where $N=8$. Kinetic Monte Carlo (KMC) simulation reveals that these models exhibit a nonequilibrium discontinuous phase transition between high- and low-density states below a critical point, $\varepsilon <{\varepsilon }_{\mathrm{c}}$, with generic two-phase coexistence (2PC) at least for smaller $N$. With some exceptions, there is an approach toward mean-field behavior with increasing $N$ (so the regime of generic 2PC shrinks, and ${\varepsilon }_{\mathrm{c}}$ approaches the mean-field value of 1/27). Additional insight into trends is provided by analysis of the exact master equations for the models via hierarchical truncation. These truncations utilize suitably tailored pair approximations which reflect the dominant nonequilibrium spatial correlations. These correlations in turn are shown to reflect the details of the autocatalytic particle creation process. For spatially heterogeneous states, the truncations produce coupled sets of lattice differential equations (LDE) which can describe orientation-dependent propagation of an interface between high- and low-density steady states for $\varepsilon <{\varepsilon }_{\mathrm{c}}$. Pair approximation values of $p=p_{\mathrm{eq}}$ where the interface is stationary, and its orientation-dependence, are in semiquantitative agreement with KMC results. This comparison accounts for propagation failure in the LDE which complicates interpretation.

We investigate the coarsening dynamics of a simplified version of the persistent voter model in which an agent can become a zealot—i.e., resistent to change opinion—at each step, based on interactions with its nearest neighbors. We show that such a model captures the main features of the original, non-Markovian, persistent voter model. We derive the governing equations for the one-point and two-point correlation functions. As these equations do not form a closed set, we employ approximate closure schemes, whose validity was confirmed through numerical simulations. Analytical solutions to these equations are obtained and well-agree with the numerical results.