In this work, we analyze the pattern formation in a delayed reaction-diffusion system on a square domain. Using bifurcation theory and amplitude equations, we reveal symmetry-breaking dynamics near criticality, including rotating waves and quasiperiodic solutions. We apply this framework to both a Ginzburg-Landau equation and a delayed predator-prey model, explaining spatiotemporal patterns such as standing and spiral waves. The main contributions are the derivation of explicit normal forms for systems with spatial symmetry and the development of a predictive approach that links model parameters to the selection and stability of nonlinear patterns.

Recurrence plots (RPs) are powerful tools for visualizing time-series dynamics; however, traditional recurrence quantification analysis often relies on global metrics, such as line counting, that can overlook system-specific, localized structures. To address this, we introduce recurrence pattern correlation (RPC), a quantifier inspired by spatial statistics that bridges the gap between qualitative RP inspection and quantitative analysis. RPC is designed to measure the correlation degree of an RP to patterns of arbitrary shape and scale. By choosing patterns with specific time lags, we visualize the unstable manifolds of periodic orbits within the Logistic map bifurcation diagram, dissect the mixed phase space of the Standard map, and track the unstable periodic orbits of the Lorenz '63 system's three-dimensional phase space. This framework reveals how long-range correlations in recurrence patterns encode the underlying properties of nonlinear dynamics, and it provides a more flexible tool to analyze pattern formation in recurrent dynamical systems.

For classical random walks on networks, the flux-fluctuation relation is an important characteristic that relates the mean flux and strength of fluctuations on the nodes. It was extensively studied before, although equivalent relations for quantum walks on networks remain unknown. In this work, a quantum version of the flux-fluctuation relation is obtained. It is valid for quantum walks on an arbitrary network, subject to the condition that the spectrum of the unitary walk operator is nondegenerate. Remarkably, for phase coherent quantum walks, the quantum flux-fluctuation relation is qualitatively similar to its classical counterpart, and quantum effects are insignificant. We numerically simulate quantum walks on periodic lattices and scale-free and Erdős-Rényi networks, and the results are consistent with the analytical quantum flux-fluctuation relation. We discuss the implications for the quantum walk dynamics if the spectrum of the unitary walk operator violate the nondegeneracy condition.

Economic complexity algorithms aim to uncover the hidden capabilities that drive economic systems. Here we present a fundamental reinterpretation of two of these algorithms, the economic complexity index (ECI) and the economic fitness and complexity (EFC), by reformulating them as optimization problems that minimize specific cost functions. We show that ECI computation is equivalent to finding eigenvectors of the network's transition matrix by minimizing the quadratic form associated with the network's Laplacian. For EFC, we derive a novel cost function that exploits the algorithm's intrinsic logarithmic structure and clarifies the role of the regularization parameter in its nonhomogeneous version. Additionally, we establish the existence and uniqueness of its solution, providing theoretical foundations for its application. This optimization-based reformulation bridges economic complexity and established frameworks in spectral theory, network science, and optimization. The theoretical insights translate into practical computational advantages: We introduce a conservative, gradient-based update rule that substantially accelerates algorithmic convergence, with potential implications for a broader class of algorithms, including the Sinkhorn-Knopp method. Finally, we apply the energetic framework to a real-world trade network, demonstrating how linkwise energy provides a direct way to identify structurally relevant and vulnerable regions of the export matrix, thus complementing and enriching standard economic complexity analyses. Beyond advancing our theoretical understanding of economic complexity indicators, this work opens new pathways for algorithmic improvements and extends applicability to general network structures beyond traditional bipartite economic networks.

The use of statistical physics models to investigate real-world networks and reveal their underlying dynamics has shown promising results and acquired increasing attention. Here, we show how exponential random-graph (ERG) models can be suitably adopted to characterize how Alzheimer's disease (AD) affects brain connectivity. Magnetic-resonance imaging (MRI) of the brain was used to define a brain connectivity network whose nodes are the different brain regions, and the links indicate the pairwise structural relationships. Based on T1-weighted MRI brain scans of 126 normal controls (NC) and 92 AD patients, ERGs were able to outline both “global” and “local” disease patterns. Our findings demonstrate that ERGs accurately highlight how AD affects brain connectivity reaching an overall classification accuracy of $0.82\pm 0.08$. Besides, ERGs outline which regions of the brain are the most affected by the disease, thus proving to be a formidable instrument also to investigate the disease pathological mechanisms; more importantly, as these effects are evaluated at patient level, they can be exploited to design innovative diagnosis support systems or to provide a novel explainable framework for decision support systems. Finally, thanks to its generality, the approach proposed in this study paves the way for further applications and investigations inquiring into the use of ERGs for other diseases and different data sources or the use of alternative models.

The article presents the results of experiments on studying the radiation heating of targets by soft x-rays (SXRs) of the Z-pinch of a wire array. The SXR power pulses had amplitudes of up to 10 TW and a duration of $\sim 6-10\mathrm{ns}$ at half-maximum. In this series of experiments, the main focus was on the dynamics of expansion of target plasma made of thin films of various substances (Mylar, Ni, Gd, Au, Bi, etc.). Numerical modeling of heating, expansion, and self-emission of the target plasma made of Mylar film with or without a metallization layer was carried out using the two-dimensional radiation hydrodynamics code ralef-2d. We compared the calculated results with experimental data on plasma expansion obtained through laser shadow probing. Already at the stage of the x-ray prepulse, we observed a strong difference in the magnitude of the plasma boundary displacement of the Mylar targets with and without gadolinium deposition, calculated using the ralef-2d model and determined using laser shadow images. After the moment of peak radiation power, the difference between the calculated and experimental data increases. It is shown experimentally that the magnetic field of the discharge current of the SXR source (Z-pinch of a tungsten wire array) has a significant effect on the dynamics of the expansion of the plasma of the targets located in the anode-cathode gap of the facility. Experiments with targets whose plasma expands in magnetic field-free regions show good agreement between the observed expansion dynamics and ralef-2d calculations.

The pseudopotential lattice Boltzmann (LB) method has significant advantages in the simulation of liquid-vapor two-phase flow and phase-transition behavior of cryogenic fluids. However, prior research on multiphase flows employing the LB method primarily utilizes the cubic Peng-Robinson equation of state, which has limited accuracy in predicting thermodynamic properties of fluids, in particular for cryogens. This study presents a thermodynamic perspective on the performance of different equations of state in LB simulations, including high-precision equations of state such as those in Helmholtz energy form and the modified Benedict-Webb-Rubin equation of state. The performance of various equations of state within the entire two-phase region, ranging from the triple-point temperature to the critical-point temperature, is comparatively evaluated. It is found that the two-phase region characteristics of equations of state, which are often overlooked in traditional thermodynamics, significantly impact simulation stability. The feasibility and superiority of high-precision equations of state in simulating cryogenic fluids are further substantiated through analysis in three key aspects: liquid-vapor coexistence density, surface tension, and spurious velocity.

We study the dynamics of user-agent interactions in virtual environments through mathematical models derived in a Lagrangian formalism. The goal is to optimize the number of agents required to solve a generic predefined task while minimizing the computational cost to achieve it. Specifically, we derived Euler-Lagrange equations of motion to describe the different ways in which agents may interact with users. The main advantage of this approach lies in its peculiarity to derive a scaling law for any interaction rule one wishes to design, ensuring that the system scales while optimizing the global impact of the interactions. By specifying an action functional over interaction trajectories and enforcing its minimization, the optimal way to allocate agents emerges naturally as Euler–Lagrange equations, embedding the entire optimization strategy directly into the formalism. This intrinsic coupling of dynamics and cost yields a universal procedure to compute the scaling laws for arbitrary interaction rules, ensuring that agent populations and computational expense grow according with environmental complexity. We illustrate the methodology with two specific example. These results also offer a foundation for further research into multi-agent dynamics and their applications in virtual environments.

Understanding contact between rough surfaces undergoing plastic deformation is crucial in many applications. We test Persson's multiscale contact mechanics theory for elastoplastic solids, assuming a constant penetration hardness. Using a numerical model based on the boundary element method, we simulate the contact between a flat rigid surface and an elastic-perfectly plastic half-space with a randomly rough surface. The theory's predictions for elastic, plastic, and total contact area agree quantitatively with the numerical results. The simulations also support the boundary conditions assumed in the theory, namely that the stress probability vanishes at both zero and yield stress. These findings reinforce the validity of the theory for systems with constant hardness.

Semi-Markov processes play an important role in the effective description of partially accessible systems in stochastic thermodynamics. They occur, for instance, in coarse-graining procedures such as state lumping and when analyzing waiting times between few visible Markovian events. The finite-time measurement of any coarse-grained observable in a stochastic system depends on the specific realization of the underlying trajectory. Moreover, the fluctuations of such observables are encoded in their rate function that follows from the rate function of the empirical measure and the empirical flow in the respective process. Derivations of the rate function of empirical measure and empirical flow in semi-Markov processes in which the sojourn time in a state is independent of the next state, a property called direction-time independence (DTI), exist in the mathematical literature, but have not received much attention in the stochastic thermodynamics community. We present an accessible derivation of the rate function of the tuple frequency, i.e., the frequency of two consecutively observed states, in discrete-time Markov chains, and extend this to the rate function of the empirical semi-Markov kernel in semi-Markov processes without DTI. From this, we derive an upper bound on the rate function of the empirical entropy production rate, which leads to a lower bound on the variance of the mean entropy production rate measured along a finite-time trajectory. We illustrate these analytical bounds with simulated data.

Synchronization of coupled oscillators is a fundamental phenomenon in physics, exemplified by the Kuramoto model. In many practical systems (robotic networks, power grids) and numerical simulations, the dynamics are inherently discrete. We prove rigorously that in the discrete-time Kuramoto model, phase locking is achieved if and only if only finitely many oscillator collisions occur. Under a small step-size regime ($\kappa h\le 1$), collision events become the sole factor determining convergence. In particular, for identical-frequency oscillators every trajectory is collision free and thus synchronizes. For heterogeneous frequencies, we derive explicit bounds on initial phase spread and frequency differences that guarantee eventual phase locking. Conversely, large time steps can prevent synchronization: we show even two identical oscillators fail to lock if $\kappa h>2$. Extensive numerical simulations illustrate both phase-locking and divergent behavior under different conditions. The finite-collisions perspective clarifies synchronization criteria in discrete networks and suggests collision avoidance as a practical diagnostic for robust timing in digital oscillator systems such as swarm robotics or microgrid control systems.

We investigate the influence of nonlinear gravity corrections, arising from the Eddington-inspired Born-Infeld (EiBI) theory on wave dynamics, stability, and energy transport processes in polytropic, viscous, and turbulent solar plasmas. Analytical and numerical analyses of the Jeans-normalized quadratic dispersion relation demonstrate that both the EiBI gravity parameter $\left(\chi \right)$ and the relative polytropic sound speed $\left(\beta \right)$ independently regulate oscillation frequencies, growth rates, phase velocities, perturbation energy partitioning, and outward acoustic energy flux. Positive $\chi$ systematically elevates oscillation frequencies, phase velocities, and outward energy flux level by $\sim 10\%$ relative to the Newtonian predictions, while larger $\beta$ enhances them by up to 55%, thereby promoting wave propagation and efficient acoustic transport. Conversely, negative $\chi$ strengthens gravitational binding and increases damping rates by $\sim 40\%$, particularly for the $g$ modes. Energy partitioning analyses reveal that the EiBI corrections fundamentally restructure the kinetic-electrostatic-gravitational energy balance. While the Newtonian gravity contributes negligibly ($<4\%$), nonzero $\chi$ channels up to one-third of oscillation energy into gravitational modes. The modal surface flux calculations further confirm that only the $p$ modes drive outward energy transport (amplification for $\chi >0$, suppression for $\chi <0$). A direct comparative analysis with four years of SDO/HMI Doppler velocity observations demonstrates a robust theoretical agreement for $\chi =3\times {10}^7{\mathrm{m}}^5{\mathrm{kg}}^{-1}{\mathrm{s}}^{-2}$, providing an empirical constraint on the solar EiBI gravity through helioseismology. These findings establish a rigorous framework for testing modified gravity theories and for advancing our understanding about solar plasma stability, helioseismic signatures, and ambient atmospheric energy transport processes.

Rotational intrusion into granular media is crucial for small body sampling but remains less studied than its non-rotational counterpart. Using a GPU-accelerated discrete element method, we investigate the resistance of a rotating cylindrical penetrometer as a function of the Froude number. Unlike quasi-static intrusion, which creates a stagnant zone ahead of the intruder, rotation disrupts this structure, inducing shear dilation both in front of and around the intruder. This results in a thin, highly mobilized layer of particles, causing the slope of the force-depth to decrease following a negative power-law relationship with increasing Froude number. As rotation intensifies, the rate of resistance reduction slows, and sliding friction becomes negligible, while rolling and torsional resistances remain significant. Furthermore, introducing cohesion shifts the granular medium's response from plastic to elasto-plastic, significantly altering the force-depth relationship and leading to resistance saturation. A brief gravity scan shows that weaker gravity modestly increases the depth-dependence of relative resistance and amplifies the influence of rotation. These findings enhance the understanding of rotational intrusion mechanisms under micro-gravity.

This study employed carbon K-edge soft x-ray absorption spectroscopy (XAS) to investigate phase-dependent intermolecular interactions in the nematic liquid-crystal molecule 4-cyano-4′-pentylbiphenyl. Temperature-dependent XAS measurements revealed discontinuous shifts in core excitation peak energies across the solid, liquid-crystal, and liquid phases. Density functional theory calculations were used to assign spectral peaks to specific functional groups, namely, biphenyl and cyano, elucidating their distinct roles in intermolecular interactions. The results indicate that π–π interactions between biphenyl rings dominate in the solid phase, whereas in the liquid-crystal phase, antiparallel dimerization is primarily driven by interactions involving cyano groups. Overall, these findings demonstrate that soft XAS, combined with theoretical modeling, can provide critical insights into the weak intermolecular interactions that govern phase behavior in soft matter systems.

We present a tabletop method to investigate how tailored laser excitation can enhance shock wave generation in water. By delivering two spatiotemporally separated laser pulses focused into a confined liquid layer, we identify an optimized excitation condition that maximizes the resulting shock pressure. Remarkably, dual-pulse laser excitation leads to an overall shock pressure that far exceeds the sum of the shock pressures generated by the individual pulses. This nonlinear amplification reveals a previously unexploited laser-matter interaction regime that overcomes saturation limits in laser-driven shock generation.

The eigenstate thermalization hypothesis (ETH) underpins much of our modern understanding of the thermalization of closed quantum many-body systems. Here, we investigate the statistical properties of observables in the eigenbasis of the Lindbladian operator of a Markovian open quantum system. We demonstrate the validity of a Lindbladian ETH ansatz through extensive numerical simulations of several physical models. To highlight the robustness of Lindbladian ETH, we consider what we dub the dilute-click regime of the model, in which one postselects only quantum trajectories with a finite fraction of quantum jumps. The average dynamics are generated by a nontrace-preserving Liouvillian, and we show that the Lindbladian ETH ansatz still holds in this case. On the other hand, the no-click limit is a singular point at which the Lindbladian reduces to a doubled non-Hermitian Hamiltonian and Lindbladian ETH breaks down.

Observing superdiffusive fluctuations from Kardar-Parisi-Zhang universality in isotropic integrable spin chains is usually challenging as it requires a fairly large number of spins in interaction. We demonstrate in this paper, in the context of classical spins, that accounting for boundary effects lowers the bar, down to a few dozen spins in some cases. Additionally, boundaries control the relaxation to stationarity, which leads to many new universal scaling functions to explore, both in periodic spin chains and for open chains with magnetization imposed by reservoirs at the ends.