Recent studies have used the Lorentzian ansatz to obtain mean-field reductions of Izhikevich neuron networks, but these approaches stop short of connecting microscopic dynamics to synchrony measures. In this work, we construct an equivalent phase model for the Izhikevich neuron and apply the Ott-Antonsen ansatz to derive mean-field equations in terms of the Kuramoto order parameter. This provides governing equations for the evolution of synchrony in networks of Izhikevich neurons. We further demonstrate that the conformal mapping originally derived for quadratic integrate-and-fire neurons remains valid for the Izhikevich model, thereby extending the link between voltage–firing-rate and phase-based descriptions to a broader and more biologically realistic neuron class. Using this mapping, we challenge the common assumption that high firing rates indicate strong synchrony, and instead show that high-amplitude oscillations in firing rate are the true signature of synchrony. This result holds across excitatory and inhibitory populations and suggests that EEG and MEG spectral power could serve as noninvasive biomarkers of underlying neuronal synchrony. Together, these findings extend mean-field reduction techniques to richer neuronal models, strengthen the bridge between mathematical theory and experimental observables, and provide new insight into the relationship between firing activity and collective neural dynamics.

We connect several notions relating the structural and dynamical properties of a graph. Among them are the topological entropy coming from the vertex shift, which is related to the spectral radius of the graph's adjacency matrix, the Randić index, and the degree assortativity. We show that, among all connected graphs with the same degree sequence, the graph having maximum entropy is characterized by a hierarchical structure; namely, it satisfies a breadth-first search ordering with decreasing degrees (BFD ordering for short). Consequently, the maximum-entropy graph necessarily has high degree assortativity; furthermore, for such a graph the degree centrality and eigenvector centrality coincide. Moreover, the notion of assortativity is related to the general Randić index. We prove that the graph that maximizes the Randić index satisfies a BFD ordering. For trees, the converse holds as well. We also define a normalized Randić function and show that its maximum value equals the difference of Shannon entropies of two probability distributions defined on the edges and vertices of the graph based on degree correlations.

We introduce an ensemble of spatial networks built from the junctions of hindered-rotation chains, incorporating directional correlations between bonds, an aspect ignored in the standard network modeling paradigm. The emergent random networks support geodesics with a wandering exponent $\xi =1/2$, and a travel-time fluctuation exponent $\chi =0$, consistent with the KPZ relation, yet violating the bound $\chi \ge 1/8$ predicted in the Poissonian framework. Transverse deviations follow the Kolmogorov distribution, indicating similarities between Brownian bridge excursions and geodesics in a random medium with correlated edges orientations. These results reveal a new universality class of Euclidean first-passage percolation, where local orientational memory reshapes transport properties and challenges existing bounds for random spatial networks.

We study the transition from classical radiation reaction, described by the Landau-Lifshitz model, to the quantum mechanical regime. The plasma is subject to a circularly polarized field where the self-consistent plasma current is the source of the electromagnetic field through Ampere's law. The radiation reaction implies wave energy loss, frequency up-conversion, and a modified distribution function. Increasing the value of the quantum $\chi$-parameter, the quantum results gradually differ from the classical ones. Moreover, the deviation between models also depends on the plasma parameters, including density and temperature. We discuss the implications of our findings.

A minimal coarse-grained model for cubic nanoparticles bound by magnetic dipolar forces is introduced, with limited site-site steric interactions. Static phase diagrams as a double function of the magnetic dipolar strength and the short-range attraction are computationally investigated for selected numbers of cubic particles. Despite some generic trends, the competition between directional magnetic interactions and the short-range anisotropic attraction with cubatic symmetry gives rise to very different structures showing linear, more spherical, or even columnar arrangements. The finite-temperature behavior explored using parallel tempering Monte Carlo simulations further suggests that the cubatic order is usually maximum at low temperature, in contrast with magnetic ordering which requires some significant thermal activation. Such a competition is also manifested in the multiple phase changes predicted to occur for specific system sizes as the result of cluster finite-size effects.

The aging transition refers to the cessation of oscillations in a network of coupled oscillators as the proportion of inactive elements increases beyond a critical threshold, and was first reported in Phys. Rev. Lett. 93, 104101 (2004) by Hiroaki Daido and Kenji Nakanishi. This is a universal phenomenon seen in biological systems. In this paper, we experimentally investigated the aging transition in a network using ten Wien-bridge oscillators for both local and nonlocal coupling configurations. The experimental results are validated by the LTspice simulator. Furthermore, it is observed that for a higher coupling strength, an abrupt transition occurs beyond which all the oscillators exhibit fixed point dynamics. This implies that, subsequent to this abrupt transition, the order parameter is independent of the fraction of inactive oscillators. This is true for both local and nonlocal couplings. Finally, we generalized our results to a globally connected network with the LTspice hybrid simulator. Thus, the present work involves the experimental verification of the aging transition using different coupling kernels.

Understanding how higher-order interactions shape the energy landscape of coupled oscillator networks is crucial for characterizing complex synchronization phenomena. Here we investigate a generalized Kuramoto model with triadic interactions, combining deterministic basin analysis, noise-induced transitions, and quantum annealing methods. We uncover a dual effect of higher-order interactions: They simultaneously expand basins for nontwisted states while contracting those of twisted states yet modify potential well depths for both. As triadic coupling strengthens, higher-winding-number states and nontwisted states gain stability relative to synchronized states. The system exhibits remarkable stability asymmetry, where states with small basins can possess deep potential wells, making them highly resistant to noise-induced transitions once formed. These findings extend quasipotential theory to high-dimensional networked systems and offer new insights for controlling synchronization in complex systems.

Radiation therapy is one of the most common cancer treatments, and dose optimization and targeting of radiation are crucial since both cancerous and healthy cells are affected. Different mathematical and computational approaches have been developed for this task. The most common mathematical approach, dating back to the late 1970s, is the linear-quadratic (LQ) model for the survival probability given the radiation dose. Most simulation models consider tissue as a continuum rather than consisting of discrete cells. While reasonable for large-scale models (e.g., human organs), continuum approaches necessarily neglect cellular-scale effects, which may play a role in growth, morphology, and metastasis of tumors. Here we propose a method for modeling the effect of radiation on cells based on the mechanobiological CellSim3D simulation model for growth, division, and proliferation of cells. To model the effect of a radiation beam, we incorporate a Monte Carlo procedure into CellSim3D with the LQ model by introducing a survival probability at each beam delivery. Effective removal of dead cells by phagocytosis was also implemented. Systems with two types of cells were simulated: stiff slowly proliferating healthy cells and soft rapidly proliferating cancer cells. For model verification, the results were compared to prostate cancer (PC-3 cell line) data for different doses, and we found good agreement. In addition, we simulated proliferating systems and analyzed the probability density of the contact forces. We determined the state of the system with respect to the jamming transition and found very good agreement with experiments.

Critically elastic materials—those that are rigid with a single state of self-stress—can be generated from parent systems with two states of self-stress by the removal of one of many constraints. We show that the elastic moduli of the resulting homogeneous and isotropic daughter systems are interrelated by a universal functional form parametrized by properties of the parent. In simulations of both spring networks and packings of soft spheres, judicious choice of parent systems and bond removal allows for the selection of a wide variety of moduli and Poisson's ratios in the critically elastic systems, providing a framework for versatile deterministic selection of mechanical properties.

We study single-variable approaches for describing stochastic dynamics with small inertia. The basic models we deal with describe passive Brownian particles and phase elements (phase oscillators, rotators, superconducting Josephson junctions) with an effective inertia in the case of a linear dissipation term and active Brownian particles in the case of a nonlinear dissipation. Elimination of a fast variable (velocity) reduces the characterization of the system state to a single variable and is formulated in four representations: moments, cumulants, the basis of Hermite functions, and the formal cumulant variant of the last. This elimination provides rigorous mathematical description for the overdamped limit in the case of linear dissipation and the overactive limit of active Brownian particles. For the former, we derive a low-dimensional equation system which generalizes the Ott–Antonsen Ansatz to systems with small effective inertia. In the latter case, we derive a Fokker–Planck-type equation with a forced drift term and an effective diffusion in one dimension, where the standard two- and three-dimensional mechanism is impossible. In the four considered representations, truncated equation chains are demonstrated to be utilitary for numerical simulation for a small finite inertia.

A hard-wall billiard is a mathematical model describing the confinement of a free particle that collides specularly and instantaneously with boundaries and discontinuities. Soft billiards are a generalization that includes a smooth boundary whose dynamics are governed by Hamiltonian equations and overcome overly simplistic representations. We study the dynamical features of an anisotropic soft-wall squircle billiard. This curve is a geometric figure that seamlessly blends the angularity of a square with the smooth curves of a circle. We characterize the billiard's emerging trajectories, exhibiting the onset of chaos and its alternation with regularity in the parameter space. We characterize the transition to chaos and the stabilization of the dynamics by revealing the nonlinearity of the parameters (squareness, ellipticity, and hardness) via the computation of Poincaré surfaces of section and the Lyapunov exponent across the parameter space. We expect our work to introduce a valuable tool to increase understanding of the onset of chaos in soft billiards.

Noether’s theorem is traditionally applied to Lagrangian systems to identify conserved quantities. In this work, we apply Noether’s theorem instead to a broad class of non-Lagrangian gradient flow partial differential equations (PDEs) arising in physics, showing how continuous symmetries constrain the evolution of such systems and, in certain special cases, still give rise to conserved quantities. We demonstrate symmetry-induced evolutionary constraints numerically on the thin-film equation with capillary and van der Waals forces, and also theoretically derive a conserved quantity for a singular fast-diffusion equation. These results not only provide a tool to analyze gradient flow PDEs; they also demonstrate the utility of Noether’s theorem beyond Lagrangians.

The multistage Adomian decomposition method (MADM) is a widely used algorithm for the numerical solution of fractional ordinary differential equations (FODEs). However, this study reveals that the traditional MADM yields distorted results for fractional-order problems due to a fundamental conceptual flaw: the improper handling of the nonlocal memory effect. By analyzing the derivation of the Adomian decomposition method we identify that the traditional multistage implementation neglects the accumulation of historical memory. A comparative analysis using a fractional FitzHugh-Nagumo neuron model demonstrates that the traditional MADM produces physically inconsistent results compared to the established predictor-corrector method. To address this, we propose a revised MADM that correctly incorporates the memory term via numerical integration. Comprehensive performance analysis reveals that the revised MADM is rigorously convergent and stable, and achieves superior absolute accuracy in the high-precision regime. Therefore, this research holds theoretical and practical value by preventing the continued use of a flawed method and by proposing a correct and efficient alternative, thereby opening new avenues for the numerical solution of FODEs.

This paper investigates absorbing-state phase transitions in opinion dynamics through a master-node network model analyzed using annealing approximation. We develop a theoretical framework examining three fundamental regimes: systems converging to complete disagreement, complete consensus, or both states depending on initial conditions. The phase behavior is governed by two key chiral parameters: $R$ measuring right-oriented influence and $L$ measuring left-oriented influence in the network interactions. Our analysis reveals a rich phase diagram featuring both continuous and discontinuous transitions between disordered and ordered phases. The discontinuous transition emerges in systems with two absorbing states, where the final configuration depends critically on initial opinion distributions. The annealing approximation provides fundamental insights into how asymmetric social influences (chirality) shape collective opinion formation, acting as a symmetry-breaking element that drives the system toward polarization or consensus.

Extensive optical measurements of canonical turbulent pipe flows have revealed the existence of structural boundary states (SBSs)—near-wall low-speed streaks strongly correlated with pairs of counter-rotating quasistreamwise vortices. In this study, we investigate the number fluctuations of these structures within the framework of statistical mechanics. Specifically, we introduce reduced degrees of freedom to model the low-speed streaks as a dilute lattice gas of hard-core particles. The Metropolis stochastic evolution provides, furthermore, a simple yet effective two-parameter model for describing SBS transitions. The lattice gas approach enables us to derive both the probability of SBS occurrence and the peculiar self-similar correlations that these structures exhibit along the streamwise direction. Our findings give additional support to the idea that the statistically stationary regimes of wall-bounded turbulent flows can be understood as Markov chains of coherent dynamical states in reduced-dimensional phase spaces.

Cavitation is a process where bubbles form and collapse within a fluid with dynamic, spatially varying pressure. This phenomenon can concentrate energy density by 12 orders of magnitude, creating light-emitting plasma or damaging nearby surfaces. A key question in cavitation theory and experiments is: What are the upper limits of energy density achievable through this spontaneous multiscale process? Among the many physical processes at play, we focus on fluid compressibility, modeled using the Tait-Murnaghan equation of state for a homentropic Euler fluid. Sonoluminescence represents the extreme limit of cavitation. Here, we examine an extreme case of experimentally realizable sonoluminescence, where spherical cavities have an initial radius that is 10 to 20 times their ambient radius and change their radius by a factor of over 100 during the collapse. To capture such extreme motion, with Mach numbers relative to ambient sound speed greater than one during the final stages of implosion, require methods beyond the classic approaches of Rayleigh and Gilmore. In this direction, we applied an all-Mach solver developed in the Basilisk framework, actively used to model bubble dynamics. Some of the reasons for its popularity include the fact that it is also expected to work for high Mach numbers, transport processes, nonspherical motion, shock wave capture, and involves low computational cost. Additionally, it has been tested for compressible motion at lower Mach numbers. Given its recent and extensive application, we endeavored to determine the specific solver's capability in resolving rapid bubble collapses. This solver was designed to handle the hydrodynamics of both the gas inside the bubble and the compressible fluid outside. However, we discovered that even at early times, when the Mach number is small and the fluid is approximately incompressible, the solver cannot accurately resolve the hydrodynamic motion within practical computational limits. To capture high Mach number motion and resolve dynamics in the sonoluminescence regime, we employed the well-established uniform bubble approximation for the ideal gas inside the bubble. Within this approximation, the all-Mach solver achieved numerically converging results describing the evolution of the bubble wall. Although compressibility slows down the collapse, these bubbles reach velocities exceeding the ambient speed of sound of the surrounding fluid. Our method works for various fluids and is applied to liquid lithium as well as water. Our results reproduce the equation-of-state-dependent asymptotic power-law region predicted by analytic calculations for water and liquid lithium in the case of an empty cavity. This confirms our method's ability to capture high Mach number motion and suggests that the asymptotic regime could be experimentally observed. When the cavity is filled with an ideal gas, the transition to Mach number greater than one in liquid lithium occurs later in the collapse than for water, making liquid lithium a possible candidate for achieving greater concentration of energy density. Furthermore, an outgoing shock wave, which can diagnose cavitation in opaque fluids such as liquid lithium, is captured without implementing an ad hoc construction algorithm for solutions based on characteristics or other approaches.

We introduce a strategy employing an adaptive genetic algorithm (GA) for iterative optimization of control sequences to generate quantum nonclassical states. Its efficacy is demonstrated by preparing spin squeezed states in an open collective spin model governed by a linear control field. Inspired by Darwinian evolution, the algorithm iteratively refines control sequences using crossover, mutation, and elimination strategies, starting from a coherent spin state within a dissipative and dephasing environment. We rigorously benchmark our method against constant control protocols and reinforcement learning, demonstrating competitive and robust performance. Furthermore, we showcase the GA's versatility by directly optimizing for metrologically relevant squeezing, achieving scalable performance, even in the presence of dissipation and thermal noise. The proposed strategy demonstrates a high state-preparation fidelity, exceeding 0.99, and provides a long time window for maintaining the spin squeezed state, even under dissipative conditions. We discuss feasible experimental implementations and potential extensions to alternative quantum systems, and the adaptability of the GA module. This research establishes the foundation for utilizing GA-like strategies in controlling quantum systems and achieving desired nonclassical states.

Tensor networks are employed to characterize the current fluctuations in one-dimensional diffusion-reaction systems. The representative system under study is a semiconducting material where holes and electrons constitute two types of charge carriers. These holes and electrons diffuse in the system with the reactions of pair-generation and -recombination occurring between them. The system is driven by imbalanced conditions imposed at two boundaries. The large deviation function encoding the full counting statistics of electric current is numerically calculated using the density matrix renormalization group. The fluctuation theorem is shown to hold for the current. Moreover, by comparing the cases where the reactions are turned on or off, it is revealed that the reactions have a damping effect on current fluctuations. This indicates an interesting inequality, suggesting that current fluctuations are upper bounded.

The $N$-step random walk, elongated in the vicinity of a disk (in 2D) or a sphere (in 3D) of radius $R$, demonstrates a nonalgebraic stretched exponential decay $P_N\sim exp(-\mathrm{const}{N}^{1/3})$ for the first-return probability $P_N$ in the double-scaling limit $N=\frac{L}{a}\gg 1,\frac{R}{a}\gg 1$ conditioned that $\frac{L}{R}=c=\mathrm{const}$. Stretching means that the length of the walk, $L=Na$ (where $a$ is the unit step length) satisfies the condition $L=cR$, where $c>\pi$ and under first return we understand the radial first arrival to a boundary. Both analytic and numerical evidence of the nonalgebraic behavior of $P_N$ are provided. Considering the model of a polymer loop stretched (inflated) by external force, we show that nonalgebraic behavior of $P_N$ affects the adsorption of a polymer at the boundary of a sticky disk in 2D, manifesting in a first-order localization transition.