Chemical reaction network (CRN) theory is widely utilized to model and analyze a wide range of biochemical phenomena. Structural transformations and reductions serve as essential tools to better understand how topological properties of a CRN are related with specific functions. In this context, graph-based representations of CRNs have been explored; however, their connections to concentration dynamics and thermodynamics remain elusive. In this study, we propose a natural transformation from the classical complex-reaction graph to a species-transition graph, leveraging the conservation laws of the stoichiometric matrix. By introducing transition matrices on the species graph, the concentration dynamics of CRNs are reinterpreted as the differences between the physically observable inflow and outflow of species. This approach enables the formal lumping of multiple reactions into fewer interactions, which we demonstrate using a realistic metabolic model of E. coli. Additionally, we define species-specific thermodynamic quantities on the species graphs and establish bounds relating them to conventional reactionwise quantities. The specieswise bounds of conventional driving forces and entropy production rates can outperform the bounds determined by reactionwise flux fluctuations, as illustrated through numerical simulations with the Brusselator model. The proposed framework unifies graph-based representations of CRNs with concentration dynamics and thermodynamic principles, offering novel insights and computational advantages for analyzing complex biochemical networks.

During the 23 April 2023 geospace storm, we observed chorus-wave-driven, energetic particle precipitation on closed magnetic field lines in the dayside magnetosphere. Simultaneously and in the ionosphere's bottom side, we observed signatures of impact ionization and strong enhancements in the ionospheric electric field, via radar detection of meter-scale turbulence, and with temporal characteristics matching those of the magnetospheric observations. We detail this in another work [M. F. Ivarsen et al., Phys. Rev. E 112, 045204 (2025)]. In the present article we place those observations into context with the dayside ionosphere and describe a remarkably similar event that took place during the May 2024 geospace superstorm. In both cases, fast, eastward-moving electric field structures were excited equatorward of the ionospheric cusp, on closed magnetic field lines, observations that challenge existing modes of explanation for electrodynamics in the cusp region, where most such observations are interpreted in the context of poleward-moving auroral forms. Instead, primarily eastward-moving electric field structures were associated with turbulent Hall currents that are perhaps characteristically excited during geospace storms by wave-particle interactions near the magnetospheric equator or by proton precipitation characteristics in the cusp, forming a parallel-plate capacitorlike effect. We propose that transient eastward electrodynamic bursts in the dayside ionosphere might be a common, albeit previously unresolved, feature of geomagnetic storms.

At night in Earth's polar regions, energetic aurorae frequently penetrate into the atmosphere, with the peculiar effect of driving turbulent electrojet currents in the bottomside ionosphere. During the day, however, Earth's plasma environment becomes highly conductive, owing to the constant flux of extreme ultraviolet radiation emitted from the Sun. The high-conductivity plasma in the dayside ionosphere can effectively short out plasma turbulence around aurorae, and so electrojet turbulence is thought rare in the dayside high-latitude ionosphere. In this paper we show observations to the contrary. During the onset of the 23 April 2023 geomagnetic storm, we observed prolific small-scale plasma turbulence in the dayside $E$ region on closed magnetic field lines just equatorward of the cusp. Using data from two orbiting satellites, we infer the locations of the cusp and the distributed presence of diffuse aurorae, through observations of electron fluxes and wave-particle interactions near the magnetospheric equator, on nearby magnetic field lines. The resulting diffuse aurorae pass electric fields and produce unstable gradients in the plasma density. The number and intensity of the falling charges momentarily overwhelm the capacity of the lower ionosphere to extinguish the strong electric fields that follow from this action, spurring the growth of transient, turbulent electrojets, or Hall currents. In the 23 April 2023 case study, we establish a correlation between observations of chorus-wave activity near the magnetospheric equator and observations of turbulent electrojets in the ionosphere on closed magnetic field lines, from which we infer a causal chain where magnetospheric plasma waves ultimately drive small-scale turbulence in the ionosphere. We show how the predictions are brought to fruition in similar supporting events. Finally, we briefly discuss the implications that this discovery bears for the electrodynamics of the dayside ionosphere. In the following paper [M. F. Ivarsen, Phys. Rev. E 112, 045203 (2025)] we follow the lengthy argument to a logical conclusion, leading to an alternative description of electrodynamics in the cusp region.

Resonances play a crucial role in media sustaining oscillatory phenomena, such as plasmas. We show with experimental results and numerical simulations that the wakefields driven by individual successive bunches in overdense plasma superpose linearly, and that their amplitude increases along the train, under optimal coupling with plasma density oscillations. We also demonstrate, for the first time, that a train of bunches with increasing charge can be used to enhance the transformer ratio of the acceleration process, hence improving the energy-transfer efficiency.

Radiative transfer in curvilinear geometries has wide applications across engineering and scientific fields. However, solving the radiative transfer equation (RTE) in curvilinear coordinate systems remains challenging due to its complexity. A universal and simple numerical method is still lacking. This paper presents a lattice Boltzmann method (LBM) for radiative transfer in curvilinear coordinates. Through Chapman-Enskog analysis, the LB model is rigorously derived from the curvilinear RTE. By incorporating the metric tensor and a curvilinear radiative transfer operator, the method maintains simplicity while being applicable to curvilinear systems. Numerical tests confirm its accuracy and stability, and asymptotic analysis proves second-order convergence. As an application, we study thermal radiative transfer in fiber lasers, providing insights for optimized fiber design. The proposed LBM offers an efficient tool for curvilinear radiative transfer problems.

Systems of particles interacting via stealthy potentials, a family of soft, long-ranged, isotropic pair potentials, possess infinitely degenerate disordered hyperuniform classical ground states of fundamental and practical interest, highlighted by their novel optical and mechanical properties. The configurational dimensionality of the ground-state manifold depends on a dimensionless parameter $\chi$ that measures the number of independently constrained degrees of freedom in a ground state. Starting from a wide class of initial two-dimensional point configurations, we study the evolution of trajectories of the collective-coordinate optimization procedure to their corresponding disordered stealthy hyperuniform ground states as a function of $\chi$ within the disordered regime ($0<\chi <1/2$). Initial conditions studied span a wide class of disordered systems, including antihyperuniform, nonhyperuniform, and hyperuniform ones. The evolution of the trajectories is quantified by computing a translational order metric and configurational proximity metric as a function of the computational time for selected values of $\chi$ within the disordered regime. The rate at which trajectories approach the ground-state manifold is fastest for those evolved from hyperuniform states and slowest for those evolved from antihyperuniform states. We observe that ground-state ensembles with distinct pair statistics are sampled by different initial conditions across a broad range of $\chi$ and that these pair statistics are generally effected by higher-order spatial correlations characterizing the initial condition. Learning how to manipulate initial conditions in the optimization procedure to target different portions of the ground-state manifold enables one to explore structurally unique stealthy ground states with designed short- up to intermediate-ranged spatial correlations for the purposes of materials discovery.

The persistent assembly and clustering in active systems, ranging from biological aggregates to synthetic active matter, is governed by the interplay of self-propulsion, environmental stimulus, and interparticle interactions. This study investigates how self-propelled particles (SPPs) dynamically organize around spatially distributed attractive points, which act as targets for directed motion. The systematic variation of alignment sensitivity, particle number, and noise reveal distinct regimes of cluster formation and stability. At low noise levels, particles exhibit coherent alignment toward attractors, forming dynamic rotating clusters whose behavior is highly sensitive to alignment rate. Increasing alignment strength along with the number of SPPs breaks rotational symmetry leading to ordered phases, while noise introduces disordered or transient phases. Single-particle motion in the presence of convex quadrilateral arrangement of attractive points reveals patterns reminiscent of deterministic limit cycles, with alignment strength acting as a tuning parameter for spatial oscillations. In the case of multiple SPPs we identify three regions depending on the strength of the aligning angular momentum and number of SPPs as disordered, ordered rotating cluster, and ordered static clusters. We observe a weakly second-order phase transition from a disordered phase to an ordered phase. The study reveals how active particles exhibit some order around competing environmental cues such as food sources.

Remote synchronization (RS) has recently attracted a lot of attention, but it is mainly focused on the synchronization among leaf nodes of a star graph and thus cannot be applied to the synchronization between distant nodes across different regions of a brain network. To understand how the distant connections of the brain functional network come from its structural network, we extend our previous bridge-connected model of two star graphs to the case of multiple connected star graphs. We surprisingly find that this extended model can show not only the RS among all the leaf nodes, but also a new form of RS between distant leaf nodes without the involvement of any middle nodes. We call the former as relay RS and the latter as distant RS. To the best of our knowledge, this is the first implementation of a distant RS in star-like graph models, and thus may open a window for applying RS to discuss the mechanisms of long connections in brain structural networks. Further, we show that there are two necessary conditions for the emergence of distant RS: (i) heterogeneous morphology of the network and (ii) asymmetric couplings between the bridge links and non-bridge links. Finally, we present a brief theoretical analysis to explain the distant RS and find that the key element is the dynamical symmetry, in contrast to the previous morphology symmetry.

We have explored the nonlinear dynamics of six common, driven, diatomic molecules using a shifted Tietz-Wei (sTW) model of their molecular potential functions. We focused on the variations in their resonances, bifurcations and multistability with changes in the spectroscopic and driving force parameters, namely the dissociation energy ($V_0$), the potential function optimization parameters ($b_h$ and $c_h$), driving frequency ($\omega$), and amplitude ($F_0$). We used the method of multiple timescales to obtain frequency response curves for the primary and secondary superharmonic resonances. The primary resonances were larger for ${\mathrm{I}}_2$ and ${\mathrm{Cl}}_2$ than for CO or ${\mathrm{O}}_2$. Variations in $F_0,b_h$, and $c_h$ had profound impacts on the primary resonance features, with higher $F_0$ and lower $V_0$ enhancing the response amplitude. Evidence for hysteresis in the frequency-response—a signature of multistability—is demonstrated. Superharmonic resonances are marked by increased amplitudes and significant hysteresis, especially for ${\mathrm{I}}_2$ and ${\mathrm{Cl}}_2$, driven by large $F_0$ at low $V_0$. Bifurcation diagrams, maximal Lyapunov exponents, and Poincaré maps were used to unravel the transitions between periodic and chaotic states. Period-doubling bifurcations, sudden chaos, and an abundance of crisis events, viz boundary, interior, and attractor-merging crises, were identified as the routes to a range of different chaotic states. Symmetry-breaking, attractor-bubbling, and multistability were all found and are reported. Coexisting attractors and their basins of attraction showed striped, fractal, and Wada-like basin structures. The results highlight the complex dynamics stemming from the interaction between spectroscopic properties and external excitations of the sTW oscillator in diatomic molecules. They carry significant implications for experimental applications.

We demonstrate that the dynamics of an observable localized at a single-site is sufficient to determine whether a many-body quantum system exhibits level statistics characteristic of random matrix theory, which is a widely used diagnostic of quantum chaos. Specifically, we analyze the spin autocorrelation function at a single site evolving under a disordered spin-1/2 chain, a setup realizable in ongoing experimental platforms. We also investigate the partial (subsystem) survival probability, recently measured in cold-atom experiments, thereby broadening discussions on detecting many-body quantum chaos via survival probability [Phys. Rev. Res. 7, 013181 (2025)]. Given the precision and timescales currently achievable, our results indicate that the detection of many-body quantum chaos through dynamical observables is feasible but constrained to small system sizes.

We investigate the diffusion of linguistic innovations on a fully connected network to understand the emergence of linguistic diversity. We employ an agent-based dynamics based on the Axelrod model, where interactions between agents are driven by homophily and social influence, with the difference that we assume that all agents share a number of common features that ensure a finite probability of pairwise interaction. We start from a homogeneous population and introduce zealots that act like agents spreading linguistic innovations, without being influenced by other agents. We analyze how different factors, such as the degree of cohesion and number of zealots in different linguistic states, determine the linguistic configurations that populations can adopt and contribute to the possible emergence of a multilinguistic community. The results are compared with those derived within the mean-field approximation.

A unique coherent bremsstrahlung (CB) regime is proposed for the generation of an isolated half-cycle attosecond pulse (AP), even for the case of a multicycle driving laser pulse, which is realized by the laser pulse interacting with the double-foil target. When the rising edge of the laser pulse interacts with the double-foil target, the AP train is generated in the reflected direction due to the fact that the relativistic electron sheet (RES) is generated periodically twice per cycle of the laser pulse. While the peak cycle of the laser pulse interacts with the target, the electrons of the second foil target were nearly completely removed, which leads to the formation of an electrostatic potential well, and then the double-foil target becomes an electrostatic storage target (EST) that can capture and store electrons coming from the second foil target. Accordingly, only one RES can be generated by the peak cycle of the laser pulse interacting with those electrons stored in the EST, and is accelerated to ultra-relativistic velocity in the transmission direction, which emits the isolated AP by the CB regime. The isolation regime of AP can be determined by the scaling law of the depletion of electrons, which is described by the ratio of the areal charge density of the double-foil target and the amplitude of the peak-cycle laser pulse. The ratio is called the generalized similarity parameter. The generalized similarity parameter is about $2/\pi$, which is predicted by the theoretical model and confirmed by the simulation results. The robustness of the isolation regime of AP is confirmed by considering different parameters of the laser pulse and plasmas, and by considering the presence of preplasma and two-dimensional effects.

Recovering coherent structures from sparse or partially sampled flow field data is inherently challenging, and traditional spectral proper orthogonal decomposition (SPOD) methods are further constrained by high computational cost, memory demands, and limited applicability. To mitigate incomplete experimental coverage and the computational constraints of high-fidelity simulations, this study proposes a spatially compressed SPOD (scSPOD) method to reconstruct global flow modes from spatially nonuniform datasets. The method integrates the assumption of spectral translation with clustering, compressed sensing, and optimization to directly recover SPOD modes from spatial subsets while preserving dominant spectral features. Validation is conducted using two representative cases: a direct numerical simulation of flow past a cylinder with a tonal spectrum and a large eddy simulation of tip leakage flow exhibiting broadband characteristics. In both cases, scSPOD accurately identifies the spatial structure of flow modes across the domain, while the quantitative reconstruction accuracy is notably high for first-order modes associated with low-rank behavior. A spectral concentration metric $\theta$ is introduced to quantify this property, with a threshold of $\theta \ge 0.75$ that ensures high reconstruction accuracy. When this condition is satisfied, the reconstruction deviation of the first-order modes remains below ${10}^{-4}$ using only $3.03\%$ of the cylinder flow data, and averages around ${10}^{-2}$ using $11.18\%$ of the leakage flow data. These results confirm the feasibility and effectiveness of scSPOD and highlight its potential for low-cost, high-fidelity flow diagnostics in complex fluid systems.

We propose ratio divergence (RD) learning for discrete energy-based models, a method that utilizes both training data and a tractable target energy function. We apply RD learning to restricted Boltzmann machines (RBMs), which are a minimal model that satisfies the universal approximation theorem for discrete distributions. RD learning combines the strength of both forward and reverse Kullback–Leibler divergence (KLD) learning, effectively addressing the “notorious” issues of underfitting with the forward KLD and mode collapse with the reverse KLD. Since the summation of forward and reverse KLD seems to be sufficient to combine the strength of both approaches, we include this learning method as a direct baseline in numerical experiments to evaluate its effectiveness. Numerical experiments demonstrate that RD learning outperforms other learning methods in terms of energy function fitting, mode-covering, and learning stability across various discrete energy-based models. Moreover, the performance gaps between RD learning and the other learning methods become more pronounced as the dimensions of target models increase.

Recent years have seen a rise in the application of machine learning techniques to aid the simulation of hard-to-sample systems that cannot be studied using traditional methods. Despite the introduction of many different architectures and procedures, a wide theoretical understanding is still lacking, with the risk of suboptimal implementations. As a first step to close this gap, we provide a complete analytic study of the widely used global annealing (also called sequential tempering) procedure applied to a shallow MADE architecture for the Curie-Weiss model. The contribution of this work is twofold: first, we give a description of the optimal weights and of the training under gradient descent optimization. Second, we compare what happens in global annealing with and without the addition of local Metropolis Monte Carlo steps. We are thus able to give theoretical insight into the best procedure to apply in this case. This work establishes a clear theoretical basis for the integration of machine learning techniques into Monte Carlo sampling and optimization.

In this paper, a unified lattice Boltzmann model is developed to solve the multiterm time-fractional mixed diffusion and diffusion-wave equations. To obtain the standard form of the equation, the Caputo derivative terms are approximated using numerical differentiation and composite integration rules. By selecting appropriate auxiliary distribution functions and equilibrium distribution functions, the macroscopic equation is properly recovered. A series of numerical simulations are performed, demonstrating that the results of the proposed method agree well with the analytical solutions. The efficiency of the proposed lattice Boltzmann model is thus validated.

In a ferroelectric nematic liquid crystal, the electrostatic interaction can induce a spontaneous cholesteric helix, even if the material is not chiral. If the liquid-crystal cell is infinitely thick, then the predicted pitch depends continuously on material parameters. Here, we consider how the prediction must be modified in a cell of finite thickness. If the Debye screening length is large enough, we find that the free energy has multiple minima. In these minima, the cholesteric pitch is locked to the cell thickness, so that the cell contains an integer number of pitches. However, if the screening length is smaller, then the cholesteric pitch can vary continuously.

The Frenkel-Kontorova model is a simple yet generic framework for the description of tribological phenomena and processes, including dry solid friction and the motion of adsorbed layers. As revealed in this work, it also reproduces qualitatively various features of complex liquids, such as, power-law subdiffusion between the ballistic and the diffusive regimes as well as a crossover from a non-Arrhenius to an Arrhenius dependence of the diffusion coefficient near the temperature, where the specific heat assumes its maximum. By systematically analyzing these thermal and kinetic properties, we also identify and clarify several misconceptions prevalent in the literature. Most notably, we show that the shear thinning with a shear-thinning exponent close to zero can be the natural consequence from enforced basin hopping: the energy drops caused by shear-induced instabilities dictate the friction-velocity dependence at medium shear rates rather than the way how shear forces reduce the free energy barriers for directed motion. Our findings thus demonstrate that even if the rheology is described by semiempirical theories such as the Eyring model, any agreement with experimental data, whether past, present, or future, may be purely coincidental.

We investigate the avalanche dynamics of thermal relaxation in glassy systems after a rapid quench by molecular simulation. We find that the particle rearrangements show local rearrangements with long-range quadrupolar displacements, and their sizes follow a power-law distribution satisfying a simple scaling relation. These results imply the relation between thermal relaxation of glassy systems, and avalanches in sheared amorphous solids and a recent theory on the thermal elastoplastic model. However, we also observe the properties unpredicted by the previous theories, including the smaller exponent of the distribution and the non-power-law growth of avalanche size against system size. Our results suggest that by viewing a glass as a thermally driven elastoplastic material, we can understand dynamics below the glass transition point, such as aging.

The main goal of this paper is twofold. First, we want to demonstrate how the forward and backward Feynman-Kac equations can be extended to account for the general form of Markov processes described by the differential Chapman-Kolmogorov equations. Second, we demonstrate specialization of these equations for different models of Markov processes, ranging from classical diffusion to more computationally challenging jump diffusion with drift, regime switching, and hybrid systems with resetting. To illustrate the power of the extended Feynman-Kac formalism, we consider different settings corresponding to various models of the stochastic process. We provide the closed-form solutions to the respective problems for an arbitrary initial (final) condition. For deterministic initial (final) conditions, the obtained results reduce to the known solutions to the respective special problems derived by different methods. We study the model with mean reversion and uncorrelated pre- and postjump states. This model is antipodal to both continuous diffusion and random walks. It is most appropriate when physical reality involves strong exogenous shocks with exponential relaxation to the mean value between these shocks, leading to a significant departure from conventional modeling assumptions. Finally, we demonstrate how naturally the generalized Feynman-Kac equations can be specialized to treat resetting (as a particular case of the uncorrelated states model) in stochastic hybrid systems.