Zixiang Yan

Online information cascades with similar final participation can nevertheless unfold along markedly different temporal and structural routes, indicating that final reach alone does not capture how collective activity develops. This raises the possibility that part of this diversity may originate from the internal dynamics of the spreading process itself. Here we examine this possibility using a minimal coevolutionary network model in which activity strength- ens opinion coupling, while opinion magnitude enhances activation. The model generates qualitatively distinct delayed and rapid spreading histories. Analysis reveals a two-stage instability structure, in which sustained activity first emerges and the resulting opinion-neutral active state subsequently loses transverse stability. Near the second threshold, this state becomes a weak saddle, producing a long-lived activity plateau before transition to a high-activity state. A center-manifold reduction further shows that the transverse pitchfork is locally subcritical along the studied parameter path. Event-driven simulations identify the slow growth of the unstable opinion mode during the plateau and link its stochastic amplification timescale to plateau residence across different network structures. These results show how an apparently settled active process can conceal internal dynamics that later drive delayed macroscopic reorganization.

As renewable energy integration continues to accelerate, transient stability challenges in modern power systems have become increasingly pronounced, particularly due to the systems’ inherent high-dimensional nonlinear dynamics. Developing a reliable and efficient method for assessing transient stability and the associated basin of attraction remains a critical yet unresolved challenge. This study focuses on the precise estimation of the basin-of-attraction boundary in phase-locked loop based voltage source converter systems, which can be described by a generalized swing equation. To address this problem, a higher-order Taylor expansion renormalization approach is proposed. This method enables the construction of a highly accurate approximation of the stable manifold that serves as the basin-of-attraction boundary, offering substantial improvements over conventional linear and second-order local approximations. The reliability and effectiveness of the proposed approach are rigorously validated through simulations under various fault scenarios in the transient stability assessment. The proposed method provides a robust tool for analyzing transient stability in modern power systems and offers new insights into the stability characterization of other nonlinear dynamical systems.

High-order network models have emerged as powerful frameworks for modeling complex dynamical systems that involve multi-body interactions in recent years. Despite their widespread adoption in prior studies, the subtle difference between high-order structures, even those of the same order, has frequently been overlooked. To fill this gap in between, this study takes four typical triadic (second-order) configurations as examples and examines their influence on complex contagion process described by the susceptible-infected-susceptible model. A novel network construction model is first proposed to generate high-order networks with one of the four triadic configurations while maintaining the average second-order degree as well as the first-order structure. Numerical simulations of contagions on these networks reveal that, while different triadic configurations do not alter the qualitative characteristics of the phase transition (i.e. from continuous to discontinuous phase transitions) in contagion processes, they have a noticeable impact on the second-order epidemic threshold for discontinuous phase transitions. Specifically, networks with 2-simplices exhibit the smallest threshold for discontinuous phase transitions, whereas those with 3-cycle structures display the largest threshold. By employing the heterogeneous mean-field approach, the critical second-order epidemic threshold for the emergence of discontinuous phase transitions is analytically derived, providing a theoretical explanation for the numerical findings.

Species separation induced by ultra-strong shocks is a fundamental topic for both inertial confinement fusion and high-energy-density experiments. However, how this phenomenon unfolds during the propagation and release phases of shocks has not been fully understood. In this study, we conduct a systematic investigation of species separation dynamics induced by strong shocks covering both steady propagation stage and shock release stage. Our study employs the non-equilibrium molecular dynamics method to explore these processes in a medium composed of two representative isotopes. Simulation results unveil distinct physical scenarios and dynamic behaviors of species separation during the two stages: During the steady propagation stage, species separation is confined to a localized region near the shock front, where the dynamics of the binary isotopic mixture are well-captured by the single-fluid approximation. In contrast, at the shock release stage, the species expand independently into the vacuum with different speeds, leading to a separation region of several orders of the mean free path. Interactions between particles play a minimal role in this process, allowing the dynamics of the mixture to be effectively described by decoupled two-phase hydrodynamic equations. Specifically, a self-similar behavior in the degree of separation and the isentropic expansion laws governing the two highly rarefied species at the shock release stage are identified, offering quantitative insights for applications.

We show that it is possible to perform a first-principles precision molecular dynamics (MD) investigation of hypervelocity gas–surface interaction (HGSI) with the help of deep potential (DP) type interaction model as a bridge. A DP type interaction model specifically designed for HGSI is trained based on dataset generated from high-precision first-principles MD (FPMD) simulations of HGSI processes at a relatively small spatial scale, and then is directly integrated into MD simulations of large spatial and temporal scales to simulate complete HGSI processes. Special care is taken in the FPMD simulations to correctly describe the van der Waals interaction, which is of particular importance to HGSI. As an illustrating example, the HGSI process of helium atoms and aluminum surface is investigated with incident velocity ranging from 5.0 to 15.0 km/s. Accommodation coefficients and reflected velocity distributions of He atoms are calculated and show significant differences with MD simulations using empirical interaction potentials, which highlights the necessity for high-accuracy interaction model in HGSI investigations. In addition, we find that it is necessary to include high-incident velocity collision data in the generation of DP type interaction potential to guarantee the accuracy of interaction model in the context of HGSI. Results of this work may help to provide more accurate theoretical benchmarks for the prediction of aerodynamic properties and thermal loads, which is essential for the design and optimization of hypervelocity vehicles.

Synergistic contagions are common in natural and social systems, with network topology playing a crucial role in shaping these dynamics. Despite extensive researches, a comprehensive understanding of how specific structural features influence synergistic contagions, especially their phase transitions, remains lacking. This study demonstrates that the spectral approach can serve as a high-precision analytical tool to describe the impact of network structure, particularly degree heterogeneity and degree correlations, on synergistic contagions. By comparing this approach with numerical simulations and conventional analytical approaches, such as the heterogeneous mean-field (HMF) approach, its high accuracy in predicting the critical synergistic strength is illustrated. Furthermore, the analysis based on the spectral approach reveals that the heterogeneity of the principal eigenvector of the network is the key structural factor determining the phase transition of synergistic contagions. As this heterogeneity increases, which can be promoted by increasing degree heterogeneity or degree correlations, the critical synergistic strength required for an explosive phase transition is enhanced.