arXiv subjects

B. Kahng

Publications and source records attributed to B. Kahng.

At least 19 recordsLinked to original sources

arXiv2026

Synchronization Pathways and Resilience in Power Grids

Ensuring a sustainable energy supply requires maintaining power-grid stability. Rotor dynamics are governed by the swing equation, which takes the form of a second-order Kuramoto model with a correlation between power and total coupling strength. Yet the microscopic mechanisms that nucleate and propagate synchronized clusters remain poorly understood. Using a minimal model motivated by empirical grid data and the \Adhoc potential method, we reveal two distinct seed cluster types and propagation pathways: a population-driven seed cluster at the center of the power distribution propagating to its tails by rotor accretion, and, for a symmetric distribution, coupling-driven seed clusters at its tails propagating inward to the center by cluster merger. These differences generate distinct order-parameter patterns, while inertia controls whether the seed clusters persist with distinct angular velocities. The same propagation pathways also govern recovery following external disturbances. We further confirm that the same selection--persistence rule holds in data-derived annealed representations of European power grids. Therefore, our results can inform strategies for sustaining stable power-grid operation. More generally, our pathway-based framework reframes synchronization by emphasizing the dynamics of cluster formation and recovery rather than relying solely on static criteria.

nlin.AO↗

arXiv2026

Breathing chimera states from purely triadic interactions

Chimera states, characterized by the coexistence of synchronized and desynchronized dynamics in identical oscillators, are typically studied in systems with pairwise interactions. Whether higher-order interactions alone can generate such symmetry-broken collective states remains unclear. Here, we show that chimera states can arise solely from triadic interactions. Furthermore, exploiting the intrinsic $\pi$-symmetry of the triadic coupling leads to bimodal phase distributions. We construct a bimodal Ott--Antonsen reduction that incorporates an asymmetry parameter via symmetry-breaking initial conditions, thereby achieving an exact low-dimensional description of the macroscopic dynamics. This allows us to derive an analytic condition for the emergence of chimera states and identify a bifurcation to a breathing chimera regime characterized by persistent oscillations. Furthermore, the reduced dynamics can be expressed as a Riccati-type equation, providing a geometric interpretation of the chimera state as a closed periodic orbit in the complex plane. Our results establish purely triadic coupling as a minimal mechanism for chimera formation and provide a tractable framework for studying symmetry-broken collective dynamics in systems dominated by many-body interactions.

physics.soc-ph↗

arXiv2026

Paths to synchronization in the Kuramoto model with inertia

Synchronization is ubiquitous across natural and synthetic systems, yet most prior studies focus on the inertia-free Kuramoto model and do so at the macroscopic level. In this study, we instead investigate the inertial Kuramoto model and analyze the kinetics of individual synchronized clusters that emerge in the underdamped dynamics, driven by the interactions among multiple synchronized clusters with different frequencies. Specifically, we explore two forms of intrinsic frequency distribution -- unimodal Gaussian and multimodal uniform -- and show that they give rise to qualitatively different synchronized clusters: a hierarchical organization for the Gaussian distribution and a homogeneous organization for the uniform distribution. This contrast leads to qualitatively different behaviors of the order parameter: for the Gaussian distribution, it increases smoothly with increasing coupling strength, while for the uniform distribution, it grows through a series of discrete jumps that trace out the size of the Devil's staircase (DS). By resolving the kinetics at the cluster level, we further find that the route to synchronization also depends on the distribution type: with a Gaussian distribution, a single dominant cluster forms and gradually entrains the remaining oscillators, whereas with a uniform distribution, synchronization proceeds via successive cluster mergers initiated from peripheral seeds associated with the high-frequency periphery. Taken together, these findings provide a new perspective on collective synchronization dynamics in inertial complex systems.

nlin.AO↗

arXiv2026

Heterogeneous Network Topology Induces the Widom Line

The Widom line, initially identified as a crossover line between liquid-like and gas-like behavior in water and supercritical fluids, separates these two types of behavior. Here, we show that an analogous line arises in spin models on scale-free networks as a consequence of degree heterogeneity, which we analyze using the annealed network approximation. For the Ashkin--Teller and Invisible Potts models, the Widom line exists within a finite range of the degree exponent. It separates two distinct ordered regimes$-$distributed spin alignment and hub-dominant alignment$-$while also giving rise to a supercritical-like state where the two alignments become indistinguishable. These results demonstrate that degree heterogeneity alone can generate mesoscopic crossovers beyond conventional phase-transition theory, opening new directions for understanding and controlling collective dynamics in complex networks.

physics.soc-ph↗

arXiv2026

Phase lag enhances synchronization in coupled oscillators with inertia

The second-order Kuramoto model with inertia exhibits different dynamical behaviors than the first-order KM without inertia. A central difference is its lower synchronization due to the emergence of multiple synchronized clusters with different frequencies. We aim to investigate how such lowered synchronization can be improved by applying external perturbations to the system in a steady state, for example, a symmetry-breaking phase lag to a subset of oscillators. We find that this phase lag steers the primary cluster along a specific path and enables it to merge with higher-order clusters, thereby enhancing global synchronization. Our results reveal a mechanism by which controlled phase lag can improve entrainment in inertial oscillator systems, with possible implications for synchronization control in inertial oscillator networks.

cond-mat.stat-mech↗

arXiv2026

AI-Driven Stabilization in Power Grids through Controlling Line Admittances

The global transition from traditional power plants to renewable energy sources introduces new challenges in grid stability, primarily because inverter-based technologies provide insufficient inertia. To address this, we introduce an artificial intelligence algorithm that autonomously stabilizes power grids by adaptively tuning admittance regulators in response to disturbances. This Adaptive Admittance Controller (AAC) algorithm not only stabilizes the system in real time but also identifies the best regulator locations, thereby unifying grid planning and real time control within a single framework. When tested on a real UK power grid, the AAC markedly reduces frequency deviations and rapidly restores nominal operation. In addition, the algorithm isolates a small number of key regulators and intervenes only on these, lowering both system complexity and cost. The AAC algorithm further reduces the nonlinearity effect, quickly stabilizing the frequency and power flow. This intelligent control scheme enables power grids to reliably return to stable operating conditions under a broad spectrum of fault scenarios. The proposed framework can also be used to mitigate cascading failures by adaptively controlling critical links in a variety of networked infrastructures, such as cascades of traffic congestion on road networks or fuse failures in energy-saving systems.

physics.soc-ph↗

arXiv2025

Cluster-Mediated Synchronization Dynamics in Globally Coupled Oscillators with Inertia

Globally coupled oscillator systems with inertia exhibit complex synchronization patterns, among which the emergence of a couple of secondary synchronized clusters (SCs) in addition to the primary cluster (PC) is especially distinctive. Although previous studies have predominantly focused on the collective properties of the PC, the dynamics of individual clusters and their inter-cluster interactions remain largely unexplored. Here, we demonstrate that multiple clusters emerge and coexist, forming a hierarchical pattern known as the Devil's Staircase. We identify three key findings by investigating individual cluster dynamics and inter-cluster interactions. First, the PC persistently suppresses the formation of SCs during its growth and even after it has fully formed, revealing the significant impact of inter-cluster interactions on cluster formation. Second, once established, SCs induce higher-order clusters exhibiting frequency resonance via inter-cluster interactions, resulting in the Devil's Staircase pattern. Third, sufficiently large SCs can destabilize and fragment the PC, highlighting the bidirectional nature of cluster interactions. We develop a coarse-grained Kuramoto model that treats each cluster as a macroscopic oscillator to capture these inter-cluster dynamics and the resulting phenomena. Our work marks a significant step beyond system-wide averages in the study of inertial oscillator systems, offering new insights into the rich dynamics of cluster formation and synchronization in real-world applications such as power grid networks.

nlin.AO↗

arXiv2025

Ashkin-Teller model with antiferromagnetic four-spin interactions: Interference effect between two conflicting issues

Spin systems have emerged as powerful tools for understanding collective phenomena in complex systems. In this work, we investigate the Ashkin--Teller (AT) model on random scale-free networks using mean-field theory, which extends the traditional Ising framework by coupling two spin systems via both pairwise and four-spin interactions. We focus on the previously unexplored antiferromagnetic regime of four-spin coupling, in which strong ordering in one layer actively suppresses the formation of order in the other layer. This mechanism captures, for example, scenarios in social or political systems where a dominant viewpoint on one issue (e.g., economic development) can inhibit consensus on another (e.g., environmental conservation). Our analysis reveals a rich phase diagram with four distinct phases -- paramagnetic, Baxter, \langle \sigma \rangle, and antiferromagnetic -- and diverse types of phase transitions. Notably, we find that the upper critical degree exponent extends to \lambda_{c2} \approx 9.237, far exceeding the conventional value of \lambda = 5$ observed in ferromagnetic systems. This dramatic shift underscores the enhanced robustness of hub-mediated spin correlations under competitive coupling, leading to asymmetric order parameters between layers and novel phase transition phenomena. These findings offer fundamental insights into systems with competing order parameters and have direct implications for multilayer biological networks, social media ecosystems, and political debates characterized by competing priorities.

physics.soc-ph↗

arXiv2025

From Spatial to Spectral: Network Renormalization via Dynamical Correlations

Network renormalization has traditionally relied on spatial adjacency-grouping nearby nodes together, but this approach fails to capture the dynamical correlations that govern system-wide behavior in scale-free networks. We present a spectral-space renormalization framework that enables coarse-graining based on dynamical coherence rather than geometric proximity. Within this framework, diffusion processes naturally constitute renormalization transformations in spectral space, yielding scaling relations that connect network dimensions with critical exponents. Building on this foundation, we develop a meta-graph reconstruction algorithm that systematically maps spectral information back into explicit topology while preserving dynamical correlations. The resulting renormalized networks uncover organizational structures that remain invisible to adjacency-based methods, including long-range correlations between structurally distant nodes that reflect coherent dynamical responses. Applications to Internet topologies, yeast regulatory networks, and European power grids demonstrate the broad applicability of this framework. The algorithm consistently extracts fractal, spectral, and random-walk dimensions with theoretical consistency across diverse systems. In power grids, it further reveals hidden failure pathways, exposing transcontinental correlations that match documented cascade patterns. In Internet networks, it reveals multiscaling behavior as the topology evolves over time. By shifting network renormalization from spatial geometry to dynamical flow, this work provides a unified foundation for understanding how information, energy, and failures propagate through complex systems, with direct implications for infrastructure resilience and network vulnerability assessment.

physics.soc-ph↗

arXiv2025

Optimal location of reinforced inertia to stabilize power grids

The increasing adoption of renewable energy sources has significantly reduced the inertia in the modernized power grid, making the system more vulnerable. One way to stabilize the grid is to add extra inertia from unused turbines, called the fast frequency response (FFR), to the existing grid. However, reinforcing inertia can cause unintended consequences, such as more significant avalanche failures. This phenomenon is known as the Braess paradox. Here, we propose a method to find the optimal position of FFR. This method is applied to the second-order Kuramoto model to find an effective position to mitigate cascading failures. To address this, we propose a method to evaluate a ratio between the positive effects of mitigation and the negative consequences. Through this analysis, we find that the peripheral area of the network is a seemingly effective location for inertia reinforcement across various reinforcement scales. This strategy provides essential insights for enhancing the stability of power grids in a time of widespread renewable energy usage.

physics.soc-ph↗

arXiv2024

Neural Graph Simulator for Complex Systems

Numerical simulation is a predominant tool for studying the dynamics in complex systems, but large-scale simulations are often intractable due to computational limitations. Here, we introduce the Neural Graph Simulator (NGS) for simulating time-invariant autonomous systems on graphs. Utilizing a graph neural network, the NGS provides a unified framework to simulate diverse dynamical systems with varying topologies and sizes without constraints on evaluation times through its non-uniform time step and autoregressive approach. The NGS offers significant advantages over numerical solvers by not requiring prior knowledge of governing equations and effectively handling noisy or missing data with a robust training scheme. It demonstrates superior computational efficiency over conventional methods, improving performance by over $10^5$ times in stiff problems. Furthermore, it is applied to real traffic data, forecasting traffic flow with state-of-the-art accuracy. The versatility of the NGS extends beyond the presented cases, offering numerous potential avenues for enhancement.

cs.LG↗

arXiv2024

Reinforcement Learning Optimizes Power Dispatch in Decentralized Power Grid

Effective frequency control in power grids has become increasingly important with the increasing demand for renewable energy sources. Here, we propose a novel strategy for resolving this challenge using graph convolutional proximal policy optimization (GC-PPO). The GC-PPO method can optimally determine how much power individual buses dispatch to reduce frequency fluctuations across a power grid. We demonstrate its efficacy in controlling disturbances by applying the GC-PPO to the power grid of the UK. The performance of GC-PPO is outstanding compared to the classical methods. This result highlights the promising role of GC-PPO in enhancing the stability and reliability of power systems by switching lines or decentralizing grid topology.

physics.soc-ph↗

arXiv2024

Hybrid Synchronization with Continuous Varying Exponent in Decentralized Power Grid

Motivated by the decentralized power grid, we consider a synchronization transition (ST) of the Kuramoto model (KM) with a mixture of first- and second-order type oscillators with fractions $p$ and $1-p$, respectively. Discontinuous ST with forward-backward hysteresis is found in the mean-field limit. A critical exponent $β$ is noticed in the spinodal drop of the order parameter curve at the backward ST. We find critical damping inertia $m_*(p)$ of the oscillator mixture, where the system undergoes a characteristic change from overdamped to underdamped. When underdamped, the hysteretic area also becomes multistable. This contrasts an overdamped system, which is bistable at hysteresis. We also notice that $β(p)$ continuously varies with $p$ along the critical damping line $m_*(p)$. Further, we find a single-cluster to multi-cluster phase transition at $m_{**}(p)$. We also discuss the effect of those features on the stability of the power grid, which is increasingly threatened as more electric power is produced from inertia-free generators.

cond-mat.stat-mech↗

arXiv2024

Entropy-Induced Phase Transitions in a Hidden Potts Model

A hidden state in which a spin does not interact with any other spin contributes to the entropy of an interacting spin system. Using the Ginzburg-Landau formalism in the mean-field limit, we explore the $q$-state Potts model with extra $r$ hidden states. We analytically demonstrate that when $1 < q \le 2$, the model exhibits a rich phase diagram comprising a variety of phase transitions such as continuous, discontinuous, two types of hybrids, and two consecutive second- and first-order transitions; moreover, several characteristics such as critical, critical endpoint, and tricritical point are identified. The critical line and critical end lines merge in a singular form at the tricritical point. Those complex critical behaviors are not wholly detected in previous research because the research is implemented only numerically. We microscopically investigate the origin of the discontinuous transition; it is induced by the competition between the interaction and entropy of the system in the Ising limit, whereas by the bi-stability of the hidden spin states in the percolation limit. Finally, we discuss the potential applications of the hidden Potts model to social opinion formation with shy voters and the percolation in interdependent networks.

cond-mat.stat-mech↗

arXiv2023

GNRK: Graph Neural Runge-Kutta method for solving partial differential equations

Neural networks have proven to be efficient surrogate models for tackling partial differential equations (PDEs). However, their applicability is often confined to specific PDEs under certain constraints, in contrast to classical PDE solvers that rely on numerical differentiation. Striking a balance between efficiency and versatility, this study introduces a novel approach called Graph Neural Runge-Kutta (GNRK), which integrates graph neural network modules with a recurrent structure inspired by the classical solvers. The GNRK operates on graph structures, ensuring its resilience to changes in spatial and temporal resolutions during domain discretization. Moreover, it demonstrates the capability to address general PDEs, irrespective of initial conditions or PDE coefficients. To assess its performance, we benchmark the GNRK against existing neural network based PDE solvers using the 2-dimensional Burgers' equation, revealing the GNRK's superiority in terms of model size and accuracy. Additionally, this graph-based methodology offers a straightforward extension for solving coupled differential equations, typically necessitating more intricate models.

cs.LG↗

arXiv2023

Unified framework for hybrid percolation transitions based on microscopic dynamics

A hybrid percolation transition (HPT) exhibits both discontinuity of the order parameter and critical behavior at the transition point. Such dynamic transitions can occur in two ways: by cluster pruning with suppression of loop formation of cut links or by cluster merging with suppression of the creation of large clusters. While the microscopic mechanism of the former is understood in detail, a similar framework is missing for the latter. By studying two distinct cluster merging models, we uncover the universal mechanism of the features of HPT-s at a microscopic level. We find that these features occur in three steps: (i) medium-sized clusters accumulate due to the suppression rule hindering the growth of large clusters, (ii) those medium size clusters eventually merge and a giant cluster increases rapidly, and (iii) the suppression effect becomes obsolete and the kinetics is governed by the Erd\H{o}s-R\'enyi type of dynamics. We show that during the second and third period, the growth of the largest component must proceed in the form of a Devil's staircase. We characterize the critical behavior by two sets of exponents associated with the order parameter and cluster size distribution, which are related to each other by a scaling relation. Extensive numerical simulations are carried out to support the theory where a specific method is applied for finite-size scaling analysis to enable handling the large fluctuations of the transition point. Our results provide a unified theoretical framework for the HPT.

cond-mat.stat-mech↗

arXiv2023

$(k,q)$-core decomposition of hypergraphs

In complex networks, many elements interact with each other in different ways. A hypergraph is a network in which group interactions occur among more than two elements. In this study, first, we propose a method to identify influential subgroups in hypergraphs, named $(k,q)$-core decomposition. The $(k,q)$-core is defined as the maximal subgraph in which each vertex has at least $k$ hypergraph degrees \textit{and} each hyperedge contains at least $q$ vertices. The method contains a repeated pruning process until reaching the $(k,q)$-core, which shares similarities with a widely used $k$-core decomposition technique in a graph. Second, we analyze the pruning dynamics and the percolation transition with theoretical and numerical methods in random hypergraphs. We set up evolution equations for the pruning process, and self-consistency equations for the percolation properties. Based on our theory, we find that the pruning process generates a hybrid percolation transition for either $k\ge 3$ \textit{or} $q\ge 3$. The critical exponents obtained theoretically are confirmed with finite-size scaling analysis. Next, when $k=q=2$, we obtain a unconventional degree-dependent critical relaxation dynamics analytically and numerically. Finally, we apply the $(k,q)$-core decomposition to a real coauthorship dataset and recognize the leading groups at an early stage.

cond-mat.stat-mech↗

arXiv2022

Prediction and mitigation of nonlocal cascading failures using graph neural networks

Cascading failures (CFs) in electrical power grids propagate nonlocally; After a local disturbance, the second failure may be distant. To study the avalanche dynamics and mitigation strategy of nonlocal CFs, numerical simulation is necessary; however, computational complexity is high. Here, we first propose an avalanche centrality (AC) of each node, a measure related to avalanche size, based on the Motter and Lai model. Second, we train a graph neural network (GNN) with the AC in small networks. Next, the trained GNN predicts the AC ranking in much larger networks and real-world electrical grids. This result can be used effectively for avalanche mitigation. The framework we develop can be implemented in other complex processes that are computationally costly to simulate in large networks.

physics.soc-ph↗