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Alignment frustration-induced swarming lattice in the Vicsek-Kuramoto model
Authors:
Yichen Lu,
Yingshan Guo,
Yiyi Zhang,
Tong Zhu,
Zhigang Zheng
Abstract:
We introduce a frustration parameter $α$ into the Vicsek-Kuramoto model of self-propelled particles. While the system exhibits conventional synchronized states, such as global phase synchronization and swarming, for low frustration ($α< π/2$), beyond the critical point $α= π/2$, a Hopf-Turing bifurcation drives a transition to a resting hexagonal lattice, accompanied by spatiotemporal patterns suc…
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We introduce a frustration parameter $α$ into the Vicsek-Kuramoto model of self-propelled particles. While the system exhibits conventional synchronized states, such as global phase synchronization and swarming, for low frustration ($α< π/2$), beyond the critical point $α= π/2$, a Hopf-Turing bifurcation drives a transition to a resting hexagonal lattice, accompanied by spatiotemporal patterns such as vortex lattices and dual-cluster lattices with oscillatory unit-cell motions. Lattice dominance is governed by coupling strength and interaction radius, with a clear parametric boundary balancing pattern periodicity and particle dynamics. Our results demonstrate that purely orientational interactions are sufficient to form symmetric lattices, challenging the necessity of spatial forces and illuminating the mechanisms driving lattice formation in active matter systems.
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Submitted 11 November, 2025;
originally announced November 2025.
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Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures
Authors:
Fanze Kong,
Chen-Chih Lai,
Yubin Lu
Abstract:
This paper proposes a data-driven learning framework for identifying governing laws of generalized diffusions with non-gradient components. By combining energy dissipation laws with a physically consistent penalty and first-moment evolution, we design a two-stage method to recover the pseudo-potential and rotation in the pointwise orthogonal decomposition of a class of non-gradient drifts in gener…
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This paper proposes a data-driven learning framework for identifying governing laws of generalized diffusions with non-gradient components. By combining energy dissipation laws with a physically consistent penalty and first-moment evolution, we design a two-stage method to recover the pseudo-potential and rotation in the pointwise orthogonal decomposition of a class of non-gradient drifts in generalized diffusions. Our two-stage method is applied to complex generalized diffusion processes including dissipation-rotation dynamics, rough pseudo-potentials and noisy data. Representative numerical experiments demonstrate the effectiveness of our approach for learning physical laws in non-gradient generalized diffusions.
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Submitted 5 August, 2025; v1 submitted 3 August, 2025;
originally announced August 2025.
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Classical and quantum curves of 5d Seiberg's theories and their 4d limit
Authors:
Oleg Chalykh,
Yongchao Lü
Abstract:
In this work, we examine the classical and quantum Seiberg-Witten curves of 5d N = 1 SCFTs and their 4d limits. The 5d theories we consider are Seiberg's theories of type $E_{6,7,8}$, which serve as the UV completions of 5d SU(2) gauge theories with 5, 6, or 7 flavors. Their classical curves can be constructed using the five-brane web construction [1]. We also use it to re-derive their quantum cur…
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In this work, we examine the classical and quantum Seiberg-Witten curves of 5d N = 1 SCFTs and their 4d limits. The 5d theories we consider are Seiberg's theories of type $E_{6,7,8}$, which serve as the UV completions of 5d SU(2) gauge theories with 5, 6, or 7 flavors. Their classical curves can be constructed using the five-brane web construction [1]. We also use it to re-derive their quantum curves [2], by employing a q-analogue of the Frobenius method in the style of [3]. This allows us to compare the reduction of these 5d curves with the 4d curves, i.e. Seiberg-Witten curves of the Minahan-Nemeschansky theories and their quantization, which have been identified in [4] with the spectral curves of rank-1 complex crystallographic elliptic Calogero-Moser systems.
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Submitted 4 November, 2024;
originally announced November 2024.
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Complex crystallographic reflection groups and Seiberg-Witten integrable systems: rank 1 case
Authors:
Philip C. Argyres,
Oleg Chalykh,
Yongchao Lü
Abstract:
We consider generalisations of the elliptic Calogero--Moser systems associated to complex crystallographic groups in accordance to [1]. In our previous work [2], we proposed these systems as candidates for Seiberg--Witten integrable systems of certain SCFTs. Here we examine that proposal for complex crystallographic groups of rank one. Geometrically, this means considering elliptic curves $T^2$ wi…
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We consider generalisations of the elliptic Calogero--Moser systems associated to complex crystallographic groups in accordance to [1]. In our previous work [2], we proposed these systems as candidates for Seiberg--Witten integrable systems of certain SCFTs. Here we examine that proposal for complex crystallographic groups of rank one. Geometrically, this means considering elliptic curves $T^2$ with $\mathbb{Z}_m$-symmetries, $m=2,3,4,6$, and Poisson deformations of the orbifolds $(T^2\times\mathbb{C})/\mathbb{Z}_m$. The $m=2$ case was studied in [2], while $m=3,4,6$ correspond to Seiberg--Witten integrable systems for the rank 1 Minahan--Nemeshansky SCFTs of type $E_{6,7,8}$. This allows us to describe the corresponding elliptic fibrations and the Seiberg--Witten differential in a compact elegant form. This approach also produces quantum spectral curves for these SCFTs, which are given by Fuchsian ODEs with special properties.
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Submitted 27 October, 2025; v1 submitted 22 September, 2023;
originally announced September 2023.
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Reservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systems
Authors:
Cheng Fang,
Yubin Lu,
Ting Gao,
Jinqiao Duan
Abstract:
The prediction of stochastic dynamical systems and the capture of dynamical behaviors are profound problems. In this article, we propose a data-driven framework combining Reservoir Computing and Normalizing Flow to study this issue, which mimics error modeling to improve traditional Reservoir Computing performance and integrates the virtues of both approaches. With few assumptions about the underl…
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The prediction of stochastic dynamical systems and the capture of dynamical behaviors are profound problems. In this article, we propose a data-driven framework combining Reservoir Computing and Normalizing Flow to study this issue, which mimics error modeling to improve traditional Reservoir Computing performance and integrates the virtues of both approaches. With few assumptions about the underlying stochastic dynamical systems, this model-free method successfully predicts the long-term evolution of stochastic dynamical systems and replicates dynamical behaviors. We verify the effectiveness of the proposed framework in several experiments, including the stochastic Van der Pal oscillator, El Niño-Southern Oscillation simplified model, and stochastic Lorenz system. These experiments consist of Markov/non-Markov and stationary/non-stationary stochastic processes which are defined by linear/nonlinear stochastic differential equations or stochastic delay differential equations. Additionally, we explore the noise-induced tipping phenomenon, relaxation oscillation, stochastic mixed-mode oscillation, and replication of the strange attractor.
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Submitted 30 July, 2023; v1 submitted 1 May, 2023;
originally announced May 2023.
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D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants
Authors:
Jin Chen,
Yongchao Lü,
Xin Wang
Abstract:
We study the quantization of the 6d Seiberg-Witten curve for D-type minimal conformal matter theories compactified on a two-torus. The quantized 6d curve turns out to be a difference equation established via introducing codimension two and four surface defects. We show that, in the Nekrasov-Shatashvili limit, the 6d partition function with insertions of codimension two and four defects serve as th…
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We study the quantization of the 6d Seiberg-Witten curve for D-type minimal conformal matter theories compactified on a two-torus. The quantized 6d curve turns out to be a difference equation established via introducing codimension two and four surface defects. We show that, in the Nekrasov-Shatashvili limit, the 6d partition function with insertions of codimension two and four defects serve as the eigenfunction and eigenvalues of the difference equation, respectively. We further identify the quantum curve of D-type minimal conformal matters with an elliptic Garnier system recently studied in the integrability community. At last, as a concrete consequence of our elliptic quantum curve, we study its RG flows to obtain various quantum curves of 5d ${\rm Sp}(N)+N_f \mathsf{F},N_f\leq 2N+5$ theories.
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Submitted 7 October, 2023; v1 submitted 10 April, 2023;
originally announced April 2023.
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A passive bias-free ultrabroadband optical isolator based on unidirectional self-induced transparency
Authors:
Haodong Wu,
Jiangshan Tang,
Mingyuan Chen,
Min Xiao,
Franco Nori,
Keyu Xia,
Yanqing Lu
Abstract:
Achieving a broadband nonreciprocal device without gain and any external bias is very challenging and highly desirable for modern photonic technologies and quantum networks. Here, we theoretically propose a passive and bias-free all-optical isolator for a femtosecond laser pulse by exploiting a new mechanism of unidirectional self-induced transparency, obtained with a nonlinear medium followed by…
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Achieving a broadband nonreciprocal device without gain and any external bias is very challenging and highly desirable for modern photonic technologies and quantum networks. Here, we theoretically propose a passive and bias-free all-optical isolator for a femtosecond laser pulse by exploiting a new mechanism of unidirectional self-induced transparency, obtained with a nonlinear medium followed by a normal absorbing medium at one side. The transmission contrast between the forward and backward directions can reach ~14.3 dB for a 2π5 fs laser pulse, implying isolation of a signal with an ultrabroad bandwidth of 200 THz. The 20 dB bandwidth is about 57 nm, already comparable with a magneto-optical isolator. This cavity-free optical isolator may pave the way to integrated nonmagnetic isolation of ultrashort laser pulses.
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Submitted 5 December, 2022;
originally announced December 2022.
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Discovering Conservation Laws using Optimal Transport and Manifold Learning
Authors:
Peter Y. Lu,
Rumen Dangovski,
Marin Soljačić
Abstract:
Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficult to identify, making it hard to analyze their dynamics and build stable predictive models. Current approaches for discovering conservation laws often depend on detailed dynamical…
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Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficult to identify, making it hard to analyze their dynamics and build stable predictive models. Current approaches for discovering conservation laws often depend on detailed dynamical information or rely on black box parametric deep learning methods. We instead reformulate this task as a manifold learning problem and propose a non-parametric approach for discovering conserved quantities. We test this new approach on a variety of physical systems and demonstrate that our method is able to both identify the number of conserved quantities and extract their values. Using tools from optimal transport theory and manifold learning, our proposed method provides a direct geometric approach to identifying conservation laws that is both robust and interpretable without requiring an explicit model of the system nor accurate time information.
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Submitted 22 August, 2023; v1 submitted 31 August, 2022;
originally announced August 2022.
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Inozemtsev System as Seiberg-Witten Integrable system
Authors:
Philip Argyres,
Oleg Chalykh,
Yongchao Lü
Abstract:
In this work we establish that the Inozemtsev system is the Seiberg-Witten integrable system encoding the Coulomb branch physics of 4d $\mathcal{N}=2$ USp(2N) gauge theory with four fundamental and (for $N \geq 2$) one antisymmetric tensor hypermultiplets. We describe the transformation from the spectral curves and canonical one-form of the Inozemtsev system in the $N=1$ and $N=2$ cases to the Sei…
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In this work we establish that the Inozemtsev system is the Seiberg-Witten integrable system encoding the Coulomb branch physics of 4d $\mathcal{N}=2$ USp(2N) gauge theory with four fundamental and (for $N \geq 2$) one antisymmetric tensor hypermultiplets. We describe the transformation from the spectral curves and canonical one-form of the Inozemtsev system in the $N=1$ and $N=2$ cases to the Seiberg-Witten curves and differentials explicitly, along with the explicit matching of the modulus of the elliptic curve of spectral parameters to the gauge coupling of the field theory, and of the couplings of the Inozemtsev system to the field theory mass parameters. This result is a particular instance of a more general correspondence between crystallographic elliptic Calogero-Moser systems with Seiberg-Witten integrable systems, which will be explored in future work.
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Submitted 12 January, 2021;
originally announced January 2021.
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Excitation of bound states in the continuum via second harmonic generations
Authors:
Lijun Yuan,
Ya Yan Lu
Abstract:
A bound state in the continuum (BIC) on a periodic structure sandwiched between two homogeneous media is a guided mode with a frequency and a wavenumber such that propagating plane waves with the same frequency and wavenumber exist in the homogeneous media. Optical BICs are of significant current interest, since they have applications in lasing, sensing, filtering, switching, and many light emissi…
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A bound state in the continuum (BIC) on a periodic structure sandwiched between two homogeneous media is a guided mode with a frequency and a wavenumber such that propagating plane waves with the same frequency and wavenumber exist in the homogeneous media. Optical BICs are of significant current interest, since they have applications in lasing, sensing, filtering, switching, and many light emission processes, but they cannot be excited by incident plane waves when the structure consists of linear materials. In this paper, we study the diffraction of a plane wave by a periodic structure with a second order nonlinearity, assuming the structure has a BIC and the frequency and wavenumber of the incident wave are one half of those of the BIC. Based on a scaling analysis and a perturbation theory, we show that the incident wave may induce a very strong second harmonic wave dominated by the BIC, and also a fourth harmonic wave that cannot be ignored. The perturbation theory reveals that the amplitude of the BIC is inversely proportional to a small parameter depending on the amplitude of the incident wave and the nonlinear coefficient. In addition, a system of four nonlinearly coupled Helmholtz equations (the four-wave model) is proposed to model the nonlinear process. Numerical solutions of the four-wave model are presented for a periodic array of circular cylinders and used to validate the perturbation results.
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Submitted 29 July, 2019;
originally announced August 2019.
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Quantitative analysis on the disparity of regional economic development in China and its evolution from 1952 to 2000
Authors:
Jianhua Xu,
Nanshan Ai,
Yan Lu,
Yong Chen,
Yiying Ling,
Wenze Yue
Abstract:
Domestic and foreign scholars have already done much research on regional disparity and its evolution in China, but there is a big difference in conclusions. What is the reason for this? We think it is mainly due to different analytic approaches, perspectives, spatial units, statistical indicators and different periods for studies. On the basis of previous analyses and findings, we have done some…
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Domestic and foreign scholars have already done much research on regional disparity and its evolution in China, but there is a big difference in conclusions. What is the reason for this? We think it is mainly due to different analytic approaches, perspectives, spatial units, statistical indicators and different periods for studies. On the basis of previous analyses and findings, we have done some further quantitative computation and empirical study, and revealed the inter-provincial disparity and regional disparity of economic development and their evolution trends from 1952-2000. The results shows that (a) Regional disparity in economic development in China, including the inter-provincial disparity, inter-regional disparity and intra-regional disparity, has existed for years; (b) Gini coefficient and Theil coefficient have revealed a similar dynamic trend for comparative disparity in economic development between provinces in China. From 1952 to 1978, except for the "Great Leap Forward" period, comparative disparity basically assumes a upward trend and it assumed a slowly downward trend from 1979 to1990. Afterwards from 1991 to 2000 the disparity assumed a slowly upward trend again; (c) A comparison between Shanghai and Guizhou shows that absolute inter-provincial disparity has been quite big for years; and (d) The Hurst exponent (H=0.5) in the period of 1966-1978 indicates that the comparative inter-provincial disparity of economic development showed a random characteristic, and in the Hurst exponent (H>0.5) in period of 1979-2000 indicates that in this period the evolution of the comparative inter-provincial disparity of economic development in China has a long-enduring characteristic.
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Submitted 28 June, 2018;
originally announced June 2018.
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Attraction of Spiral Waves by Localized Inhomogeneities with Small-World Connections in Excitable Media
Authors:
Xiaonan Wang,
Ying Lu,
Minxi Jiang,
Qi Ouyang
Abstract:
Trapping and un-trapping of spiral tips in a two-dimensional homogeneous excitable medium with local small-world connections is studied by numerical simulation. In a homogeneous medium which can be simulated with a lattice of regular neighborhood connections, the spiral wave is in the meandering regime. When changing the topology of a small region from regular connections to small-world connecti…
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Trapping and un-trapping of spiral tips in a two-dimensional homogeneous excitable medium with local small-world connections is studied by numerical simulation. In a homogeneous medium which can be simulated with a lattice of regular neighborhood connections, the spiral wave is in the meandering regime. When changing the topology of a small region from regular connections to small-world connections, the tip of a spiral waves is attracted by the small-world region, where the average path length declines with the introduction of long distant connections. The "trapped" phenomenon also occurs in regular lattices where the diffusion coefficient of the small region is increased. The above results can be explained by the eikonal equation and the relation between core radius and diffusion coefficient.
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Submitted 23 December, 2003;
originally announced December 2003.