Article
Physics, Fluids & Plasmas
Jonathan A. D. Wattis
Summary: This study proposes a model for a chain of particles coupled by nonlinear springs, in which each mass has an internal mass and all interactions are assumed to be nonlinear. The paper demonstrates how to construct an asymptotic solution using multiple timescales and a consistency condition. The results show that the dynamics are governed by NLS for certain combinations of nonlinearity, but a Ginzburg-Landau equation is obtained when both nonlinearities have quadratic components.
Article
Physics, Fluids & Plasmas
M. M. Lee, E. G. Charalampidis, S. Xing, C. Chong, P. G. Kevrekidis
Summary: This work focuses on the study of time-periodic solutions, including breathers, in a nonlinear lattice with alternating contacts of strain hardening and strain softening. The existence, stability, and bifurcation structure of these solutions, as well as the system dynamics with damping and driving, are systematically studied. It is found that the presence of nonlinearity causes the linear resonant peaks in the system to bend towards the frequency gap. Time-periodic solutions within the frequency gap closely resemble Hamiltonian breathers when damping and driving are small. In the Hamiltonian limit, a nonlinear Schrodinger equation is derived through multiple scale analysis to construct both acoustic and optical breathers, which match well with numerically obtained breathers in the Hamiltonian limit.
Article
Automation & Control Systems
Pieter van Goor, Tarek Hamel, Robert Mahony
Summary: This article proposes a novel filter, the equivariant filter (EqF), which poses the observer state on the symmetry group, linearizes global error dynamics derived from the equivariance of the system, and applies EKF design principles. We show that exploiting the equivariance of the system output can reduce linearization error and improve filter performance. Simulation experiments of an example application demonstrate that the EqF significantly outperforms the EKF and the reduced linearization error leads to a clear improvement in performance.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Mathematics, Applied
Bo Liu
Summary: This paper investigates the anomaly formula and functoriality of equivariant Bismut-Cheeger eta forms with perturbation operators for a compact Lie group action, and constructs a new analytic model for the equivariant differential K-theory on compact manifolds with finite stabilizers. The results provide insights on the well-definedness of the push-forward map, addressing a question raised by Bunke and Schick (2009).
SCIENCE CHINA-MATHEMATICS
(2021)
Article
Mathematics, Applied
Jinling Zhou, Yu Yang, Cheng-Hsiung Hsu
Summary: We study the traveling waves of a discrete diffusive waterborne pathogen model with general incidence. The existence and non-existence of traveling waves are determined by the basic reproduction number R0 and the minimum wave speed c*. We establish the traveling waves connecting the disease-free equilibrium and endemic equilibrium when R0 > 1 and c ≥ c*, using the Schauder fixed point theorem, technique of Lyapunov function, and the limiting argument. The non-existence of traveling waves can be verified using the comparison principle and the method of Laplace transform when R0 ≤ 1 or R0 > 1 and c < c*. Our results show that the diffusion rates of infectious individuals and bacteria in water can increase the minimum wave speed.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Computer Science, Information Systems
Diego Patino, John W. Branch
Summary: CPMA is a new method for medial axis pruning that is noise-robust and equivariant to isometric transformations. It utilizes the discrete cosine transform to create smooth versions of a shape and computes a score function to filter out spurious branches. The method has been compared extensively with state-of-the-art pruning methods and has shown competitive results in various datasets.
Article
Physics, Multidisciplinary
Yaroslav Kartashov, Fangwei Ye, Vladimir V. Konotop, Lluis Torner
Summary: The photonic moire patterns created by two mutually twisted periodic sublattices in quadratic nonlinear media can allow the formation of parametric solitons, with the geometry of the pattern significantly impacting the conditions for soliton excitation and the properties of soliton families. The geometry also broadens the phase-mismatch bandwidth for soliton generation compared to latticeless structures.
PHYSICAL REVIEW LETTERS
(2021)
Article
Engineering, Aerospace
Zhetao Zhang, Haijun Yuan, Xiufeng He, Bofeng Li, Jianghui Geng
Summary: Global navigation satellite system is widely used for navigation and positioning, but it faces challenges in resolving ambiguities in high occlusion and reflection environments. This article proposes a best integer equivariant (BIE) estimation method with quality control (QC) to improve positioning performance. The method includes an improved multipath processing approach and a modified outlier identification procedure. Two experiments validate the effectiveness of the proposed method, which shows improved precision and reliability in positioning.
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS
(2023)
Article
Mathematics, Applied
Jinbing Chen, Dmitry E. Pelinovsky
Summary: We study the traveling periodic waves of the discrete modified Korteweg-de Vries equation and analyze their modulational stability using a nonlinearization method. Numerical approximations show that the dnoidal solutions are modulationally stable while the cnoidal solutions are modulationally unstable. This has significant implications for understanding the propagation of algebraic solitons and the dynamic generation of rogue waves on different wave backgrounds.
PHYSICA D-NONLINEAR PHENOMENA
(2023)
Article
Mathematics
Peter Bonventre, Luis A. Pereira
Summary: The study introduces genuine equivariant operads as a hybrid structure between operads and coefficient systems. It proves a theorem establishing the equivalence between equivariant operads and genuine equivariant operads. One specific application is the construction of explicit models for the N-infinity-operads of Blumberg and Hill.
ADVANCES IN MATHEMATICS
(2021)
Article
Physics, Multidisciplinary
J. Sanz, A. Frolian, C. S. Chisholm, C. R. Cabrera, L. Tarruell
Summary: In this study, we demonstrate the rapid control of interatomic interactions in a Bose-Einstein condensate by coherently coupling two atomic states with opposite signs of scattering lengths. The elastic and inelastic scattering properties of the system are measured, and good agreement with a theoretical model is found. The formation of bright solitons by dressed-state atoms in the attractive regime is observed, and the response of the system to an interaction quench from repulsive to attractive values is studied, revealing the development of modulational instability into a bright soliton train.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Particles & Fields
Daniel Sheinbaum, Omar Antolin Camarena
Summary: This study focused on symmorphic crystalline interacting gapped systems, deriving a classification under adiabatic evolution that includes a complete classification for non-degenerate ground states and some invariants for degenerate states based on equivariant characteristic classes. Unlike traditional assumptions, this study does not require the emergence of a relativistic field theory, the assumption that phases form a topological spectrum, or the restriction to systems with short-range entanglement, stability against stacking with trivial systems, or the existence of quasi-particles.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Multidisciplinary Sciences
H. Dehne, A. Reitenbach, A. R. Bausch
Summary: By utilizing DNA specificity, depletion forces, and geometric constraints for precise control, the dynamic and fully reversible assembly of DNA-functionalized particles was achieved, demonstrating autonomous oscillating structure formation on the meso-scale.
NATURE COMMUNICATIONS
(2021)
Article
Physics, Particles & Fields
Zichun Hao, Raghav Kansal, Javier Duarte, Nadezda Chernyavskaya
Summary: Significant work has been done in developing machine learning models for various tasks in high energy physics, such as classification, simulation, and anomaly detection. However, models adapted from other domains may lack the necessary biases suited to HEP data, such as equivariance to inherent symmetries. To address this, the Lorentz group autoencoder is proposed, which is equivariant with respect to the proper, orthochronous Lorentz group and has a latent space in the representations of the group. Experimental results on LHC jets show that this model outperforms baseline models on compression, reconstruction, and anomaly detection metrics. The equivariant model also improves the explainability of potential anomalies discovered by ML models.
EUROPEAN PHYSICAL JOURNAL C
(2023)
Article
Mathematics
Bo Liu, Xiaonan Ma
Summary: In this paper, we define the equivariant infinitesimal 77-form and compare it with the equivariant 77-form modulo exact forms using a locally computable form. As a result, we obtain the singular behavior of the equivariant 77-form modulo exact forms as a function on the acting Lie group.
ADVANCES IN MATHEMATICS
(2022)
