Article
Mathematics
Pavel E. Ryabov, Sergei V. Sokolov
Summary: The article examines a model system of a dynamically symmetric rigid body with a suspension point that oscillates at high frequency. After the averaging process, the system is reduced to Hamilton equations with two degrees of freedom, exhibiting Liouville integrability, which describes the dynamics of a Lagrange top with an oscillating suspension point. The paper presents a bifurcation diagram of the moment mapping and uses it to illustrate the stability analysis of singular points, including rank zero and rank one.
Article
Mathematics, Applied
Maxim Idriss Tametang Meli, Gervais Dolvis Leutcho, David Yemele
Summary: The non-linear analysis of undesired vibrations on hybrid electric vehicle (HEV) powertrains is studied in this paper, introducing a new mathematical model and detailing the stability, instability, and multistability phenomena of the system. The research reveals rich and complex dynamic behaviors in such systems, different from some rare cases reported in HEV models previously.
Article
Instruments & Instrumentation
Yu Alexahin, V Kapin
Summary: This paper explores the potential of space-charge compensation in the Fermilab Booster rapid cycling synchrotron using multiple electron columns, demonstrating the significant promise of this technique.
JOURNAL OF INSTRUMENTATION
(2021)
Article
Instruments & Instrumentation
B. Cathey, G. Stancari, A. Valishev, T. Zolkin
Summary: The McMillan electron lens will be implemented in the Fermilab Integrable Optics Test Accelerator, describing its physics and discussing its implications for experimental design.
JOURNAL OF INSTRUMENTATION
(2021)
Article
Engineering, Mechanical
Zhimin Wang, Guoguang Jin, Dong Liang, Zhan Wei, Boyan Chang, Yang Zhou
Summary: In this study, a dynamic modeling and analysis method for a planar six-bar feeding mechanism with multi-clearance lubricated joints is proposed based on the Newton-Euler equation. The influence of clearance size, crank speed, and viscosity coefficient of lubricant on the dynamic behavior of the mechanism is comprehensively revealed under dry friction and lubrication conditions. The bifurcation and chaotic behavior of the mechanism under lubrication condition are emphatically studied, and the combined effect of crank speed and clearance size on the nonlinear behavior of the mechanism is investigated.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
S. S. Baturin
Summary: In this paper, a method of constructing a discrete nonlinear accelerator lattice is presented, along with an integrator that has an approximate integral of motion. The integrator, which is connected to a real lens arrangement, preserves a Hamiltonian in normalized coordinates with a given accuracy. By utilizing known algorithms of high-order symplectic integrators, several nonlinear lattices are generated. A new lattice design based on the Ruth and Yoshida integrators is proposed, which can be experimentally tested at existing accelerator facilities and Paul traps.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Mathematics, Interdisciplinary Applications
Wang Mei-Qi, Ma Wen-Li, Chen En-Li, Chang Yu-Jian, Wang Cui-Yan
Summary: This paper introduces the use of fractional order differentiation to accurately describe the stress relaxation behavior of viscoelastic materials and establishes a non-linear dynamic model. By studying the influence of non-linear factors and fractional order terms on the stability of the system, it is found that the system exhibits chaotic behavior under different parameter disturbances, and reducing linear damping widens the range of chaotic states the system can exhibit.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Ernest Fontich, Arturo Vieiro
Summary: We study a one-parameter family of 2-DOF Hamiltonian systems with a Hamiltonian-Hopf bifurcation at an equilibrium point. The normal form theory is reviewed, and the behavior of the splitting of 2D invariant manifolds is investigated when there are homoclinic orbits to the complex-saddle equilibrium point. Symmetries of the normal form are utilized to reduce the dynamics to a family of area-preserving Poincare maps, allowing for the derivation of an explicit upper bound for the splitting of separatrices. The results are illustrated with a concrete example and a separatrix map is derived to analyze the chaotic dynamics near the 2D invariant manifolds.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Engineering, Mechanical
Prashant N. Kambali, Amirhassan Abbasi, C. Nataraj
Summary: This paper focuses on the nonlinear modeling and analysis of the COVID-19 pandemic. It explores the impact of vaccination and the observed oscillations in infections. By incorporating a nonlinear Susceptible, Infected, & Immune model with dynamic transmission rate and vaccination policy, the study analyzes stability, bifurcations, and dynamics using US data as a starting point. Further parametric analysis reveals the influence of imperfect vaccination on the occurrence of sustained epidemic equilibria. This work highlights the importance of systematic nonlinear dynamic analysis in pandemic modeling and demonstrates the significant influence of vaccination and transmission rate on the disease's persistent dynamics.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Annelies De Meulenaere, Sonja Hohloch
Summary: A one-parameter family of integrable systems on a compact 4-dimensional symplectic manifold is studied, transitioning smoothly from a system with elliptic-elliptic singular points to a semitoric system with a specific distribution of singular points. At t = 1/2, the system exhibits two focus-focus fibres with a unique shape.
JOURNAL OF NONLINEAR SCIENCE
(2021)
Article
Engineering, Mechanical
Jinying Guo, Huailong Shi, Ren Luo, Jing Zeng
Summary: The study examines the stability and bifurcation characteristics under nonlinear wheel/rail contact, finding that an exponent fitting is more appropriate for simulating flange effects. It also discusses the significant impact of linear and nonlinear terms of rolling radius on bifurcation and critical speeds.
NONLINEAR DYNAMICS
(2021)
Article
Engineering, Mechanical
Runeng Zhou, Yongpeng Gu, Jiang Cui, Gexue Ren, Suyuan Yu
Summary: This paper investigates the Hopf bifurcation behavior in gas foil bearing-rotor systems and provides insights into the nonlinear dynamic characteristics of systems with supercritical or subcritical Hopf bifurcations. The research demonstrates that systems with a supercritical Hopf bifurcation exhibit better dynamic characteristics, and parameter analysis shows that foil stiffness and aspect ratio have significant effects on the type of bifurcation.
NONLINEAR DYNAMICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Fatma Ata, Ali Demirci, Cihangir Ozemir
Summary: The study focuses on the dynamics of opinion transitions within a group of individuals, incorporating a nonlinear system with a leader effect and non-linear potential for analysis. The results demonstrate the distinctions between stable states in parameter space, showcasing the potential for further research on how leaders influence a large group of people. Through bifurcation analysis, the study also identifies the mechanism of imperfect pitchfork bifurcation as one of the transition mechanisms between different final group states.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics, Applied
Wei Wang, Baolin Li, Shuangyan Liu, Zon -Han Wei
Summary: The study aims to develop a rolling magnet multistable electromagnetic-induction energy harvester (RM-MEH) that can scavenge energy from a wide frequency range. The RM-MEH, designed based on a magnetic levitation rolling magnet, possesses the advantage of low damping. Through an investigation of the mechanics, the study demonstrates that different configurations with monostable, bistable, and tristable states can be achieved with proper parameters. Numerical simulations show that these configurations can achieve large-amplitude oscillation in a wide frequency range. Nonlinear dynamics are analyzed under constant frequency excitation, and multiple vibrational patterns are verified. The study also discusses the vibration isolation characteristics of the system by considering the electromagnetic force of the RM-MEH. Overall, the demonstration of the novel RM-MEH expands the approach to achieving multistable oscillation and provides a new way of thinking for designing nonlinear energy harvesters.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Engineering, Multidisciplinary
Hongchuan Cheng, Yimin Zhang, Wenjia Lu, Zhou Yang
Summary: A mathematical model is presented to study the dynamic properties of rotor-bearing coupling system under various effects, and the impact of typical parameters on the mechanical characteristics of the rotor system is analyzed. The results offer theoretical support for controlling the rotor-bearing system and studying the nonlinear vibration mechanism in practical applications.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Instruments & Instrumentation
F. Sannibale, D. Filippetto, H. Qian, C. Mitchell, F. Zhou, T. Vecchione, R. K. Li, S. Gierman, J. Schmerge
REVIEW OF SCIENTIFIC INSTRUMENTS
(2019)
Article
Physics, Mathematical
Chad Mitchell
JOURNAL OF MATHEMATICAL PHYSICS
(2019)
Article
Physics, Nuclear
Kilean Hwang, Chad Mitchell, Robert Ryne
PHYSICAL REVIEW ACCELERATORS AND BEAMS
(2020)
Article
Physics, Nuclear
Yongjun Li, Kilean Hwang, Chad Mitchell, Robert Rainer, Robert Ryne, Victor Smaluk
Summary: A numerical method to design nonlinear DBA and MBA lattices with approximate invariants of motion is investigated. By tuning existing lattices, it is possible to improve instability thresholds and reduce feedback gain.
PHYSICAL REVIEW ACCELERATORS AND BEAMS
(2021)
Article
Optics
Chad E. Mitchell, Robert D. Ryne, Kilean Hwang
Summary: Measures of discrepancy between probability distributions are important in artificial intelligence and machine learning. This paper describes how these measures can be used as numerical diagnostics for simulations involving charged-particle beams, providing sensitive measures of important dynamical processes in nonlinear or high-intensity systems.
Article
Physics, Nuclear
Chad E. Mitchell, Robert D. Ryne, Kilean Hwang, Sergei Nagaitsev, Timofey Zolkin
Summary: This paper describes how to determine the dynamical frequencies of motion as functions of integrals in the absence of explicitly known action-angle variables, and provides several examples.
PHYSICAL REVIEW ACCELERATORS AND BEAMS
(2021)
Article
Physics, Fluids & Plasmas
Chad E. Mitchell, Robert D. Ryne, Kilean Hwang
Proceedings Paper
Computer Science, Artificial Intelligence
Ji Qiang, Chad Mitchell, Albert Qiang
2016 IEEE CONGRESS ON EVOLUTIONARY COMPUTATION (CEC)
(2016)