Qualitative behavior of the Lorenz‐like chaotic system describing the flow between two concentric rotating spheres

Zhang, Fuchen; Liao, Xiaofeng; Zhang, Guangyun

doi:10.1002/cplx.21784

Cited by 3 publications

(2 citation statements)

References 27 publications

(27 reference statements)

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“…The five-mode Navier-Stokes equations in Fourier series on a torus have been built [25,[29][30][31]. As the movement of the film scrape is driven by the rotor of the BLDCM, there are no other force controls.…”

Section: Molecular-distillation-navier-stokes Equationmentioning

confidence: 99%

Generation and analysis of the chaos phenomenon in the molecular-distillation-Navier–Stokes (MDNS) nonlinear system

Qin,

Li,

Jiang

et al. 2024

Front. Phys.

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Introduction: For the Navier-Stokes equation, one of the most essential tasks should be to study its completeness of the complex nonlinear systems. Also, its nature and physical practical applications would be depth explored. Moreover, as one of the routes to chaos, this equation with an external force has been investigated numerically in 1989. Recently, some information is worth noting that when the high symmetry was imposed on the velocity field, the complex nonlinear motions should occur even lead to the chaos phenomenon. However, most of the published papers are based on theoretical studies and rarely deal with the above results, which lost of the match between them and the integrity of the scientific system.Methods: This study analyzed the molecular distillation process in detail based on the basic theory of nonlinear chaotic systems. Then, the mathematical model for the process of molecular distillation with one brushless DC motor (BLDCM) is built and named the Molecular-Distillation-Navier-Stokes (MDNS) equation. Also, its complex and potentially chaotic behaviors and chaotic processes are first discovered and demonstrated, such as chaotic attractors, chaotic co-attractors, phase portraits, time-domain waveforms, Lyapunov exponent spectrums, Poincare maps, the bifurcation diagrams, and so on.Results: The good agreement among theoretical analysis, simulation and experimental results verifies the practicability and flexibility of the configured model.Discussion: The related conclusions have supplemented and improved the theoretical system for the Navier Stokes equations. Also, it reflects the significance in molecular distillation processes. Meanwhile, the novel research direction for the fields of the chaotic nonlinear and complex industrial systems have been explored and discovered.

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Section: Molecular-distillation-navier-stokes Equationmentioning

confidence: 99%

Generation and analysis of the chaos phenomenon in the molecular-distillation-Navier–Stokes (MDNS) nonlinear system

Qin,

Li,

Jiang

et al. 2024

Front. Phys.

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“…Robot tracking planning of redundant robotic manipulators is to achieve the motion actions to steer the end-effector along with the desired trajectories in the energy optimal system [1][2][3]. Tracking planning is an important part in engineering robotic applications, such as telecommunication [4], energetic optimization [5], and welding manufacturing [6]. Redundancy of the manipulators is defined as possessing more degrees of freedom (DOF) than the number that the given tasks are required to use.…”

Section: Introductionmentioning

confidence: 99%

A Repeatable Optimization for Kinematic Energy System with Its Mobile Manipulator Application

et al. 2019

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For repeatable motion of redundant mobile manipulators, the flexible base platform and the redundant manipulator have to be returned to the desired initial position simultaneously after completing the given tasks. To remedy deviations between initial position and desired position of each kinematic joint angle, a special kind of repeatable optimization for kinematic energy minimization based on terminal-time Zhang neural network (TTZNN) with finite-time convergence is proposed for inverse kinematics of mobile manipulators. It takes the advantages that each joint of the manipulator is required to return to the desired initial position not considering the initial orientation of itself for realizing repeatable kinematics control. Unlike the existed training methods, such an optimization of kinematic energy scheme based on TTZNN can not only reduce the convergent position error of each joint to zero in finite time, but also improve the convergent precision. Theoretical analysis and verifications show that the proposed optimal kinematic energy scheme accelerates the convergent rate, which is tended to be applied in practical robot kinematics. Simulation results on the manipulator with three mobile wheels substantiate the timeliness and repetitiveness of the proposed optimization scheme.

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Memory reduction for numerical solution of differential equations using compressive sensing

Unni

Chandra

Kumar

2017

2017 IEEE 13th International Colloquium on Signal Processing &Amp; Its Applications (CSPA)

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Qualitative behavior of the Lorenz‐like chaotic system describing the flow between two concentric rotating spheres

Cited by 3 publications

References 27 publications

Generation and analysis of the chaos phenomenon in the molecular-distillation-Navier–Stokes (MDNS) nonlinear system

Generation and analysis of the chaos phenomenon in the molecular-distillation-Navier–Stokes (MDNS) nonlinear system

A Repeatable Optimization for Kinematic Energy System with Its Mobile Manipulator Application

Memory reduction for numerical solution of differential equations using compressive sensing

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