scholarly journals (In-)stability of singular equivariant solutions to the Landau–Lifshitz–Gilbert equation

2013 ◽  
Vol 24 (6) ◽  
pp. 921-948 ◽  
Author(s):  
JAN BOUWE VAN DEN BERG ◽  
J. F. WILLIAMS

In this paper, we use formal asymptotic arguments to understand the stability properties of equivariant solutions to the Landau–Lifshitz–Gilbert model for ferromagnets. We also analyse both the harmonic map heatflow and Schrödinger map flow limit cases. All asymptotic results are verified by detailed numerical experiments, as well as a robust topological argument. The key result of this paper is that blowup solutions to these problems are co-dimension one and hence both unstable and non-generic.

2017 ◽  
Vol 14 (01) ◽  
pp. 1750007
Author(s):  
Masoumeh Hosseini Nasab ◽  
Gholamreza Hojjati ◽  
Ali Abdi

Considering the methods with future points technique from second derivative general linear methods (SGLMs) point of view, makes it possible to improve their stability properties. In this paper, we extend the stability regions of a modified version of E2BD formulas to optimal one and show its effectiveness by numerical verifications. Also, implementation issues, with numerical experiments, of these methods are investigated in a variable step-size mode.


Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.


2003 ◽  
Vol 2003 (2) ◽  
pp. 109-117
Author(s):  
R. Lowen ◽  
C. Verbeeck

This paper studies the stability properties of the concepts of local compactness introduced by the authors in 1998. We show that all of these concepts are stable for contractive, expansive images and for products.


1968 ◽  
Vol 78 (1) ◽  
pp. 91-103 ◽  
Author(s):  
G. P. Szegö ◽  
C. Olech ◽  
A. Cellina

Author(s):  
W. T. van Horssen ◽  
O. V. Pischanskyy ◽  
J. L. A. Dubbeldam

In this paper the forced vibrations of a linear, single degree of freedom oscillator (sdofo) with a time-varying mass will be studied. The forced vibrations are due to small masses which are periodically hitting and leaving the oscillator with different velocities. Since these small masses stay for some time on the oscillator surface the effective mass of the oscillator will periodically vary in time. Not only solutions of the oscillator equation will be constructed, but also the stability properties, and the existence of periodic solutions will be discussed.


2021 ◽  
Vol 50 (6) ◽  
pp. 1799-1814
Author(s):  
Norazak Senu ◽  
Nur Amirah Ahmad ◽  
Zarina Bibi Ibrahim ◽  
Mohamed Othman

A fourth-order two stage Phase-fitted and Amplification-fitted Diagonally Implicit Two Derivative Runge-Kutta method (PFAFDITDRK) for the numerical integration of first-order Initial Value Problems (IVPs) which exhibits periodic solutions are constructed. The Phase-Fitted and Amplification-Fitted property are discussed thoroughly in this paper. The stability of the method proposed are also given herewith. Runge-Kutta (RK) methods of the similar property are chosen in the literature for the purpose of comparison by carrying out numerical experiments to justify the accuracy and the effectiveness of the derived method.


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