Numerical methods for the Landau-Lifshitz-Gilbert equation

Banas L. Numerical methods for the Landau-Lifshitz-Gilbert equation. In: Li Z, Vulkov L, Wasniewski J, eds. Numerical analysis and its applications : third international conference ; revised selected papers. NAA 2004, Rousse, Bulgaria, June 29 - July 3, 2004. Lecture Notes in Computer Science. Vol 3401. Berlin: Springer; 2005: 158-165

Approximation of reachable sets using optimal control algorithms

To appearInternational audienceNumerical experiences with a method for the approximation of reachable sets of nonlinear control systems are reported. The method is based on the formulation of suitable optimal control problems with varying objective functions, whose discretization by Euler's method lead to finite dimensional non-convex nonlinear programs. These are solved by a sequential quadratic programming method. An efficient adjoint method for gradient computation is used to reduce the computational costs. The discretization of the state space is more efficiently than by usual sequential realization of Euler's method and allows adaptive calculations or refinements. The method is illustrated for two test examples. Both examples have non-linear dynamics, the first one has a convex reachable set, whereas the second one has a non-convex reachable set

Approximation of reachable sets using optimal control and support vector machines

We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorithm and represents the set approximation as a sublevel set of a function chosen in a reproducing kernel Hilbert space. In some sense, the method can be considered as an extension to the optimal control algorithm approach recently developed by Baier, Gerdts and Xausa. The convergence of the method is illustrated numerically for selected examples

Diode Like Attributes in Magnetic Domain Wall Devices via Geometrical Pinning for Neuromorphic Computing

Neuromorphic computing (NC) is considered as a potential vehicle for implementing energy-efficient artificial intelligence (AI). To realize NC, several materials systems are being investigated. Among them, the spin-orbit torque (SOT) -driven domain wall (DW) devices are one of the potential candidates. To implement these devices as neurons and synapses, the building blocks of NC, researchers have proposed different device designs. However, the experimental realization of DW device-based NC is only at the primeval stage. In this study, we have proposed and investigated pine-tree-shaped DW devices, based on the Laplace force on the elastic DWs, for achieving the synaptic functionalities. We have successfully observed multiple magnetization states when the DW was driven by the SOT current. The key observation is the asymmetric pinning strength of the device when DW moves in two opposite directions (defined as, xhard and xeasy). This shows the potential of these DW devices as DW diodes. We have used micromagnetic simulations to understand the experimental findings and to estimate the Laplace pressure for various design parameters. The study leads to the path of device fabrication, where synaptic properties are achieved with asymmetric pinning potential

Design Of Feedback Control For Active Mass Dampers Of Excited Structures

Annually, our world experiences thousands of seismic events that are the cause of hundreds of structural disasters and human fatalities. The objective of the presented research is to contribute to the world’s social, economic, and environmental needs by designing an optimized feedback control for active mass dampers (AMDs) by reducing oscillations. The optimal design will meet the required specifications and maintain a structure’s quasi-ideal, static position throughout a seismic event. The system’s equation of motion (EOM) is derived by using the Lagrangian Method and the free-body diagram. All the simulated and experimental responses of the AMD-1 system are obtained using MATLAB and Simulink. The experimental data is collected from various tests performed on a single-story building model. The techniques utilized for improvement of the AMD’s feedback control include parameter estimation, eigenvalue assignment, and linear quadratic regulation (LQR). As success is achieved with the AMD feedback control, future research can focus on idealizing the AMD’s performance in a system with multiple degrees of freedom