Estimating T2 from surface NMR FID data using a forward model based on the full-Bloch equation

Abstract Undesired forces during human-robot interaction limit training effectiveness with rehabilitation robots. Thus, avoiding such undesired forces by improved mechanics, sensorics, kinematics, and controllers are the way to increase exoskeleton transparency. In this paper, the arm therapy exoskeleton ARMin IV+ was used to compare the differences in transparency offered by using the previous feed-forward model-based controller, with a disturbance observer in a study. Systematic analysis of velocity-dependent effects of controller transparency in single- and multi-joint scenarios performed in this study highlight the advantage of using disturbance observers for obtaining consistent transparency behavior at different velocities in single-joint and multi-joint movements. As the main result, the concept of the disturbance observer sets a new benchmark for ARMin transparency.

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The Bloch equation for spin dynamics in electron storage rings: Computational and theoretical aspects

International Journal of Modern Physics A ◽

10.1142/s0217751x19420326 ◽

2019 ◽

Vol 34 (36) ◽

pp. 1942032 ◽

Cited By ~ 1

Author(s):

Klaus Heinemann ◽

Daniel Appelö ◽

Desmond P. Barber ◽

Oleksii Beznosov ◽

James A. Ellison

Keyword(s):

Mathematical Model ◽

Spin Diffusion ◽

Spin Dynamics ◽

High Energy ◽

Bloch Equation ◽

Storage Rings ◽

Electron Storage ◽

Model Based ◽

Spin Flip ◽

Electron Storage Rings

In this paper, we describe our work on spin polarization in high-energy electron storage rings which we base on the Full Bloch equation (FBE) for the polarization density and which aims towards the [Formula: see text] option of the proposed Future Circular Collider (FCC-ee) and the proposed Circular Electron Positron Collider (CEPC). The FBE takes into account non spin-flip and spin-flip effects due to synchrotron radiation including the spin-diffusion effects and the Sokolov–Ternov effect with its Baier–Katkov generalization as well as the kinetic-polarization effect. This mathematical model is an alternative to the standard mathematical model based on the Derbenev–Kondratenko formulas. For our numerical and analytical studies of the FBE, we develop an approximation to the latter to obtain an effective FBE. This is accomplished by finding a third mathematical model based on a system of stochastic differential equations (SDEs) underlying the FBE and by approximating that system via the method of averaging from perturbative ODE theory. We also give an overview of our algorithm for numerically integrating the effective FBE. This discretizes the phase space using spectral methods and discretizes time via the additive Runge–Kutta (ARK) method which is a high-order semi-implicit method. We also discuss the relevance of the third mathematical model for spin tracking.

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An approximate fast-mapping approach to the surface NMR forward problem

Geophysical Journal International ◽

10.1093/gji/ggaa044 ◽

2020 ◽

Vol 221 (2) ◽

pp. 928-937

Author(s):

Denys Grombacher ◽

Mason Andrew Kass ◽

Esben Auken ◽

Jakob Juul Larsen

Keyword(s):

Matrix Multiplication ◽

Coefficient Matrix ◽

Bloch Equation ◽

Forward Model ◽

Fast Mapping ◽

Polynomial Representation ◽

Mapping Approach ◽

Simple Matrix ◽

The Look ◽

Cent Error

SUMMARY A surface nuclear magnetic resonance (NMR) forward model based on the full-Bloch equation improves the accuracy of the forward response given an arbitrary excitation pulse and a wider range of relaxation conditions. However, the full-Bloch solution imposes a significant slowdown in inversion times compared to the traditional forward model. We present a fast-mapping approach capable of dramatic increases in inversion speeds with minimal sacrifices in forward response accuracy. We show that the look-up tables used to calculate the transverse magnetization and the full surface NMR forward response are smoothly varying functions of the underlying T2* and T2 values. We exploit this smoothness to form a polynomial representation of the look-up tables and surface NMR forward responses, where a fast-mapping approximation of each are reduced to a simple matrix multiplication. Accurate approximations with less than 1 per cent error can be produced using 21 coefficient representations of the look-up tables for each B1 value and for the signal expected from a particular depth layer for a particular pulse moment. In essence, the proposed fast-mapping approach front-loads all expensive calculations and stores the results in a compressed form as a coefficient matrix containing less than a half a million elements. This allows all subsequent inversions to be performed at greatly improved speeds.

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Inverse Optimization of Design Parameters in a Hybrid Solar Pond System With External Heat Addition

Volume 6: Energy ◽

10.1115/imece2019-11117 ◽

2019 ◽

Author(s):

Abhishek Kumar ◽

Ranjan Das

Keyword(s):

Solar Radiation ◽

El Paso ◽

Global Solar Radiation ◽

External Heat ◽

Forward Model ◽

Design Parameters ◽

Geometrical Parameters ◽

Heat Addition ◽

Model Based ◽

Solar Pond

Abstract External heat supply to solar ponds from various types of solar collectors is a feasible alternative that significantly enhances its performance. In this work, various design parameters in a hybrid solar pond with external heat addition from Evacuated Tube Solar Collector (ETSC) are evaluated using an inverse approach. A forward model based on heat balance equations is solved for various zones of the solar pond to predict temperatures attained by its storage zone under a given climatic condition. Bryant and Colbeck’s relation is used to account for the diminution of the solar radiation as it travels from upper layers of the solar pond to its bottom layers. The relevant differential equations are solved using a Runge-Kutta fourth order scheme. The component of heat addition from ETSC is added to the forward model in the storage zone’s equation. Heat added from ETSC is considered proportional to the fraction of the aperture area to the pond’s base area, the thermal efficiency of ETSC and global solar radiation incident on ETSC. Both the forward model of the solar pond and combined solar pond and ETSC model were validated with previous experimental and numerical studies available in the literature for El Paso, USA, and Melbourne, Australia. An inverse model based on genetic algorithm is proposed for evaluating the set of geometrical parameters of ETSC and solar pond in order to derive a required performance from the combined solar pond-ETSC system.

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