Analytical solution of the time-dependent Bloch NMR flow equations: a translational mechanical analysis

Awojoyogbe, Bamidele O.

doi:10.1016/j.physa.2004.03.061

Cited by 29 publications

(16 citation statements)

References 29 publications

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“…where M y (x) are the time independent NMR transverse magnetizations, 4k are the 4k-order Boubaker polynomials, Based on the conditions which may conform to the real-time experimental arrangements, we obtained a second order non homogeneous differential equation from the Bloch NMR flow equation [34,35] at Larmor frequency:…”

Section: Mathematical Analysismentioning

confidence: 99%

Flow Dynamics in Restricted Geometries: A Mathematical Concept Based on Bloch NMR Flow Equation and Boubaker Polynomial Expansion Scheme

Awojoyogbe¹,

Dada²,

Boubaker³

et al. 2013

JAMP

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Computational techniques are invaluable to the continued success and development of Magnetic Resonance Imaging (MRI) and to its widespread applications. New processing methods are essential for addressing issues at each stage of MRI techniques. In this study, we present new sets of non-exponential generating functions representing the NMR transverse magnetizations and signals which are mathematically designed based on the theory and dynamics of the Bloch NMR flow equations. These signals are functions of many spinning nuclei of materials and can be used to obtain information observed in all flow systems. The Bloch NMR flow equations are solved using the Boubaker polynomial expansion scheme (BPES) and analytically connect most of the experimentally valuable NMR parameters in a simplified way for general analyses of magnetic resonance imaging with adiabatic condition.

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Section: Mathematical Analysismentioning

confidence: 99%

Flow Dynamics in Restricted Geometries: A Mathematical Concept Based on Bloch NMR Flow Equation and Boubaker Polynomial Expansion Scheme

Awojoyogbe¹,

Dada²,

Boubaker³

et al. 2013

JAMP

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“…Bloch equations in NMR can be simulated numerically and analytically (see, for details, [11][12][13][14][15][16]). The time-fractional order Bloch equation having fractional derivative in Caputo sense is solved in [17].…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi Polynomials

Singh¹,

Srivástava

2020

Applied Sciences

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In the present paper, we numerically simulate fractional-order model of the Bloch equation by using the Jacobi polynomials. It arises in chemistry, physics and nuclear magnetic resonance (NMR). It also arises in magnetic resonance imaging (MRI) and electron spin resonance (ESR). It is used for purity determination, provided that the molecular weight and structure of the compound is known. It can also be used for structural determination. By the study of NMR, chemists can determine the structure of many compounds. The obtained numerical results are compared and simulated with the known solutions. Accuracy of the proposed method is shown by providing tables for absolute errors and root mean square errors. Different orders of the time-fractional derivatives results are illustrated by using figures.

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“…For example, the Bloch NMR equations has shown good success in the study biological and physiological properties of living tissue [1,2]. Besides medical applications, the Bloch NMR equations were used to investigate the thermodynamic properties of system e.g.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modelling of Bloch NMR to Explain the Rashba Energy Features

Emetere¹

2013

WJCMP

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The Bloch NMR as an analytical tool was able to address the fundamental features in the learning of spintronics. Beside confirming past assertions on the Rashba spin-orbit interaction, thermal motion of hole and electron spin and features of the quantum well, it was also able to explain the condition necessary for Rashba splitting within the quantum well. When the Rashba energy is 43 meV, it modified the Ehrenfest's theorem to hold for an external magnetic field. The confinement potential which is the strength of the Rashba spin-orbit interaction was shown to be controlled magnetically.

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Analytical solution of the time-dependent Bloch NMR flow equations: a translational mechanical analysis

Cited by 29 publications

References 29 publications

Flow Dynamics in Restricted Geometries: A Mathematical Concept Based on Bloch NMR Flow Equation and Boubaker Polynomial Expansion Scheme

Flow Dynamics in Restricted Geometries: A Mathematical Concept Based on Bloch NMR Flow Equation and Boubaker Polynomial Expansion Scheme

Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi Polynomials

Mathematical Modelling of Bloch NMR to Explain the Rashba Energy Features

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