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

2020 ◽  
Vol 10 (8) ◽  
pp. 2850 ◽  
Author(s):  
Harendra Singh ◽  
H. M. Srivastava

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.

2007 ◽  
Vol 30 (4) ◽  
pp. 41
Author(s):  
A. Dechant

On the morning of October 10, 2003, the residents of New York awoke to find that an entire page of their beloved paper, The Times, had been usurped for the sole purpose of flagrant self-promotion and protestation. On his own behalf, Dr. Raymand Damadian had purchased a one page spread bemoaning his exclusion in the Nobel Prize for Medicine that year which had previously been awarded to Paul Laterbur and Peter Mansfield for their contributions to the development of Magnetic Resonance Imaging (MRI). Over the course of the next few months, the public was to witness a series of such articles proclaiming that a shameful wrong had been committed, and that the truth would eventually prove Dr. Damadian’s accusations. That truth lay in the early theoretical and technical foundations that led to the discovery of MRI. Described just after the Second World War, nuclear magnetic resonance (NMR) was hailed as a breakthrough in physical chemistry for which Felix Bloch and Edward Purcell were awarded the Nobel Prize in Physics in 1952. Two decades later, in 1971, Dr. Damadian discovered that differences between the NMR signals of cancerous and normal tissue might provide a rapid means of cancer detection. However, Laterbur and Mansfield were the first to actually demonstrate images of live tissue using the application of magnetic gradients – the key to modern MRI. Though speculation exists that Dr. Damadian may have been excluded from the prize due to his religious beliefs or political rivalry, only time will reveal the whole truth when the Nobel files are opened 50 years hence. Bradley W. The Nobel Prize: Three Investigators Allowed but Two Were Chosen. Journal of Magnetic Resonance Imaging 2004; 19:520. Laterbur P. Image formation by induced local interactions: examples of employing nuclear magnetic resonance. Nature 1973; 242:190-191. Mansfield P, Grannell P. “NMR diffraction in solids?” Journal of Physics C: Solid State Physics 1973; 63:L433-L426.


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