In Depth Analysis of Stretch Function Resulting from Solving the Generalize Fractional-Order Bloch Equations Using Fractional Calculus

In this paper the stretch function resulting from solving the fractional-order Bloch equations using fractional calculus was discussed. This function has promising results to represent diffusion signal decay from MRI images. Conventional analyses of (DWI) measurements resolve the normalized magnetization decay profiles in terms of discrete and mono-exponential components with distinct lifetimes. In complex, heterogeneous biological and biophysical samples such as tissue, multi-exponential decay functions can appear to provide truer representation to normalized magnetization decay profile than the assumption of a mono-exponential decay, but the assumption of multiple discrete components is arbitrary and is often erroneous. Moreover, interactions, between both normalized magnetization and with their environment, can result in complex normalized magnetization decay profiles that represent a continuous distribution of lifetimes. The purpose in this paper is to study different factors that influence the stretch function strength, clarity, and contrast of MRI magnetization signal relaxation by manipulating the anomalous diffusion parameters Δ,δ,Gz,β and μ. of Bloch equations. Through this study, it was found that complex normalized magnetization decay profiles behave like stretch exponential function inside power law. Further developments of this study may be useful in optimizing anomalous diffusion in tissues with neurodegenerative, and ischemic diseases.

Storage of quantum coherences as phase-labelled local polarization in solid-state nuclear magnetic resonance

Nuclear spins are promising candidates for quantum information processing because their good isolation from the environment precludes the rapid loss of quantum coherence. Many strategies have been developed to further extend their decoherence times. Some of them make use of decoupling techniques based on the Carr–Purcell and Carr–Purcell–Meiboom–Gill pulse sequences. In many cases, when applied to inhomogeneous samples, they yield a magnetization decay much slower than that of the Hahn echo. However, we have proved that these decays cannot be associated with longer decoherence times, as coherences remain frozen. They result from coherences recovered after their storage as local polarization and thus they can be used as memories. We show here how this freezing of the coherent state, which can subsequently be recovered after times longer than the natural decoherence time of the system, can be generated in a controlled way with the use of field gradients. A similar behaviour of homogeneous samples in inhomogeneous fields is demonstrated. It is emphasized that the effects of inhomogeneities in solid-state nuclear magnetic resonance, independently of their origin, should not be disregarded, as they play a crucial role in multipulse sequences.

A New Measuring System for Determining the Magnetic Viscosity in Permanent Magnets

A new system for measuring magnetic viscosity in bulk hard magnetic materials base on a pulsed field method is presented. After the magnetizing field pulse, the stray field of the sample, which is proportional to the magnetic moment, is measured with a compensated set of two Hall probes. The set of Hall probes is driven with an AC voltage source and the Hall voltage is detected using a lock-in amplifier. By this method the system is able to measure the time dependence of the magnetization (viscosity). The magnetic viscosity coefficient (S) is obtained through a linear fitting of the magnetization decay versus ln t. Two typical Nd-Fe-B samples were measured and good agreement with the results from the traditional viscosity experiment was obtained.