396 research outputs found
Application of Time-Fractional Order Bloch Equation in Magnetic Resonance Fingerprinting
Magnetic resonance fingerprinting (MRF) is one novel fast quantitative
imaging framework for simultaneous quantification of multiple parameters with
pseudo-randomized acquisition patterns. The accuracy of the resulting
multi-parameters is very important for clinical applications. In this paper, we
derived signal evolutions from the anomalous relaxation using a fractional
calculus. More specifically, we utilized time-fractional order extension of the
Bloch equations to generate dictionary to provide more complex system
descriptions for MRF applications. The representative results of phantom
experiments demonstrated the good accuracy performance when applying the
time-fractional order Bloch equations to generate dictionary entries in the MRF
framework. The utility of the proposed method is also validated by in-vivo
study.Comment: Accepted at 2019 IEEE 16th International Symposium on Biomedical
Imaging (ISBI 2019
Wannier-Stark resonances in optical and semiconductor superlattices
In this work, we discuss the resonance states of a quantum particle in a
periodic potential plus a static force. Originally this problem was formulated
for a crystal electron subject to a static electric field and it is nowadays
known as the Wannier-Stark problem. We describe a novel approach to the
Wannier-Stark problem developed in recent years. This approach allows to
compute the complex energy spectrum of a Wannier-Stark system as the poles of a
rigorously constructed scattering matrix and solves the Wannier-Stark problem
without any approximation. The suggested method is very efficient from the
numerical point of view and has proven to be a powerful analytic tool for
Wannier-Stark resonances appearing in different physical systems such as
optical lattices or semiconductor superlattices.Comment: 94 pages, 41 figures, typos corrected, references adde
- …