General Analytical Solutions of the Bloch Equations
General Analytical Solutions of the Bloch Equations ... Direct Cartesian-Space Solutions of Generalized Bloch Equations in the Rotating Frame. 1995, Journal of ...
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Analytic solutions to the Bloch equations for amplitude- and - JETP
a monochromatic field with variable amplitude, analytic so- lutions are known for ... general formalism to solve the Bloch equations ( 1 ) with co- efficients which ...
[ e_070_04_0639.pdf - Read/Download File
Bloch equations
Bloch equations. – With and without relaxation. – With RF and Relaxation. – Transformation into rotating frame. – Steady state solutions. • Absorption and ...
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On unorthodox solutions of the Bloch equations
Aug 22, 2012 ... Keywords: analytic solutions * Bloch equations * two-level system ... it had long remained unnoticed that Torrey's general solution (1) had been.
[ 1208.5736 - Read/Download File
Exceptional Points For Parameter Estimation In Open - arXiv.org
The Bloch equation is the simplest example of a quantum Master equation. ... Kossakowski and Sudarshan (L-GKS) obtained the general structure of the .... Such figures were obtained in the study of analytical solutions for the Bloch equation.
[ 1411.6364 - Read/Download File
ANALYTICAL SOLUTION TO BLOCH EQUATIONS FOR CW
Close-form solutions of NMR Bloch equation with ﬂow dependent ... get the particular and general solution of the resulting differential equation using certain ...
[ KIC000001-odoh & De.pdf - Read/Download File
Project 1 - UO Atom Optics - University of Oregon
We developed a program that is used to solve the optical Bloch equations for the two-level atom ... to compare the numerical and analytical solutions for ρee. ..... Figure 2.1: general plot of numerical solutions Ω = Γ, tstep = 0.01, ntraj = 10000. 9 ...
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Revisiting the Bloch Equation through Averaging
analytic solution to the Bloch equation is developed in this paper. The method is .... The general form of the Bloch equation, without consid- ering spin diffusion ...
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Fast approximate solution of Bloch equation for simulation of RF
In this paper, we present an original method for solving the Bloch equation ... for simple test objects (such as cylinders, spheres or ellipsoids) analytical ... The basic idea for numerical simulation of MRI images is to solve repeatedly the Bloch.
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Analytic solutions to the two-state problem for chirped pulses
An analytic solution of the undamped Bloch equation is presented for a class of pulses that ... solution of Rosen and Zener was generalized by Bambini and.
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Bloch equations revisited: New analytical solutions for the
coupled equations are solved numerically (11). We have given analytical solution to the general- ized Bloch equations in the rotating frame without any.
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Article PDF - IOPscience
Nov 16, 2015 ... have paved the way for a general theory of quantum open systems. Davies [23] ..... study of analytical solutions for the Bloch equation [53–55].
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Mathematical concept of the Bloch flow equations for general
ABSTRACT: The recent analytical solutions to the Bloch NMR equations for a general RF ... den applications of blood flow and general physiological fluid flow ...
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Numerical solution of the Bloch equations provides insights into the
spectra obtained with an aqueous solution of a paramagnetic. CEST agent containing .... Bloch equations for the general three-pool case in which exchange also ..... it does not result in exact analytical solutions in the form of simple equations.
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MRI notes, p. 1-33 - EECS
Oct 28, 2009 ... As usual, we begin by describing the general physical phenomena that underly the MR ...... Solutions to the Bloch equation when applied RF=0.
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Transient Decay of Longitudinal Magnetization in Heterogeneous
A general method of solving equations governing the transient response of ... derived implicit solution to the coupled Bloch equations is re- formulated using this ... With this formula- tion. we provide an analytical and explicit solution to the full.
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7 Interaction of Atoms With a Classical Light Field
or more general. (b+ .... This leads to the Bloch equations in the rotating frame: .... A more lengthy calculation provides an analytical solution for the case of near-.
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Analytical Solutions of a Three Dimensional Time-Dependent - Hikari
Keywords: Bloch NMR, Schrodinger Equation, Characteristics Energy, Wave function,. Potential. 1. .... Applying an assumed general solution of ( ). , therefore. ( ).
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General solution to gradient-induced transverse - Duke University
Nov 14, 2011 ... limit; however, our approach yields a single analytical solution suitable in all ... shown to be the eigenfunction of the Bloch-Torrey equation.
[ PhysRevA.84.053411.pdf - Read/Download File
PDF - Ideals
The proposed method is further generalized to correct B0 inhomogeneity effects and ..... equation and analytical approximate solutions of the Bloch equation are ...
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