scholarly journals The Rabi problem with elliptical polarization

2020 ◽  
Vol 75 (11) ◽  
pp. 937-962
Author(s):  
Heinz-Jürgen Schmidt
Keyword(s):  
Floquet Theory ◽  
Equation Of Motion ◽  
Quantum Spin ◽  
Heun Equation ◽  
Elliptical Polarization ◽  
Third Order ◽  
Polynomial Coefficients ◽  
Resonance Frequencies ◽  
Classical Quantum ◽  
Elliptically Polarized

AbstractWe consider the solution of the equation of motion of a classical/quantum spin subject to a monochromatical, elliptically polarized external field. The classical Rabi problem can be reduced to third-order differential equations with polynomial coefficients and hence solved in terms of power series in close analogy to the confluent Heun equation occurring for linear polarization. Application of Floquet theory yields physically interesting quantities like the quasienergy as a function of the problem’s parameters and expressions for the Bloch–Siegert shift of resonance frequencies. Various limit cases are thoroughly investigated.

Calibration of pneumotachographs using a calibrated syringe

2003 ◽  
Vol 95 (2) ◽  
pp. 571-576 ◽  
Author(s):  
Yongquan Tang ◽  
Martin J. Turner ◽  
Johnny S. Yem ◽  
A. Barry Baker
Keyword(s):  
Calibration Method ◽  
Linear Range ◽  
Data Sets ◽  
Constant Flow ◽  
Calibration Constant ◽  
Third Order ◽  
Polynomial Coefficients ◽  
Calibration Curves ◽  
Order Polynomial ◽  
Better Than

Pneumotachograph require frequent calibration. Constant-flow methods allow polynomial calibration curves to be derived but are time consuming. The iterative syringe stroke technique is moderately efficient but results in discontinuous conductance arrays. This study investigated the derivation of first-, second-, and third-order polynomial calibration curves from 6 to 50 strokes of a calibration syringe. We used multiple linear regression to derive first-, second-, and third-order polynomial coefficients from two sets of 6–50 syringe strokes. In part A, peak flows did not exceed the specified linear range of the pneumotachograph, whereas flows in part B peaked at 160% of the maximum linear range. Conductance arrays were derived from the same data sets by using a published algorithm. Volume errors of the calibration strokes and of separate sets of 70 validation strokes ( part A) and 140 validation strokes ( part B) were calculated by using the polynomials and conductance arrays. Second- and third-order polynomials derived from 10 calibration strokes achieved volume variability equal to or better than conductance arrays derived from 50 strokes. We found that evaluation of conductance arrays using the calibration syringe strokes yields falsely low volume variances. We conclude that accurate polynomial curves can be derived from as few as 10 syringe strokes, and the new polynomial calibration method is substantially more time efficient than previously published conductance methods.

scholarly journals Origin of the residual line width under frequency-switched Lee–Goldburg decoupling in MAS solid-state NMR

2020 ◽  
Vol 1 (1) ◽  
pp. 13-25 ◽  
Author(s):  
Johannes Hellwagner ◽  
Liam Grunwald ◽  
Manuel Ochsner ◽  
Daniel Zindel ◽  
Beat H. Meier ◽  
...  
Keyword(s):  
Solid State ◽  
Line Width ◽  
Floquet Theory ◽  
Pulse Sequence ◽  
Second Order ◽  
Magic Angle ◽  
Line Broadening ◽  
Third Order ◽  
Order Error ◽  
Error Terms

Abstract. Homonuclear decoupling sequences in solid-state nuclear magnetic resonance (NMR) under magic-angle spinning (MAS) show experimentally significantly larger residual line width than expected from Floquet theory to second order. We present an in-depth theoretical and experimental analysis of the origin of the residual line width under decoupling based on frequency-switched Lee–Goldburg (FSLG) sequences. We analyze the effect of experimental pulse-shape errors (e.g., pulse transients and B1-field inhomogeneities) and use a Floquet-theory-based description of higher-order error terms that arise from the interference between the MAS rotation and the pulse sequence. It is shown that the magnitude of the third-order auto term of a single homo- or heteronuclear coupled spin pair is important and leads to significant line broadening under FSLG decoupling. Furthermore, we show the dependence of these third-order error terms on the angle of the effective field with the B0 field. An analysis of second-order cross terms is presented that shows that the influence of three-spin terms is small since they are averaged by the pulse sequence. The importance of the inhomogeneity of the radio-frequency (rf) field is discussed and shown to be the main source of residual line broadening while pulse transients do not seem to play an important role. Experimentally, the influence of the combination of these error terms is shown by using restricted samples and pulse-transient compensation. The results show that all terms are additive but the major contribution to the residual line width comes from the rf-field inhomogeneity for the standard implementation of FSLG sequences, which is significant even for samples with a restricted volume.

Vibration Analysis of Drug Delivery CNTs Using Transfer Matrix Method

2011 ◽  
Author(s):  
Anooshiravan Farshidianfar ◽  
Ali A. Ghassabi ◽  
Mohammad H. Farshidianfar ◽  
Mohammad Hoseinzadeh
Keyword(s):  
Boundary Conditions ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Equation Of Motion ◽  
Beam Model ◽  
Multi Wall Carbon Nanotubes ◽  
Resonance Frequencies ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

The free vibration and instability of fluid-conveying multi-wall carbon nanotubes (MWCNTs) are studied based on an Euler-Bernoulli beam model. A theory based on the transfer matrix method (TMM) is presented. The validity of the theory was confirmed for MWCNTs with different boundary conditions. The effects of the fluid flow velocity were studied on MWCNTs with simply-supported and clamped boundary conditions. Furthermore, the effects of the CNTs’ thickness, radius and length were investigated on resonance frequencies. The CNT was found to posses certain frequency behaviors at different geometries. The effect of the damping corriolis term was studied in the equation of motion. Finally, a useful simplification is introduced in the equation of motion.

Variational formulation for weakly nonlinear perturbations of ideal magnetohydrodynamics

2011 ◽  
Vol 77 (5) ◽  
pp. 589-615 ◽  
Author(s):  
M. HIROTA
Keyword(s):  
Coupling Coefficient ◽  
Displacement Vector ◽  
Lagrange Equation ◽  
Natural Extension ◽  
Equation Of Motion ◽  
Nonlinear Phenomena ◽  
Lie Series ◽  
Third Order ◽  
Weakly Nonlinear ◽  
Ideal Magnetohydrodynamics

AbstractA new equation of motion that governs weakly nonlinear phenomena in ideal magnetohydrodynamics (MHDs) is derived as a natural extension of the well-known linearized equation of motion for the displacement field. This derivation is made possible by expanding the MHD Lagrangian explicitly up to third order with respect to the displacement of plasma, which necessitates an efficient use of the Lie series expansion. The resultant equation of motion (i.e. the Euler–Lagrange equation) includes a new quadratic force term which is responsible for various mode–mode coupling due to the MHD nonlinearity. The third-order potential energy serves to quantify the coupling coefficient among resonant three modes and its cubic symmetry proves the Manley–Rowe relations. In contrast to earlier works, the coupling coefficient is expressed only by the displacement vector field, which is already familiar in the linear MHD theory, and both the fixed and free boundary cases are treated systematically.

A Legendre Polynomials Based Method for Stability Analysis of Milling Processes

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Ye Ding ◽  
XiaoJian Zhang ◽  
Han Ding
Keyword(s):  
Time Domain ◽  
Legendre Polynomials ◽  
Floquet Theory ◽  
Space Form ◽  
Equation Of Motion ◽  
Analytical Prediction ◽  
Numerical Examples ◽  
Dynamic Map ◽  
Delay Differential ◽  
Time Periodic

This paper presents a time-domain approach for a semi-analytical prediction of stability in milling using the Legendre polynomials. The governing equation of motion of milling processes is expressed as a delay-differential equation (DDE) with time periodic coefficients. After the DDE being re-expressed in state-space form, the state vector is approximated by a series of Legendre polynomials. With the help of the Legendre–Gauss–Lobatto (LGL) quadrature, a discrete dynamic map is formulated to approximate the original DDE, and utilized to predict the milling stability based on Floquet theory. With numerical examples illustrating the efficiency and accuracy of the proposed approach, an experimental example validates the method.

Multicritical Points from Mean Field Renormalization Group

1998 ◽  
Vol 12 (18) ◽  
pp. 1813-1821 ◽  
Author(s):  
D. Peña Lara ◽  
J. A. Plascak ◽  
J. Ricardo de Souza
Keyword(s):  
Renormalization Group ◽  
Tricritical Point ◽  
Mean Field ◽  
Transverse Field ◽  
Quantum Spin ◽  
Group Method ◽  
Third Order ◽  
Multicritical Points ◽  
Unique Manner ◽  
Field Renormalization

The mean field renormalization group method is extended to study tri-critical phenomena. By taking into account the third-order terms in the expansion of the magnetizations of the different clusters with respect to the symmetry breaking fields, together with the scaling assumption of the magnetization at a first-order fixed point, one additional equation is obtained which locates, in an unique manner, the tricritical point. This approach is applied in the study of the classical spin-σ Blume–Capel model and the quantum spin-1/2 anisotropic Heisenberg model in the presence of a transverse field as well as with Dzyaloshinsky–Moriya interactions.

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