On the magnetic resonance of an alined spin-assembly

1972 ◽  
Vol 330 (1581) ◽  
pp. 265-270 ◽  
Keyword(s):  
Steady State ◽  
Magnetic Resonance ◽  
Equations Of Motion ◽  
Double Resonance ◽  
Relaxation Times ◽  
Spin Orientation ◽  
Optical Double Resonance ◽  
Set Up ◽  
Slow Passage ◽  
Steady State Solutions

The state of a spin-assembly of arbitrary J , undergoing magnetic resonance, is characterized by the multipole components p q k of the instantaneous spin-polarization which describe spin-orientation ( k = 1), spin-alinement ( k = 2), etc. Equations of motion analogous to Bloch’s equations ( k = 1) are set up for the multipole components of different k , introducing terms which describe phenomenologically ( a ) the pumping of the longitudinal multipole components ( q = 0), and ( b ) the independent but anisotropic relaxation of multipole components of different k . Steady-state solutions are obtained. In particular, the slow-passage magnetic resonance functions for the alinement components, which involve three relaxation times, are calculated explicitly. For the particular case of isotropic relaxation, these resonance functions reduce to the form originally derived for optical double resonance for a J = 1 assembly. It is emphasized that the damping constant which is involved is that for alinement.

The solution conformation of prostacyclin as determined by high field proton magnetic resonance techniques

1980 ◽  
Vol 58 (10) ◽  
pp. 974-983 ◽  
Author(s):  
George Kotovych ◽  
Gerdy H. M. Aarts ◽  
Tom T. Nakashima ◽  
Glen Bigam
Keyword(s):  
Magnetic Resonance ◽  
Correlation Time ◽  
Proton Magnetic Resonance ◽  
Double Resonance ◽  
Relaxation Times ◽  
Segmental Motion ◽  
Solution Conformation ◽  
Nmr Spectrum ◽  
H Nmr ◽  
The Difference

The proton magnetic resonance (1H nmr) spectrum at 400 MHz of prostacyclin at pH 10.4 in glycine buffer has been completely analyzed utilizing homonuclear double resonance, inversion recovery, and difference nOe experiments. The spectral analysis shows that the two protons at C-4 are non-equivalent even though they are removed from the asymmetric centres at C-8 and C-9 by five bonds. The difference nOe measurements verify the configuration at C-5.Proton longitudinal relaxation times (T1) were measured at 400 and 200 MHz. From the T1 frequency dependence, effective rotational correlation times ranging from 2.3 × 10−10 to 3.0 × 10−10 s were calculated for H-5, H-9, H-11, and H-15. This indicates that the portion of the molecule encompassed by these protons has a longer correlation time than is observed for the C-2 and the C-17 to C-19 protons, for which the average correlation time is 1.2 × 10−10 s. Hence the aliphatic side chains have more segmental motion.

Passive Stability and Active Control in a Rhythmic Task

2007 ◽  
Vol 98 (5) ◽  
pp. 2633-2646 ◽  
Author(s):  
Kunlin Wei ◽  
Tjeerd M. H. Dijkstra ◽  
Dagmar Sternad
Keyword(s):  
Steady State ◽  
Active Control ◽  
Human Performance ◽  
Passive Control ◽  
Basin Of Attraction ◽  
Relaxation Times ◽  
Passive Dynamics ◽  
Passive Stability ◽  
Set Up ◽  
Boundary Of Stability

Rhythmically bouncing a ball with a racket is a task that affords passively stable solutions as demonstrated by stability analyses of a mathematical model of the task. Passive stability implies that no active control is needed as errors die out without requiring corrective actions. Empirical results from human performance demonstrated that actors indeed exploit this passive dynamics in steady-state performance, thereby reducing computational demands of the task. The present study investigated the response to perturbations of different magnitudes designed on the basis of the model's basin of attraction. Humans performed the task in a virtual reality set-up with a haptic interface. Relaxation times of the performance errors showed significantly faster returns than predicted from the purely passive model, indicative of active error corrections. Systematic adaptations in the racket trajectories were a monotonic function of the perturbation magnitudes, indicating that active control was applied in proportion to the perturbation. These results did not indicate any sensitivity to the boundary of stability. Yet the influence of passive dynamics was also seen: the pattern of relaxation times in the major performance variable ball height was consistent with qualitative predictions derived from the basin of attraction and racket accelerations at contact were generally negative signaling use of passive stability. These findings suggest that the fast return back to steady state was assisted by passive properties of the task. It was concluded that actors used a blend of active and passive control for all sizes of perturbations.

Modal Analysis to Interpret Localization Phenomena in Two Nonlinear Tuned Mass Dampers

2021 ◽  
Author(s):  
Yuji Harata ◽  
Takashi Ikeda
Keyword(s):  
Steady State ◽  
Modal Analysis ◽  
Equations Of Motion ◽  
Harmonic Excitation ◽  
Mode Shapes ◽  
Response Curves ◽  
Tuned Mass Dampers ◽  
Second Mode ◽  
Steady State Solutions ◽  
Modal Coordinates

Abstract This study investigates localization phenomena in two identical nonlinear tuned mass dampers (TMDs) installed on an elastic structure, which is subjected to external, harmonic excitation. In the theoretical analysis, the mode shapes of the system are determined, and the modal equations of motion are derived using modal analysis. These equations are demonstrated as forming an autoparametric system in which external excitation directly acts on the first and third vibration modes, whereas the second vibration mode is indirectly excited due to the nonlinear coupling with the other modes. Van der Pol’s method is employed to obtain the frequency response curves for both physical and modal coordinates. The two TMDs vibrate in phase for the first and third modes, but vibrate out of phase for the second mode. Consequently, when all modes appear, the two TMDs may vibrate at different amplitudes, i.e., localization phenomena may occur because the TMD motions are expressed by the summation of motions for all modes. The numerical calculations clarify that the localization phenomena may occur in the two TMDs when all three modes appear simultaneously. Moreover, there are two steady-state solutions of the harmonic oscillations for the second mode with identical amplitudes; however, their phases differ by π. Hence, which TMD vibrates at higher amplitudes depends on which of these two steady-state solutions for the phase.

A high field proton magnetic resonance study of the solution conformation of thromboxane B2

1980 ◽  
Vol 58 (11) ◽  
pp. 1111-1117 ◽  
Author(s):  
George Kotovych ◽  
Gerdy H. M. Aarts
Keyword(s):  
Magnetic Resonance ◽  
High Field ◽  
Double Resonance ◽  
Relaxation Times ◽  
Chair Conformation ◽  
Rotational Correlation Time ◽  
Coupling Constants ◽  
Solution Conformation ◽  
Dipolar Relaxation ◽  
Rotational Correlation

The solution conformation of thromboxane B2 (TXB2) has been studied using high-field nuclear magnetic resonance techniques. In CDCl3, both anomers are present in solution with 76% 11α-OH TXB2 and 24% 11β-OH TXB2. In CD3OD, the predominant anomer is 11β-OH TXB2 (80%) while the concentration of 11α-OH TXB2 is 20%. The proton resonances were assigned at 400 MHz using double resonance techniques. The analysis of the vicinal coupling constants indicates that the six-membered ring is present in solution in a chair conformation with both of the aliphatic side chains equatorial. Proton longitudinal relaxation times were measured at 25 °C in CDCl3 for H-2, H-11β, H-12, H-13, H-14, and H-17 to H-19, both at 200 MHz and at 400 MHz. From the frequency dependence of these dipolar relaxation times, the rotational correlation times were evaluated. Within experimental error, all of the values are similar in magnitude (~ 2.0 × 10−10 s) indicating that this is the molecular rotational correlation time.

Some Recent Developments in High Resolution Nuclear Magnetic Resonance

1972 ◽  
Vol 26 (4) ◽  
pp. 421-430 ◽  
Author(s):  
Edwin D. Becker
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
High Resolution ◽  
Nuclear Overhauser Effect ◽  
Double Resonance ◽  
Relaxation Times ◽  
Nuclear Magnetic Resonance Spectra ◽  
Recent Developments ◽  
Nuclear Overhauser ◽  
Nuclear Magnetic

Techniques for studying high resolution nuclear magnetic resonance spectra have been considerably broadened in recent years. The most far reaching development—pulse Fourier transform (FT) methods—is discussed in detail. Applications of FT techniques to measurement of relaxation times and to enhancement of weak signals, especially from natural abundance 13C, are reviewed. Double resonance methods, particularly the nuclear Overhauser effect, and the use of lanthanide shift reagents are also covered in this “mini-review.”

Effects of Bearing and Shaft Asymmetries on the Resonant Oscillations of a Rotor-Dynamic System

1996 ◽  
Vol 118 (1) ◽  
pp. 107-114
Author(s):  
R. Ganesan
Keyword(s):  
Steady State ◽  
Dynamic System ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Mass Unbalance ◽  
Asymmetric Rotor ◽  
Amplitude And Frequency Modulation ◽  
Rotor Dynamic ◽  
Steady State Solutions

Parametric steady-state vibrations of an asymmetric rotor while passing through primary resonance and the associated stability behavior are analyzed. The undamped case is considered and the equations of motion are rewritten in a from suitable for applying the method of multiple scales. Sensitivity to the bearing as well as shaft asymmetries of the oscillations due to unbalance excitation is evaluated. Expressions for amplitude and frequency modulation functions are obtained and are specialized to yield the steady-state solutions near primary resonance. Frequency-amplitude relationships that result from combined parametric and mass unbalance excitations are derived. Stability regions in the parameter space are obtained based on the time evolution of the amplitude and phase of the steady-state motions. The effects of bearing asymmetry on the amplitude and phase of the resonant oscillations are brought out. The sensitivity of vibrational and stability characteristics to various rotor-dynamic system parameters is illustrated through a numerical investigation.

scholarly journals Lineshape of Magnetic Resonance and its Effects on Free Induction Decay and Steady-State Free Precession Signal Formation

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
C. H. Ziener ◽  
M. Uhrig ◽  
T. Kampf ◽  
V. J. F. Sturm ◽  
F. T. Kurz ◽  
...  
Keyword(s):  
Steady State ◽  
Magnetic Resonance ◽  
Free Induction Decay ◽  
Relaxation Times ◽  
Fast Method ◽  
Signal Decay ◽  
Microscopic Field ◽  
Free Induction ◽  
Vessel Networks ◽  
Sequence Parameters

Magnetic resonance imaging based on steady-state free precision (SSFP) sequences is a fast method to acquire T1, T2, and T2∗-weighted images. In inhomogeneous tissues such as lung tissue or blood vessel networks, however, microscopic field inhomogeneities cause a nonexponential free induction decay and a non-Lorentzian lineshape. In this work, the SSFP signal is analyzed for different prominent tissue models. Neglecting the effect of non-Lorentzian lineshapes can easily result in large errors of the determined relaxation times. Moreover, sequence parameters of SSFP measurements can be optimized for the nonexponential signal decay in many tissue structures.

Autoparametric interaction in a double pendulum system

2012 ◽  
Vol 226 (8) ◽  
pp. 1971-1986
Author(s):  
Matthew P Cartmell ◽  
Ivana Kovacic ◽  
Miodrag Zukovic
Keyword(s):  
Steady State ◽  
Numerical Solutions ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Equations Of Motion ◽  
Double Pendulum ◽  
Pendulum System ◽  
Right Hand ◽  
The Right ◽  
Steady State Solutions

This article investigates a four-degree-of-freedom mechanical model comprising a horizontal bar onto which two identical pendula are fitted. The bar is suspended from a pair of springs and the left-hand-side pendulum is excited by means of a harmonic torque. The article shows that autoparametric interaction is possible by means of typical external and internal resonance conditions involving the system natural frequencies and excitation frequency, yielding an interesting case when the right-hand-side pendulum does not oscillate, but stays at rest. It is demonstrated that applying the standard method of multiple scales to this system leads to slow-time and subsequently steady-state equations representative of periodic responses; however, in common with previous findings reported in the literature for systems of four or more interacting modes, global solutions are not obtainable. This article then concentrates on discussing a proposed new modification to the method of multiple scales in which the effect of detuning is accentuated within the zeroth-order perturbation equations and it is then demonstrated that the numerical solutions from this approach to multiple scales yield results that are virtually indistinguishable from those obtained from direct numerical integration of the equations of motion. It is also shown that the algebraic structure of the steady-state solutions for the modified multiple scales analysis is identical to that obtained from a harmonic balance analysis for the case when the right-hand-side pendulum is decoupled. This particular decoupling case is prominent from examination of both the original equations of motion and the steady-state solutions irrespective of the analysis undertaken. This article concludes by showing that the translation and rotation of the bar are, in this particular case, mutually coupled and opposite in sign.

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