Motion characterization

Fig. 3. The basic Hahn sequence for the measurement of the transverse relaxation time T2. Any precession motion characterized by the frequency v in the rotating frame is refocused. This precession may arise either from chemical shift or from Bq inhomogeneity (symbolized by the shaded area, which has been strongly reduced for visualization purposes owing to the fast decay of the fid, it should in fact extend to the whole circle).

Abernathy and Sharp employed a similar idea, although in a more simplified form 130). They also worked in terms of a spin Hamiltonian varying with time in discrete steps and let the Hamiltonian contain the Zeeman and the ZFS interactions. They assumed, however, that the ZFS interaction was constant in the molecule-fixed (P) frame and that variation of the Hamiltonian originated only from fluctuation of the P frame with respect to the laboratory frame. These fluctuations were described in terms of Brownian reorientational motion, characterized by a time interval, x, (related to the rotational correlation time x ) and a Gaussian distribution of angular steps. 

The Spin. How can we reconcile spin s = 1 and Eq = 0 Spin is a constant, identical for all photons of arbitrary energy E. Hence, it is independent of energy and, therefore, it does not depend of the state of motion characterized by go. Also, evidently, spin cannot be a property of a nonexistent rest mass. Therefore, spin is associated with what ... 

The experimental results were rather surprising. It appeared that no significant difference existed between the average values of mixing efficiency, heat transfer coefficient and pressure drop obtained in a pulsed flow and those obtained in a constant flow of the same mean rate, probably because of the very low pulsation frequency, which is superimposed to a turbulent motion characterized by frequences three orders of magnitude higher. Thus, as far as only average values are concerned, the... 

In Table 1, S2 is the general order parameter describing bond motions at the ps-ns time scale, te is the characteristic correlation time for these motions and Rex is the conformational exchange term representing motions on the ps-ms time scale. Internal motions on the ps-ns time scale are considered as the superposition of fast and slow motions characterized by S2 and if as well as Ss2 and ts. Here, S2 = Ss2Sf2 and t, [Pg.52]

The external forces may be optical tweezers, microneedles, or the viscous load of the substance that is carried. These generalized forces create motion, characterized by an average velocity v, and average rate of ATP consumption JT. Molecular motors mostly operate far from equilibrium, and the velocity and rate of ATP consumptions are not linear functions of the forces. However, in the vicinity of the linear region, where A kBT, linear relations hold... 

The highly ordered fluid motion characterized by smooth streamlines is called laminar. The highly disordered fluid motion that typically occurs at high velocities is characterized by velocity fluctuations is called turbulent. The random and rapid fluctuations of groups of fluid panicles, called eddies, provide an additional mechanism for momentum and heat transfer. 

For completeness it is mentioned that the transformations between different sets of coordinates describing the same motion, characterize a branch of classical mechanics named kinematics which is fundamentally mathematical methods, and is not based on physical principles. 

In turbulent flow of liquid, random pulsation motions characterized by a set of pulsation velocities are imposed on average movement with velocity 1/ in a certain direction. Turbulent pulsations are characterized not only by velocities, but also by distances at which these velocities undergo noticeable change. These distances are referred to as pulsation scales and are denoted as 2. The set of values X represents a spectrum of turbulent pulsations varying from 0 up to a maximal value, having the order of linear scale of cross-sectional area of current flow. So, at motion in a pipe of diameter I the greatest value X is equal to I. Every pulsation movement is characterized by its Reynolds number Re = Xuxjv, where... 

Mode Motion characterized by a time constant, due to specific effects. 

In the above description of local motions, characterizes the segmental modes. In order to know whether these segmental motions observed by NMR in bulk at temperatures well above the glass-transition temperature belong to the glass-transition processes, it is of interest to compare the variations of Ti as a function of temperature with the predictions of the Williams-Landel-Ferry (WLF) equation [19]. The WLF equation describes the frequency dependence of the motional processes associated with the glass-transition phenomena. It can be written as [20]... 

Properties.—Carbon-13 and field-dependent proton spin-lattice relaxation times have been measured as a function of temperature and molecular weight for solutions of polycarbonates in CDCI3. The spin-lattice relaxation times were interpreted in terms of segmental motion, characterized by the sharp cut-off model of Jones and Stockmayer, for phenyl group rotation and methyl group rotation. ... 

Several types of results were obtained from the application of the slip-predictable stochastic model with the geophysical ground motion characterization. These included the development of synthetic ground motion attenuation laws, simulation of time histories, computation of risk-consistent response spectra, statistical analysis of durations of strong ground motion, and estimation of power spectral densities. In this paper we present a sampling of the estimated forecasts useful for structural response and damage analysis. 

Phenomena called light, heat, X rays, radio waves, are all part of the total electr spectrum (Fig. 2). These various forms of radiant energy travel through space in wave-like motions characterized by their wave-lengths or by their frequencies of vibration. 

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