Incoherent motion

Suppose we offset this motion by applying a Galilean transformation x = x +Pt ). In the new reference frame, the system will move just as it did in the old reference frame but, because a — /pqt = / i P )t/A, its diffusion is slowed down by a Lorentz-Fitzgerald-like time factor 1-/3. Intuitively, as some of the resources of the random walk computer are shifted toward producing coherent macroscopic motion (uniform motion of the center of mass), fewer resources will remain available for the task of producing incoherent motion (diffusion). [tofI89]... 

R. A. Marcus In the case of the reaction Klippenstein and I studied, which showed two transition states [1], the motion was that largely of heavy atoms rather than hydrogen atoms. We assumed incoherent motion between the two, though in some systems, such as the one you treated, coherence can certainly be important. In your ketene system was tunneling involved in passage through the two barriers ... 

McKeefry DJ, Watson JDG, Frackowiak RSJ, Fong K and Zeki S 1997 The activity in human areas V1W2, V3, and V5 during the perception of coherent and incoherent motion. Neuroimage 5, 1-12. 

Le Bihan D, Breton E, Lallemand D, Grenier P, Cabanis E, Laval-Jeantet M (1986) MR imaging of intravoxel incoherent motions application to diffusion and perfusion in neurologic disorders. Radiology 161 401-407... 

Obviously, the magic angle spinning techniques described briefly above rely on coherent averaging out of resonance line-broadening interactions. An alternative approach is to cause solids to assume the incoherent motion of molecules in the liquid phase. Essentially, two such methods exist. The first is the so-called ultra-fine particle NMR (UFPNMR) method which was proposed originally by Yesinowski [21 ] and developed further by Kimura [22,23]. The second is the sonically induced narrowing of the NMR spectra of solids (SINNMR) that was demonstrated recently by Homer et al. [24,25]. 

Ultrasonic manipulation of particles in suspension lies at the heart of SINNMR. The incoherent motion necessary for line-narrowing is thought to be generated from a number of ultrasonic effects. 

In heterogeneous solid-liquid systems cavitation often involves the asymmetrical collapse of cavitation bubbles near a solid surface to produce localized microjets of high-velocity liquids that impinge on the solid surface. When directed at the surface of an individual particle in a SINNMR experiment, the microjets are able to produce the required rotation as well as translation of the particle. There is strong evidence that cavitational effects provide the largest contribution to the incoherent motion of particles used in SINNMR. 

It is important to acknowledge that there are a number of ways in which a narrowed resonance could be generated from experiments of the type described above, but which might not result from the incoherent motion of the solid particles used. 

The coherent molecular motion initiated by the pump pulse can survive for a long time in (low pressure) gasses. In solution, incoherent motion will set in when the solutes start to interact with the solvent shell. Probing of molecular motion in the latter case, after the early-time coherent dynamics, will therefore represent an ensemble average which can contain a variety of different motions. 

The photodissociation of I2 dissolved in CCI4 was studied (at a concentration of 29 x 10 3 mol/L). Although the process might look quite simple, it is actually quite complex. Several excited electronic states of I2 participates in the process and after the dissociation, the solvent cage may trap the atoms leading to geminate recombination or the atoms may escape from the solvent cage and recombine with other partners. With the time resolution available at a pulsed synchrotron source ( 100 ps), it is not possible to directly follow atomic motion, i.e., the dynamics of the chemical bond. Furthermore, it is expected that incoherent motion will set in... 

Reineker, P. (1982). Exciton Dynamics in Molecular Crystals and Aggregates. Stochastic Liouville Equation Approach Coupled Coherent and Incoherent Motion, Optical Lineshapes, Magnetic Resonance Phenomena. Springer Tracts in Modern Physics, Vol. 94, Springer, Berlin, Heidelberg. 

Figure Bl.14.12. Study of the temporal fluctuation of motion in a quail egg at the incubation times 119 h and 167 h. Spatial phase encoding of the y-dimension was omitted to increase the rapidity of the imaging experiment. Profiles were obtained by ID Fourier transformation of echoes which were acquired in the presence of a readout gradient for frequency encoding of the x-coordinate. A strong gradient pulse pair for (spatially) incoherent motion weighting was applied during the evolution period of the magnetization. A series of subsequent single-scan profiles were measured at the two different incubation times 119 h (a) and 167 h...

Incoherent flow is often referred to as pseudo-diffusion. An apparent diffusion coefficient which can be significantly bigger than the self-diffusion coefficient is then defined. Pulse sequences to measure coherent flow (figure B 1.14.9) can also be used for (spatially) incoherent motion although the theory has to be reconsidered at this point [M, M and M] ... 

Fig. 7.17 The lineshape of ESR lines for a purely incoherent motion of the excitation energy between A and B. coa and cob are the eigenfrequencies of the localised states. The jump probability P between A and B is given in units of /z (coA-cog). From [14], [15].

The hopping probabilities between the two one-dimensional stacks in sublattices I and II are found from the analysis of the ESR spectra at room temperature to be Pi n = 1.6 10 s and Pn = 2.8 10 s. Their ratio is about the same as the Boltzmann factor, exp(-AE/feT) = 0.8 at T= 300 K, and the energy difference between I and II is AE/hc = 50 cm . The incoherent motion of the triplet excitons between the one-dimensional stacks is thus at least 1000 times slower than that within the stacks the triplet excitons in DBN crystals are therefore indeed one-dimensional. 

Muon Spin Relaxation refers to the observation of incoherent motions of the muon spins which result in a loss of polarization with time. This will occur if the magnetic field sensed by the ensemble of implanted muons is broadly distributed. If the local field each muon sees in addition fluctuates randomly during a muon s life we observe what is called dynamic depolarization , but also a stationary distributed field causes depolarization by phase incoherence ( static depolarization ). These two cases must be clearly distinguished. The situation corresponds to the two relaxation times Ty (spin-lattice) and Ti (spin-spin) in NMR. Muon Spin Relaxation measurements can be carried out without observing spin rotation and thus are possible in zero applied field or with a longitudinally applied field (i.e., a field applied parallel to the muon spin direction at the moment of implantation). Longitudinal field measurements are the most appropriate way to obtain a clear distinction between static and dynamic muon spin depolarization. Muon Spin Relaxation hence mostly refers to zero or longitudinal field (iSR. 

For incoherent motion, a diffusion equation is used with perpendicular diffusion coefficient D,... 

This condition is easily rewritten as t T > 0.25h for coherent motion and as > 0.35h for incoherent motion. 

We assume a random walk, i.e., an incoherent motion, for the spin carrier. In practice this assumption is not restrictive. Coherence or incoherence of the motion is essentially a question of time scale. A motion appears coherent, i.e., ballistic, as long as it is not interrupted by any kind of collision. After a collision the memory is left and the motion appears incoherent. In spin dynamics studies the time scale to probe the motion corresponds to the Larmor periods in the applied magnetic fields, typically 10" and 10" s for the nuclear and electron spins, respectively. This is longer than the usual collision times of charge carriers in conducting materials. 

There are several possible ways of inducing the necessary incoherent motion of particles to facilitate their resonance line narrowing. An obvious way is to produce a fluidized bed in the NMR sample tube, but this has been tried without success. An alternative is to utilize the effects of Brownian motion where molecular bombardment of fine particles in suspension can cause their incoherent motion. The latter approach (ultrafine particle NMR) has been demonstrated using very small particles (nm size) that were perceived to be necessary to respond appropriately to Brownian motion. The necessity to use extremely small particles for this type of experiment is open to question because many experiments in the author s laboratory have shown that micrometre sized particles, suspended in density matched liquids, respond to Brownian motion and yield resonances that are significantly reduced relative to those from static solids. 

Another way of inducing appropriate incoherent motion of suspended particles, and producing narrow... 

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