Transit times, average

The Boltzmaim weight appears implicitly in the way the states are chosen. The fomi of the above equation is like a time average as calculated in MD. The MC method involves designing a stochastic algorithm for stepping from one state of the system to the next, generating a trajectory. This will take the fomi of a Markov chain, specified by transition probabilities which are independent of the prior history of the system. 

The average linear velocity u of the mobile phase in terms of the column length L and the average linear velocity of eluent (which is measured by the transit time of a nonretained solute) is... 

Laminar and Turbulent Flow, Reynolds Number These terms refer to two distinct types of flow. In laminar flow, there are smooth streamlines and the fuiid velocity components vary smoothly with position, and with time if the flow is unsteady. The flow described in reference to Fig. 6-1 is laminar. In turbulent flow, there are no smooth streamlines, and the velocity shows chaotic fluctuations in time and space. Velocities in turbulent flow may be reported as the sum of a time-averaged velocity and a velocity fluctuation from the average. For any given flow geometry, a dimensionless Reynolds number may be defined for a Newtonian fluid as Re = LU p/ I where L is a characteristic length. Below a critical value of Re the flow is laminar, while above the critical value a transition to turbulent flow occurs. The geometry-dependent critical Reynolds number is determined experimentally. 

What is the relation between the turnover time To the average transit time and the average age ta, in a reservoir where all particles" spend an equal time in the reservoir ... 

The Bragg scattering of X-rays by a periodic lattice in contrast to a Mossbauer transition is a collective event which is short in time as compared to the typical lattice vibration frequencies. Therefore, the mean-square displacement (x ) in the Debye-Waller factor is obtained from the average over the ensemble, whereas (r4) in the Lamb-Mossbauer factor describes a time average. The results are equivalent. 

Colonic residence time is considerably longer than in other parts of the GIT, and it is also more variable. The transit time can be as short as several hours to as long as 50 60 hours. Transit along the colon is characterized by abrupt movement and long periods of stasis. In one study of 49 healthy subjects the average colonic residence time was 35 hours with the following times associated with different regions 11 hours in the... 

Location Average length/diameter (cm) Average surface area (m2) Average pH (range) Enzymes and others Mean transit times Microflora per gram content... 

The structure of the blood capillary wall is complex and varies in different organs and tissues. It consists of a single layer of endothelial cells joined together by intercellular junctions. Each endothelial cell, on an average, is 20-40 pm long, 10-15 pm wide, and 0.1-0.5 pm thick, and contains 10,000-15,000 uniform, spherical vesicles called plasmalemmal vesicles. These vesicles range in size between 60 and 80 nm in diameter. About 70% of these vesicles open on the luminal side of the endothelial surface, and the remaining open within the cytoplasm. Plasmalemmal vesicles are believed to be involved in the pinocytic transport of substances across the endothelium. The transition time of pinocytic vesicles across the cell is... 

Fig. 8.3. Average transit time in the small intestine measured using y-scintigraphy following administration of various pharmaceutical dosage forms to humans. Data from reference [611-... 

In the forthcoming sections we will consider several methods that have been used to derive different integral relaxation times for cases where both drift and diffusion coefficients do not depend on time, ranging from the considered mean transition time and to correlation times and time scales of evolution of different averages. 

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