Mean stay time

In molecular energy terms, adsorption occurs when a molecule loses sufficient energy to the atoms in a surface by exciting them vibrationally or electronically to become effectively bound to the surface. An ensemble of adsorbed molecules is called an adlayer (or monolayer if only a single molecular layer forms), and the average time of stay of a molecule upon the surface is called the mean stay time. 

Vilenskiy, V. D. (1970). The influence of natural radioactive atmospheric dust in determining the mean stay time of lead-210 in the troposphere. Izv. Acad. Sci. USSR, Atmos. Oceanic Phys. 6, 307-310. 

During plug flow, all material passes through the vessel without any mixing, and eaeh fluid element stays in the vessel for exaetly the same length of time. Eor a step input, the front or interfaee between the traeer and non-traeer fluids traverses down the vessel and exits at the other end in a time equal to the mean residenee time f. Therefore, the E(6) eurve is a step funetion and is expressed as... 

The cutoff point in residence time between what we chose to consider as active and as stagnant fluid depends on the accuracy of predictions of vessel performance. In most cases material which stays in a vessel twice the mean residence time can, with negligible error, be taken as stagnant. 

In the pulmonary region, air velocities are too low to impact particles small enough to reach that region, and the mechanisms of deposition are sedimentation and Brownian diffusion. The efficiency of both processes depends on the length of the respiratory cycle, which determines the stay time in the lung. If the cycle is 15 breaths/min, the stay time is of the order of a second. Table 7.1 shows the distance fallen in one second and the root mean square distance travelled by Brownian diffusion in one second by unit density particles (Fuchs, 1964). Sedimentation velocity is proportional to particle density, but Brownian motion is independent of density. Table 7.1 shows that sedimentation of unit density particles is more effective in causing deposition than Brownian diffusion when dp exceeds 1 pm, whereas the reverse is true if dp is less than 0.5 pm. For this reason, it is appropriate to use the aerodynamic diameter dA equal to pj dp when this exceeds 1 pm, but the actual diameter for submicrometre particles. 

Once again Fit) can be calculated from Eq. 9.2-36 in conjunction with Eq. 9.2-28. Figure 9.11 plots the RTD function F(t) versus reduced time t/t and compares it to the RTD function of Newtonian laminar flow in a pipe and that in a well-stirred vessel. The RTD function in the melt extruder is quite narrow, approaching plug-type flow. Only about 5% of the flow rate stays more than twice the mean residence time in the extruder. 

Fig. 3. Comparison of METH-induced CPP in single histamine receptor gene knockout mice. Mice were injected 1 mg/kg of METH or saline every other day, and confined for 30 min to a compartment designed to condition the place preference. The CPP score were calculated using the staying time of mouse in each compartment for 15 min before and after the conditioning. Each value represents the mean S.E.M. of 6-18 mice. Statistical analysis was performed by means of one-way ANOVA followed by Tukey s test ( p < 0.05, p < 0.01).

This exponential decay is typical of first-order processes as shown previously. Thus, there is an exponential distribution of residence times some molecules will spend little time in the reactor while others will stay very long. The mean residence time is ... 

Here, is the correlation time for the molecular motion of the C—H vector, meaning the time (or the life time) in which the C—H vector stays in the same direction without any motion. Figure 3.5 shows Tj, T2 and NOE as functions of t, which are obtained using Equation (3.17). 

The particle stays at a site for a mean residence time x then instantaneously it jumps to a neighboring site i.e. the jump time is negligibly small compared to the residence time r = (zxy denotes the jump rate. 

Therefore the half-life of a particle in a stirred-flow reactor is equal to 0.69 times the space-time. Some molecules will spend very little time in the reactor some will stay very long. But the mean residence time is equal to the nominal residence time V/ V. Indeed ... 

A variable that affects the plastification rate should have some impact on the processing rate. The mixing quality and the average time that the polymer stays in the extruder will direcdy affect the final product properties. The mean residence time is related to the transport delay time, which has enormous impact on the stability of feedback loops over the length of the extruder [18-20]. 

As a consequence of this observation, the essential dynamics of the molecular process could as well be modelled by probabilities describing mean durations of stay within different conformations of the system. This idea is not new, cf. [10]. Even the phrase essential dynamics has already been coined in [2] it has been chosen for the reformulation of molecular motion in terms of its almost invariant degrees of freedom. But unlike the former approaches, which aim in the same direction, we herein advocate a different line of method we suggest to directly attack the computation of the conformations and their stability time spans, which means some global approach clearly differing from any kind of statistical analysis based on long term trajectories. 

The simplest approximation to make is simply that the initial distribution of live" sites is completely random and that any site-site correlations are negligible i.e. we first take a conventional Mean-Field approach (see section 7.4). In this case, the equilibrium density can be written down almost by inspection. The probability of a site having value 1 (= p) is equal to the probability that it had value 1 on the previous time step multiplied by the probability that it stays equal to 1 (i.e. the probability that a site has either 2 or 3 live neighboring sites) plus the probability that the site was previously equal to 0 multiplied by the probability that it become 1 (i.e. that it is surrounded by exactly 3 live sites). Letting p and p represent the density at times t and t + 1, respectively, simple counting yields ... 

Yazdanpanah et al. (2002) calculated the resource use and cost for different stages of HIV infection in France based on a clinical database of HIV-infected patients between 1994 and 1998. The total costs attributable to bed-day and day-care inpatient care included the mean cost of each inpatient day times the length of stay, as well as total number of laboratory tests, dosage and quantity of medications, and total number of procedures. The total cost attributable to outpatient care included the mean physician and nurse fees per visit, as well as total number of laboratory tests and total number of procedures. In the absence of an AIDS-deflning event, the average total cost of care ranged from US 797 per person-month in the highest CD4 stratum to US 1,261 per person-month in the lowest CD4 stratum. 

Despite the differences between the estimated derivatives values, the computed profiles of the specific MAb production rate are quite similar. Upon inspection of the data, it is seen that during the batch period (up to t=2I2 h), qM is decreasing almost monotonically. It has a mean value of about 0.5 /ug/(l(f cells-h). Throughout the dialyzed continuous operation of the bioreactor, the average qM is about 0.6 fxg/(l(f cells-h) and it stays constant during the steady state around time... 

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