Scaling limit

From the requirement that a smooth crossover between Eqs. (29) and (31) for t = rR should take place, one can estimate the diffusion constant as Dn oc Wf /N, i.e., in the scaling limit Dj does not depend on the tube size D. 

Human or natural actions that significantly alter the erosion resistance of the ground surface can lead to dramatic increases in erosion rates. Channel networks dissect natural landscapes down to a fine-scale limit controlled by a threshold of channel initiation (Montgomery and Dietrich, 1992). In effect, channels begin where sufficient discharge collects to overcome the erosion resistance of the ground surface (Horton, 1945 Montgomery and Dietrich, 1988). Consequently, human or natural actions... 

Once plotted, a new menu bar appears with plot options. The plot can be displayed as points, connected, or as a bar chart. The data can be presented on linear or log axes, with or without grid. Text can be placed on the display in a variety of sizes and types. Lines or arrows can be drawn or areas filled. The user can edit all axis labels and titles if desired. Re-scaling is accomplished by means of the shrink and zoom options or by entering exact scale limits. Multiple curves can be annotated with keyed symbols. Plot coordinates are displayed in real time as the operator moves the mouse over the plot. 

Better chemistry through confinement economy of scale limits and expenditure of scale-up micro reactors origin from microfabrication expert opinions general advantages of micro flow hybrid construction industry s efforts chip micro reactors numbering-up vision of computer-like chemical workstation [205]. 

Filaments in chaotic flows experience complex time-varying stretching histories. Computational studies indicate that within chaotic regions, the distribution of stretches, A, becomes self-similar, achieving a scaling limit. 

Like tetrasulfur tetranitride, salts of trisulfur trinitride and of pentasulfur tetran-itride (particularly alkali-metal salts) are heat- and friction-sensitive explosives. Preparation on a scale limited to 1 g, and care in use of spatulae or in preparation of samples for IR examination is recommended. 

Within their scaling limits, OODBs traditionally have vastly outperformed relational databases. 

Frank DJ, Dennard RH, Nowak E, Solomon PM, Taur Y, Wong H-SP (2001) Device scaling limits of Si MOSEETs and their application dependencies. Proc IEEE 90 259-288... 

Extraction Relatively simple scaleup Scale limited by availability of source potential for contamination form sonrce material... 

There are inherent scale limitations in the time and space dimensions covered by laboratory studies. The applicability of the near field geochemical models derived from laboratory observations have to be applied to long-term, large-scale situations like the ones involved in the safety assessment of nuclear waste repositories. Hence, there is a need to test the models developed from laboratory investigations in field situations that are related to the ones to be encountered in repository systems. 

In one test, 0.5 g was sealed in a thermal stability bomb and the temp was raised 5°C/min. At ca 120°, a violent exothermic reaction occurred, rupturing the burst diaphragm of the app at 1800 psi. Another test conducted on a 0.5 g sample at 60°C resulted in sudden de-compn after 3 hrs at that temp. The sample temp rose sharply and exceeded the scale limit of 250°C. The same tests on the 2.6 Dichloro deriv (qv) showed similar, but less severe, instability. 

The ranking scale limit values of the index were set considering the results that would be obtained if all tests yielded a response of 20% to the same concentration or dilution. Each interval of the reference scale was arbitrarily fixed according to valued judgment taking into account the authors experience. 

Semiat, R., Hasson, D., Zelmanov, G. and Hemo, I. (2004) Threshold scaling limits of RO concentrates flowing in a long waste disposal pipeline. Water... 

However, scale-up of this type of system is limited due to the fact that oxygen transfer is a function of the area of the wave-containing liquid surface. Since the area increases with the square and the volume with the third power of a linear dimension, it is expected that this technology will reach a scale limit. Nevertheless, the companies that market this type of bioreactor offer bioreactors up to at least 500 L working volume (Wave Biotech, 2006). 

For the high-density scaling limit of KFEc[n], Gorling and Levy [11], using their adiabatic perturbation theory, arrived at... 

Related Calculations. Use the method given here for any uniform viscous liquid—oil, gasoline, kerosene, mercury, etc.—handled by a centrifugal pump. Be careful to use Fig. 6.32 only within its scale limits do not extrapolate. The method presented here is that developed by the Hydraulic Institute. For new developments in the method, be certain to consult the latest edition of the Hydraulic Institute—Standards. 

Scale-limited. A measuring instrument is said to be scale-limited if the experimental uncertainty in that instrument is smaller than the smallest division readable on its scale. Therefore the experimental uncertainty is taken to be half the smallest readable increment on the scale. 

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