Pareto’s law


As in the experiments, the simulation results also show dynamie sealing at late times. The sealing fimetion (kR(x)) at late times has the large /x behaviour. S (y) known as Porod s law [13, 16]. This result is  [c.742]

Another way to think of bad actor management is to liken it to Pareto s law, where 20 per cent of the components are causing 80 per cent of the problems. Many of the causes previously identified in connection with machinery component failure modes lend hand to bad actor management however, some of the more significant are listed as follows  [c.1045]

Keywords compressibility, primary-, secondary- and enhanced oil-recovery, drive mechanisms (solution gas-, gas cap-, water-drive), secondary gas cap, first production date, build-up period, plateau period, production decline, water cut, Darcy s law, recovery factor, sweep efficiency, by-passing of oil, residual oil, relative permeability, production forecasts, offtake rate, coning, cusping, horizontal wells, reservoir simulation, material balance, rate dependent processes, pre-drilling.  [c.183]

Yj(r), and interface distribution fiinction, gj(r), is shown in figure Bl.9.12. In general, we find the values of the long period calculated from different methods, such as a conventional analysis by using Bragg s law, the correlation fiinction and the interface distribution fiinction, to be quite different. However, their trends as fiinctions of time and temperature are usually similar. The ordering of these long periods indicates the heterogeneity of the lamellar distributions in the morphology [35].  [c.1408]

The potential energy function given in Eq. (32) contains bonded and non-bonded terms to evaluate the energy of a molecule or molecular system. The non-bonded Coulomb and van der Waals contributions need special attention, because every atom interacts with every other atom in the system. Mathematically expressed by a double sum, it is obvious that the major part of the computing time is consumed by these sums. To speed up simulations, these interactions were simply truncated at a fixed distance, typically 8-10 A. From another look at the potential energy function in Eq. (32), it becomes obvious that the truncation after such a short distance is only a minor problem in the case of the van der Waals interactions. The Lennard-Jones potential uses the distance between two interacting atoms i and j in the power of-6 and -12, so the function becomes very small at the cutoff distance. The problem is much more serious for the electrostatic part of the non-bonded interaction, because Coulomb s law uses the reciprocal of the distance r,j, resulting in long-range electrostatic interactions. The unscreened interaction of two full charges on opposite sides of a protein is still significant. At 100 A, the electrostatic interaction is greater than 3 kcal moT [26].  [c.368]

Given that some electrons and ions are present in the discharge gas from any of the previously described processes (cosmic radiation, thermal emission, photoelectric effect, piezoelectric spark), the applied voltage causes the charged species to drift toward the respective positive and negative electrodes, thereby constituting a small current flow. There is also another process that is important — some ions and electrons recombine to form neutral gas atoms again. Therefore, the electric current is the difference between the rate at which electrons and ions are produced and drift to the electrodes and the rate at which they disappear through electron/ion recombination. (Sometimes this occurs at the walls of the discharge vessel.) As the voltage increases, electrons and ions drift to the electrodes more rapidly and the current rises, seen in region A-B in Figure 6.8. At first, the relationship between the current flowing and the voltage applied is approximately in accord with Ohm s law. However, as the voltage is increased, the current begins to rise less in accord with Ohm s law until, at an applied electric field of about 10 V/m, there is no further increase in current because insufficient numbers of electrons and ions are formed to offset the drift to the electrodes and recombination. At this point, increasing the voltage does not increase the current, which is said to be saturated. This situation is represented by the straight section, B-C. The steady current is given by the equation, / = (q/r), in which q and r are, respectively, the rates at which electrons and ions are formed and then removed by recombination. This part of the discharge is not self-sustaining because  [c.40]

The driving force in diffusion involves differences in the concentration of the diffusing substance. The molecular diffusion of a gas into a hquid is dependent on the characteristics of the gas and the hquid, the temperature of the hquid, the concentration deficit, the gas to hquid contact area, and the period of contact. Diffusion may be expressed by Pick s law (13,14)  [c.339]

Cytochemical techniques can be combined with light-scattering and absorption measurements to provide five-part Diffs. Cytochemistry concerns the chemical reactions of ceU components. The reactions for automated white blood ceU differential analysis include those that bind chromophores to the granules of white ceU types, based on the presence of various substrates and enzymes in the granules. These reactions yield products suitable for light-scattering and optical absorption measurements. Other reactions exploit the differential resistance of white ceU types to cytoplasmic stripping by the lysing action of surfactants. The reaction products are suitable for light-scattering and aperture impedance measurements. Optical absorption measurements made on intact cells in suspension are different from those made on dissolved hemoglobin. Measurements made on intact cells involve reduced overall scattering intensity and do not obey Beer s Law measurements made on solutions involve dissolved chromophores and do obey Beer s law (see Specthoscopy).  [c.404]

Temperature Considerations. The inlet, detector, and the oven compartment where the column is kept, are usuahy controhed at different temperatures, because each part serves a different function that is best performed in a specified temperature range. In practice, the maximum oven temperature expected to be reached in the course of an analysis that is high enough to achieve the desired result in minimum time is chosen. This temperature should also be low enough to minimize the probabhity of column Hquid-phase degradation. Generahy, retention time is halved for every 30°C the temperature is increased. The injection port s temperature is usuahy slightly higher than the maximum oven temperature, but low enough to minimize thermal degradation or thermal rearrangement of sample components. Ideahy, the thermal energy in the injection port wih cause instantaneous vaporization without causing a loss of separation efficiency by spreading the sample over a large volume. The detector temperature is usuahy 10—30°C higher than the injector, but low enough to avoid thermal degradation of the column s Hquid phase in that part of the column near the detector.  [c.109]

The specific regulations of the U.S. DOT are found in the Code of Federal Regulations (CFR) Title 49, Parts I00-I99. A key part of CFR 49 is Part 172.lOI a portion which is illustrated as Table 21-17.  [c.1944]

The only problem with the foregoing approach to molecular interactions is that the accurate solution of Schrddinger s equation is possible only for very small systems, due to the limitations in current algorithms and computer power. Eor systems of biological interest, molecular interactions must be approximated by the use of empirical force fields made up of parametrized tenns, most of which bear no recognizable relation to Coulomb s law. Nonetheless the force fields in use today all include tenns describing electrostatic interactions. This is due at least in part to the following facts.  [c.95]

Of particular interest in the usage of polymers is the permeability of a gas, vapour or liquid through a film. Permeation is a three-part process and involves solution of small molecules in polymer, migration or diffusion through the polymer according to the concentration gradient, and emergence of the small particle at the outer surface. Hence permeability is the product of solubility and diffusion and it is possible to write, where the solubility obeys Henry s law,  [c.102]

Diffusion plays an important part in peak dispersion. It not only contributes to dispersion directly (i.e., longitudinal diffusion), but also plays a part in the dispersion that results from solute transfer between the two phases. Consider the situation depicted in Figure 4, where a sample of solute is introduced in plane (A), plane (A) having unit cros-sectional area. Solute will diffuse according to Fick s law in both directions ( x) and, at a point (x) from the sample point, according to Ficks law, the mass of solute transported across unit area in unit time (mx) will be given by  [c.243]

The wood mat environment during hot-pressing is rather different in industrial boards since the size of the panel is a determining parameter as regards internal permeability and steam flow. For example Humphrey and Bolton [218,228] found pressures three times higher in industrial boards than in laboratory boards as well as differences in heating rates. In reality steam pressure increases until the degassing period begins. The edge effect appears clearly on steam pressure curves (the curve shifts progressively to lower pressure nearer the site is to the board edge) as a gradient of pressure develops from the board center to the edges. Gas flow through particleboard can be described by Darcy s law which shows that increasing the length of the steam path, hence the dimensions of the wood mat with all the other parameters held constant, will result in a smaller volumetric steam flow rate. Clearly, a given steam volume at 100 mm from the board edge will escape from the edge with greater ease than an equivalent steam volume in the board center. This leads to greater steam accumulation in the board center than in sites nearer to the board edges. Thus, the steam pressure gradient, which is observed during particleboard pressing, is merely the result of Darcy s law and the gradient is steeper towards the board edges. As resin hardening is strongly temperature dependent [16,83], the lower temperature due to lower steam pressure at the board edges will noticeably decrease the cure rate of the adhesive with consequent fall off of board properties at the edges. This is supported by the dry internal bond (IB) strength results for industrial OSB panels [226,227] showing that a temperature difference of 25°C induces a strength reduction of 0.25 MPa, or expressed in percentage, a decrease of approximately 70% in IB strength. This is furthermore related to density profile at the different sites. Samples at the board edge show a much lower core layer density than in the board middle. As the difference noticed was shown not to be ascribed to a  [c.1096]

A vapor poeket on the exchanger s low-pressure side can create a cushion that may greatly diminish the pressure transient s intensity. A transient analysis may not be required if sufficient low-pressure side vapor exists (although tube rupture should still be considered as a viable relief scenario). However, if the low-pressure fluid is liquid from a separator that has a small amount of vapor from flashing across a level control valve, the vapor pocket may collapse after the pressure has exceeded the fluid s bubble point. The bubble point will be at the separator pressure. Transient analysis will prediet a gradually inereasing pressure until the pressure reaches the bubble point. Then, the pressure will increase rapidly. For this ease, a transient analysis should be considered.  [c.49]

Poe and Martire expanded Giddings work and derived equations for the observed plate height in general (35). Although these authors only elaimed applieability to GC, LC, and SFC, it appears that their equations are applieable to all of the forms of unified ehromatography mentioned earlier. Poe and Martire arrived at these equations by expressing Giddings equations in terms of density rather than pressure (Boyle s law is not followed by the non-ideal fluids often used as unified ehromatography mobile phases, although the density-volume produet is always eonstant), and by ineluding the density influenee on loeal retention faetors and loeal plate height. They reported the following  [c.166]

Figure 40.2 illustrates the transmission of forces through liquids. For Pascal s law to become effective for practical applications, a piston or ram confined within a close tolerance cylinder was needed. It was not until the latter part of the eighteenth century that methods were developed that could make the snugly fitted parts required making hydraulic systems practical.  [c.585]

During the last 5-10 years optical networks of all varieties have become a very important part of the World s communications infrastmcture for data transmission. The new focus has become the transmission of multi-gigabit infonnation over moderate distances at low cost. These requirements are profoundly affecting the design criteria for optoelectronics devices and components. In addition, coarse and dense wavelength division multiplexed systems are being developed to increase bandwidth. The essence of wavelength division multiplexing is the simultaneous transmission of many optical data channels each at a different wavelength on a single optical fibre. Systems with as many as 40, 1-10 Gbit optical channels are becoming commercially available. Low-cost components will be the key factor in detennining how rapidly this technology will be deployed tliroughout the communications infrastmcture.  [c.2874]

Heavy oils and especially bitumens contain high concentrations of resins (30-40%) and asphaltenes (<20%). Most heavy oils and bitumens are thought to be derivatives of lighter, conventional crude oils that have lost part or all of their straight-chain alkane contents along with some of their low-molecular-weight cyclic hydrocarbons through processes taking place in the oil reservoirs. Heavy oils are also abundant in heteroatom (N, O, S)-containing molecules, organometallics, and colloidally dispersed clays and clay organics. The prominent metals associated with petroleum are nickel, vanadium [mainly in the form of vanadyl ions (VO )], and iron. Some of these metals are (in part) bound to porphyrins to form metalloporphyrins.  [c.131]

Lee, D. G. 1969, in Augustine, R. L. (ed.), Oxidation, VoL 1, chapters 1 2, M. Dekker New York Lee, D. G. van den Engh, M. 1973, in Trahanovsky, W. S. (ed.), Oxidation in Organic Chemistry, Part B, Academic Press New York London Lee, E. Shin, Kim, T. S. 1990, J. Am. Chem. Soc. 112, 260  [c.373]

Recently, a unique approach for using the correlation fiinction method has been demonstrated to extract morphological variables in crystalline polymers from time-resolved syncluotron SAXS data. The principle of the calculation is based on two alternative expressions of Porod s law using the fonu of interference fiinction [33. 36]. This approach enables a continuous estimate of the Porod constant, corrections for liquid scattering  [c.1408]

Before looking more elosely at these, it is important to reeognize another eategory of pump-probe Raman experiments. These are often referred to as transient Raman pump-probe studies. In these, a given system is pumped mto a transient eondition sueh as an exeited vibronie state, or a photoehemieal event sueh as dissoeiation or radieal fonnation [, M ai d Ml- Sueh pumping ean be aehieved by any means—even by high energy radiation [66, 67 and 68]—though nonnally laser pumping is used. The produet(s) fonned by the pump step is then studied by a Raman probe (often simply spontaneous Raman, sometimes CARS). Sinee the transient state is nonnally at low eoneentrations, the Raman probing seeks out resonant enhaneement, as we are deseribing, and also means must be taken to stay away from the lumineseenee baekground that is invariably eaused by the pump event. Often, time gated Fourier transfonn Raman in the near-IR is employed  [c.1202]

Hence, it is necessary to correct the temperature change observed to the value it would have been if there was no leak. This is achieved by measuring the temperature of the calorimeter for a time period both before and after the process and applying Newton s law of cooling. This correction can be reduced by using the teclmique of adiabatic calorimetry, where the temperature of the jacket is kept at the same temperature as the calorimeter as a temperature change occurs. This teclmique requires more elaborate temperature control and it is prunarily used in accurate heat capacity measurements at low temperatures.  [c.1901]

The sun radiates approximately as a blackbody, with an effective temperature of about 6000 K. The total solar flux is 3.9 x 10 W. Using Wien s law, it has been found that the frequency of maximum solar radiation intensity is 6.3 x 10 s (X = 0.48 /rm), which is in the visible part of the spectrum 99% of solar radiation occurs between the frequencies of 7.5 X 10 s (X = 4/um) and 2 x 10 s (X = 0.15/um) and about 50% in the visible region between 4.3 x 10 s (X = 0.7 /rm) and 7.5 X 10 s (X = 0.4 /Ltm). The intensity of this energy flux at the distance of the earth is about 1400 W m on an area normal to a beam of solar radiation. This value is called the solar constant. Due to the eccentricity of the earth s orbit as it revolves around the sun once a year, the earth is closer to the sun in January (perihelion) than in July (aphelion). This results in about a 7% difference in radiant flux at the outer limits of the atmosphere between these two times.  [c.246]

Colorado, a moment now marked as a turning point in environmental protection, and one that had immediate consequences for developers interested in harnessing the energy of water. In the same year that Carson released Silcm Spring, Murray Bookchin offered a parallel warning in his book Our Synthetic Envirouincut. It is in this context that the success of Carson s work makes sense. Her writings complemented other actions. Still, it was Carson s lay appeal—her refusal to use technical and scientific jargon—that popularized this ecological vision and catapulted concerns about nature into the mainstream of American life, making the environment a crucial part of the agenda in any future technological decisions.  [c.223]

Some organic compounds can be in solution with water and the mixture may still be a flammable mixture. The vapors above these mixtures such as ethanol, methanol, or acetone can form flammable mixtures with air. Bodurtha [39] and Albaugh and Pratt [47] discuss the use of Raoult s law (activity coefficients) in evaluating the effects. Figures 7-52A and B illustrate the vapor-liquid data for ethyl alcohol and the flash point of various concentrations, the shaded area of flammability limits, and the UEL. Note that some of the plots are calculated and bear experimental data verification.  [c.496]

After the breakup of the ancient world, there were few new developments for many centuries. Then, over a comparatively short period, beginning near the end of the seventeenth century, Italian physicist, Evangelista Torricelle, French Physicist, Edme Mariotte and later Daniel Bernoulli conducted experiments to study the force generated by the discharge of water through small openings in the sides of tanks and through short pipes. During the same period, Blaise Pascal, a French scientist, discovered the fundamental law for the science of hydraulics. Pascal s law states that an increase in pressure on the surface of a confined fluid is transmitted throughout the confining vessel or system without any loss of pressure.  [c.585]

The potential advantages of LPG concern essentially the environmental aspects. LPG s are simple mixtures of 3- and 4-carbon-atom hydrocarbons with few contaminants (very low sulfur content). LPG s contain no noxious additives such as lead and their exhaust emissions have little or no toxicity because aromatics are absent. This type of fuel also benefits often enough from a lower taxation. In spite of that, the use of LPG motor fuel remains static in France, if not on a slightly downward trend. There are several reasons for this situation little interest from automobile manufacturers, reluctance on the part of automobile customers, competition in the refining industry for other uses of and fractions, (alkylation, etherification, direct addition into the gasoline pool). However, in 1993 this subject seems to have received more interest (Hublin et al., 1993).  [c.230]

The experiment can obviously be criticized on two grounds first, it does not determine the instantaneous fluxes, but rather their integrals over Che period of the experiment and, second, conditions are not strictly isobartc because of the difference in head of mercury which develops as diffusion proceeds. Graham was aware of the problem of interpretation posed by the developing pressure difference indeed he remarks that his conclusion is "distorted" when the porous structure of the plug is too loose, and correctly attributes the "distortion" to the influence of bulk flow driven by the pressure gradient. The difficulty is eliminated, of course, if the height of the tube is continually adjusted so that Che mercury surfaces inside and outside remain Level. Because of Its integral nature, Graham s experiment does not prove Chat the ratio of the instantaneous fluxes of the two gases is at all times the inverse ratio of the square roots of their densities, but at least it is not inconsistent with such a hypothesis. Since the pressures and temperatures are the same in all his experiments, and the pressures are sufficiently low that the gases behave ideally, volume flow is proportional to molar flow and density is proportional to molecular weight, and this hypothesis can therefore be expressed in the form  [c.51]

PdCl2 is stable, but it has low solubility in water and organic solvents. It is soluble in dilute HCl and becomes soluble in organic solvents by forming a PdCl2(PhCN)2 complex[2]. M2PdCl4 (M = Li, Na, K) are soluble in water, lower alcohols, and some organic solvents. Pd(OAc)2 is commercially available and is stable and soluble in organic solvents. It can be prepared from metallic Pd by dissolving it in AcOH containing nitric acid[3]. Sometimes the quality of Pd(OAc)2 is variable[4] and it may contain nitrate anion. It becomes partially insoluble in organic solvents by forming a polymer. In such a case, Pd(OAc)2 is purified by dissolving it in hot benzene and concentrating the benzene solution after removing the insoluble part. Pure Pd(acac)2 can be obtained a.s needle-like crystals by recrystallization.  [c.2]

The results of Hickman for the adsorption of butane at 273 K on samples of ball-milled artificial graphite, are of particular interest in the present context. The graphite was milled for 1040 hours and the isotherms of butane were measured on samples withdrawn at intervals. The monolayer capacity increased almost sixty-fold during this period, from 2-S to 14Smgg, yet all six of the isotherms showed a steep fall at the same relative pressure of 0-5. (The low pressure hysteresis, cf. Fig. 3.23, was almost certainly an extraneous effect, caused by swelling.) The pore structure must have varied widely throughout the series, so that the constancy of this closure point is all the more striking it is difficult to find any reason why all the pore systems should show a peak in size distribution at r = 19-2 A, the Kelvin value corresponding to p/p° = 0-5.  [c.156]

Where Is the Equivalence Point In discussing acid-base titrations and com-plexometric titrations, we noted that the equivalence point is almost identical with the inflection point located in the sharply rising part of the titration curve. If you look back at Figures 9.8 and 9.28, you will see that for acid-base and com-plexometric titrations the inflection point is also in the middle of the titration curve s sharp rise (we call this a symmetrical equivalence point). This makes it relatively easy to find the equivalence point when you sketch these titration curves. When the stoichiometry of a redox titration is symmetrical (one mole analyte per mole of titrant), then the equivalence point also is symmetrical. If the stoichiometry is not symmetrical, then the equivalence point will lie closer to the top or bottom of the titration curve s sharp rise. In this case the equivalence point is said to be asymmetrical. Example 9.12 shows how to calculate the equivalence point potential in this situation.  [c.337]

Scale of Operation Molecular photoluminescence can be used for the routine analysis of trace and ultratrace analytes in macro and meso samples. Detection limits for fluorescence spectroscopy are strongly influenced by the analyte s quantum yield. For analytes with f > 0.5, detection limits in the picomolar range are possible when using a high-quality spectrofluorometer. As an example, the detection limit for quinine sulfate, for which f is 0.55, is generally between 1 ppb and 1 ppTr (part per trillion). Detection limits for phosphorescence are somewhat poorer than those for fluorescence, with typical values in the nanomolar range for low-temperature phos-phorometry and in the micromolar range for room-temperature phosphorometry using a solid substrate.  [c.432]


See pages that mention the term Pareto’s law : [c.177]    [c.374]    [c.180]    [c.215]    [c.163]    [c.334]    [c.44]    [c.87]    [c.167]    [c.337]    [c.1243]    [c.2074]    [c.2123]    [c.102]    [c.657]    [c.338]    [c.502]   
Plant Engineer's Handbook (2001) -- [ c.1121 ]