Fixed-time

Data transmission rate per foot is a function of both pulse frequency and rate of penetration. Sensors acquire and transmit data samples at fixed time intervals and therefore the sampling per foot is a function of rate of penetration. Current tools allow a real time sampling and transmission rate similar to wireline tools as long as the penetration rate does not exceed about 100 ft/h. If drilling progresses faster or if there are significant variations in penetration rate, resampling by depth as opposed to time intervals may be required. 

In Austria, as well as all over Europe, the first and repetition tests of all pressure equipments including steam drums are required for security reasons within fixed time intervals. These repetitive inspections are done differently in the most European countries, but most time these inspections include, according to the European Pressure Equipment Directive" and the specific national law any kind of over-pressurisation (e.g. hydrotest) and visual inside inspection. 

As a result of the fixed time-mdependent rate constant k E), N t) decays exponentially, i.e. 

Correlated events are related in time and this time relation can be measured either with respect to an external clock or to the events themselves. Random or uncorrelated events bear no fixed time relation to each other but, on the other... 

Referring to figure BLIP. 7 consider electrons from the event under study as well as from other events all arriving at the two detectors. The electrons from the event under study are correlated in time and result in a peak in the time spectrum centred approximately at the delay time. There is also a background level due to events that bear no fixed time relation to each other. If the average rate of tlie background events in each detector is R and i 2> then the rate that two such events will be recorded within time Ax is given by i g, where... 

Examples of typical TOF spectra obtained from 4 keV Ar impinging on a Si 100] surface with chemisorbed FI2O and FI2 are shown in figure B 1.23.6 [35]. Peaks due to Ar scattering from Si and recoiled FI, O and Si are observed. The intensities necessary for stnictural analysis are obtamed by integrating the areas of fixed time windows under these peaks. 

Slurry or slip casting provides a relatively inexpensive way to fabricate unifonn-thickness, thin-wall, or large cross section shapes [4o, 44, 45, 46, 42 aiid 48]. For slip casting, a slurry is first poured into a porous mould. Capillary suction then draws the liquid from the slurry to fonn a higher solids content, close-packed, leather-hard cast on the inner surface of the mould. In a fixed time, a given wall thickness is fonned, after which the excess slurry is drained. 

The interactive studies were followed by a series of batch calculations in which the xenon atom was dragged at a constant rate from the cavity to a location well into the solvent (total distance of approximately 1.8 nm, depending on the starting location of the xenon atom) in fixed time intervals Ixitween 1... 

Finite difference techniques are used to generate molecular dynamics trajectories with continuous potential models, which we will assume to be pairwise additive. The essential idea is that the integration is broken down into many small stages, each separated in time by a fixed time 6t. The total force on each particle in the configuration at a time t is calculated as the vector sum of its interactions with other particles. From the force we can determine the accelerations of the particles, which are then combined with the positions and velocities at a time t to calculate the positions and velocities at a time t + 6t. The force is assumed to be constant during the time step. The forces on the particles in their new positions are then determined, leading to new positions and velocities at time t - - 2St, and so on. 

The earliest examples of analytical methods based on chemical kinetics, which date from the late nineteenth century, took advantage of the catalytic activity of enzymes. Typically, the enzyme was added to a solution containing a suitable substrate, and the reaction between the two was monitored for a fixed time. The enzyme s activity was determined by measuring the amount of substrate that had reacted. Enzymes also were used in procedures for the quantitative analysis of hydrogen peroxide and carbohydrates. The application of catalytic reactions continued in the first half of the twentieth century, and developments included the use of nonenzymatic catalysts, noncatalytic reactions, and differences in reaction rates when analyzing samples with several analytes. 

In Example 13.1 the initial concentration of analyte is determined by measuring the amount of unreacted analyte at a fixed time. Sometimes it is more convenient to measure the concentration of a reagent reacting with the analyte or the concentration of one of the reaction s products. The one-point fixed-time integral method can still be applied if the stoichiometry is known between the analyte and the species being monitored. For example, if the concentration of the product in the reaction... 

The one-point fixed-time integral method has the advantage of simplicity since only a single measurement is needed to determine the analyte s initial concentration. As with any method relying on a single determination, however, a... 

Fixed-time integral methods are advantageous for systems in which the signal is a linear function of concentration. In this case it is not necessary to determine the concentration of the analyte or product at times ti or f2, because the relevant concentration terms can be replaced by the appropriate signal. For example, when a pseudo-first-order reaction is followed spectrophotometrically, when Beer s law... 

An alternative to a fixed-time method is a variable-time method, in which we measure the time required for a reaction to proceed by a fixed amount. In this case the analyte s initial concentration is determined by the elapsed time, Af, with a higher concentration of analyte producing a smaller Af. For this reason variabletime integral methods are appropriate when the relationship between the detector s response and the concentration of analyte is not linear or is unknown. In the one-point variable-time integral method, the time needed to cause a desired change in concentration is measured from the start of the reaction. With the two-point variable-time integral method, the time required to effect a change in concentration is measured. 

If the rate is measured at a fixed time, then both k and are constant, and a calibration curve of (rate)f versus [A]o can be used for the quantitative analysis of the analyte. 

The reaction is now first-order in substrate, and the rate of the reaction can be used to determine the substrate s concentration by a fixed-time method. 

Sensitivity The sensitivity for a one-point fixed-time integral method of analysis is improved by making measurements under conditions in which the concentration of the monitored species is larger rather than smaller. When the analyte s concentration, or the concentration of any other reactant, is monitored, measurements are best made early in the reaction before its concentration has substantially decreased. On the other hand, when a product is used to monitor the reaction, measurements are more appropriately made at longer times. For a two-point fixed-time integral method, sensitivity is improved by increasing the difference between times t and f2. As discussed earlier, the sensitivity of a rate method improves when using the initial rate. 

Equation 13.14 shows how [A]o is determined for a two-point fixed-time integral method in which the concentration of A for the pseudo-first-order reaction... 

X is the wavelength and at a fixed time-say, t = 0-one full wave is traced out over a distance X. 

Relative to CO2 on a volume basis. A more useful way to compare the relative warming potentials is to consider the lifetimes of the species and integrate the efficiencies over a fixed time interval, usually 100 years (see Ref. 8). 

The decay constant is the key to the mixing rate number defined for Re > lO" by N/ D/TY = 0.5 for a disk flat blade turbine (DFBT), and N/ (D/TY = 0.9 for the propeUer. Therefore, power required to achieve any degree of uniformity in a fixed time is proportional to D and D for DFBT and propeUer, respectively. 

The thermal design of tank coils involves the determination of the area of heat-transfer surface required to maintain the contents of the tank at a constant temperature or to raise or lower the temperature of the contents by a specified magnitude over a fixed time. 

Batch Reactor In a batch reactor, the reactants are added to the reactor at the start of the reaction. The reactants are allowed to react in the reactor for a fixed time. No feed is added or product withdrawn during this time. The reaction products are removed at the end of the batch. 

In fact, (3.22) is the usual stationary phase approximation, performed however for an infinitedimensional path integral, which picks up the trajectories with classical action S. Further, at fixed time t we take the integral over Xi again in the stationary phase approximation, which gives... 

Fig. 7.9. Measurements of the degree of conversion of ct p silicon nitride at a fixed time and various temperatures are thought to show the strong influence of shock modification on the high temperature dissolution [84B01].

From the ergonomics perspective, some level of automation was desirable. This was because the worker was in a high stress situation and had to make a relatively difficult decision. A semiautomatic system in which blowdown would occur automatically after a fixed time period following coincident red alarms (given no worker veto) would appear to have the advantages... 

For a continuous SMB process, the specific identified amount or batch produced is defined by unit of time in such a way that ensures a homogeneous material and quality within specified limits. In the case of a continuous SMB production run a batch is defined by the amount produced in a fixed time interval. A time limitation during manufacturing using SMB is established by the same fixed time interval as the batch. The duration of the production phase is thus established, which does not affect the quality of the drug substance [66]. 

A futures contract is an agreement that calls for a seller to deliver to a buyer a specified quantity and quality of an identified commodity, at a fixed time in the future, at a price agreed to when the contract is made. An option on a commodity futures contract gives the buyer of the option the right to convert the option into a futures contract. Energy futures and options contracts arc used by energy producers, petroleum refin-... 

Provision of a fixed time-frame installation program. 

Conducting interim progress reviews Interim progress reviews typically occur on a fixed time schedule, such as daily or weekly. They may also occur when some problem in performance is observed or at the completion of a significant step toward the accomplishment of the project. 

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