Deterministic, definition

In 1997, the World Petroleum Congress (WPG) and the Society of Petroleum Engineers (SPE) jointly published petroleum resei ve definitions that added the element of probability to the deterministic definitions in common use. The WPC/SPE definitions build on the SEC definitions by including probabilistic estimates. 

While the procedure proposed in this pubUcation uses the performance goal as a measure of the required reliability of any structure, system or component (including safety barriers), the defence in depth approach implies a deterministic definition of defence levels and barriers. This approach allows consideration of administrative measures and operating procedures as part of the defence in depth levels . Therefore, in the proposed framework, the... 

The definitions above are an abbreviated version of those used in a veiy complex and financially significant exercise with the ultimate goal of estimating resei ves and generating production forecasts in the petroleum industry. Deterministic estimates are derived largely from pore volume calculations to determine volumes of either oil nr gas in-place (OIP, GIP). This volume when multiplied by a recovery factor gives a recoverable quantity of oil or natural gas liquids—commonly oil in standard barrels or natural gas in standard cubic feet at surface conditions. Many prefer to use barrels of oil equivalency (BOE) or total hydrocarbons tor the sum of natural gas, natural gas liquids (NGL), and oil. For comparison purposes 6,000 cubic feet of gas is considered to be equivalent to one standard barrel on a British thermal unit (Btu) basis (42 U.S. gallons). 

While the explicit deterministic structure of such rules - by which me mean the set of sites whose value is fixed by values of other sites - appears as [ai-i t),ai t), ai+i t) Gift + 1), there may also exist an implicit underlying deterministic structure not immediately obvious from the definition of the rule itself. It may be... 

Initially, it was assumed that the HlV-1 population is infinite, evolution is deterministic, and antiretroviral resistance development is definite (Coffin 1995). However, our research amongst others has demonstrated that the effective population size, defined as the average number of HIV variants that produces infectious progeny is relatively small (Leigh Brown 1997 Leigh Brown and Richman 1997 Nijhnis et al. 1998). This can be explained because the majority of virus particles that are produced harbor deleterious mutations resulting in noninfectious virus. Also limited target cell availability and inactivation of potentially infectious viruses by the host... 

This is the same equation of motion that is satisfied by the original coordinate qa(t), except that the stochastic driving term is absent. The relative dynamics is therefore deterministic. We have chosen the notation accordingly and left out the index a in the definition (41) of Aq (although, of course, we cannot expect the relative dynamics to remain noiseless in the full nonlinear system). Although noiseless, the relative dynamics is still dissipative because Eq. (43) retains the damping term. 

According to Stuart A. Kauffman (1991) there is no generally accepted definition for the term complexity . However, there is consensus on certain properties of complex systems. One of these is deterministic chaos, which we have already mentioned. An ordered, non-linear dynamic system can undergo conversion to a chaotic state when slight, hardly noticeable perturbations act on it. Even very small differences in the initial conditions of complex systems can lead to great differences in the development of the system. Thus, the theory of complex systems no longer uses the well-known cause and effect principle. 

DEFINITION A two-tape one-way deterministic finite state acceptor M = (K1,K2,I,6,qo,qa,qr) consists of ... 

In this definition, we allow our deterministic pdas to block (rather than enter a DEAD state). We can adapt our previous construction to show that under these definitions ... 

THEOREM 8.4 The reversal of the interpreted value language of a monadic recursion scheme with r tests is an (r+1)-definite deterministic context-free language. 

Since is deterministic, the expected value in this definition is with respect to the composition PDF. However,... 

There is also no single, commonly accepted technical definition of (proved) reserves, and in the above definition many words are ambiguous and without any quantification a major drawback of the deterministic approach. 

The risk index in Equation 6.2 is expressed in terms of risk (i.e., the probability that an adverse response will occur during an individual s lifetime). This definition is consistent with the fundamental objective of developing a risk-based hazardous waste classification system. However, the use of health risk per se in calculating the risk index presents some difficulties because risk is not proportional to dose for substances that cause deterministic effects. For this type of substance, the risk is presumed to be zero at any dose below a nominal threshold. Since the allowable dose should always be less than the threshold in order to prevent the occurrence of adverse responses, expressing the risk index in terms of risk would result in an indeterminate value and, more importantly, a lack of distinction between doses near the nominal thresholds and lower doses of much less concern. For any hazardous substance, including carcinogens for which risk is assumed to be proportional to dose without threshold, it is generally useful to express the risk index as the ratio of a calculated dose [e.g., sieverts, mg (kg d)-1] to an allowable dose that corresponds to an allowable risk ... 

In deterministic theory we started with the definition of a compartment as a kinetically homogeneous amount of material. The equivalent definition in stochastic theory is that the probability of a unit participating in a particular transfer out of a compartment, at any time, is the same for all units in the compartment. 

In this chapter, we explain the technique of sequential bifurcation and add some new results for random (as opposed to deterministic) simulations. In a detailed case study, we apply the resulting method to a simulation model developed for Ericsson in Sweden. In Sections 1.1 to 1.3, we give our definition of screening, discuss our view of simulation versus real-world experiments, and give a brief indication of various screening procedures. 

Deterministic dynamics of biochemical reaction systems can be visualized as the trajectory of (ci(t), c2(t), , c v(0) in a space of concentrations, where d(t) is the concentration of ith species changing with time. This mental picture of path traced out in the N-dimensional concentration space by deterministic systems may prove a useful reference when we deal with stochastic chemical dynamics. In stochastic systems, one no longer thinks in terms of definite concentrations at time t rather, one deals with the probability of the concentrations being xu x2, , Wy at time t ... 

With suitable definitions of search functions, EA methods can also be used to locate more features on the PES than just low-energy local and global minima. Chaudhury et al. [144,145] have implemented methods for finding first-order saddle points and reaction paths, applying them to LJ clusters up to n=30. It remains to be tested, however, if these method can be competitive with deterministic exhaustive searches for critical points for small systems [146], on the one hand, and with the large arsenal of methods for finding saddles and reaction paths between two known minima for larger systems [63], on the other hand. 

The mass balance of the retained solid is described by Eq. (4.280). The Mint deterministic model results from the coupling of this relation vfith the definition of the filtration coefficient. The result is written in Eq. (4.281) for the start time of the filtration and in Eq. (4.282) for the remaining filtration time. Here a is the detachment coefficient of the retained particle its dimension is T h... 

---