Deterministic method

With a chain length of n the number of conformers is 3(n-l), thus hexane has 243 conformations and decane 19,683 (these are only non-degenerate if each carbon is uniquely substituted). 

With a chain length of n the number of conformers is 3(n 1) thus, hexane has 

243 conformations and decane 19683 (these are only non-degenerate if each carbon is uniquely substituted). 

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Keywords deterministic methods, STOllP, GllP, reserves, ultimate recovery, net oil sands, area-depth and area-thickness methods, gross rock volume, expectation curves, probability of excedence curves, uncertainty, probability of success, annual reporting requirements, Monte-Carlo simulation, parametric method... 

The other parameters used in the calculation of STOMP and GIIP have been discussed in Section 5.4 (Data Interpretation). The formation volume factors (B and Bg) were introduced in Section 5.2 (Reservoir Fluids). We can therefore proceed to the quick and easy deterministic method most frequently used to obtain a volumetric estimate. It can be done on paper or by using available software. The latter is only reliable if the software is constrained by the geological reservoir model. 

Molecular Dynamics and Monte Carlo Simulations. At the heart of the method of molecular dynamics is a simulation model consisting of potential energy functions, or force fields. Molecular dynamics calculations represent a deterministic method, ie, one based on the assumption that atoms move according to laws of Newtonian mechanics. Molecular dynamics simulations can be performed for short time-periods, eg, 50—100 picoseconds, to examine localized very high frequency motions, such as bond length distortions, or, over much longer periods of time, eg, 500—2000 ps, in order to derive equiUbrium properties. It is worthwhile to summarize what properties researchers can expect to evaluate by performing molecular simulations ... 

Deterministic methods. Deterministic methods follow a predetermined search pattern and do not involve any guessed or random steps. Deterministic methods can be further classified into direct and indirect search methods. Direct search methods do not require derivatives (gradients) of the function. Indirect methods use derivatives, even though the derivatives might be obtained numerically rather than analytically. 

Stochastic methods do not need auxiliary information, such as derivatives, in order to progress. They only require an objective function for the search. This means that stochastic methods can handle problems in which the calculation of the derivatives would be complex and cause deterministic methods to fail. 

Also, it is possible to combine stochastic and deterministic methods as hybrid methods. For example, a stochastic method can be used to control the structural changes and a deterministic method to control the changes in the continuous variables. This can be useful if the problem involves a large number of integer variables, as for such problems, the tree required for branch and bound methods explodes in size. 

Deterministic methods are easier to visualize and simpler to implement. However, these represent poor physical and statistical pictures. The spur energy (62.5 eV) needed for best agreement between deterministic calculation and experiment is not supported by the mean energy loss of high-energy electrons in water-producing spurs, which is somewhat less than 40 eV (Pimblott et ai, 1990). 

The different theoretical models for analyzing particle deposition kinetics from suspensions can be classified as either deterministic or stochastic. The deterministic methods are based on the formulation and solution of the equations arising from the application of Newton s second law to a particle whose trajectory is followed in time, until it makes contact with the collector or leaves the system. In the stochastic methods, forces are freed of their classic duty of determining directly the motion of particles and instead the probability of finding a particle in a certain place at a certain time is determined. A more detailed classification scheme can be found in an overview article [72]. 

The use of uncertainty conscious schedulers - schedulers which consider the uncertain parameters already at the scheduling stage - have the potential to lead to a significant increase in the profit compared to deterministic methods. However, the resulting optimization problems are usually of large scale and it is difficult to solve them within the short period of time available in a real-time environment. 

Despite this assertion, if you are new to AI you may already feel doubt creeping up on you AI is beginning to seem like a slippery concept. It is difficult to believe that a method that is less precise than deterministic methods such as calculus could outperform them. Yet the choice of ways to tackle a scientific problem that AI offers provides opportunities for inventiveness in use that are generally absent from traditional methods, and this is one of its strengths. 

More sophisticated calculations (14,20), using either stochastic Monte Carlo or deterministic methods, are able to consider not only different Irradiating particles but also reactant diffusion and variations In the concentration of dissolved solutes, giving the evolution of both transient and stable products as a function of time. The distribution of species within the tracks necessitates the use of nonhomogeneous kinetics (21,22) or of time dependent kinetics (23). The results agree quite well with experimental data. 

Measurement of dietary exposure to pesticides has historically relied upon deterministic methods that assign finite values to both the pesticide residue level and the food consumption estimates to yield a point estimate of exposure. The calculations are relatively simple, but consideration needs to be given to the accuracy of the assumptions concerning residue level and food consumption. 

While deterministic methods are still quite useful in determining long-term, chronic exposures to pesticides, they are being replaced with probabilistic methods for the analysis of acute (short-term) exposures. These probabilistic methods take advantage of improvements in computational capabilities. 

The present investigation applies deterministic methods of continuous mechanics of multiphase flows to determine the mean values of parameters of the gaseous phase. It also applies stochastic methods to describe the evolution of polydispersed particles and fluctuations of parameters [4]. Thus the influence of chaotic pulsations on the rate of energy release and mean values of flow parameters can be estimated. The transport of kinetic energy of turbulent pulsations obeys the deterministic laws. 

Deterministic methods Methods in which all biological, chemical, physical, and environmental parameters are assnmed to be constant and accurately specihed. 

The environmental concentration of a stressor, either measured or estimated, is compared with an effect concentration such as an LC50 (lethal concentration to kill 50% of individuals in a theoretical population in a set period of time) or no observed effect concentration (NOEC) [31, 32]. These are simple ratios of single exposure and effects values and may be used to express hazard or relative safety. This deterministic method uses point estimates to represent one or more factors in a risk assessment and treats them as if they were fixed and precisely known [33]. The calculation of HQs... 

There are many possible reverberation algorithms that can be constructed by adding absorptive losses to allpass feedback loops, and these reverberators can sound very good. However, the design of these reverberators has to date been entirely empirical. There is no way to specify in advance a particular reverberation time function A(co), nor is there a deterministic method for choosing the filter parameters to eliminate tonal coloration. 

The deterministic methods in Section 2.2.1 numerically solve the differential equations, thus determining the macroscopic composition of the system at a given time. On the contrary, the KMC method determines the time of change (reaction) of a species with the use of a random number generated with an appropriate distribution.89 The result is the system s composition, as well. 

In the past, catalyst design has been mainly based on heuristics more recently, deterministic methods have started to evolve. Heuristics describes methods by which knowledge is acquired in a logical but non-mathematical manner. In this way also, trial-and-error procedures may be considered to be of the heuristic... 

Since chemical reaction engineering considerations apply to nondcterministic as well as deterministic methods they will be briefly dealt with separately. The interaction of chemical kinetics and transport processes and their effect on catalyst activity and selectivity in reaction networks will be emphasized. Some attention will be also paid to catalyst deactivation. 

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