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Deterministic

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... [Pg.153]

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. [Pg.155]

It is very important to make classification of dynamic models and choose an appropriate one to provide similarity between model behavior and real characteristics of the material. The following general classification of the models is proposed for consideration deterministic, stochastic or their combination, linear, nonlinear, stationary or non-stationary, ergodic or non-ergodic. [Pg.188]

It is possible to limit our choice for stochastic modeling by stationary, linear, nonlinear, and ergodic models in combination with deterministic function. In this case the following well studied models can be proposed for the accepted concept [1] ... [Pg.189]

Standard procedures that are used for testing of construction materials are based on square pulse actions or their various combinations. For example, small cyclic loads are used for forecast of durability and failure of materials. It is possible to apply analytical description of various types of loads as IN actions in time and frequency domains and use them as analytical deterministic models. Noise N(t) action as a rule is represented by stochastic model. [Pg.189]

Gyorgyi L and Field R J 1992 A three-variable model of deterministic chaos in the Belousov-Zhabotinsky reaction Nature 355 808-10... [Pg.1117]

Miller R J D 1994 Energetics and dynamics of deterministic protein motion Acc. Chem. Res. 27 145-50... [Pg.2000]

C.D. Maranas, IP. Androulakis and C.A. Floudas, A deterministic global optimization approach for the protein folding problem, pp. 133-150 in Global minimization of nonconvex energy functions molecular conformation and protein folding (P. M. Pardalos et al., eds.), Amer. Math. Soc., Providence, RI, 1996. [Pg.223]

Another difference is related to the mathematical formulation. Equation (1) is deterministic and does not include explicit stochasticity. In contrast, the equations of motion for a Brownian particle include noise. Nevertheless, similar algorithms are adopted to solve the two differential equations as outlined below. The most common approach is to numerically integrate the above differential equations using small time steps and preset initial values. [Pg.266]

A related algorithm can be written also for the Brownian trajectory [10]. However, the essential difference between an algorithm for a Brownian trajectory and equation (4) is that the Brownian algorithm is not deterministic. Due to the existence of the random force, we cannot be satisfied with a single trajectory, even with pre-specified coordinates (and velocities, if relevant). It is necessary to generate an ensemble of trajectories (sampled with different values of the random force) to obtain a complete picture. Instead of working with an ensemble of trajectories we prefer to work with the conditional probability. I.e., we ask what is the probability that a trajectory being at... [Pg.266]

Consider a numerical solution of the Newton s differential equation with a finite time step - At. In principle, since the Newton s equations of motion are deterministic the conditional probability should be a delta function... [Pg.268]

Other methods which are applied to conformational analysis and to generating multiple conformations and which can be regarded as random or stochastic techniques, since they explore the conformational space in a non-deterministic fashion, arc genetic algorithms (GA) [137, 1381 simulation methods, such as molecular dynamics (MD) and Monte Carlo (MC) simulations 1139], as well as simulated annealing [140], All of those approaches and their application to generate ensembles of conformations arc discussed in Chapter II, Section 7.2 in the Handbook. [Pg.109]

This is a question of reaction prediction. In fact, this is a deterministic system. If we knew the rules of chemistry completely, and understood chemical reactivity fully, we should be able to answer this question and to predict the outcome of a reaction. Thus, we might use quantum mechanical calculations for exploring the structure and energetics of various transition states in order to find out which reaction pathway is followed. This requires calculations of quite a high degree of sophistication. In addition, modeling the influence of solvents on... [Pg.542]

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 ... [Pg.165]

Very early in the study of radioactivity it was deterrnined that different isotopes had different X values. Because the laws of gravity and electromagnetism were deterministic, an initial concept was that when each radioactive atom was created, its lifetime was deterrnined, but that different atoms were created having different lifetimes. Furthermore, these different lifetimes were created such that a collection of nuclei decayed in the observed manner. Later, as the probabiUstic properties of quantum mechanics came to be accepted, it was recognised that each nucleus of a given radioactive species had the same probabiUty for decay per unit time and that the randomness of the decays led to the observed decay pattern. [Pg.446]

Fig. 3. Schematic diagram of a deterministic air quality model, showing the model components and interactions (1) where each of the boxes involves a large... Fig. 3. Schematic diagram of a deterministic air quality model, showing the model components and interactions (1) where each of the boxes involves a large...
Deterministic air quaUty models describe in a fundamental manner the individual processes that affect the evolution of pollutant concentrations. These models are based on solving the atmospheric diffusion —reaction equation, which is in essence the conservation-of-mass principle for each pollutant species... [Pg.379]

CAD /CAM techniques have provided the framework for using the computer as a tool in the drawing and analysis of chemical stmctures and, more recently, in the use of chemical stmctures to design reaction pathways and new products. The essential elements in these appHcations of CAD/CAM are that the possible stmctures are relatively deterministic and that allowable changes in stmcture through reaction are governed by thermodynamic, stoichiometric, and steric constraints. [Pg.63]

Lin, C. C., and L. A. Segel. Mathematics Applied to Deterministic Frob-lems in the Natural Sciences, Macmillan, New York (1974). [Pg.423]

QRA is fundamentally different from many other chemical engineering activities (e.g., chemistry, heat transfer, reaction kinetics) whose basic property data are theoretically deterministic. For example, the physical properties of a substance for a specific application can often be established experimentally. But some of the basic property data used to calculate risk estimates are probabilistic variables with no fixed values. Some of the key elements of risk, such as the statistically expected frequency of an accident and the statistically expected consequences of exposure to a toxic gas, must be determined using these probabilistic variables. QRA is an approach for estimating the risk of chemical operations using the probabilistic information. And it is a fundamentally different approach from those used in many other engineering activities because interpreting the results of a QRA requires an increased sensitivity to uncertainties that arise primarily from the probabilistic character of the data. [Pg.2]

Another popular approach to the isothennal (canonical) MD method was shown by Nose [25]. This method for treating the dynamics of a system in contact with a thennal reservoir is to include a degree of freedom that represents that reservoir, so that one can perform deterministic MD at constant temperature by refonnulating the Lagrangian equations of motion for this extended system. We can describe the Nose approach as an illustration of an extended Lagrangian method. Energy is allowed to flow dynamically from the reservoir to the system and back the reservoir has a certain thermal inertia associated with it. However, it is now more common to use the Nose scheme in the implementation of Hoover [26]. [Pg.59]

An algorithm for performing a constant-pressure molecular dynamics simulation that resolves some unphysical observations in the extended system (Andersen s) method and Berendsen s methods was developed by Feller et al. [29]. This approach replaces the deterministic equations of motion with the piston degree of freedom added to the Langevin equations of motion. This eliminates the unphysical fluctuation of the volume associated with the piston mass. In addition, Klein and coworkers [30] present an advanced constant-pressure method to overcome an unphysical dependence of the choice of lattice in generated trajectories. [Pg.61]

The critical characteristic on each component was analysed, calculated from the analysis and the value obtained was plotted against the process capability indices, Cpk and Cp, for the characteristic in question. See Appendix V for descriptions of the 21 components analysed, including the values of Cp and Cp from the SPC data supplied. Note that some components studied have a zero process capability index. This is a default value given if the process capability index calculated from the SPC data had a mean outside either one of the tolerance limits, which was the case for some of the components submitted. Although it is recognized that negative process capability indices are used for the aim of process improvement, they have little use in the analyses here. A correlation between positive values (or values which are at least within the tolerance limits) will yield a more deterministic relationship between design capability and estimated process capability. [Pg.57]

Figure 2.15(a) shows the relationship between and Cp for the component characteristics analysed. Note, there are six points at q = 9, Cp = 0. The correlation coefficient, r, between two sets of variables is a measure of the degree of (linear) association. A correlation coefficient of 1 indicates that the association is deterministic. A negative value indicates an inverse relationship. The data points have a correlation coefficient, r = —0.984. It is evident that the component manufacturing variability risks analysis is satisfactorily modelling the occurrence of manufacturing variability for the components tested. [Pg.57]

The movement from the deterministic design criteria as described by equation 4.1 to the probability based one described by equation 4.2 has far reaching effects on design (Haugen, 1980). The particular change which marks the development of modern engineering reliability is the insight that probability, a mathematical theory, can be utilized to quantify the qualitative concept of reliability (Ben-Haim, 1994). [Pg.135]

Figure 4.2 Comparison of the probabilistic and deterministic design approaches... Figure 4.2 Comparison of the probabilistic and deterministic design approaches...

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30 Containment systems Deterministic method

A common description of the deterministic and stochastic models

A deterministic model

Acceleration deterministic model

Allowable Risks from Exposure to Substances That Cause Stochastic or Deterministic Effects

Analysis Step 3—Perform Deterministic Computations

Analytical models, deterministic

Analytical models, deterministic model formulations

Approach deterministic

Chaos, chemical deterministic

Complex Deterministic Models

Continuous-deterministic reaction kinetics

Demand deterministic

Design deterministic

Deterministic Analyses

Deterministic Compartmental Models

Deterministic Fractals, or How to Draw Entertaining Patterns

Deterministic Kinetic Analysis

Deterministic Model Formulation

Deterministic Molecular Models

Deterministic Mueller matrix

Deterministic Region

Deterministic Responses from Radiation Exposure

Deterministic Risk Index for Hazardous Chemical Constituents

Deterministic Seismic Hazard Analysis

Deterministic Synthesis

Deterministic Trajectory Models

Deterministic acoustic models, synthesis with

Deterministic and Stochastic Methods

Deterministic and probabilistic assessment

Deterministic and stochastic models

Deterministic annealing

Deterministic assessment

Deterministic canonical ensembles

Deterministic cellular automata

Deterministic chaos

Deterministic chaos, fundamentals

Deterministic chaotic properties

Deterministic chaotic systems

Deterministic collision operator

Deterministic considerations

Deterministic data, definition

Deterministic demand assessment

Deterministic description

Deterministic design approach

Deterministic dynamic system

Deterministic dynamics

Deterministic dynamics, transition path

Deterministic effects

Deterministic endpoints

Deterministic equation

Deterministic equivalent program

Deterministic evolution

Deterministic exposure assessments

Deterministic exposure estimates

Deterministic finite automaton

Deterministic functions

Deterministic generation

Deterministic global algorithm

Deterministic global optimization

Deterministic global optimization modeling

Deterministic hazard assessment

Deterministic history

Deterministic integral equation

Deterministic kinetic modeling

Deterministic kinetics

Deterministic laws

Deterministic logic algorithm

Deterministic method, computer codes

Deterministic methods

Deterministic methods, risk assessment

Deterministic mixed lubrication model

Deterministic model dietary exposure

Deterministic model dietary exposure estimation

Deterministic modeling

Deterministic modeling techniques

Deterministic models

Deterministic models boundary conditions

Deterministic models definition

Deterministic models description

Deterministic models theorem

Deterministic path

Deterministic phrasing prediction

Deterministic planning

Deterministic procedure

Deterministic processes motion

Deterministic projection

Deterministic radiation exposure

Deterministic randomness

Deterministic rate equations

Deterministic responses

Deterministic responses definition

Deterministic rule approaches

Deterministic rules

Deterministic safety analysis

Deterministic scheduler

Deterministic search

Deterministic selection

Deterministic signals

Deterministic simulations

Deterministic step

Deterministic strategy

Deterministic synthesis methods

Deterministic synthesis models

Deterministic technique

Deterministic variation coefficient

Deterministic versus Probabilistic Methods

Deterministic, classical mechanics

Deterministic, definition

Deterministic, derivative formulation

Deterministics series

Diffusion, deterministic-chaotic

Discrete deterministic steps

Dose-Response Assessment for Chemicals That Cause Deterministic Effects

Dose-response assessment deterministic responses

Dose-response relationships deterministic responses

Empirical deterministic functions

Error deterministic

Estimation errors deterministic

Flows deterministic, mixing

Fractals deterministic

Gene Expression Deterministic Description

Genetic-determinists

Implicit deterministic structures

Intonation Synthesis with Deterministic Acoustic Models

Kinetic processes macroscopic, deterministic kinetics

Known Deterministic Coupling

Linear deterministic

Macroscopic, Deterministic Chemical Kinetics

Mass action kinetic deterministic models

Mathematical model deterministic

Measures of Deterministic Responses

Minimally Diluted Deterministic Rules

Model deterministic models

More General Deterministic Thermostats

Numerical techniques deterministic approach

Objectives deterministic methods

Optimization deterministic

Optimization deterministic local methods

Optimization methods, deterministic

Phrasing prediction deterministic approaches

Planning deterministic models

Process deterministic

Process, continuous deterministic

Process, continuous deterministic discrete stochastic

Reconstruction deterministic

Residue deterministic

Risk Index for Multiple Substances That Cause Deterministic Responses

Risk index, deterministic

Risk index, deterministic responses

Safety assessments deterministic

Selection deterministic approach

Serial Supply Chain with Deterministic Demand and Fixed Ordering Costs

Signal, deterministic component

Simulation models, deterministic

Simulation models, deterministic model formulations

Simulations continuous-deterministic

Stochastic Versus Deterministic Description

Stochastic and deterministic processes

Stochastic vs. Deterministic Models

System deterministic

Theory deterministic

Thresholds for Deterministic Effects

Tier 2 (deterministic) uncertainty analysis

Time evolution deterministic dynamics

Time-dependent deterministic sampling

Transition rule deterministic

Turbulence deterministic theory

Turbulence, deterministic

Turbulence, deterministic approach

Vibrational analysis deterministic vibration

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