Numerical artifacts

The heightened appreciation of resonance problems, in particular, has been quite recent [63, 62], and contrasts the more systematic error associated with numerical stability that grows systematically with the discretization size. Ironically, resonance artifacts are worse in the modern impulse multiple-timestep methods, formulated to be symplectic and reversible the earlier extrapolative variants were abandoned due to energy drifts. 

If the At satisfies the following equation, then the solution will not oscillate from node to node (a numerical artifact). See Ref. 106. 

Numerous attempts have been made to develop hybrid methodologies along these lines. An obvious advantage of the method is its handiness, while its disadvantage is an artifact introduced at the boundary between the solute and solvent. You may obtain agreement between experiments and theory as close as you desire by introducing many adjustable parameters associated with the boundary conditions. However, the more adjustable parameters are introduced, the more the physical significance of the parameter is obscured. 

Fig. 6.7. The predicted, one-dimensional, mean-bulk temperatures versus location at various times are shown for a typical powder compact subjected to the same loading as in Fig. 6.5. It should be observed that the early, low pressure causes the largest increase in temperature due to the crush-up of the powder to densities approaching solid density. The "spike in the temperature shown on the profiles at the interfaces of the powder and copper is an artifact due to numerical instabilities (after Graham [87G03]).

An overview is provided by figure 4.7 plot (a) shows the numerically determined attractor sets for all 2.9 < a < 4 plot (b) - lest it be thought that the white regions in plot (a) are artifacts of the printing process - shows a blowup view of the windowed region within one of those wide white bands in plot (a). The general behavior is summarized as follows ... 

Algebraically equivalent formulation as used in pocket calculators (beware of numerical artifacts when using Eqs. (2.7-2.9) cf. Table 1.1) ... 

Of all the requirements that have to be fulfilled by a manufacturer, starting with responsibilities and reporting relationships, warehousing practices, service contract policies, airhandUng equipment, etc., only a few of those will be touched upon here that directly relate to the analytical laboratory. Key phrases are underlined or are in italics Acceptance Criteria, Accuracy, Baseline, Calibration, Concentration range. Control samples. Data Clean-Up, Deviation, Error propagation. Error recovery. Interference, Linearity, Noise, Numerical artifact. Precision, Recovery, Reliability, Repeatability, Reproducibility, Ruggedness, Selectivity, Specifications, System Suitability, Validation. 

The act of manipulating numbers on calculators of finite accuracy leads to numerical artifacts. (See Table l.l.) - ... 

An example of mechanism (1) is given in Section 1.1.2 Essentially, numerical artifacts are due to computational operations that result in a number, the last digits of which were corrupted by numerical overflow or truncation. The following general rules can be set up for simple operations ... 

A further incentive for supplying file JUNGLE2.dat is the possibility of smuggling in some numerical artifacts of the type that often crop up even in one s own fine, though just a bit hastily concocted, compilations (see JUN-GLE3.dat) ... 

Note. If the N dimensions yield very different numerical values, such as 105 3 mmol/L, 0.0034 0.02 meter, and 13200 600 pg/ml, the Euclidian distances are dominated by the contributions due to those dimensions for which the differences A-B, AS, or BS are numerically large. In such cases it is recommended that the individual results are first normalized, i.e., x = (x - Xn,ean)/ 5 t, where Xmean and Sx are the mean and standard deviation over all objects for that particular dimension X, by using option (Transform)/(Normalize) in program DATA. Use option (Transpose) to exchange columns and rows beforehand and afterwards The case presented in sample file SIEVEl.dat is different the individual results are wt-% material in a given size class, so that the physical dimension is the same for all rows. Since the question asked is are there differences in size distribution , normalization as suggested above would distort tbe information and statistics-of-small-numbers artifacts in the poorly populated size classes would become overemphasized. 

Since MPC dynamics yields the hydrodynamic equations on long distance and time scales, it provides a mesoscopic simulation algorithm for investigation of fluid flow that complements other mesoscopic methods. Since it is a particle-based scheme it incorporates fluctuations, which are essential in many applications. For macroscopic fluid flow averaging is required to obtain the deterministic flow fields. In spite of the additional averaging that is required the method has the advantage that it is numerically stable, does not suffer from lattice artifacts in the structure of the Navier-Stokes equations, and boundary conditions are easily implemented. 

Although this collision rule conserves momentum and energy, in contrast to the original version of MPC dynamics, phase space volumes are not preserved. This feature arises from the fact that the collision probability depends on AV so that different system states are mapped onto the same state. Consequently, it is important to check the consistency of the results in numerical simulations to ensure that this does not lead to artifacts. 

Of all the ancient metallic artifacts that have been left from antiquity, coins are among the most numerous. Since ancient times coins have generally been made from coinage metals or, mostly, from coining alloys, whose chemical and physical properties and economic qualities make them suitable to be used for this purpose. Until the twentieth century, gold, silver, copper, and their alloys were practically the only metals from which coinage was made. All these metals and alloys have the following properties ... 

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