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Numerical instabilities Subject

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]). 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]).
We have tried several tricks to avoid the numerical instabilities, such as setting some quantities beyond a threshold equal to zero or subjecting the c-coefficients to an upper bound condition. None of these tricks was fully satisfactory, but the use of extremal pairs worked in all cases. [Pg.40]

The quantum mechanical treatment of a three-dimensional atom-diatom reactive system is one of the main subjects of theoretical chemistry [1]. About a decade ago when the first numerical results for the H + H2 reactions appeared in print [2] it seemed that the problem was solved. However, difficulties associated with numerical instabilities and with the bifurcation into two nonsyrametric product channels slowed progress with this kind of treatment. This situation caused a change in the order of priorities whereas previously most of the effort was directed toward developing algorithms for yielding "exact cross sections, now it is mostly aimed at developing reliable approximations. [Pg.167]

The mechanism of squeezing is a rather comphcated phenomenon to analyse, but relative simple approximation methods exist which suffice in most cases. Care has to be taken with more sophisticated methods such as Finite Element Methods giving the illusion of more precision. Current FEM s are not well suited to model large deformation problems like squeezing as excessive mesh distortions generally cause numerical instabilities. The subject FEM model should only be used to identify the failure mechanism and not to model the resulting deformations. [Pg.234]

Forced-Convection Flow. Heat transfer in pol3rmer processing is often dominated by the uVT flow advectlon terms the "Peclet Number" Pe - pcUL/k can be on the order of 10 -10 due to the polymer s low thermal conductivity. However, the inclusion of the first-order advective term tends to cause instabilities in numerical simulations, and the reader is directed to Reference (7) for a valuable treatment of this subject. Our flow code uses a method known as "streamline upwindlng" to avoid these Instabilities, and this example is intended to illustrate the performance of this feature. [Pg.274]

Ya.B. s more recent papers have been devoted to the study of nonlinear problems. In 1966 Ya.B. turned his attention to the stabilizing effect of accelerated motion through a hot mixture of a boundary of intersection of two flame fronts, convex in the direction of propagation, and proposed an approximate model of a steady cellular flame. G. I. Sivashinsky, on the basis of this work, proposed a nonlinear model equation of thermodiffusional instability which describes the development of perturbations of a bent flame in time and, together with J. M. Michelson, studied its solution near the stability boundary Le = Lecrit. It was shown numerically that the flat flame is transformed into a three-dimensional cellular one with a non-steady, chaotically pulsating structure. The formation of a two-dimensional cellular structure was also the subject of a numerical investigation by A. P. Aldushin, S. G. Kasparyan and K. G. Shkadinskii, who obtained steady flames in a wider parameter interval. [Pg.302]

The pure samples of Ba2YCu30y prepared from the nitrates were placed on a watch glass which was transferred to a desiccator containing water in place of the desiccant. After 48 hours, the sample was removed and subjected to visual and x-ray analysis. The black product contained numerous aggregated white particles. The x-ray analysis of the product is shown in Figure 11 and indicates the formation of BaC03. These results would indicate that the product is attacked by moist air and the instability of Ba2YCu30y will present problems for any practical device application. [Pg.77]

Of course, even in presence of Nekhoroshev stability, evolution of the actions is possible on the very long exponential times typical of Arnold d diffusion (Arnold 1964), but this kind of instability is outside the subject of this article (see Lega, Guzzo and Froeschle 2003 for a numerical study). [Pg.176]

Historically, pnibhshed values of the h/h concentration of both tissue and body fluids from healthy subjects have varied greatly. These great differences were attributed to numerous variables, such as age, sex, dietary habits, physiological conditions, environmental factors and numerous other X-factors. Given the delicate nature and the instability of biological samples, it has been concluded that improper sample collection methods and manipulation drastically affects the iodine content of biological matrices. [Pg.378]

Developing a quantitative theory of the conditions for shear localization is the subject of ongoing numerical (finite element-based) research. Key earlier papers are (Recht 1964) in which the instability criterion dx/dy = 0 was first applied, (Semiatin and Rao 1983) in which it was argued that dx/dy needed to be substantially negative and (Hou and Komanduri 1997) in which the complexities of temperature distributions in shear localized chips were examined in more detail than in previous work. Adiabatic shearing has been the subject of a number of general reviews, for example, Walley (2007), and books, for example, Bai and Dodd (1992). These mention but do not have a main focus on machining. Walley (2007) mentions nine earlier reviews. [Pg.31]

Huynh et al. [92] conducted a numerical study of capillary instability of a jet subject to two superposed disturbances. The stuface disturbance, C was composed of the superposition of two wave numbers ... [Pg.32]

Clearly, data derived from experiment are measurements, and are therefore subject to margins of error. Random errors (such as those observed in the measurement of our piece of string) arise from instabilities of the radiation source, sensitivity of the detection device, etc. But this is not the only source of error in our experiments. When we measured our piece of string, if it turned out that the ruler was in some way defective, then a systematic error would be present, which would affect all our measurements to the same degree. Systematic errors in experiments can arise from the methods we use to process the data. For example, we use a parameterized model in a least-squares refinement. Any assumptions we make in that model (e.g. the choice of molecular symmetry) and any numerical treatment of the data as we process them will affect the results we obtain. [Pg.38]


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See also in sourсe #XX -- [ Pg.439 ]




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