Computer comparison example

A key feature of the DSMC technique in comparison to continuum methods is its relatively high computational expense. To allow the decoupling between molecular motion and intermolecular collisions to occur in a physically accurate way, the time-step used in the DSMC technique must be smaller than the mean time between collisions. Similarly, the size of the cells employed in the DSMC computational grid must be of the order of the local mean free path everywhere in the flow domain. These physical restrictions on the size of the numerical parameters results in the time steps and cell sizes employed in DSMC calculations being usually significantly smaller than those employed in continuum computations. For this reason, significant work has been performed in the optimization of the DSMC technique for different types of computer hardware. Examples of specific implementations are described in Refs. 23-26. 

Yields from AGB stars are provided by a number of authors. Many AGB yields available in the literature are from synthetic AGB computations that use fitting formula to estimate the evolution during the TP-AGB. Synthetic AGB models have successfully been used to model AGB populations [76], and compute stellar yields [161,162,163,79]. The yields published by Forestini Charbonnel [112] employed a combination of full, or detailed, AGB models and synthetic. The AGB yields of [164], [103], [105], and [24] were computed from detailed AGB model computations. An example of the yields from Karakas Lattanzio [24] are shown in Figure 30. The yields have been weighted by the initial mass function of Kroupa, Tout, Gilmore [165], and we show results from the Z = 0.02 (solar), 0.008 (LMC) and 0.004 (SMC) metallicity models. For comparison we also show the yields from a number of different synthetic AGB calculations, and from [164] see the figure caption for details. 

Sathyagal et al (1995) give a striking demonstration of the solution of the inverse problem using both computer-simulated data and as experimental data with liquid drops in a stirred liquid-liquid dispersion. The computer-simulated examples provide for a direct comparison of the... 

In addition, the mirrors are adjustable, so that unimportant areas can be ignored. Light re-emmited from the surfaee is detected, and the detector signal is transmitted to a computer programmed with acceptable deviation levels for comparison with a reference component. Tolerance levels can vary for different areas of the same test piece they may, for example, be higher on a ground section than on adjacent unmachined areas. 

As an example for an efficient yet quite accurate approximation, in the first part of our contribution we describe a combination of a structure adapted multipole method with a multiple time step scheme (FAMUSAMM — fast multistep structure adapted multipole method) and evaluate its performance. In the second part we present, as a recent application of this method, an MD study of a ligand-receptor unbinding process enforced by single molecule atomic force microscopy. Through comparison of computed unbinding forces with experimental data we evaluate the quality of the simulations. The third part sketches, as a perspective, one way to drastically extend accessible time scales if one restricts oneself to the study of conformational transitions, which arc ubiquitous in proteins and are the elementary steps of many functional conformational motions. 

Nevertheless, the technique suffers from a severe time scale problem -the trajectories are computed for (at most) a few nanoseconds. This is far too short compared to times required for many processes in biophysics. For example, the ii to T conformational transition in hemoglobin lasts tens of microseconds [1], and the typical time for ion migration through the gramicidin channel is hundreds of nanoseconds. This limits (of course) our ability to make a meaningful comparison to experiments, using MD. 

FIG. 13-95 Comparison of computed stage temperatures with plant data for the example of Fig. 13-94. 

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

Fig. 7 gives an example of such a comparison between a number of different polymer simulations and an experiment. The data contain a variety of Monte Carlo simulations employing different models, molecular dynamics simulations, as well as experimental results for polyethylene. Within the error bars this universal analysis of the diffusion constant is independent of the chemical species, be they simple computer models or real chemical materials. Thus, on this level, the simplified models are the most suitable models for investigating polymer materials. (For polymers with side branches or more complicated monomers, the situation is not that clear cut.) It also shows that the so-called entanglement length or entanglement molecular mass Mg is the universal scaling variable which allows one to compare different polymeric melts in order to interpret their viscoelastic behavior. 

A comparison between Gl, G2, G2(MP2) and G2(MP2,SVP) is shown in Table 5.2 for the reference G2 data set the mean absolute deviations in kcal/mol vary from 1.1 to 1.6 kcal/mol. There are other variations of tlie G2 metliods in use, for example involving DFT metliods for geometry optimization and frequency calculation or CCSD(T) instead of QCISD(T), with slightly varying performance and computational cost. The errors with the G2 method are comparable to those obtained directly from calculations at the CCSD(T)/cc-pVTZ level, at a significantly lower computational cost. ... 

Yaw s et al. [141] present a useful technique for estimating overhead and bottoms recoveries with a very good comparison with tray-to-tray computer calculations. The procedure suggested uses an example from the reference with permission ... 

Many anodic oxidations involve an ECE pathway. For example, the neurotransmitter epinephrine can be oxidized to its quinone, which proceeds via cyclization to leukoadrenochrome. The latter can rapidly undergo electron transfer to form adrenochrome (5). The electrochemical oxidation of aniline is another classical example of an ECE pathway (6). The cation radical thus formed rapidly undergoes a dimerization reaction to yield an easily oxidized p-aminodiphenylamine product. Another example (of industrial relevance) is the reductive coupling of activated olefins to yield a radical anion, which reacts with the parent olefin to give a reducible dimer (7). If the chemical step is very fast (in comparison to the electron-transfer process), the system will behave as an EE mechanism (of two successive charge-transfer steps). Table 2-1 summarizes common electrochemical mechanisms involving coupled chemical reactions. Powerful cyclic voltammetric computational simulators, exploring the behavior of virtually any user-specific mechanism, have... 

Another important insight obtained from this example is related to the number of Monte Carlo trials which must be averaged to obtain a comparison value to the experimentally observed quantities. In order to produce a reasonable estimate of the distribution a suitable ratio of shimmer to measurement error must be achieved. A reasonable value based on experience only was found to be 0.2. In this example 100 Monte Carlo trials were required. With such a large number of trials computer logistics are an important concern. The details of the computer run and of the mapping procedure are discussed by Duever (7 ). ... 

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