Benchmarks

Woon D E 1994 Benchmark calculations with correlated molecular wavefunctions. 5. The determination of accurate ab initio intermolecular potentials for He2, Ne2, and A 2 J. Chem. Phys. 100 2838... 

Barker J A and Rettner C T 1992 Accurate potentiai energy surface for Xe/Pt(111) a benchmark gas-surface interaction potentiai J. Chem. Phys. 97 5844... 

Day P N and Truhlar D G 1991 Benchmark calculations of thermal reaction rates. II. Direct calculation of the flux autocorrelation function for a canonical ensemble J. Chem. Phys. 94 2045-56... 

The situation is very different in indirect gap materials where phonons must be involved to conserve momentum. Radiative recombination is inefficient, resulting in long lifetimes. The minority carrier lifetimes in Si reach many ms, again in tire absence of defects. It should be noted tliat long minority carrier lifetimes imply long diffusion lengtlis. Minority carrier lifetime can be used as a convenient quality benchmark of a semiconductor. 

We employ the general scheme presented above as a starting point in our discussion of various approaches for handling the R-T effect in triatomic molecules. We And it reasonable to classify these approaches into three categories according to the level of sophistication at which various aspects of the problem are handled. We call them (1) minimal models (2) pragmatic models (3) benchmark treatments. The criterions for such a classification are given in Table I. 

The BDD approach has been applied in a number of studies that employ the parameters derived from the experimental findings [77-85]. The approach has been extended by Duxbury an co-workers, particularly Alijah in its present version, involving the new stretch-bender Hamiltonian [84,85], which follows the idea by HBl [60], it approaches the methods we tentatively call benchmark. ... 

Fig. 3. Average computation time for one step using EGO.VIII on a DEC-Alpha 3300L workstation (175 MHz) for simulation systems of varying size. The insets show some of the protein-water systems used for the benchmark simulations.

The first finite element schemes for differential viscoelastic models that yielded numerically stable results for non-zero Weissenberg numbers appeared less than two decades ago. These schemes were later improved and shown that for some benchmark viscoelastic problems, such as flow through a two-dimensional section with an abrupt contraction (usually a width reduction of four to one), they can generate simulations that were qualitatively comparable with the experimental evidence. A notable example was the coupled scheme developed by Marchal and Crochet (1987) for the solution of Maxwell and Oldroyd constitutive equations. To achieve stability they used element subdivision for the stress approximations and applied inconsistent streamline upwinding to the stress terms in the discretized equations. In another attempt, Luo and Tanner (1989) developed a typical decoupled scheme that started with the solution of the constitutive equation for a fixed-flow field (e.g. obtained by initially assuming non-elastic fluid behaviour). The extra stress found at this step was subsequently inserted into the equation of motion as a pseudo-body force and the flow field was updated. These authors also used inconsistent streamline upwinding to maintain the stability of the scheme. 

The outlined scheme is shown to yield stable solutions for non-zero Weissenberg number flows in a number of benchmark problems (Swarbric and Nassehi, 1992b). However, the extension of this scheme to more complex problems may involve modifications such as increasing of elemental subdivisions for stress calculations from 3 x 3 to 9 x 9 and/or the discretization of the stress field by biquadratic rather than bi-linear sub-elements. It should also be noted that satisfaction of the BB condition in viscoelastic flow simulations that use mixed formulations is not as clear as the case of purely viscous regimes. 

The potential energy is never known in an absolute sense but is always measured relative to some arbihary benchmark. Let us set the potential energy to zero at the equilibrium bond length, Vq = 0, which is the bottom of the potential energy well. 

Among the few systems that can be solved exactly are the particle in a onedimensional box, the hydrogen atom, and the hydrogen molecule ion Hj. Although of limited interest chemically, these systems are part of the foundation of the quantum mechanics we wish to apply to atomic and molecular theory. They also serve as benchmarks for the approximate methods we will use to treat larger systems. 

D. F. Feller, MSRC Ah Initio Methods Benchmark Suite—A Measurement of Hardware and Software Performance in the Area of Electronic Structure Methods WA Battelle Pacific Northwest Labs, Richland (1993). 

The program can be run either in a serial or parallel execution mode. Both execution modes were stable when tested on a multiprocessor Linux system. Parallel calculations can be run either on parallel computers or networked workstations. Benchmark information is available at the website listed below. 

Monuron Monzomte Moody diagram Mooney viscometer Mooney viscometers MOPAC 5.0 benchmark 4-79Mo-Permalloy Mopping asphalt Morantel [20574-50-9]... 

SPEC benchmark Special-duty propane Special effects Specialty chemicals... 

In the past, commodity chemicals were generally priced on the basis of ROl. Capital cost was the most critical item, and those elements that ate related to capital cost were the principal factors in the selling price (excluding taw material cost in some cases). On this basis, a satisfactory ROl resulted in acceptable values for other criteria such as ROS or sales margin. Many analysts favor ROS as a benchmark for comparison because it is up to date and simple and because it is increasingly difficult to determine a tme ROl based on what profits might be on plants built under indation and expensive capital and constmction costs. 

G. T. Seaborg, "Transuranium Elements, Products of Modem Alchemy," Benchmark Papers in Physical Chemisty and Chemical Physics, Vol. 1, Dowden, Hutchison Ross, Stroudsburg, Pa., 1978. 

Market prices are extremely volatile and follow cycles of advance and decline related to fluctuations ia global iaventories and world economic forces. For example, for northern bleached softwood kraft, which is considered a global benchmark pulp grade, market price went from 840/t ia 1990 down to 440/t ia 1993 as a result of oversupply and worldwide recession (3). By 1995 virtually all of the price losses had been recovered. 

D. Matheson, J. E. Matheson, and M. M. Menke, ReND Decision Quality Association Benchmarking Stuff, Strategic Decisions Group, Menlo Park, Calif., 1993. 

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