Superiority

Predictions for the other isobaric systems (experimental data of Sinor, Steinhauser, and Nagata) show good agreement. Excellent agreement is obtained for the system carbon tetrachlor-ide-methanol-benzene, where the binary data are of superior quality. 

Equation (7-8). However, for liquid-liquid equilibria, the equilibrium ratios are strong functions of both phase compositions. The system is thus far more difficult to solve than the superficially similar system of equations for the isothermal vapor-liquid flash. In fact, some of the arguments leading to the selection of the Rachford-Rice form for Equation (7-17) do not apply strictly in the case of two liquid phases. Nevertheless, this form does avoid spurious roots at a = 0 or 1 and has been shown, by extensive experience, to be marltedly superior to alternatives. 

At present time, metal-ceramic technology is quite expensive and its superior performance pays only in specific applications. 

For special applications such as air coupled testing a special programmable transmitter board was developed. This transmitter generates rectangular and burst signals, which increase the acoustical power in an optimized frequency range, and provides a superior signal-to-noise ratio. 

The water quality (air content) and the water flow influenced the measurements using one channel. Therefore the four channel system was first tested in the laboratory with a stationary tube. The best results were obtained using tap water and a well controlled flow in a water-filled chamber. A great difference in the concentration of air in the different grades of water was obvious, and the tap water was superior to soft water during these measurements. 

The situation is complicated, however, because some of the drag on a skidding tire is due to the elastic hysteresis effect discussed in Section XII-2E. That is, asperities in the road surface produce a traveling depression in the tire with energy loss due to imperfect elasticity of the tire material. In fact, tires made of high-elastic hysteresis material will tend to show superior skid resistance and coefficient of friction. 

Sonoelectrochemistry has been employed in a number of fields such as in electroplating for the achievement of deposits and films of higher density and superior quality, in the deposition of conducting polymers, in the generation of highly active metal particles and in electroanalysis. Furtlienuore, the sonolysis of water to produce hydroxyl radicals can be exploited to initiate radical reactions in aqueous solutions coupled to electrode reactions. 

These various techniques were recently applied to molecular simulations [11, 20]. Both of these articles used the rotation matrix formulation, together with either the explicit reduction-based integrator or the SHAKE method to preserve orthogonality directly. In numerical experiments with realistic model problems, both of these symplectic schemes were shown to exhibit vastly superior long term stability and accuracy (measured in terms of energy error) compared to quaternionic schemes. 

When considering the construction of exactly symmetric schemes, we are obstructed by the requirement to find exactly symmetric approximations to exp(—ir/f/(2fi,)). But it is known [10], that the usual stepsize control mechanism destroys the reversibility of the discrete solution. Since we are applying this mechanism, we now may use approximations to exp —iTH/ 2h)) which are not precisely symmetric, i.e., we are free to take advantage of the superior efficiency of iterative methods for evaluating the matrix exponential. In the following, we will compare three different approaches. 

In most cases, this Lanczos-based technique proves to be superior to the Chebyshev method introduced above. It is the method of choice for the application problems of class 2b of Sec. 2. The Chebyshev method is superior only in the case that nearly all eigenstates of the Hamiltonian are substantially occupied. 

The work presented in this paper was the result of the joint effort with the following colleagues. For the simulations on catalysis Simonetta larlori (IBM Italy), Franco Buda (Scuola NormaJe Superiore, Pisa, Italy) and Gerard van Doremaele (DSM Research) were involved. For the work on polyethylene the simulations were performed by Joost Hageman, with help from Martina Heinemann and Rob de Groot (all University of Nijmegen, The Netherlands). 

Besides structure and substructure searches, Gmclin provides a special search strategy for coordiuation compouuds which is found in no other database the ligand search system, This superior search method gives access to coordination compounds from a completely different point of view it is possible to retrieve all coordination compounds with the same ligand environment, independently of the central atom or the empirical formula of the compound. 

While INDO calciilaiioii s have more pariuiieiers an d are som ewh ill more complex that CXDO ciilciilatioim. they require csseii tiiilly no extra computation time and in most siluiilions they are superior to CNDO ciilculatioiis. 

In a united atomforce field the van der Waals centre of the united atom is usually associated v ilh the position of the heavy (i.e. non-hydrogen) atom. Thus, for a united CH3 or CH2 group the vem der Waals centre would be located at the carbon atom. It would be more accurate to associate the van der Waals centre with a position that was offset slightly from the carbon position, in order to reflect the presence of the hydrogen atoms. Toxvaerd has developed such a model that gives superior performance for alkemes than do the simple united atom models, particularly for simulations at high pressures [Toxvaerd 1990]. In... 

Sutton and Chen extended the potential to longer range to enable the study of certain problems such as the interactions between clusters of afoms [Sutton and Chen 1990]. Their objective was to combine the superior Fiimis-Sinclair description of short-range interactions with a van der Waals tail to model the long-range interactions. The form of the Sutton-Chen potential is ... 

This study shows that the steepest descent method can actually be superior to conjugate gradients when the starting structure is some way from the minimum. However, conjugate gradients is much better once the initial strain has been removed. 

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