Supercomputer approach

Before the advent of modem computer-aided mathematics, most mathematical models of real chemical processes were so idealized that they had severely limited utility— being reduced to one dimerrsion and a few variables, or Unearized, or limited to simplified variability of parameters. The increased availability of supercomputers along with progress in computational mathematics and numerical functional analysis is revolutionizing the way in which chemical engineers approach the theory and engineering of chemical processes. The means are at hand to model process physics and chenustry from the... 

One example of such a new approach is the hypercube architecture, in which many processors are linked together as a team to solve a single problem. A well-integrated team of cheap processing units can potentially outperform the most sophisticated single-processor machine. In addition, since each processor can have its own dedicated memory, the total system can have both more memory than current supercomputers and more memory in use at any given moment. 

One Important aspect of the supercomputer revolution that must be emphasized Is the hope that not only will It allow bigger calculations by existing methods, but also that It will actually stimulate the development of new approaches. A recent example of work along these lines Involves the solution of the Hartree-Fock equations by numerical Integration In momentum space rather than by expansion In a basis set In coordinate space (2.). Such calculations require too many fioatlng point operations and too much memory to be performed In a reasonable way on minicomputers, but once they are begun on supercomputers they open up several new lines of thinking. 

Consistently, the agreement with experiment is about 1% for geometric parameters and 5-10% for force constants. On the other hand, binding energies are found to be usually too large by l-2eV per atom. The computational efforts in the LDF approach scale with the third power in the number of orbitals. Consequently, the speed and memory capabilities of supercomputers will allow the study of systems with a hundred atoms and more. 

Time scales for various motions within biopolymers (upper) and nonbiological polymers (lower). The year scale at the bottom shows estimates of when each such process might be accessible to brute force molecular simulation on supercomputers, assuming that parallel processing capability on supercomputers increases by about a factor of 1,000 every 10 years (i.e., one order of magnitude more than Moore s law) and neglecting new approaches or breakthroughs. Reprinted with permission from H.S. Chan and K. A. Dill. Physics Today, 46, 2, 24, (1993). 

Contemporary computer-assisted molecular simulation methods and modern computer technology has contributed to the actual numerical calculation of solvent effects on chemical reactions and molecular equilibria. Classical statistical mechanics and quantum mechanics are basic pillars on which practical approaches are based. On top of these, numerical methods borrowed from different fields of physics and engineering and computer graphics techniques have been integrated into computer programs running in graphics workstations and modem supercomputers (Zhao et al., 2000). 

The description of electron motion and electronic states that is at the heart of all of chemistry is included in wave function theory, which is also referred to as self-consistent-field (SCF) or, by honouring its originators, Hartree-Fock (HF) theory [7]. In principle, this theory also includes density functional theory (DFT) approaches if one uses densities derived from SCF densities, which is common but not a precondition [2] therefore, we treat density functional theory in a separate section. Many approaches based on wave function theory date back to when desktop supercomputers were not available and scientists had to reduce the computational effort by approximating the underlying equations with data from experiment. This approach and its application to the elucidation of reaction mechanisms are outlined in Section 7.2.3. 

Now the technique provides the basis for simulating concentrated suspensions at conditions extending from the diffusion-dominated equilibrium state to highly nonequilibrium states produced by shear or external forces. The results to date, e.g., for structure and viscosity, are promising but limited to a relatively small number of particles in two dimensions by the demands of the hydrodynamic calculation. Nonetheless, at least one simplified analytical approximation has emerged [44], As supercomputers increase in power and availability, many important problems—addressing non-Newtonian rheology, consolidation via sedimentation and filtration, phase transitions, and flocculation—should yield to the approach. 

Most of the present discussion has been concerned with applications of REPs within the framework of otherwise essentially orbital-based calculations. On the other hand, a recent application 110) involved a quantum Monte Carlo (QMC) procedure. [A useful overview of Monte Carlo electronic structure work has been given by Ceperly and Alder 111). ] Currently, QMC offers little, if any, competition for conventional calculations in that the computer time required to reduce statistical errors to acceptable limits increases rapidly as a function of atomic number and is excessive for all but the smallest systems. Recent fluorine calculations required nearly 100 hours of supercomputer time 112). Although, on the surface, it would appear totally impractical, the appeal of this approach in the context of heavy-element work is its avoidance of extensive basis sets and enormous configuration expansions that plague present studies. 

The descriptive, classificatory and comparative approach to analysis of structures also depends on computing. It is no longer feasible to pursue these studies with physical models. Beyond the obvious mechanical problems, there is the logistical catastrophe the amount of space and materiel increases linearly with the number of structures to be examined. In addition, there is no way to save and restore structures. It is therefore necessary to apply computer graphics to draw representations of structures. The importance of supercomputers in studies of this kind will lie not only in the feasibility of large calculations that are rot possible at present, but in the conversion of many tasks from batch mode to interactive. 

Many current models treat ventilation loss based on the assumption of a well-mixed space. Furtaw et al. (1996) conducted experiments with pre-set ventilation rates and constant source strengths. These authors showed that rooms with high ventilation rates behave as well-mixed spaces, and that the ventilation rate accurately accounts for steady-state levels and ventilation loss when the source is turned off. At lower ventilation rates, mixing is not uniform and concentrations near the source deviate from those further away. However, once the source is turned off, the ventilation rate accurately accounts for the observed decrease in air concentration. The assumption of a well-mixed room is questionable in the case in which there are few activities and no mixing of air currents. In such cases, diffusion and multiple-zone models can be used to more realistically capture spatial heterogeneity (Furtaw et al., 1996 Nicas, 1996, 1998). Another approach for estimation is a fluid dynamics model utilizing a supercomputer (Matoba et al., 1994a). 

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