Features of Computer Simulations

The kinetic scheme used in the computer simulations of this thesis is meant to represent a TR-SP-PLP experiment at zero percent conversion in bulk, and comprises the following reactions  

Ray [34] has discussed several different methodologies (also analytical ones) for calculation of MWDs. A more recent, though very brief discussion on simulation techniques can be found in [35] with particular attention for the commercial package PREDICI. Rees [36] has discussed several aspects of numerical simulations in more detail. 

The subscript g- is added to all radical concentrations to indicate that these are coarse grained populations thus denotes the total radical concentration in grain number /. 

With respect to the termination reaction, the lUPAC preferred factor 2 is used to describe the bimolecular termination reaction [42, 43]. However, although not common practice for general kinetic equations [e.g. 44], this prefactor was used for both i-i reactions as well as for i-j reactions  

The origin of the factor 2 in equation 3.12 lies in the fact that 2 identical radicals disappear simultaneously from the reaction mixture, where the factor 2 in equation 3.13 is a permutation factor. This latter factor arises as an /-mer can encounter ay-mer or the other way around, ay -mer encountering an /-mer. The advantage of this notation is the termination rate coefficient now only relates to the rate of diffusion and not to stoichiometric (or other) factors. In other words, if i equals j, then the rate coefficient k / and kl - are identical, which would not be the case if the above notation would not be used. 

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But a computer simulation is more than a few clever data structures. We need algorithms to manipulate our system. In some way, we have to invent ways to let the big computer in our hands do things with the model that is useful for our needs. There are a number of ways for such a time evolution of the system the most prominent is the Monte Carlo procedure that follows an appropriate random path through configuration space in order to investigate equilibrium properties. Then there is molecular dynamics, which follows classical mechanical trajectories. There is a variety of dissipative dynamical methods, such as Brownian dynamics. All these techniques operate on the fundamental degrees of freedom of what we define to be our model. This is the common feature of computer simulations as opposed to other numerical approaches. 

Single crystals of /S-A1203 are essentially two dimensional conductors. The conducting plane has hexagonal symmetry (honeycomb lattice). This characteristic feature made -alumina a useful model substance for testing atomistic transport theory, for example with the aid of computer simulations. Low dimensionality and high symmetry reduce the computing time of the simulations considerably (e.g., for the calculation of correlation factors of solid solutions). 

Thus this feature is extremely useful with electrolyte systems, reducing the number of computer simulations necessary to find the correct control strategy. With this design to specifications feature, FRACHEM/ECES has been used to determine a proper caustic injection rate to reduce the ammonia and hydrogen sulfide concentrations to meet EPA specifications without inordinate amounts ot stripping steam. 

As announced above these findings are in astonishing agreement with the heuristic pictures of the diffusion mechanism discussed in the framework of some microscopic diffusion models. But, besides being free of the conceptual drawbacks (the ad hoc assumptions) of the classical diffusion models, the MD method of computer simulation of diffusion in polymers makes it possible to get an even closer look at the diffusion mechanism and explain from a true atomistic level well known experimental findings. For example the results reported in (119,120) on the hopping mechanism reveal the following additional features. 

It is thus apparent from the simple but quite feasible example of the tank liquid level system that stiffness can easily become a significant feature of the simulation of a process plant. While stiffness in such a small simulation as this will not cause a major computational burden, stiffness in a larger process plant system will result in a very significant slowing of the integration, and special measures need to be taken to counter its influence. 

In spite of appealing features, the Gaussian approximation has a very serious defect it predicts a size exponent v = 2/d which is too big, in contradiction to the results of computer simulations and experiments for real polymers. 

A remarkable feature of van der Waals equation is its ability to calculate with reasonable accuracy the volumes of both liquid and vapour phases at equilibrium. This property made it attractive for some technical calculations, but a real breakthrough arrived only because of computer simulation. Slightly modifications have shown a surprising capacity to be adapted to various applications. 

The selection of streams is determinant for efficient heat integration. Most of the studies are based on results issued from a process simulator. Automatic transfer of data to the Pinch software is a current feature of many simulation systems, commonly called data extraction , which sometimes is assisted by an expert system. However, the user should be aware about possible problems in heat integration caused by inappropriate stream extraction, even if it is computer-assisted. Hereafter some recommendations ... 

Two major classical simulation techniques, molecular dynamics and Monte Carlo, have been applied to simulation of water-metal interfaces. We first discuss features common to both methodologies and then describe aspects unique to each. The field of computer simulations is an actively evolving one, despite being more than 40 years old. Even for the particular case of water-metal interfaces, many variations exist on the central theme of how best to carry out these calculations. In this chapter, we limit our discussion to the most significant (in our opinion) techniques in use for metal-water interfaces. 

Of course such observables only yield a rather indirect information on the nuclear equation of state. Early investigations of the supernova required a soft equation of state characterized by a compressibility as low as K 140 MeV. A stiffer EOS would not allow sufficient energy to be stored during the collapse such that the subsequent explosion would not reach the surface. Taking into account additional features like effects of neutron heating, a different composition or a rotation of the progenitor star may allow for a supernova even with a stiffer EOS. On the other hand it turned out that also the comparison of experimental data of relativistic heavy ion collisions with corresponding results of computer simulations does not provide a unique answer for the properties of the EOS. Early calculations seemed to show a preference for a stiff EOS with a compressibility as... 

This article describes stochastic computer simulations of the local segmental dynamics of synthetic polymers. Particular attention is given to local dynamics in solution. Related work involving experimental methods, analytical theory, and molecular dynamics simulations will also be discussed. An introduction to the concepts involved in stochastic simulations will be presented. Methods of characterizing local segmental dynamics will also be described. The main portion of the article describes various features of the simulated dynamics. The approximations inherent in stochastic approaches and their influence on the observed dynamics will be discussed. Issues of cooperativity in conformational transitions will be highlighted. 

Over the past decade or so there have been several significant advances both in experimental techniques, and in the power of computer simulation, that have led to an ongoing reappraisal of our understanding of pol5uner crystallization. In the following, some attempt is made to outline the most significant features of these new ideas and to point the interested reader toward the literature. 

The status of computer simulations of electric double layers is briefly summarized and a road map for solving the important problems in the atomic scale simulation of interfacial electrochemical processes is proposed. As examples efforts to simulate screening in electric double layers are described. Molecular dynamics simulations on systems about 4 nm thick, containing up to 1600 water molecules and NaQ at IM to 3M concentration, displayed the main features of double layers at charged metal surfaces including bulk electrolyte zone, diffuse ionic layer that screens the charge on the electrode and a layer of oriented water next to the surface. 

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