Loose modelling techniques

On the whole, loose modelling techniques tend to be very easy to implement, but their synthesis parameters are not straightforward to control because they bear little relation to the acoustic world. Computer technology also inspired a few loose modelling techniques, such as Walsh synthesis and synthesis by binary instruction. 

Loose modelling techniques (discussed in Chapter 2) tend to provide synthesis parameters that bear little relation to the acoustic world. They are usually based entirely upon conceptual mathematical formulae. It is often difficult to predict the outcome and to explore the potential of a loose model. Frequency modulation (FM) is a typical example of loose modelling. FM is a powerful technique and extremely easy to program but difficult to operate computer simulations of Yamaha s acclaimed DX7 synthesiser, for example, are relatively easy to implement on a computer. Nevertheless, it is apparent that the relationship between a timbre and its respective synthesis parameters is far from intuitive. Apart from John Chowning, the inventor of FM synthesis, only a few people have managed to master the operation of this technique. 

Almost every method, from the most dense and formal ones to those based on the most loosely defined sketches and drawings, stakes a claim to being abstract. The formal ones have a precise idea of what kinds of things are omitted in the abstraction and exactly what it means to correctly implement that abstraction they also share our idea of a conformance relation with a justification Refinement is a well-established technique in the formal methods community. The ideas of protocol refinement and data reification (model or state refinement) have been separately but quite thoroughly worked out elsewhere. 

The present text is aimed partly at chemists, to encourage more of us to be less afraid of the mathematics, but also with the hope of catching the attention of mathematicians, engineers, etc., who should find that the chemical world offers exemplary non-linearities which can be realized in practice as well as in numero. The book is loosely divided into two unequal parts. The main thrust is to introduce a variety of the techniques used by the non-linear kineticist, with special attention to particularly simple model schemes. This part encompasses chapters 2 to 13. Other readers may prefer to begin with real experimental results, and these are presented in chapters 14 and 15. 

Abstract. The synthesis and study of dendrimers has been truly dramatic in the last ten years. This review gives a brief introduction to some of the key concepts and main synthetic strategies in dendrimer chemistry. The focus of the chapter is a survey of modern analytical techniques and physical characterization of dendrimers. Results of model calculations and experiments probing the dimensions and conformation of dendrimers are reviewed. In the final sections the experimental work on dendrimer-polymer hybrids is highlighted. The dense spherical conformation of dendrimers has been combined with the loose random-coil conformation of ordinary polymers to form new hybrids with potentially interesting new properties. 

Molecular mechanics is a simple technique for scanning the potential energy surface of a molecule, molecular ion, crystal lattice or solvate. The model is based on a set of functions which may or may not be based on chemical and physical principles. These functions are parameterized based on experimental data. That is, the potential energy surface is not computed by fundamental theoretical expressions but by using functions whose parameters are derived empirically by reproducing experimentally observed data. Molecular mechanics then is, similar to a neural network, completely dependent on the facts that it has been taught. The quality of results to be obtained depends on the choice of the experimental data used for the parameterization. Clearly, the choice of potential energy functions is also of some importance. The most common model used is loosely derived from... 

Fig. 4. Technique for monitoring platelet aggregation in the partially obstructed left circumflex coronary artery of the dog. Electromagnetic flow probes measure blood flow. Partial obstruction of the coronary artery with a plastic Lexan cylinder results in episodic cyclical reductions in coronary blood flow that are due to platelet-dependent thrombus formation. Every 2-3 mm the thrombus must be mechanically shaken loose to restore blood. For detailed application of the Folts model, see Sullivan et al. (1992) Folts, Rowe (1974, 1988) and Folts et al. (1976, 1982).

In solution, the H-NMR spectra of la-MeCN and la-2MeCN did not give separate resonances for included MeCN and free MeCN. Therefore, a rapid equilibrium between included MeCN and free MeCN in solution is expected. Even in the solid state, the included MeCN is only loosely bound in the calixarene cavity and it can be completely removed in vacuo (0.1 mm Hg) in one day. However, the structure is important as a model for the calixarene part of the more complex molecules described below which, though they were often obtained in crystalline form, always failed to diffract sufficiently to allow X-ray structure determination. Instead it is necessary to rely on spectroscopic techniques, comparing the NMR spectra with that of the parent calixarene whose structure is known (Figure 1). 

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