Three-phase search

In a binary diagram the position of the three-phase line can be calculated utilising a method whereby the step size is changed when a phase boundary is reached. For example, the calculation begins with an alloy in the (a 4- 0) phase held. The temperature is increased by 10°C steps and its composition maintained so that it exists in the (a + 0) phase field. At each new step the stability of the liquid is checked. Once the liquid becomes stable the previous temperature is used as a start point and the temperature step is decreased. This process is repeated with subsequent decreased step sizes until a the temperature is defined within a critical step size. This method is cumbersome and more intelligent searching routines can be used. But in the end the temperature will be defined within a critical step size. Alternatively, the temperature where the activity/chemical potential of A and B in the three phases is equal can be explicitly calculated. 

Once the IND application is accepted, three phases of human trials must be conducted. Phase I studies are typically performed on a small number of normal subjects, usually not more than 30 volunteers, generally by clinical pharmacologists. The purpose of the phase I smdy is to determine the metabolism of the drug in humans and a safe dosage range, and to search for any extremely common toxic effects that were not detected in the prior animal studies. 

In order to search for the optimum, the relations between variables must be given to an optimization algorithm. This is here provided by the model equations developed by Mariano et al. [3]. The model calculates all mass and heat transfers, besides the hydrogenation reaction rate. Since there are three phases (the catalysts is solid, the hydrogen is a gas and the o-cresol is liquid), both reactants must come to the solid pores, where the reaction takes place, and the unreacted reactants and the reaction product must then leave the catalyst particle. All these phenomena are accounted for by partial differential equations for mass and energy balances for each component in each phase. 

Scaling theory can be used to design microemulsions for important applications such as enhanced oil recovery. The salinities of brines in oil reservoirs range from potable to saturated at elevated temperature and pressure. When a reservoir of high salinity has been flooded previously with fresh water, the brine salinity can also vary greatly within the reservoir. To find a suitable surfactant requires a laborious search for a formulation with the correct optimal salinity for each reservoir. Thus (see Fig. 16.8), there has been a desire to find a surfactant that would form three phases over the broadest range of salinities and have ultralow interfacial tensions for those phases at the same time. However, there are thermodynamic limits on the extent to which these goals can be simultaneously met. 

An accident investigation is a search process and can only partly be planned in advance. It is thus recommended that the SMORT analysis of an accident is divided into different phases and that the procedure above is repeated for each phase. A full SMORT analysis may involve three phases levels 1 plus 2 level 3 and finally level 4. The report from one phase is used as input to the SMORT analyses in subsequent phases. 

The traditional approach to SS has been the "three phase" search. The first step Involves some form of full structure screen in which from several hundred to a thousand or more precalculated screen bits are used to quickly eliminate 90 to 99.9 percent of the structures. This is generally followed by a step in which candidate atoms are located in the remaining structures for each substructure atom and finally, an atom by atom mapping of the substructure into the structure is performed. 

DENDRAL followed a three-stage procedure. In the first phase, the so-called plan, prior knowledge, and heuristics were used to deduce a set of constraints. Constraints could be, for example, the exemption of large sets of candidate solutions or the suggestion for a extensive search over limited classes of solutions. 

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