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- Author or Editor: L. Vincent x
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It has been shown that the ESS Maximum Principle, used to find evolutionarily stable strategies, is applicable to a large class of population dynamic models. These include both differential and difference equation models. To date, this principle has been used to find an evolutionarily stable strategy (ESS) for single-stage systems. That is, systems in which the density of all individuals of a given species or phenotype are represented by a scalar. There are many situations in which more detail is needed in order to properly model the state of a system (e.g. within a given species or phenotype, juveniles may effect the fitness of adults and vice versa). In this case, the density of a species or phenotype is more properly represented by a vector. Each component of the vector represents the density of a particular life stage. We show here that the ESS Maximum Principle may be extended to include multistage systems in a very natural way. In the scalar case, we have used a scalar G-function (fitness generating function) to model the system and formulate the ESS Maximum Principle. We have shown that it is necessary for the G-function, when evaluated at equilibrium, to take on a maximum with respect to the ESS strategy. Here we show, for multistage systems that a G-matrix may be used to model the system and the ESS Maximum Principle may be stated in terms of a G-matrix. In this case the real part of the dominant eigenvalue of the G-matrix, when evaluated at equilibrium, must take on a maximum with respect to the ESS strategy. Two multistage examples are given to illustrate use of the theory.
Abstract
In the case of a complex mechanism of two parallel independent reactions, peak maximum evolution methods and model-fitting methods give only a mean value of the kinetic parameters, while isoconversional methods are useful to describe the complexity of the mechanism. Isothermal and non-isothermal isoconversional methods can be used to elucidate the kinetics of the process. Nevertheless, isothermal isoconversional methods can be limited by restrictions on the temperature regions experimentally available because of duration times or detection limits.
Abstract
The fracture toughness of blends of polypropylene terephthalate (PPT) with polyethylene terephthalate (PET) and polybutylene terephthalate (PBT) were investigated. Binary blends were prepared comprising 10:90, 30:70, 50:50, 70:30 and 90:10 mass/mass%. The fracture toughness was determined for each blend using the essential work of fracture (EWF) method and thin film double edge notched tension (DENT) specimens. The specific essential work of fracture, w e, values obtained for blends of PET/PPT ranged from 27.33 to 37.38 kJ m–2 whilst PBT/PPT blends yielded values ranging from 41.78 to 64.23 kJ m–2. Differential scanning calorimetry (DSC) was employed to assess whether or not crystallinity levels influence the mechanical properties evaluated. The fracture toughness of PPT deteriorated with PET incorporation. However, high we values exceeding that of pure PPT were obtained for PBT/PPT blends across the composition range studied.
Abstract
The essential work of fracture (EWF) method has been used to study the relationship between molecular structure and thin film fracture toughness for three ductile polyesters at ambient temperature. The fracture toughness of PPT is of particular interest. Successful fracture characterisation of thin film polyesters has been achieved by the EWF method using double edge notched tension (DENT) specimens. The specific essential work of fracture, w e, for polyethylene terephthalate (PET), polypropylene terephthalate (PPT) and polybutylene terephthalate (PBT) films is found to be 35.542.56, 41.033.23 and 31.348.60 kJ m–2, respectively. Differential scanning calorimetry (DSC) has been employed to investigate the crystallinity of the polymers concerned and the effect of this on their EWF values.
