Creation of a complex butterfly attractor using a novel Lorenz-type system

A novel Lorenz-type system of nonlinear differential equations is proposed. Unlike the original Lorenz system, where the chaotic dynamics remain confined to the positive half-space with respect to the Z state variable due to a limiting threshold effect, the proposed system enables bipolar swing of this state variable. In addition, the classical set of parameters (a, b, c) controlling the behavior of the Lorenz system are reduced to a single parameter, namely a. Two possible modes of operation are admitted by the system; switching between these two modes results in the creation of a complex butterfly chaotic attractor. Numerical simulations and results from an experimental setup are presented

Experimental quantification and modelling of attrition of infant formulae during pneumatic conveying

Infant formula is often produced as an agglomerated powder using a spray drying process. Pneumatic conveying is commonly used for transporting this product within a manufacturing plant. The transient mechanical loads imposed by this process cause some of the agglomerates to disintegrate, which has implications for key quality characteristics of the formula including bulk density and wettability. This thesis used both experimental and modelling approaches to investigate this breakage during conveying. One set of conveying trials had the objective of establishing relationships between the geometry and operating conditions of the conveying system and the resulting changes in bulk properties of the infant formula upon conveying. A modular stainless steel pneumatic conveying rig was constructed for these trials. The mode of conveying and air velocity had a statistically-significant effect on bulk density at a 95% level, while mode of conveying was the only factor which significantly influenced D[4,3] or wettability. A separate set of conveying experiments investigated the effect of infant formula composition, rather than the pneumatic conveying parameters, and also assessed the relationships between the mechanical responses of individual agglomerates of four infant formulae and their compositions. The bulk densities before conveying, and the forces and strains at failure of individual agglomerates, were related to the protein content. The force at failure and stiffness of individual agglomerates were strongly correlated, and generally increased with increasing protein to fat ratio while the strain at failure decreased. Two models of breakage were developed at different scales; the first was a detailed discrete element model of a single agglomerate. This was calibrated using a novel approach based on Taguchi methods which was shown to have considerable advantages over basic parameter studies which are widely used. The data obtained using this model compared well to experimental results for quasi-static uniaxial compression of individual agglomerates. The model also gave adequate results for dynamic loading simulations. A probabilistic model of pneumatic conveying was also developed; this was suitable for predicting breakage in large populations of agglomerates and was highly versatile: parts of the model could easily be substituted by the researcher according to their specific requirements.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

Factors relating to motivation to change behaviour in individuals who are overweight: application of the health belief model

Background: Obesity is the most important health challenge faced at a global level and represents a rapidly growing problem to the health of populations. Given the escalating global health problem of obesity and its co-morbidities, the need to re-appraise its management is more compelling than ever. The normalisation of obesity within our society and the acceptance of higher body weights have led to individuals being unaware of the reality of their weight status and gravity of this situation. Recognition of the problem is a key component of obesity management and it remains especially crucial to address this issue. A large amount of research has been undertaken on obesity however, limited research has been undertaken using the Health Belief Model. Aim: The aim of the research was to determine factors relating to motivation to change behaviour in individuals who perceive themselves to be overweight and investigate whether the constructs of the Health Belief Model help to explain motivation to change behaviour. Method: The research design was quantitative, correlational and cross-sectional. The design was guided by the Health Belief Model. Data Collection: Data were collected online using a multi-section and multi-item questionnaire, developed from a review of the theoretical and empirical research. Descriptive and inferential statistical analyses were employed to describe relationships between variables. Sample: A sample of 202 men and women who perceived themselves to be overweight participated in the research. Results: Following multivariate regression analysis, perceived barriers to weight loss and perceived benefits of weight loss were significant predictors of motivation to change behaviour. The perceived barriers to weight loss which were significant were psychological barriers to weight loss (p =<0.019) and environmental barriers to physical activity (p=<0.032).The greatest predictor of motivation to change behaviour was the perceived benefits of weight loss (p<0.001). Perceived susceptibility to obesity and perceived severity of obesity did not emerge as significant predictors in this model. Total variance explained by the model was 33.5%. Conclusion: Perceived barriers to weight loss and perceived benefits of weight loss are important determinants of motivation to change behaviour. The current study demonstrated the limited applicability of the Health Belief Model constructs to motivation to change behaviour, as not all core dimensions proved significant predictors of the dependant variable.