Unsteady natural convection within a porous enclosure of sinusoidal corrugated side walls

Numerically investigation of free convection within a porous cavity with differential heating has been performed using modified corrugated side walls. Sinusoidal hot left and cold right walls are assumed to receive sudden differentially heating where top and bottom walls are insulated. Air is considered as working fluid and is quiescent, initially. Numerical experiments reveal 3 distinct stages of developing pattern including initial stage, oscillatory intermediate and finally steady state condition. Implicit Finite Volume Method with TDMA solver is used to solve the governing equations. This study has been performed for the Rayleigh numbers ranging from 100 to 10,000. Outcomes have been reported in terms of isotherms, streamline, velocity and temperature plots and average Nusselt number for various Ra, corrugation frequency and corrugation amplitude. The effects of sudden differential heating and its resultant transient behavior on fluid flow and heat transfer characteristics have been shown for the range of governing parameters. The present results show that the transient phenomena are enormously influenced by the variation of the Rayleigh Number with corrugation amplitude and frequency.

Insight into the fractional calculus via a spreadsheet

Many students of calculus are not aware that the calculus they have learned is a special case (integer order) of fractional calculus. Fractional calculus is the study of arbitrary order derivatives and integrals and their applications. The article begins by stating a naive question from a student in a paper by Larson (1974) and establishes, for polynomials and exponential functions, that they can be deformed into their derivative using the μ-th order fractional derivatives for 0<μ<1. Through the power of Excel we illustrate the continuous deformations dynamically through conditional formatting. Some applications are discussed and a connection made to mathematics education.

The renormalization group: A perturbation method for the graduate curriculum

In this paper the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. Lett., 73 (1994), pp.1311-1315; Phys. Rev. E, 54 (1996), pp.376-394] is presented in a pedagogical way to increase its visibility in applied mathematics and to argue favorably for its incorporation into the corresponding graduate curriculum.The method is illustrated by some linear and nonlinear singular perturbation problems. Key word. © 2012 Society for Industrial and Applied Mathematics.

The renormalization group and the implicit function theorem for amplitude equations

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

Secular series and renormalization group for amplitude equations

We have developed a technique that circumvents the process of elimination of secular terms and reproduces the uniformly valid approximations, amplitude equations, and first integrals. The technique is based on a rearrangement of secular terms and their grouping into the secular series that multiplies the constants of the asymptotic expansion. We illustrate the technique by deriving amplitude equations for standard nonlinear oscillator and boundary-layer problems. © 2008 The American Physical Society.

The story of the men’s white shirt

The classic white dress shirt is familiar and omnipresent in men’s fashion. As a result, we tend to be unaware that for more than 200 years this singular item of apparel, which is essentially unadulterated in form from the late 19th century, has been able to define and represent status, wealth and fashion norms. The history underlying this garment is rich and, in the main part, untold.

Including nonequilibrium interface kinetics in a continuum model for melting nanoscaled particles

The melting temperature of a nanoscaled particle is known to decrease as the curvature of the solid-melt interface increases. This relationship is most often modelled by a Gibbs--Thomson law, with the decrease in melting temperature proposed to be a product of the curvature of the solid-melt interface and the surface tension. Such a law must break down for sufficiently small particles, since the curvature becomes singular in the limit that the particle radius vanishes. Furthermore, the use of this law as a boundary condition for a Stefan-type continuum model is problematic because it leads to a physically unrealistic form of mathematical blow-up at a finite particle radius. By numerical simulation, we show that the inclusion of nonequilibrium interface kinetics in the Gibbs--Thomson law regularises the continuum model, so that the mathematical blow up is suppressed. As a result, the solution continues until complete melting, and the corresponding melting temperature remains finite for all time. The results of the adjusted model are consistent with experimental findings of abrupt melting of nanoscaled particles. This small-particle regime appears to be closely related to the problem of melting a superheated particle.

Frequency-motivated observer design for the prediction of parametric roll resonance control applications in marine systems

This work deals with estimators for predicting when parametric roll resonance is going to occur in surface vessels. The roll angle of the vessel is modeled as a second-order linear oscillatory system with unknown parameters. Several algorithms are used to estimate the parameters and eigenvalues of the system based on data gathered experimentally on a 1:45 scale model of a tanker. Based on the estimated eigenvalues, the system predicts whether or not parametric roll occurred. A prediction accuracy of 100% is achieved for regular waves, and up to 87.5% for irregular waves.

Injury narrative text classification : a preliminary study

Description of a patient's injuries is recorded in narrative text form by hospital emergency departments. For statistical reporting, this text data needs to be mapped to pre-defined codes. Existing research in this field uses the Naïve Bayes probabilistic method to build classifiers for mapping. In this paper, we focus on providing guidance on the selection of a classification method. We build a number of classifiers belonging to different classification families such as decision tree, probabilistic, neural networks, and instance-based, ensemble-based and kernel-based linear classifiers. An extensive pre-processing is carried out to ensure the quality of data and, in hence, the quality classification outcome. The records with a null entry in injury description are removed. The misspelling correction process is carried out by finding and replacing the misspelt word with a soundlike word. Meaningful phrases have been identified and kept, instead of removing the part of phrase as a stop word. The abbreviations appearing in many forms of entry are manually identified and only one form of abbreviations is used. Clustering is utilised to discriminate between non-frequent and frequent terms. This process reduced the number of text features dramatically from about 28,000 to 5000. The medical narrative text injury dataset, under consideration, is composed of many short documents. The data can be characterized as high-dimensional and sparse, i.e., few features are irrelevant but features are correlated with one another. Therefore, Matrix factorization techniques such as Singular Value Decomposition (SVD) and Non Negative Matrix Factorization (NNMF) have been used to map the processed feature space to a lower-dimensional feature space. Classifiers with these reduced feature space have been built. In experiments, a set of tests are conducted to reflect which classification method is best for the medical text classification. The Non Negative Matrix Factorization with Support Vector Machine method can achieve 93% precision which is higher than all the tested traditional classifiers. We also found that TF/IDF weighting which works well for long text classification is inferior to binary weighting in short document classification. Another finding is that the Top-n terms should be removed in consultation with medical experts, as it affects the classification performance.

Novel solutions for a model of wound healing angiogenesis

We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al (2000 IMA J. Math. App. Med. 17 395–413) assuming two conjectures hold. In the previous work, the authors showed that for certain parameter values, a heteroclinic orbit in the phase plane representing a smooth travelling wave solution exists. However, upon varying one of the parameters, the heteroclinic orbit was destroyed, or rather cut-off, by a wall of singularities in the phase plane. As a result, they concluded that under this parameter regime no travelling wave solutions existed. Using techniques from geometric singular perturbation theory and canard theory, we show that a travelling wave solution actually still exists for this parameter regime. We construct a heteroclinic orbit passing through the wall of singularities via a folded saddle canard point onto a repelling slow manifold. The orbit leaves this manifold via the fast dynamics and lands on the attracting slow manifold, finally connecting to its end state. This new travelling wave is no longer smooth but exhibits a sharp front or shock. Finally, we identify regions in parameter space where we expect that similar solutions exist. Moreover, we discuss the possibility of more exotic solutions.

Canards in advection-reaction-diffusion systems in one spatial dimension

This thesis contains a mathematical investigation of the existence of travelling wave solutions to singularly perturbed advection-reaction-diffusion models of biological processes. An enhanced mathematical understanding of these solutions and models is gained via the identification of canards (special solutions of fast/slow dynamical systems) and their role in the existence of the most biologically relevant, shock-like solutions. The analysis focuses on two existing models. A new proof of existence of a whole family of travelling waves is provided for a model describing malignant tumour invasion, while new solutions are identified for a model describing wound healing angiogenesis.

Epistemological lens : birth, death and ecology of documentary practices

This paper considers the epistemological life cycle of the camera lens in documentary practices. The 19th century industrial economies that manufactured and commercialised the camera lens have engendered political and economic contingencies on documentary practices to sustain a hegemonic and singular interpretive epistemology. Colonial documentary practices are considered from the viewpoint of manipulative hegemonic practices - all of which use the interpretive epistemology of the camera lens to capitalise a viewpoint which is singular and possesses the power to sustain its own status and economic privilege. I suggest that decolonising documentary practices can be nurtured in what Boaventura de Sousa Santos proposes as an 'ecology of knowledges' (Andreotti, Ahenakew, & Cooper 2011) - a way of including the epistemologies of cultures beyond the 'abyssal' (Santos), outside the limits of epistemological dominance. If an 'epistemicide' (Santos) of indigenous knowledges in the dominant limits has occurred then in an ecology of knowledges the limits become limitless and what were once invisible knowledges, come into their own ontological and epistemological being: as free agents and on their own terms. In an ecology of knowledges, ignorance and blindness may still exist but are not privileged. The decolonisation of documentary practices inevitably destabilises prevailing historicities and initiates ways for equal privilege to exist between multiple epistemologies.

Butterfly catastrophe for fronts in a three-component reaction–diffusion system

We study the dynamics of front solutions in a three-component reaction–diffusion system via a combination of geometric singular perturbation theory, Evans function analysis, and center manifold reduction. The reduced system exhibits a surprisingly complicated bifurcation structure including a butterfly catastrophe. Our results shed light on numerically observed accelerations and oscillations and pave the way for the analysis of front interactions in a parameter regime where the essential spectrum of a single front approaches the imaginary axis asymptotically.

Stability analysis of STATCOM in distribution networks

This chapter presents the stability analysis based on bifurcation theory of the distribution static compensator (DSTATCOM) operating both in current control mode as in voltage control mode. The bifurcation analysis allows delimiting the operating zones of nonlinear power systems and hence the computation of these boundaries is of interest for practical design and planning purposes. Suitable mathematical representations of the DSTATCOM are proposed to carry out the bifurcation analyses efficiently. The stability regions in the Thevenin equivalent plane are computed for different power factors at the Point of Common Coupling (PCC). In addition, the stability regions in the control gain space are computed, and the DC capacitor and AC capacitor impact on the stability are analyzed in detail. It is shown through bifurcation analysis that the loss of stability in the DSTATCOM is in general due to the emergence of oscillatory dynamics. The observations are verified through detailed simulation studies.

Patient perspectives of using a web based intervention program for patients with type 2 diabetes and acute coronary syndrome

Introduction Research highlights patients with dual diagnoses of type 2 diabetes and acute coronary syndrome (ACS) have higher readmission rates and poorer health outcomes than patients with singular chronic conditions. Despite this, there is a lack of education programs targeted for this dual diagnosis population to improve self-management and decrease negative health outcomes. There is evidence to suggest that internet based interventions may improve health outcomes for patients with singular chronic conditions, however there is a need to develop an evidence base for ACS patients with comorbid diabetes. There is a growing awareness of the importance of a participatory model in developing effective online interventions. That is, internet interventions are more effective if end users’ perceptions of the intervention are incorporated in their final development prior to testing in large scale trials. Objectives This study investigated patients’ perspectives of the web-based intervention designed to promote self-management of the dual conditions in order to refine the intervention prior to clinical trial evaluation. Methods An interpretive approach with thematic analysis was used to obtain deeper understanding regarding participants’ experience when using web-application interventions for patients with ACS and type 2 diabetes. Semi-structured interviews were undertaken on a purposive sample of 30 patients meeting strict inclusion and exclusion criteria to obtain their perspectives on the program. Results Preliminary results indicate patients with dual diagnoses express more complex needs than those with a singular condition. Participants express a positive experience with the proposed internet intervention and emerging themes include that the web page is seen as easy to use and comforting as a support, in that patients know they are not alone. Further results will be reported as they become available. Conclusion The results indicate potential for patient acceptability of the newly developed internet intervention for patients with ACS and comorbid diabetes. Incorporation of patient perspectives into the final development of the intervention is likely to maximise successful outcomes of any future trials that utilise this intervention. Future quantitative evaluation of the effectiveness of the intervention is being planned.