Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.

An analytical tool that quantifies cellular morphology changes from three-dimensional fluorescence images

The most common software analysis tools available for measuring fluorescence images are for two-dimensional (2D) data that rely on manual settings for inclusion and exclusion of data points, and computer-aided pattern recognition to support the interpretation and findings of the analysis. It has become increasingly important to be able to measure fluorescence images constructed from three-dimensional (3D) datasets in order to be able to capture the complexity of cellular dynamics and understand the basis of cellular plasticity within biological systems. Sophisticated microscopy instruments have permitted the visualization of 3D fluorescence images through the acquisition of multispectral fluorescence images and powerful analytical software that reconstructs the images from confocal stacks that then provide a 3D representation of the collected 2D images. Advanced design-based stereology methods have progressed from the approximation and assumptions of the original model-based stereology(1) even in complex tissue sections(2). Despite these scientific advances in microscopy, a need remains for an automated analytic method that fully exploits the intrinsic 3D data to allow for the analysis and quantification of the complex changes in cell morphology, protein localization and receptor trafficking. Current techniques available to quantify fluorescence images include Meta-Morph (Molecular Devices, Sunnyvale, CA) and Image J (NIH) which provide manual analysis. Imaris (Andor Technology, Belfast, Northern Ireland) software provides the feature MeasurementPro, which allows the manual creation of measurement points that can be placed in a volume image or drawn on a series of 2D slices to create a 3D object. This method is useful for single-click point measurements to measure a line distance between two objects or to create a polygon that encloses a region of interest, but it is difficult to apply to complex cellular network structures. Filament Tracer (Andor) allows automatic detection of the 3D neuronal filament-like however, this module has been developed to measure defined structures such as neurons, which are comprised of dendrites, axons and spines (tree-like structure). This module has been ingeniously utilized to make morphological measurements to non-neuronal cells(3), however, the output data provide information of an extended cellular network by using a software that depends on a defined cell shape rather than being an amorphous-shaped cellular model. To overcome the issue of analyzing amorphous-shaped cells and making the software more suitable to a biological application, Imaris developed Imaris Cell. This was a scientific project with the Eidgenössische Technische Hochschule, which has been developed to calculate the relationship between cells and organelles. While the software enables the detection of biological constraints, by forcing one nucleus per cell and using cell membranes to segment cells, it cannot be utilized to analyze fluorescence data that are not continuous because ideally it builds cell surface without void spaces. To our knowledge, at present no user-modifiable automated approach that provides morphometric information from 3D fluorescence images has been developed that achieves cellular spatial information of an undefined shape (Figure 1). We have developed an analytical platform using the Imaris core software module and Imaris XT interfaced to MATLAB (Mat Works, Inc.). These tools allow the 3D measurement of cells without a pre-defined shape and with inconsistent fluorescence network components. Furthermore, this method will allow researchers who have extended expertise in biological systems, but not familiarity to computer applications, to perform quantification of morphological changes in cell dynamics.

Numerical methods for strong solutions of stochastic differential equations : an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

The analytical solution and numerical solution of the fractional diffusion-wave equation with damping

Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusionwave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An implicit difference approximation is constructed. Stability and convergence are proved by the energy method. Finally, two numerical examples are presented to show the effectiveness of this approximation.

Analytical benchmark solutions for steel frame structures subject to local buckling effects

Application of "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A research project has been conducted with the aim of developing concentrated plasticity methods suitable for practical advanced analysis of steel frame structures comprising non-compact sections. This paper contains a comprehensive set of analytical benchmark solutions for steel frames comprising non-compact sections, which can be used to verify the accuracy of simplified concentrated plasticity methods of advanced analysis. The analytical benchmark solutions were obtained using a distributed plasticity shell finite element model that explicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. A brief description and verification of the shell finite element model is provided in this paper.

Innovative methods for assessing viability of diversification into new markets : a study based on an engineering consultancy

This study resulted in the development of a decision making tool for engineering consultancies looking to diversify into new markets. It reviewed existing decision tools used by contractor's entering new markets to develop a bespoke tool for engineering consultants to establish more rigor around the decision making process rather than rely purely on the intuition of company executives. The tool can be used for developing medium and long term company strategies or as a quick and efficient way to assess the viability of new market opportunities when they arise. A combination of Delphi and Analytical Hierarchy Process was selected as the basis of the decision theory.

Emerging methods in using GIS to analyse Barmah Forest virus disease in Queensland, Australia

Barmah Forest virus (BFV) disease is an emerging mosquito-borne disease in Australia. We aimed to outline some recent methods in using GIS for the analysis of BFV disease in Queensland, Australia. A large database of geocoded BFV cases has been established in conjunction with population data. The database has been used in recently published studies conducted by the authors to determine spatio-temporal BFV disease hotspots and spatial patterns using spatial autocorrelation and semi-variogram analysis in conjunction with the development of interpolated BFV disease standardised incidence maps. This paper briefly outlines spatial analysis methodologies using GIS tools used in those studies. This paper summarises methods and results from previous studies by the authors, and presents a GIS methodology to be used in future spatial analytical studies in attempt to enhance the understanding of BFV disease in Queensland. The methodology developed is useful in improving the analysis of BFV disease data and will enhance the understanding of the BFV disease distribution in Queensland, Australia.

Anatomy of a trending topic : Methods for the visualisation of retweet chains [Anatomie eines Trending Topics: Methoden zur Visualisierung von Retweet-Ketten]

Twitter and other social networking sites play an ever more present role in the spread of current events. The dynamics of information dissemination through digital network structures are still relatively unexplored, however. At what time an issue is taken up by whom? Who forwards a message when to whom else? What role do individual communication participants, existing digital communities or the technical foundations of each network platform play in the spread of news? In this chapter we discuss, using the example of a video on a current sociopolitical issue in Australia that was shared on Twitter, a number of new methods for the dynamic visualisation and analysis of communication processes. Our method combines temporal and spatial analytical approaches and provides new insights into the spread of news in digital networks. [Social media dienen immer häufger als Disseminationsmechanismen für Medieninhalte. Auf Twitter ermöglicht besonders die Retweet-Funktion den schnellen und weitläufgen Transfer von Nachrichten. In diesem Beitrag etablieren neue methodische Ansätze zur Erfassung, Visualisierung und Analyse von Retweet-Ketten. Insbesondere heben wir hervor, wie bestehende Netzwerkanalysemethoden ergänzt werden können, um den Ablauf der Weiterleitung sowohl temporal als auch spatial zu erfassen. Unsere Fallstudie demonstriert die verbreitung des videoclips einer am 9. Oktober 2012 spontan gehaltenen Wutrede der australischen Premierministerin Julia Gillard, in der sie Oppositionsführer Tony Abbott als Frauenhasser brandmarkte. Durch die Erfassung von Hintergrunddaten zu den jeweiligen NutzerInnen, die sich an der Weiterleitung des Videoclips beteiligten, erstellen wir ein detailliertes Bild des Disseminationsablaufs im vorliegenden Fall. So lassen sich die wichtigsten AkteurInnen und der Ablauf der Weiterleitung darstellen und analysieren. Daraus entstehen Einblicke in die allgemeinen verbreitungsmuster von Nachrichten auf Twitter].

Household carbon emission research: An analytical review of measurement, influencing factors and mitigation prospects

Greenhouse gas (GHG) emissions are simultaneously exhausting the world's supply of fossil fuels and threatening the global climate. In many developing countries, significant improvement in living standards in recent years due to the accelerating development of their economies has resulted in a disproportionate increase in household energy consumption. Therefore, a major reduction in household carbon emissions (HCEs) is essential if global carbon reduction targets are to be met. To do this, major Organisation for Economic Co-operation and Development (OECD) states have already implemented policies to alleviate the negative environmental effects of household behaviors and less carbon-intensive technologies are also proposed to promote energy efficiency and reduce carbon emissions. However, before any further remedial actions can be contemplated, though, it is important to fully understand the actual causes of such large HCEs and help researchers both gain deep insights into the development of the research domain and identify valuable research topics for future study. This paper reviews existing literature focusing on the domain of HCEs. This critical review provides a systematic understanding of current work in the field, describing the factors influencing HCEs under the themes of household income, household size, age, education level, location, gender and rebound effects. The main quantification methodologies of input–output models, life cycle assessment and emission coefficient methods are also presented, and the proposed measures to mitigate HCEs at the policy, technology and consumer levels. Finally, the limitations of work done to date and further research directions are identified for the benefit of future studies.

Effective Cell-Centred Time-Domain Maxwell's Equations Numerical Solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed.