Development and parameterization of a rain- and fire-driven model for exploring elephant effects in African savannas

We describe the development and parameterization of a grid-based model of African savanna vegetation processes. The model was developed with the objective of exploring elephant effects on the diversity of savanna species and structure, and in this formulation concentrates on the relative cover of grass and woody plants, the vertical structure of the woody plant community, and the distribution of these over space. Grid cells are linked by seed dispersal and fire, and environmental variability is included in the form of stochastic rainfall and fire events. The model was parameterized from an extensive review of the African savanna literature; when available, parameter values varied widely. The most plausible set of parameters produced long-term coexistence between woody plants and grass, with the tree-grass balance being more sensitive to changes in parameters influencing demographic processes and drought incidence and response, while less sensitive to fire regime. There was considerable diversity in the woody structure of savanna systems within the range of uncertainty in tree growth rate parameters. Thus, given the paucity of height growth data regarding woody plant species in southern African savannas, managers of natural areas should be cognizant of different tree species growth and damage response attributes when considering whether to act on perceived elephant threats to vegetation. © 2007 Springer Science+Business Media B.V.

Coil enhancements for high efficiency wireless power transfer applications

Achieving high efficiency with improved power transfer range and misalignment tolerance is the major design challenge in realizing Wireless Power Transfer (WPT) systems for industrial applications. Resonant coils must be carefully designed to achieve highest possible system performance by fully utilizing the available space. High quality factor and enhanced electromagnetic coupling are key indices which determine the system performance. In this paper, design parameter extraction and quality factor optimization of multi layered helical coils are presented using finite element analysis (FEA) simulations. In addition, a novel Toroidal Shaped Spiral (TSS) coil is proposed to increase power transfer range and misalignment tolerance. The proposed shapes and recommendations can be used to design high efficiency WPT resonator in a limited space.

Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation

Wound healing and tumour growth involve collective cell spreading, which is driven by individual motility and proliferation events within a population of cells. Mathematical models are often used to interpret experimental data and to estimate the parameters so that predictions can be made. Existing methods for parameter estimation typically assume that these parameters are constants and often ignore any uncertainty in the estimated values. We use approximate Bayesian computation (ABC) to estimate the cell diffusivity, D, and the cell proliferation rate, λ, from a discrete model of collective cell spreading, and we quantify the uncertainty associated with these estimates using Bayesian inference. We use a detailed experimental data set describing the collective cell spreading of 3T3 fibroblast cells. The ABC analysis is conducted for different combinations of initial cell densities and experimental times in two separate scenarios: (i) where collective cell spreading is driven by cell motility alone, and (ii) where collective cell spreading is driven by combined cell motility and cell proliferation. We find that D can be estimated precisely, with a small coefficient of variation (CV) of 2–6%. Our results indicate that D appears to depend on the experimental time, which is a feature that has been previously overlooked. Assuming that the values of D are the same in both experimental scenarios, we use the information about D from the first experimental scenario to obtain reasonably precise estimates of λ, with a CV between 4 and 12%. Our estimates of D and λ are consistent with previously reported values; however, our method is based on a straightforward measurement of the position of the leading edge whereas previous approaches have involved expensive cell counting techniques. Additional insights gained using a fully Bayesian approach justify the computational cost, especially since it allows us to accommodate information from different experiments in a principled way.

High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

In this paper, a class of unconditionally stable difference schemes based on the Pad´e approximation is presented for the Riesz space-fractional telegraph equation. Firstly, we introduce a new variable to transform the original dfferential equation to an equivalent differential equation system. Then, we apply a second order fractional central difference scheme to discretise the Riesz space-fractional operator. Finally, we use (1, 1), (2, 2) and (3, 3) Pad´e approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations. Matrix analysis is used to show the unconditional stability of the proposed algorithms. Two examples with known exact solutions are chosen to assess the proposed difference schemes. Numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space-fractional hyperbolic equation.

A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2)O(n2) and computational cost of O(n3)O(n3) down to n and O(nlogn)O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

Subdiffusion equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we consider the time distributed-order and Riesz space fractional diffusions on bounded domains with Dirichlet boundary conditions. Here, the time derivative is defined as the distributed-order fractional derivative in the Caputo sense, and the space derivative is defined as the Riesz fractional derivative. First, we discretize the integral term in the time distributed-order and Riesz space fractional diffusions using numerical approximation. Then the given equation can be written as a multi-term time–space fractional diffusion. Secondly, we propose an implicit difference method for the multi-term time–space fractional diffusion. Thirdly, using mathematical induction, we prove the implicit difference method is unconditionally stable and convergent. Also, the solvability for our method is discussed. Finally, two numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation

In this paper, we consider a two-sided space-fractional diffusion equation with variable coefficients on a finite domain. Firstly, based on the nodal basis functions, we present a new fractional finite volume method for the two-sided space-fractional diffusion equation and derive the implicit scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the implicit fractional finite volume method and conclude that the method is unconditionally stable and convergent. Finally, some numerical examples are given to show the effectiveness of the new numerical method, and the results are in excellent agreement with theoretical analysis.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

Prediction of GMA welding characteristic parameter by artificial neural network system

Nowadays, demand for automated Gas metal arc welding (GMAW) is growing and consequently need for intelligent systems is increased to ensure the accuracy of the procedure. To date, welding pool geometry has been the most used factor in quality assessment of intelligent welding systems. But, it has recently been found that Mahalanobis Distance (MD) not only can be used for this purpose but also is more efficient. In the present paper, Artificial Neural Networks (ANN) has been used for prediction of MD parameter. However, advantages and disadvantages of other methods have been discussed. The Levenberg–Marquardt algorithm was found to be the most effective algorithm for GMAW process. It is known that the number of neurons plays an important role in optimal network design. In this work, using trial and error method, it has been found that 30 is the optimal number of neurons. The model has been investigated with different number of layers in Multilayer Perceptron (MLP) architecture and has been shown that for the aim of this work the optimal result is obtained when using MLP with one layer. Robustness of the system has been evaluated by adding noise into the input data and studying the effect of the noise in prediction capability of the network. The experiments for this study were conducted in an automated GMAW setup that was integrated with data acquisition system and prepared in a laboratory for welding of steel plate with 12 mm in thickness. The accuracy of the network was evaluated by Root Mean Squared (RMS) error between the measured and the estimated values. The low error value (about 0.008) reflects the good accuracy of the model. Also the comparison of the predicted results by ANN and the test data set showed very good agreement that reveals the predictive power of the model. Therefore, the ANN model offered in here for GMA welding process can be used effectively for prediction goals.

The space of make: A topological account of the studio

Approaches to art-practice-as-research tend to draw a distinction between the processes of creative practice and scholarly reflection. According to this template, the two sites of activity – studio/desk, work/writing, body/mind – form the ‘correlative’ entity known as research. Creative research is said to be produced by the navigation of world and thought: spaces that exist in a continual state of tension with one another. Either we have the studio tethered to brute reality while the desk floats free as a site for the fluid cross-pollination of texts and concepts. Or alternatively, the studio is characterized by the amorphous, intuitive play of forms and ideas, while the desk represents its cartography, mapping and fixing its various fluidities. In either case, the research status of art practice is figured as a fundamentally riven space. However, the nascent philosophy of Speculative Realism proposes a different ontology – one in which the space of human activity comprises its own reality, independent of human perception. The challenge it poses to traditional metaphysics is to rethink the world as if it were a real space. When applied to practice-led research, this reconceptualization challenges the creative researcher to consider creative research as a contiguous space – a topology where thinking and making are not dichotomous points but inflections in an amorphous and dynamic field. Instead of being subject to the vertical tension between earth and air, a topology of practice emphasizes its encapsulated, undulating reality – an agentive ‘object’ formed according to properties of connectedness, movement and differentiation. Taking the central ideas of Quentin Meillassoux and Graham Harman as a point of departure, this paper will provide a speculative account of the interplay of spatialities that characterise the author’s studio practice. In so doing, the paper will model the innovative methodological potential produced by the analysis of topological dimensions of the studio and the way they can be said to move beyond the ‘geo-critical’ divide.

Optimal electricity distribution framework for public space: Assessing renewable energy proposals for Freshkills Park, New York City

Integrating renewable energy into public space is becoming more common as a climate change solution. However, this approach is often guided by the environmental pillar of sustainability, with less focus on the economic and social pillars. The purpose of this paper is to examine this issue in the speculative renewable energy propositions for Freshkills Park in New York City submitted for the 2012 Land Art Generator Initiative (LAGI) competition. This paper first proposes an optimal electricity distribution (OED) framework in and around public spaces based on relevant ecology and energy theory (Odum’s fourth and fifth law of thermodynamics). This framework addresses social engagement related to public interaction, and economic engagement related to the estimated quantity of electricity produced, in conjunction with environmental engagement related to the embodied energy required to construct the renewable energy infrastructure. Next, the study uses the OED framework to analyse the top twenty-five projects submitted for the LAGI 2012 competition. The findings reveal an electricity distribution imbalance and suggest a lack of in-depth understanding about sustainable electricity distribution within public space design. The paper concludes with suggestions for future research.

Urban public space and the marginalisation of children and young people

In the 21st century city, public space for a range of users, but especially children and young people, has come under threat. Watson proposed that “public space itself has come under attack from several directions-thematisation, enclosure into malls and other controlled spaces, and privatisation, or from urban planning and design interventions to erase its uniqueness”. Largely as a result of these trends, Scott observed that “young urbanites form a marginalised age class movement is restricted, out of fear and distrust, within aims to protect, monitored by city surveillance methods within the security-obsessed fabric”. The use of public space by children and young people is a contentious issue in a number of countries and a range of measures deployed to control public space curtail the rights of children and young people to claim the space for their use through curfews, oppressive camera surveillance and at times, the unwarranted attentions of police and private security personnel.

Collecting in an urban context: Relationships between collections and space in the home

Collecting has become a popular hobby within Western society, with collectables including anything from ‘bottle tops’ to ‘skyscrapers’. As the nature and size of these collections can impact upon the use of space in the home, the purpose of this study is to explore the relationship between the collections, space in the home and the impacts on others. This qualitative study explores the experiences of 11 Australian collectors, investigating the motivations, practices and adaption techniques used within their urban home environment. The themes of sentimentality, sociability and spatial tensions, including physical, personal and use of space are discussed within the context of their home and family environments. Overall the practice of collecting objects is a complex, varied, sentimental and sociable activity, providing enjoyment, knowledge and friendships. Space can be a central consideration to the practice of collecting as collections shape and are shaped by the available space in a household.

Towards strongly consistent online HMM parameter estimation using one-step Kerridge inaccuracy

In this paper, we propose a novel online hidden Markov model (HMM) parameter estimator based on the new information-theoretic concept of one-step Kerridge inaccuracy (OKI). Under several regulatory conditions, we establish a convergence result (and some limited strong consistency results) for our proposed online OKI-based parameter estimator. In simulation studies, we illustrate the global convergence behaviour of our proposed estimator and provide a counter-example illustrating the local convergence of other popular HMM parameter estimators.