A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation

This paper aims to develop a meshless approach based on the Point Interpolation Method (PIM) for numerical simulation of a space fractional diffusion equation. Two fully-discrete schemes for the one-dimensional space fractional diffusion equation are obtained by using the PIM and the strong-forms of the space diffusion equation. Numerical examples with different nodal distributions are studied to validate and investigate the accuracy and efficiency of the newly developed meshless approach.

Multi-action recognition via stochastic modelling of optical flow and gradients

In this paper we propose a novel approach to multi-action recognition that performs joint segmentation and classification. This approach models each action using a Gaussian mixture using robust low-dimensional action features. Segmentation is achieved by performing classification on overlapping temporal windows, which are then merged to produce the final result. This approach is considerably less complicated than previous methods which use dynamic programming or computationally expensive hidden Markov models (HMMs). Initial experiments on a stitched version of the KTH dataset show that the proposed approach achieves an accuracy of 78.3%, outperforming a recent HMM-based approach which obtained 71.2%.

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.

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.

Vote as you go : Blending interfaces for community engagement into the urban space

This paper presents a series of studies on situated interfaces for community engagement. Firstly, we identify five recurring design challenges as well as four common strategies used to overcome them. We then assess the effectiveness of these strategies through field studies with public polling interfaces. We developed two very different polling interfaces in the form of (1) a web application running on an iPad mounted on a stand, allowing one vote at a time, and (2) a playful full-body interaction application for a large urban screen allowing concurrent participation. We deployed both interfaces in an urban precinct with high pedestrian traffic and equipped with a large urban screen. Analysing discoverability and learnability of each scenario, we derive insights regarding effective ways of blending community engagement interfaces into the built environment, while attracting the attention of passers-by and communicating the results of civic participation.

Fractional models in space for diffusive processes in heterogeneous media with applications in cell motility and electrical signal propagation

This work addresses fundamental issues in the mathematical modelling of the diffusive motion of particles in biological and physiological settings. New mathematical results are proved and implemented in computer models for the colonisation of the embryonic gut by neural cells and the propagation of electrical waves in the heart, offering new insights into the relationships between structure and function. In particular, the thesis focuses on the use of non-local differential operators of non-integer order to capture the main features of diffusion processes occurring in complex spatial structures characterised by high levels of heterogeneity.

The effect of BCMO1 gene variants on macular pigment optical density in young healthy Caucasians

Background Serum lutein (L) and zeaxanthin (Z) positively correlate with macular pigment optical density (MPOD), hence the latter is a valuable indirect tool for measuring L and Z content in the macula. L and Z have been attributed antioxidant capacity and protection from certain retinal diseases but their uptake within the eye is thought to depend on genetic, age and environmental factors. In particular gene variants within beta-carotene monooxygenase (BCMO1) are thought to modulate MPOD in the macula. Objectives: To determine the effect of BCMO1 single nucleotide polymorphisms (SNPs) rs11645428, rs6420424 and rs6464851 on macular pigment optical density (MPOD) in a cohort of young healthy participants of Caucasian origin with normal ocular health. Design In this cohort study, MPOD was assessed in 46 healthy participants (22 male and 24 female) with a mean age of 24 ± 4.0 years (range 19-33). The three SNPs, rs11645428, rs6420424, rs6564851 that have established associations with MPOD were determined using MassEXTEND (hME) Sequenom assay. One-way analysis of variance (ANOVA) was performed on groups segregated into homozygous and heterozygous BCMO1 genotypes. Correlations between body mass index (BMI), iris colour, gender, central retinal thickness (CRT), diet and MPOD were investigated. Results MPOD did not significantly vary with BCMO1 rs11645428 (F2,41 = 0.700, p = 0.503), rs6420424 (F2,41 = 0.210, p = 0.801) nor rs6464851 homozygous or heterozygous genotypes (F2,41 = 0,13, p = 0.88), in this young healthy cohort. The combination of these three SNPs into triple genotypes based on plasma conversion efficiency did not affect MPOD (F2,41 = 0.07, p = 0.9). There was a significant negative correlation with MPOD and central retinal thickness (r = - 0.39, p = 0.01) but no significant correlation between BMI, iris colour, gender and MPOD. Conclusion Our results indicate that macular pigment deposition within the central retina is not dependent on BCMO1 gene variants in young healthy people. We propose that MPOD is saturated in younger persons and/or other gene variant combinations determine its deposition.