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.

Robot navigation using human cues: A robot navigation system for symbolic goal-directed exploration

In this paper we present for the first time a complete symbolic navigation system that performs goal-directed exploration to unfamiliar environments on a physical robot. We introduce a novel construct called the abstract map to link provided symbolic spatial information with observed symbolic information and actual places in the real world. Symbolic information is observed using a text recognition system that has been developed specifically for the application of reading door labels. In the study described in this paper, the robot was provided with a floor plan and a destination. The destination was specified by a room number, used both in the floor plan and on the door to the room. The robot autonomously navigated to the destination using its text recognition, abstract map, mapping, and path planning systems. The robot used the symbolic navigation system to determine an efficient path to the destination, and reached the goal in two different real-world environments. Simulation results show that the system reduces the time required to navigate to a goal when compared to random exploration.

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.

Is the sun too bright in Queensland? An approach to robust outdoor colour beacon detection

Using cameras onboard a robot for detecting a coloured stationary target outdoors is a difficult task. Apart from the complexity of separating the target from the background scenery over different ranges, there are also the inconsistencies with direct and reflected illumination from the sun,clouds, moving and stationary objects. They can vary both the illumination on the target and its colour as perceived by the camera. In this paper, we analyse the effect of environment conditions, range to target, camera settings and image processing on the reported colours of various targets. The analysis indicates the colour space and camera configuration that provide the most consistent colour values over varying environment conditions and ranges. This information is used to develop a detection system that provides range and bearing to detected targets. The system is evaluated over various lighting conditions from bright sunlight, shadows and overcast days and demonstrates robust performance. The accuracy of the system is compared against a laser beacon detector with preliminary results indicating it to be a valuable asset for long-range coloured target detection.

Design of a four-rotor aerial robot

The design and fabrication of a proto-type four-rotor vertical take-off and landing (VTOL) aerial robot for use as indoor experimental robotics platform is presented. The flyer is termed an X4-flyer. A development of the dynamic model of the system is presented and a pilot augmentation control design is proposed.

Robust sensing for a 3,500 tonne field robot

The mining industry is highly suitable for the application of robotics and automation technology since the work is arduous, dangerous and often repetitive. This paper discusses a robust sensing system developed to find and trade the position of the hoist ropes of a dragline. Draglines are large `walking cranes' used in open-pit coal mining to remove the material covering the coal seam. The rope sensing system developed uses two time-of-flight laser scanners. The finding algorithm uses a novel data association and tracking strategy based on pairing rope data.

Modeling and control of a 3500 tonne mining robot

Draglines are extremely large machines that are widely used in open-cut coal mines for overburden stripping. Since 1994 we have been working toward the development of a computer control system capable of automatically driving a dragline for a large portion of its operating cycle. This has necessitated the development and experimental evaluation of sensor systems, machines models, closed-loop control controllers, and an operator interface. This paper describes our steps toward the goal through scale-model and full-scale field experimentation.

Robot control of a 3,500 tonne mining machine

The mining industry is highly suitable for the application of robotics and automation technology since the work is arduous, dangerous and often repetitive. This paper describes the development of an automation system for a physically large and complex field robotic system - a 3,500 tonne mining machine (a dragline). The major components of the system are discussed with a particular emphasis on the machine/operator interface. A very important aspect of this system is that it must work cooperatively with a human operator, seamlessly passing the control back and forth in order to achieve the main aim - increased productivity.

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.

A robot application to marine vessel inspection

Seagoing vessels have to undergo regular inspections, which are currently performed manually by ship surveyors. The main cost factor in a ship inspection is to provide access to the different areas of the ship, since the surveyor has to be close to the inspected parts, usually within arm's reach, either to perform a visual analysis or to take thickness measurements. The access to the structural elements in cargo holds, e.g., bulkheads, is normally provided by staging or by 'cherry-picking' cranes. To make ship inspections safer and more cost-efficient, we have introduced new inspection methods, tools, and systems, which have been evaluated in field trials, particularly focusing on cargo holds. More precisely, two magnetic climbing robots and a micro-aerial vehicle, which are able to assist the surveyor during the inspection, are introduced. Since localization of inspection data is mandatory for the surveyor, we also introduce an external localization system that has been verified in field trials, using a climbing inspection robot. Furthermore, the inspection data collected by the robotic systems are organized and handled by a spatial content management system that enables us to compare the inspection data of one survey with those from another, as well as to document the ship inspection when the robot team is used. Image-based defect detection is addressed by proposing an integrated solution for detecting corrosion and cracks. The systems' performance is reported, as well as conclusions on their usability, all in accordance with the output of field trials performed onboard two different vessels under real inspection conditions.