Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by a Caputo fractional derivative, and the second order space derivative by a symmetric fractional derivative. First, a method of separating variables expresses the analytical solution of the TSS-FDE in terms of the Mittag--Leffler function. Second, we propose two numerical methods to approximate the Caputo time fractional derivative: the finite difference method; and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term

Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPE-NST), which involve the Caputo time fractional derivative (CTFD) of order α ∈ (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order μ ∈ (1, 2). Approximating the CTFD and RSFD using the L1-algorithm and shifted Grunwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.

Computationally efficient numerical methods for time- and space-fractional Fokker–Planck equations

Fractional Fokker–Planck equations have been used to model several physical situations that present anomalous diffusion. In this paper, a class of time- and space-fractional Fokker–Planck equations (TSFFPE), which involve the Riemann–Liouville time-fractional derivative of order 1-α (α(0, 1)) and the Riesz space-fractional derivative (RSFD) of order μ(1, 2), are considered. The solution of TSFFPE is important for describing the competition between subdiffusion and Lévy flights. However, effective numerical methods for solving TSFFPE are still in their infancy. We present three computationally efficient numerical methods to deal with the RSFD, and approximate the Riemann–Liouville time-fractional derivative using the Grünwald method. The TSFFPE is then transformed into a system of ordinary differential equations (ODE), which is solved by the fractional implicit trapezoidal method (FITM). Finally, numerical results are given to demonstrate the effectiveness of these methods. These techniques can also be applied to solve other types of fractional partial differential equations.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative and the second order space derivative by the symmetric fractional derivative. Firstly, a method of separating variables is used to express the analytical solution of the tss-fde in terms of the Mittag–Leffler function. Secondly, we propose two numerical methods to approximate the Caputo time fractional derivative, namely, the finite difference method and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results are presented to demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Making space and place for the knowledge economy : knowledge-based development of Australian cities

The impact of what has been broadly labelled the knowledge economy has been such that, even in the absence of precise measurement, it is the undoubted dynamo of today’s global market, and an essential part of any global city. The socio-economic importance of knowledge production in a knowledge economy is clear, and it is an emerging social phenomenon and research agenda in geographical studies. Knowledge production, and where, how and by whom it is produced, is an urban phenomenon that is poorly understood in an era of strong urbanisation. This paper focuses on knowledge community precincts as the catalytic magnet infrastructures impacting on knowledge production in cities. The paper discusses the increasing importance of knowledge-based urban development within the paradigm of the knowledge economy, and the role of knowledge community precincts as instruments to seed the foundation of knowledge production in cities. This paper explores the knowledge based urban development, and particularly knowledge community precinct development, potentials of Sydney, Melbourne and Brisbane, and benchmarks this against that of Boston, Massachusetts.

Making space and place for knowledge production : socio-spatial development of knowledge community precincts

In the knowledge era the importance of making space and place for knowledge production is clearly understood worldwide by many city administrations that are keen on restructuring their cities as highly competitive and creative places. Consequently, knowledge-based urban development and socio-spatial development of knowledge community precincts have taken their places among the emerging agendas of the urban planning and development practice. This chapter explores these emerging issues and scrutinizes the development of knowledge community precincts that have important economic, social and cultural dimensions on the formation of competitive and creative urban regions. The chapter also sheds light on the new challenges for planning discipline, and discusses the need for and some specifics of a new planning paradigm suitable for dealing with 21st Century’s socio-economic development and urbanization problems.

Distributed orthogonal space-time block codes with adaptive diversity gain

In this paper we present a novel distributed coding protocol for multi-user cooperative networks. The proposed distributed coding protocol exploits the existing orthogonal space-time block codes to achieve higher diversity gain by repeating the code across time and space (available relay nodes). The achievable diversity gain depends on the number of relay nodes that can fully decode the signal from the source. These relay nodes then form space-time codes to cooperatively relay to the destination using number of time slots. However, the improved diversity gain is archived at the expense of the transmission rate. The design principles of the proposed space-time distributed code and the issues related to transmission rate and diversity trade off is discussed in detail. We show that the proposed distributed space-time coding protocol out performs existing distributed codes with a variable transmission rate.

The embodied hybrid space : designing ubiquitous computing towards an amplification of situated real world experiences

The emergence of mobile and ubiquitous computing technology has created what is often referred to as the hybrid space – a virtual layer of digital information and interaction opportunities that sit on top of and augment the physical environment. Embodied media materialise digital information as observable and sometimes interactive parts of the physical environment. The aim of this work is to explore ways to enhance people’s situated real world experience, and to find out what the role and impact of embodied media in achieving this goal can be. The Edge, an initiative of the State Library of Queensland in Brisbane, Australia, and case study of this thesis, envisions to be a physical place for people to meet, explore, experience, learn and teach each other creative practices in various areas related to digital technology and arts. Guided by an Action Research approach, this work applies Lefebvre’s triad of space (1991) to investigate the Edge as a social space from a conceived, perceived and lived point of view. Based on its creators’ vision and goals on the conceived level, different embodied media are iteratively designed, implemented and evaluated towards shaping and amplifying the Edge’s visitor experience on the perceived and lived level.

Reverse immigration

This book (256 pages, written in Korean) is a critical essay that reviews, questions, and criticises Korean and Eastern immigrants’ thinking and behaviour styles in Australia from their cultural perspectives, and discuss and proposes a creative cultural dimension for their better life in a multicultural context. Multiculturalism is not supportive of Eastern cultures because of individualistic collection of cultures, while transculturalism facilitates nurture of their culture in a community-oriented way within multicultural circumstances. Korean and Eastern immigrants, sharing oriental cultural systems and values, should approach to the Australian multicultural context with transculturalism which allows creating new cultural values in collaboration with and by participation into local communities. ------------------------------------------------------------ Many Eastern immigrants live in their own ethnic communities without or less interacting with Australian (communities). The author defines this phenomenon as “reverse immigration”. Reverse immigration refers to re-immigrating to their ethnic community in Australia or to their birth country despite they did not anticipate that this would happen to them before immigration to Australia. The author argues that Easterners’ collectivistic culture often devalues individuality and vice versa. Cultural clash between West and East often forces the immigrants to choose reverse immigration because of their lack of understanding of Western culture and their cultural characteristics such as low individuality, high power distance, and high uncertainty avoidance. For example, a vague boundary between individualist and collectivist in a collectivistic context (within their ethnic group) often leads to maladjustment to local communities and enhancement of cultural conservatism. The author proposes that the cultural clash can be overcome by cross-cultural activities named “transculturalism”. To Eastern immigrants, transculturalism can be achieved by acculturation of their two predominant cultures, the third-person perspective and generalised others. In a multicultural context, the former refers to the ability to share another person's feelings and emotions as if they were your own, and the latter does the ability to manage community and public expectations. When both cultural values are used for quality interactions between East and West, they allow Eastern immigrants to be more creative and critical and Australian to be more socially inclusive and culturally tolerant. With these discussions, the author discusses cultural differences throughout the book with four topics (chapters) and proposes transculturalism as a solution to the reverse immigration. ------------------------------------------------------------ Chapter 1 criticises Koreans’ attitudes and methods towards learning English that is less pragmatic and practical, but more likely to be a scholarly study. The author explains that Koreans’ non-pragmatic towards learning English has been firmly built based on their traditional systems and values that Koreans view English as a discipline and an aim of academic achievements rather than a means of communication. Within their cultural context, English can be perceived as more than a language, but something like vastly superior to their language and culture. Their collectivistic culture regards English as an unreachable and heterogeneous one that may threaten their cultural identity, so that “scholarly studying” is only the way to achieve (not learn) it. This discourages the immigrants to engage and involve in daily dialogues by “using” English as a second language. The author further advises the readers to be aware of Eastern collectivistic culture in communication and interaction that sometimes completely reverses private and public topics in a Western context. This leads them to feel that they have no content to talk to natives. ------------------------------------------------------------ Chapter 2 compares between Korea and Australia in terms of their educational systems and values, and proposes how Eastern overseas students can achieve critical and creative thinking within a Western educational setting. Interestingly, this chapter includes an explanation of why Eastern overseas students easily fail assessments including essay writing, oral presentations and discussions. One of the reasons the author explains is that Eastern students are not familiar to criticise others and think creatively, especially when they recognise that their words and ideas may harm the collectivistic harmony. Western educational systems focuses on enhancement of individuality such as self-confidence, self-esteem, and self-expression, while Eastern educational systems foster group-oriented values such as interpersonal relationship, and strong moral and spiritual values. Yet, the author argues that the collectivistic approach to criticism and creativity is often more critical and creative than Western individuals when they know what they are supposed to do for a group (or a community). Therefore, Eastern students need to think their cultural merits and demerits by using an individual perspective rather than generalised others’ perspective. The latter often discourages individual participation in a community, and the generalised others in a Western culture is weaker than Eastern. Furthermore, Western educational systems do not educate students to transform (loose) their individuality to fit into a group or a community. Rather they cultivate individuality for community prosperity. ------------------------------------------------------------ Chapter 3 introduces various cases of reverse immigration in workplaces that many immigrants return to their country or their ethnic community after many trials for acculturation. Reverse immigration is unexpected and not planned before immigration, so that its emotional embarrassment increases such severe social loneliness. Most Eastern immigrant workers have tried to adjust themselves in this new cultural environment at the early stages of immigration. However, their cultural features of collectivism, high power distance, high uncertainty avoidance, and long-term oriented cultures suppress individual initiative and eliminate the space for experiments in ways of acculturation. The author argues that returning to their ethnic community (physically and psychologically) leads to two significant problems: their distorted parenting and becoming more conservatives. The former leads the first generation of immigrants to pressure their children to pursue extrinsic or materialist values, such as financial success, fame and physical appearance, rather than on intrinsic values, while the latter refers to their isolated conservative characters because of their remoteness from the changes of their own country. The author also warns that their ethnic and religious groups actively strengthens immigrants’ social loneliness and systematically discourages immigrants’ interests and desire to be involving into local communities. The ethnic communities and leaders have not been interacting with Australian local communities and, as a result, are eager to conserve outdated cultural systems values. Even they have a tendency to weed out those people who wish to settle down within Australian local communities. They believe that those people can threaten their community’s survival and continuity. ------------------------------------------------------------ Chapter 4 titled multiculturalism argues that Korean and Eastern immigrants should more precisely understand Australia as a multicultural society in a way of collaboratively creating new cultural values. The author introduces multiculturalism with its definitions and history in Australia and argues the limitations of multiculturalism from an Easterner’s perspective. With well known tragedies of the second generations of U.S. immigrants, Cho Seung-Hui, a university student, massacred 32 people on the Virginia Tech before committing suicide and Hidal Hassan, an Army psychiatrist, killed 13 people at Fort Hood and the responses of ethnic community, the author explains that their mental illness may be derived from their parents’ (or ethnic group) culturally isolated attitude and socially static viewpoint of U.S. (Western system and values). The author insists that multiculturalism may restrict Eastern immigrants’ engagement and involvement in local communities. Multiculturalism has been systematically and historically developed based on Western systems and cultural values. In other words, multiculturalism requires high self-confidence and self-esteem that Eastern immigrants less prioritise them. It has been generally known that Easterners put more weight on human relationship than Westerners, but the author claims that this is not true. Within an individualistic culture, Westerners are more interested in building person-to-person connections and relationships. While Easterners are more interested in how individuals can achieve a sense of belonging within a group and a community. Therefore, multiculturalism is an ideology which forces Eastern immigrants to discard their strong desire to be part of a group and does not give a sense of belonging. In a consequence, the author advises that Eastern immigrants should aim towards “transculturalism” which allows them to actively participate in and contribute to their multicultural community. Transculturalism does not ask Easterners to discard their cultural values, but enables them to be a collectivistic individualist (a community leader) who is capable of developing new cultural values in a more creative and productive way. Furthermore, transculturalism encourages Western Australians in a multicultural context to collaborate with ethnic minorities to build a better community.