Analytical solutions of the multi-term modified power law wave equations in a finite domain

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi term time-space fractional models including fractional Laplacian.

Numerical methods for solving the multi-term time-fractional wave-diffusion equations

In this paper, the multi-term time-fractional wave diffusion equations are considered. The multiterm time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Analytical solutions for the two- and three-dimensional time-fractional telegraph equations by the method of separating variables

In this paper, a method of separating variables is effectively implemented for solving a time-fractional telegraph equation (TFTE) in two and three dimensions. We discuss and derive the analytical solution of the TFTE in two and three dimensions with nonhomogeneous Dirichlet boundary condition. This method can be extended to other kinds of the boundary conditions.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Determining the optimal proportion of design in design-build request for proposals (RFPs)

The design-build (DB) system is a popular and effective delivery method of construction projects worldwide. After owners decide to procure their projects through the DB system, they may wish to determine the optimal proportion of design to be provided in the DB request for proposals (RFPs), which serve as solicitations for design-builders and describe the scope of work. However, this presents difficulties to DB owners and there is little, if any, systematic research in this area. This paper reports on an empirical study in the USA entailing both an online questionnaire survey and Delphi survey to identify and evaluate the factors influencing owners’ decisions in determining the proportion of design to include in DB RFPs. Eleven factors are identified, i.e. (1) clarity of project scope; (2) applicability of performance specifications; (3) desire for design innovation; (4) site constraints; (5) availability of competent design-builders; (6) project control requirements; (7) user group involvement level; (8) third party requirements; (9) owner experience with DB; (10) project complexity; and (11) schedule constraints. A statistically significant agreement on the eleven factors was also obtained from the (mainly non-owner) Delphi experts. Although some of the experts hold different opinions on how these factors affect the proportion of design, these findings furnish various stakeholders with a better understanding of the delivery process of DB projects and the appropriate provision of project information in DB RFPs. As the result is mainly industry opinion concerning the optimal proportion of design, in addition and for completeness, future studies should be conducted to obtain a big picture of the optimal proportion of design by means of seeking owners’ inputs.

Perceptions of physical versus virtual design studio education

While the studio environment has been promoted as an ideal educational setting for project-based disciplines associated with the art and design, few qualitative studies have been undertaken in a comprehensive way, with even fewer giving emphasis to the teachers and students and how they feel about changing their environment. This situation is problematic given the changes and challenges facing higher education, including those associated with new technologies such as online learning. In response, this paper describes a comparative study employing grounded theory to identify and describe teachers’ and students’ perceptions of the physical design studio (PDS) as well as the virtual design studio (VDS) of architectural students in an Australian university. The findings give significance to aspects of design education activities and their role in the development of integrated hybrid learning environments.

Flexible airport terminal design : towards a framework

Flexibility is a key driver of any successful design, specifically in highly unpredictable environment such as airport terminal. Ever growing aviation industry requires airport terminals to be planned and constructed in such a way that will allow flexibility for future design, alteration and redevelopment. The concept of flexibility in terminal design is a relatively new initiative, where existing rules or guidelines are not adequate to assist designers. A shift towards flexible design concept would allow terminal buildings to be designed to accommodate future changes and to make passengers’ journey as simple, timely and hassle free as possible. Currently available research indicates that a theoretical framework on flexible design approach for airport terminals would facilitate the future design process. The generic principles of flexibility are investigated in the current research to incorporate flexible design approaches within the process of an airport terminal design. A conceptual framework is proposed herein, which is expected to ascertain flexibility to current passenger terminal facilities within their corresponding locations as well as in future design and expansion.

A holistic blended design studio model : a basis for exploring and expanding learning opportunities

While the studio environment has been promoted as an ideal educational setting for project-based disciplines, few qualitative studies have been undertaken in a comprehensive way (Bose, 2007). This study responds to this need by adopting Grounded Theory methodology in a qualitative comparative approach. The research aims to explore the limitations and benefits of a face-to-face (f2f) design studio as well as a virtual design studio (VDS) as experienced by architecture students and educators at an Australian university in order to find the optimal combination for a blended environment to maximize learning. The main outcome is a holistic multidimensional blended model being sufficiently flexible to adapt to various setting, in the process, facilitating constructivist learning through self-determination, self-management, and personalization of the learning environment.

Design process excludes users : the co-creation activities between user and designer

User needs are a fundamental element of design. If the design process does not properly reflect user needs, the design will be severely compromised. Therefore, it is worthwhile to investigate how the user is, and user needs are, understood in the design process. In this article, three accepted linear process models for web site and interactive media design are reviewed in terms of the designer and user participation. The article then proposes a user-evolving collaborative design process which is built on co-creation activities between designer and user. Co-creation activities across the entire design process structurally and ontologically reposition the users, and user needs, centrally, which allows the designers to holistically approach to the user needs through building a partnership with the users. Co-creation creates an equal evolving participatory process between user and designer towards sharing values and knowledge and creating new domains of collective creativity.

Privacy by design : Does it matter for social networks?

Privacy is an important component of freedom and plays a key role in protecting fundamental human rights. It is becoming increasingly difficult to ignore the fact that without appropriate levels of privacy, a person’s rights are diminished. Users want to protect their privacy - particularly in “privacy invasive” areas such as social networks. However, Social Network users seldom know how to protect their own privacy through online mechanisms. What is required is an emerging concept that provides users legitimate control over their own personal information, whilst preserving and maintaining the advantages of engaging with online services such as Social Networks. This paper reviews “Privacy by Design (PbD)” and shows how it applies to diverse privacy areas. Such an approach will move towards mitigating many of the privacy issues in online information systems and can be a potential pathway for protecting users’ personal information. The research has also posed many questions in need of further investigation for different open source distributed Social Networks. Findings from this research will lead to a novel distributed architecture that provides more transparent and accountable privacy for the users of online information systems.