A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

Amplitude equations and asymptotic expansions for multi-scale problems

In this paper we introduce a new technique to obtain the slow-motion dynamics in nonequilibrium and singularly perturbed problems characterized by multiple scales. Our method is based on a straightforward asymptotic reduction of the order of the governing differential equation and leads to amplitude equations that describe the slowly-varying envelope variation of a uniformly valid asymptotic expansion. This may constitute a simpler and in certain cases a more general approach toward the derivation of asymptotic expansions, compared to other mainstream methods such as the method of Multiple Scales or Matched Asymptotic expansions because of its relation with the Renormalization Group. We illustrate our method with a number of singularly perturbed problems for ordinary and partial differential equations and recover certain results from the literature as special cases. © 2010 - IOS Press and the authors. All rights reserved.

Resonant generation of the second harmonic of a surface wave on a plasma-metal boundary

The process of resonant generation of the second harmonic of the surface wave, propagating along the external magnetic field at the plasma-metal boundary is considered. The periodic process of the energy exchange between the first and the second harmonics of the wave is investigated as well. It is shown that the process under study is periodic one. The analytical expressions are obtained and numerical estimations are presented for characteristic time of nonlinear energy exchange. The self-action effect of main frequency wave is account for harmonics interaction. It is shown that the effect leads to nonlinear phenomena attenuation, which expresses in narrowing possible value interval of harmonics amplitudes during energy exchange process and in increasing the nonlinear interaction time.

Agency problems of corporate philanthropy

Evaluating agency theory and optimal contracting theory views of corporate philanthropy, we find that as corporate giving increases, shareholders reduce their valuation of firm cash holdings. Dividend increases following the 2003 Tax Reform Act are associated with reduced corporate giving. Using a natural experiment, we find that corporate giving is positively (negatively) associated with CEO charity preferences (CEO shareholdings and corporate governance quality). Evidence from CEO-affiliated charity donations, market reactions to insider-affiliated donations, its relation to CEO compensation, and firm contributions to director-affiliated charities indicates that corporate donations advance CEO interests and suggests misuses of corporate resources that reduce firm value.

Do instructional attributes pose multicollinearity problems? An empirical exploration

It is commonly perceived that variables ‘measuring’ different dimensions of teaching (construed as instructional attributes) used in student evaluation of teaching (SET) questionnaires are so highly correlated that they pose a serious multicollinearity problem for quantitative analysis including regression analysis. Using nearly 12000 individual student responses to SET questionnaires and ten key dimensions of teaching and 25 courses at various undergraduate and postgraduate levels for multiple years at a large Australian university, this paper investigates whether this is indeed the case and if so under what circumstances. This paper tests this proposition first by examining variance inflation factors (VIFs), across courses, levels and over time using individual responses; and secondly by using class averages. In the first instance, the paper finds no sustainable evidence of multicollinearity. While, there were one or two isolated cases of VIFs marginally exceeding the conservative threshold of 5, in no cases did the VIFs for any of the instructional attributes come anywhere close to the high threshold value of 10. In the second instance, however, the paper finds that the attributes are highly correlated as all the VIFs exceed 10. These findings have two implications: (a) given the ordinal nature of the data ordered probit analysis using individual student responses can be employed to quantify the impact of instructional attributes on TEVAL score; (b) Data based on class averages cannot be used for probit analysis. An illustrative exercise using level 2 undergraduate courses data suggests higher TEVAL scores depend first and foremost on improving explanation, presentation, and organization of lecture materials.

An exploratory study into managing value creation in tourism service firms: Understanding value creation phases at the intersection of the tourism service firm and their customers

To satisfy customers, managers of tourism services need to understand their customers' value requirements and then develop a unique service value offering based on those requirements. This understanding underpins their effort to provide superior value to customers and deliver the proposed services through employees. Problematically, previous work on value creation (i.e. customer value) has focused separately on either the firm or customer. This theoretical separation does not allow investigation of whether there may be discrepancies between what value firms offer and what value customers perceive they have received. We bring tourism service firms (manager and employee) and customers together and examine the nature of a tourism service provider's value proposition, its contribution to the value offering, and subsequent impact on customers' perceived-value-in-use. We focus on the important role that employees play as boundary spanning workers in the value creation phases, linking the tourism service provider and customer.

A game of balance and disguise: Examining experiential value and game attributes in social marketing m-games

Experiential value is an important driver of customer repeat behaviour and is necessary for achieving sustained behaviour. Understanding the value gained by consumers is particularly important when adopting innovative techniques, such as new technology. Social marketing (behaviour change) practice is increasingly using the technology of mobile games (m-games), yet there is little scholarly research to explain how these games can create experiential value for the user, or which game attributes influence this value. A key finding of this thesis is the importance of achieving a balance between entertainment value and behaviour value through the use of key game attributes relating to disguise and performance. The research offers a contribution to address current managerial problems faced by social marketing practitioners looking to employ m-games to achieve behavioural outcomes.

Cumulative effects on the change of residual value in PPP projects: A comparative case study

Public private partnerships (PPPs) have been adopted widely to provide public facilities and services. According to the PPP agreement, PPP projects would be transferred to the public sector. However, problems related to the subsequent management of ongoing PPP projects have not been studied thoroughly. Residual value risk (RVR) can occur if the public sector cannot obtain the project in the desired conditions as required in the agreement when a project is being transferred. RVR has been identified as an important risk in PPPs and has greatly influenced the outputs of the projects. In order to further observe the change of residual value (RV) during the process of PPP projects and to reveal the internal mechanism for reducing the RVR, a comparative case study of two PPP projects in mainland China and Hong Kong was conducted. Based on the case study, different factors leading to RVR and a series of key risk indicators (KRIs) were identified. The comparison demonstrates that RVR is an important risk that could influence the success of PPP projects. The cumulative effects during the concession period can play significant roles in the occurrence of RVR. Additionally, the cumulative effects in different cases can make the RVR different because of different stakeholders’ efforts on the projects and ways to treat RVR. Finally, alternatives for the public sector to treat RVR were proposed. The findings of this research can reduce RVR and improve the performance of PPP projects.

The shifting value of design in the Australian Architecture Industry

Architects regularly employ design as a problem-solving tool in the built environment. Within the design process, architects apply design thinking to reframe problems as opportunities, take advantage of contradictory information to develop new solutions, and differentiate outcomes based on context. This research aims to investigate how design can be better positioned to develop greater differentiated value to an architect’s current service offering, and how design as a strategy could be applied as a driver of business innovation within the Australian architecture industry. The research will explore literature relating to the future of architecture, the application of design thinking, and the benefits of strategic design. The future intent of the research is to develop strategies that improve the value offering of architects, and develop design led solutions that could be applied successfully to the business of architecture.

A three-dimensional hybrid smoothed finite element method (H-SFEM) for nonlinear solid mechanics problems

This paper presents a novel three-dimensional hybrid smoothed finite element method (H-SFEM) for solid mechanics problems. In 3D H-SFEM, the strain field is assumed to be the weighted average between compatible strains from the finite element method (FEM) and smoothed strains from the node-based smoothed FEM with a parameter α equipped into H-SFEM. By adjusting α, the upper and lower bound solutions in the strain energy norm and eigenfrequencies can always be obtained. The optimized α value in 3D H-SFEM using a tetrahedron mesh possesses a close-to-exact stiffness of the continuous system, and produces ultra-accurate solutions in terms of displacement, strain energy and eigenfrequencies in the linear and nonlinear problems. The novel domain-based selective scheme is proposed leading to a combined selective H-SFEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The proposed 3D H-SFEM is an innovative and unique numerical method with its distinct features, which has great potential in the successful application for solid mechanics problems.

A computer code for enclosed natural convection in the boundary layer regime

A computer code is developed for the numerical prediction of natural convection in rectangular two-dimensional cavities at high Rayleigh numbers. The governing equations are retained in the primitive variable form. The numerical method is based on finite differences and an ADI scheme. Convective terms may be approximated with either central or hybrid differencing for greater stability. A non-uniform grid distribution is possible for greater efficiency. The pressure is dealt with via a SIMPLE type algorithm and the use of a fast elliptic solver for the solenoidal velocity correction field significantly reduces computing times. Preliminary results indicate that the code is reasonably accurate, robust and fast compared with existing benchmarks and finite difference based codes, particularly at high Rayleigh numbers. Extension to three-dimensional problems and turbulence studies in similar geometries is readily possible and indicated.

Lowering grain boundary resistance of BaZr0.8Y0.2O3−δ with LiNO3 sintering-aid improves proton conductivity for fuel cell operation

A novel sintering additive based on LiNO3 was used to overcome the drawbacks of poor sinterability and low grain boundary conductivity in BaZr0.8Y0.2O3-δ (BZY20) protonic conductors. The Li-additive totally evaporated during the sintering process at 1600°C for 6 h, which led to highly dense BZY20 pellets (96.5% of the theoretical value). The proton conductivity values of BZY20 with Li sintering-aid were significantly larger than the values reported for BZY sintered with other metal oxides, due to the fast proton transport in the "clean" grain boundaries and grain interior. The total conductivity of BZY20-Li in wet Ar was 4.45 × 10-3 S cm-1 at 600°C. Based on the improved sinterability, anode-supported fuel cells with 25 μm-thick BZY20-Li electrolyte membranes were fabricated by a co-firing technique. The peak power density obtained at 700°C for a BZY-Ni/BZY20-Li/La0.6Sr0.4Co0.2Fe 0.8O3-δ (LSCF)-BZY cell was 53 mW cm-2, which is significantly larger than the values reported for fuel cells using electrolytes made of BZY sintered with the addition of ZnO and CuO, confirming the advantage of using Li as a sintering aid.