Effective Cell-Centred Time-Domain Maxwell's Equations Numerical Solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed.

Some Remarks on the Approximation of Transitional Density in Stochastic Differential Equations

Aijt-Sahalia (2002) introduced a method to estimate transitional probability densities of di®usion processes by means of Hermite expansions with coe±cients determined by means of Taylor series. This note describes a numerical procedure to ¯nd these coe±cients based on the calculation of moments. One advantage of this procedure is that it can be used e®ectively when the mathematical operations required to ¯nd closed-form expressions for these coe±cients are otherwise infeasible.

Organizational ambidexterity and corporate entrepreneurship : the differential effects on venturing, innovation and renewal processes

Most corporate entrepreneurship studies have focused on either innovation, venturing or strategic renewal making comparison between the antecedents of all three aspects of corporate entrepreneurship difficult. Moreover, studies on corporate entrepreneurship hardly address organizational antecedents, while simultaneously managing and organizing CE and mainstream activities has been seen as a major challenge for incumbent firms. Our findings show that organizational ambidexterity has strong and differential effects on venturing, innovation and renewal. We find, for example, that innovation is affected by horizontal integration, while strategic renewal is significantly influenced by integration on top management team level.

Is the sum more than the corporate entrepreneurship parts? the different effects of social capital on innovation, venturing, and renewal processes

Principal Topic Although corporate entrepreneurship is of vital importance for long-term firm survival and growth (Zahra and Covin, 1995), researchers still struggle with understanding how to manage corporate entrepreneurship activities. Corporate entrepreneurship consists of three parts: innovation, venturing, and renewal processes (Guth and Ginsberg, 1990). Innovation refers to the development of new products, venturing to the creation of new businesses, and renewal to redefining existing businesses (Sharma, and Chrisman, 1999; Verbeke et al., 2007). Although there are many studies focusing on one of these aspects (cf. Burgelman, 1985; Huff et al., 1992), it is very difficult to compare the outcomes of these studies due to differences in contexts, measures, and methodologies. This is a significant lack in our understanding of CE, as firms engage in all three aspects of CE, making it important to compare managerial and organizational antecedents of innovation, venturing and renewal processes. Because factors that may enhance venturing activities may simultaneously inhibit renewal activities. The limited studies that did empirically compare the individual dimensions (cf. Zahra, 1996; Zahra et al., 2000; Yiu and Lau, 2008; Yiu et al., 2007) generally failed to provide a systematic explanation for potential different effects of organizational antecedents on innovation, venturing, and renewal. With this study we aim to investigate the different effects of structural separation and social capital on corporate entrepreneurship activities. The access to existing and the development of new knowledge has been deemed of critical importance in CE-activities (Floyd and Wooldridge, 1999; Covin and Miles, 2007; Katila and Ahuja, 2002). Developing new knowledge can be facilitated by structurally separating corporate entrepreneurial units from mainstream units (cf. Burgelman, 1983; Hill and Rothaermel, 2003; O'Reilly and Tushman, 2004). Existing knowledge and resources are available through networks of social relationships, defined as social capital (Nahapiet and Ghoshal, 1998; Yiu and Lau, 2008). Although social capital has primarily been studied at the organizational level, it might be equally important at top management level (Belliveau et al., 1996). However, little is known about the joint effects of structural separation and integrative mechanisms to provide access to social capital on corporate entrepreneurship. Could these integrative mechanisms for example connect the separated units to facilitate both knowledge creation and sharing? Do these effects differ for innovation, venturing, and renewal processes? Are the effects different for organizational versus top management team integration mechanisms? Corporate entrepreneurship activities have for example been suggested to take place at different levels. Whereas innovation is suggested to be a more bottom-up process, strategic renewal is a more top-down process (Floyd and Lane, 2000; Volberda et al., 2001). Corporate venturing is also a more bottom-up process, but due to the greater required resource commitments relative to innovation, it ventures need to be approved by top management (Burgelman, 1983). As such we will explore the following key research question in this paper: How do social capital and structural separation on organizational and TMT level differentially influence innovation, venturing, and renewal processes? Methodology/Key Propositions We investigated our hypotheses on a final sample of 240 companies in a variety of industries in the Netherlands. All our measures were validated in previous studies. We targeted a second respondent in each firm to reduce problems with single-rater data (James et al., 1984). We separated the measurement of the independent and the dependent variables in two surveys to create a one-year time lag and reduce potential common method bias (Podsakoff et al., 2003). Results and Implications Consistent with our hypotheses, our results show that configurations of structural separation and integrative mechanisms have different effects on the three aspects of corporate entrepreneurship. Innovation was affected by organizational level mechanisms, renewal by integrative mechanisms on top management team level and venturing by mechanisms on both levels. Surprisingly, our results indicated that integrative mechanisms on top management team level had negative effects on corporate entrepreneurship activities. We believe this paper makes two significant contributions. First, we provide more insight in what the effects of ambidextrous organizational forms (i.e. combinations of differentiation and integration mechanisms) are on venturing, innovation and renewal processes. Our findings show that more valuable insights can be gained by comparing the individual parts of corporate entrepreneurship instead of focusing on the whole. Second, we deliver insights in how management can create a facilitative organizational context for these corporate entrepreneurship activities.

Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.

Closed-form design equations for decoupling networks of small arrays

Small element spacing in compact arrays results in strong mutual coupling between the array elements. A decoupling network consisting of reactive cross-coupling elements can alleviate problems associated with the coupling. Closed-form design equations for the decoupling networks of symmetrical arrays with two or three elements are presented.