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.

The theatre programme : a public discourse at a staging of Maxwell Anderson's "Anne of the Thousand Days"

The term ’public discourses’ describes a range of texts or signifiers that inform the conditions of audience reception. Public discourses include myriad written, visual, spatial, auditory and sensory texts experienced by an audience at a particular theatrical event. Ric Knowles first introduced this term in his recent work Reading the Material Theatre. Whereas Knowles was interested in how public discourses modified the conditions of reception, my broader research is to explore how these public discourses become texts in themselves. This paper will discuss one public discourse, the theatre programme, as it related to a staging of Maxwell Anderson’s Anne of the Thousand Days at the Brisbane Powerhouse in June 2006. The significance of the programme was explored at symposiums held after the performances. Audiences generally view programmes before a performance and after a performance and its significance as a written text changes. The program became a sign vehicle that worked to expound and explicate the meaning of the play for the audience. This public discourse became a significant written text contributing to the textual whole of the theatrical event.

The three faces of Maxwell�s equations

In dealing with electromagnetic phenomena and in particular the phenomena of optics, despite the recognition of the quanta of light people tend to talk of the amplitudes and field strengths, as if the electromagnetic field were a classical field. For example we measure the wavelength of light by studying interference fringes. In this paper we study the inter-relationship of three ways of looking at the problem: in terms of classical wave fields, wave function of the photon; and the quantized wave field. The comparison and contrasts of these three modes of description are carefully analyzed in this paper. The ways in which these different modes complement our intuition and insight are also discussed.

Gaussian-Maxwell beams

Gaussian-beam-type solutions to the Maxwell equations are constructed by using results from relativistic front analysis, and the propagation characteristics of these beams are analyzed. The rays of geometrical optics are shown to be the trajectories of energy flow, as given by the Poynting vector. The longitudinal components of the field vectors in the direction of the beam axis, though small, are shown to be essential for a consistent description.

Paraxial Maxwell beams: transformation by general linear optical systems

Extending the work of earlier papers on the relativistic-front description of paraxial optics and the formulation of Fourier optics for vector waves consistent with the Maxwell equations, we generalize the Jones calculus of axial plane waves to describe the action of the most general linear optical system on paraxial Maxwell fields. Several examples are worked out, and in each case it is shown that the formalism leads to physically correct results. The importance of retaining the small components of the field vectors along the axis of the system for a consistent description is emphasized.

Steady mixed convection stagnation-point flow of upper convected Maxwell fluids with magnetic field

The steady MHD mixed convection flow of a viscoelastic fluid in the vicinity of two-dimensional stagnation point with magnetic field has been investigated under the assumption that the fluid obeys the upper-convected Maxwell (UCM) model. Boundary layer theory is used to simplify the equations of motion. induced magnetic field and energy which results in three coupled non-linear ordinary differential equations which are well-posed. These equations have been solved by using finite difference method. The results indicate the reduction in the surface velocity gradient, surface heat transfer and displacement thickness with the increase in the elasticity number. These trends are opposite to those reported in the literature for a second-grade fluid. The surface velocity gradient and heat transfer are enhanced by the magnetic and buoyancy parameters. The surface heat transfer increases with the Prandtl number, but the surface velocity gradient decreases.

Steady flow of a maxwell fluid in a porous cylindrical annulus with circular cross-section

When a fluid with memory is injected into any flow region some assumptions regarding the initial state of stress have to be made in order to determine the state of stress at any subsequent instant. For a Maxwell fluid, it is assumed that the fluid near the surface of injection is suddenly stressed and responds by starting flow in accordance with the mechanical model chosen. The flow of a Maxwell fluid with a single relaxation time has been determined under the above assumption in the following two cases: (i) annulus between two porous concentric circular cylinders, and (ii) space between two porous and infinitely extending parallel plates. The nature of flow in the present case is similar to that of the Reiner-Rivlin fluids obtained by Narasimhan2).

Flow of a maxwell liquid fluid between two rotating coaxial cones having the same vertex

We consider the secondary flows arising in the motion of a Maxwell fluid between two rotating coaxial cones having the same vertex. We find that in any meridian plane passing through the common axis of the cones, the flow field is divided into two regions. Such a division of flow field was first reported by Bhatnagar and Rathna.

Moore meets maxwell

Moore's Law has driven the semiconductor revolution enabling over four decades of scaling in frequency, size, complexity, and power. However, the limits of physics are preventing further scaling of speed, forcing a paradigm shift towards multicore computing and parallelization. In effect, the system is taking over the role that the single CPU was playing: high-speed signals running through chips but also packages and boards connect ever more complex systems. High-speed signals making their way through the entire system cause new challenges in the design of computing hardware. Inductance, phase shifts and velocity of light effects, material resonances, and wave behavior become not only prevalent but need to be calculated accurately and rapidly to enable short design cycle times. In essence, to continue scaling with Moore's Law requires the incorporation of Maxwell's equations in the design process. Incorporating Maxwell's equations into the design flow is only possible through the combined power that new algorithms, parallelization and high-speed computing provide. At the same time, incorporation of Maxwell-based models into circuit and system-level simulation presents a massive accuracy, passivity, and scalability challenge. In this tutorial, we navigate through the often confusing terminology and concepts behind field solvers, show how advances in field solvers enable integration into EDA flows, present novel methods for model generation and passivity assurance in large systems, and demonstrate the power of cloud computing in enabling the next generation of scalable Maxwell solvers and the next generation of Moore's Law scaling of systems. We intend to show the truly symbiotic growing relationship between Maxwell and Moore!

Steady mixed convection flow of Maxwell fluid over an exponentially stretching vertical surface with magnetic field and viscous dissipation

The steady mixed convection flow and heat transfer from an exponentially stretching vertical surface in a quiescent Maxwell fluid in the presence of magnetic field, viscous dissipation and Joule heating have been studied. The stretching velocity, surface temperature and magnetic field are assumed to have specific exponential function forms for the existence of the local similarity solution. The coupled nonlinear ordinary differential equations governing the local similarity flow and heat transfer have been solved numerically by Chebyshev finite difference method. The influence of the buoyancy parameter, viscous dissipation, relaxation parameter of Maxwell fluid, magnetic field and Prandtl number on the flow and heat transfer has been considered in detail. The Nusselt number increases significantly with the Prandtl number, but the skin friction coefficient decreases. The Nusselt number slightly decreases with increasing viscous dissipation parameter, but the skin friction coefficient slightly increases. Maxwell fluid reduces both skin friction coefficient and Nusselt number, whereas buoyancy force enhances them.

James Clerk Maxwell e a unidade do mundo: modelos e metáforas na construção de teorias científicas

Esta é uma pesquisa sobre o uso de metáforas na construção de modelos por parte do físico escocês James Clerk Maxwell. O objetivo da pesquisa foi buscar compreender de que maneira o uso de metáforas e modelos é legítimo na ciência e em que medida contribui para seu sucesso. Além disso, busca compreender em que medida o uso de artifícios como modelos e analogias entre ramos distintos da ciência são impulsionadores de sucesso explicativo e preditivo da teoria do físico estudado. Explora as crenças teológicas e filosóficas do autor, que vê o mundo como unidade, permitindo a analogia entre ramos distintos da física. Seus desenvolvimentos em torno de teorias como calor, cores, óptica, magnetismo e eletricidade permitem evidenciar essa visão em todo o seu trabalho. Maxwell é considerado inaugurador de nova metodologia com o uso de modelos e metáforas. Explora o desenvolvimento da teoria das cores, da descrição matemática da estabilidade dos anéis de Saturno e o desenvolvimento da teoria dos gases como preâmbulo à discussão da teoria do eletromagnetismo. Descreve o desenvolvimento teórico do eletromagnetismo em seus diversos momentos. A construção da teoria do eletromagnetismo evidencia paulatino abandono do mecanicismo, uso intenso de modelos e metáforas temporários e ênfase na quantificação e no uso de experimentos. Discute o relacionamento de Maxwell com as discussões filosóficas, sociais e teológicas de sua época, seu engajamento em atividades práticas nesse sentido e suas influências científicas e filosóficas. Descreve e discute os textos filosóficos do cientista, em que se evidenciam sua ontologia, suas crenças teológicas e sua concepção de analogias. Discute a questão do uso de analogias em ciência e compara diversos autores que abordam o tema. A metodologia utilizada foi a de levantamento bibliográfico com análise crítica da literatura do autor e de seus comentadores, além de comentário crítico sobre os textos primários e secundários. Conclui que o sucesso científico de Maxwell deve-se à sua aposta numa unidade do mundo garantida por Deus, bem como na unidade entre o mundo e a mente humana, posturas que mostraram ser bem-sucedidas quando aplicadas à metodologia científica. Conclui também pela legitimidade e necessidade do uso de metáforas e modelos no empreendimento científico.