Search results for: formalism

Authors: Kamaran Fathulla

Abstract:

Human creativity knows no bounds. More than a millennia ago humans have expressed their knowledge on cave walls and on clay artefacts. Using visuals such as diagrams and paintings have always provided us with a natural and intuitive medium for expressing such creativity. Making sense of human generated visualisation has been influenced by western scientific philosophies which are often reductionist in their nature. Theoretical frameworks such as those delivered by Peirce dominated our views of how to make sense of visualisation where a visual is seen as an emergent property of our thoughts. Others have reduced the richness of human-generated visuals to mere shapes drawn on a piece of paper or on a screen. This paper introduces an alternate framework where the centrality of human functioning is given explicit and richer consideration through the multi aspectual philosophical works of Herman Dooyeweerd. Dooyeweerd's framework of understanding reality was based on fifteen aspects of reality, each having a distinct core meaning. The totality of the aspects formed a ‘rainbow’ like spectrum of meaning. The thesis of this approach is that meaningful human functioning in most cases involves the diversity of all aspects working in synergy and harmony. Illustration of the foundations and applicability of this approach is underpinned in the case of humans use of diagramming for creative purposes, particularly within an educational context. Diagrams play an important role in education. Students and lecturers use diagrams as a powerful tool to aid their thinking. However, research into the role of diagrams used in education continues to reveal difficulties students encounter during both processes of interpretation and construction of diagrams. Their main problems shape up students difficulties with diagrams. The ever-increasing diversity of diagrams' types coupled with the fact that most real-world diagrams often contain a mix of these different types of diagrams such as boxes and lines, bar charts, surfaces, routes, shapes dotted around the drawing area, and so on with each type having its own distinct set of static and dynamic semantics. We argue that the persistence of these problems is grounded in our existing ways of understanding diagrams that are often reductionist in their underpinnings driven by a single perspective or formalism. In this paper, we demonstrate the limitations of these approaches in dealing with the three problems. Consequently, we propose, discuss, and demonstrate the potential of a nonreductionist framework for understanding diagrams based on Symbolic and Spatial Mappings (SySpM) underpinned by Dooyeweerd philosophy. The potential of the framework to account for the meaning of diagrams is demonstrated by applying it to a real-world case study physics diagram.

Keywords: SySpM, drawing style, mapping

Procedia PDF Downloads 238

Authors: P. Naderi, M. N. Ouarzazi, S. C. Hirata, H. Ben Hamed, H. Beji

Abstract:

The stability of mixed convection in a Newtonian fluid medium heated from below and cooled from above, also known as the Poiseuille-Rayleigh-Bénard problem, has been extensively investigated in the past decades. To our knowledge, mixed convection in porous media has received much less attention in the published literature. The present paper extends the mixed convection problem in porous media for the case of a viscoelastic fluid flow owing to its numerous environmental and industrial applications such as the extrusion of polymer fluids, solidification of liquid crystals, suspension solutions and petroleum activities. Without a superimposed through-flow, the natural convection problem of a viscoelastic fluid in a saturated porous medium has already been treated. The effects of the viscoelastic properties of the fluid on the linear and nonlinear dynamics of the thermoconvective instabilities have also been treated in this work. Consequently, the elasticity of the fluid can lead either to a Hopf bifurcation, giving rise to oscillatory structures in the strongly elastic regime, or to a stationary bifurcation in the weakly elastic regime. The objective of this work is to examine the influence of the main horizontal flow on the linear and characteristics of these two types of instabilities. Under the Boussinesq approximation and Darcy's law extended to a viscoelastic fluid, a temporal stability approach shows that the conditions for the appearance of longitudinal rolls are identical to those found in the absence of through-flow. For the general three-dimensional (3D) perturbations, a Squire transformation allows the deduction of the complex frequencies associated with the 3D problem using those obtained by solving the two-dimensional one. The numerical resolution of the eigenvalue problem concludes that the through-flow has a destabilizing effect and selects a convective configuration organized in purely transversal rolls which oscillate in time and propagate in the direction of the main flow. In addition, by using the mathematical formalism of absolute and convective instabilities, we study the nature of unstable three-dimensional disturbances. It is shown that for a non-vanishing through-flow, general three-dimensional instabilities are convectively unstable which means that in the absence of a continuous noise source these instabilities are drifted outside the porous medium, and no long-term pattern is observed. In contrast, purely transversal rolls may exhibit a transition to absolute instability regime and therefore affect the porous medium everywhere including in the absence of a noise source. The absolute instability threshold, the frequency and the wave number associated with purely transversal rolls are determined as a function of the Péclet number and the viscoelastic parameters. Results are discussed and compared to those obtained from laboratory experiments in the case of Newtonian fluids.

Keywords: instability, mixed convection, porous media, and viscoelastic fluid

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