O Intuitivo e o Lógico no Conhecimento Matemático: análise de uma proposta pedagógica em relação a abordagens filosóficas atuais e ao contexto educacional da matemática

In this paper, we consider Meneghetti & Bicudo's proposal (2003) regarding the constitution of mathematical knowledge and analyze it with respect to the following two focuses: in relation to conceptions of mathematical knowledge following the fundamentalist crisis in mathematics; and in the educational context of mathematics. The investigation of the first focus is done analyzing new claims in mathematical philosophy. The investigation of the second focus is done firstly via a theoretical reflection followed by an examination of the implementation of the proposal in the process of development of didactic materials for teaching and learning Mathematics. Finally, we present the main results of the application of one of those materials.

O intuitivo e o lógico no conhecimento matemático: análise de uma proposta pedagógica em relação a abordagens filosóficas atuais e ao contexto educacional da matemática

In this paper, we consider Meneghetti & Bicudo's proposal (2003) regarding the constitution of mathematical knowledge and analyze it with respect to the following two focuses: in relation to conceptions of mathematical knowledge following the fundamentalist crisis in mathematics; and in the educational context of mathematics. The investigation of the first focus is done analyzing new claims in mathematical philosophy. The investigation of the second focus is done firstly via a theoretical reflection followed by an examination of the implementation of the proposal in the process of development of didactic materials for teaching and learning Mathematics. Finally, we present the main results of the application of one of those materials.

Two-degree-of-freedom vortex-induced vibration of circular cylinders with very low aspect ratio and small mass ratio

The investigation of vortex-induced vibration on very short cylinders with two degrees of freedom has drawn the attention of a large number of researchers. Some investigations on such a problem are carried out in order to have a better understanding of the physics involved in vortex-induced motions of floating bodies such as offshore platforms. In this paper, experiments were carried out in a recirculating water channel over the range of Reynolds number 6000aspect ratios (0.3≤L/D≤2.0) were shown and the results were discussed in depth. Conversely to what would be expected for cylinders with very low aspect ratio, the results showed large motions in the transverse direction with maximum amplitudes around 1.5 diameters for cylinders with L/D=2.0, despite being smaller when the aspect ratio is reduced. Moreover, the response amplitudes presented high values around 0.4 diameters in the in-line direction. In fact, the large transverse motions were related to a strong coupling with the in-line responses, visibly identified in the plots of nondimensional frequency, as well as by the trajectories in the XY-plane, Lissajous figures, particularly in the case of m⁎=1.00 and L/D=2.0, when 8-shape trajectories were clearly observed. The case of m⁎=1.00 deserves more attention because of its smaller amplitude compared to the cases with the same aspect ratio and a larger mass ratio. This counter-intuitive behavior seems to be related to the energy transferring process from the steady stream to the oscillatory hydroelastic system. Finally, it is noteworthy that the characteristic of the “Strouhal-like” number decreases when the aspect ratio decreases, as also observed in previous works available in the literature, most of them for stationary cylinders.

Two-degree-of-freedom vortex-induced vibration of circular cylinders with very low aspect ratio and small mass ratio

The investigation of vortex-induced vibration on very short cylinders with two degrees of freedom has drawn the attention of a large number of researchers. Some investigations on such a problem are carried out in order to have a better understanding of the physics involved in vortex-induced motions of floating bodies such as offshore platforms. In this paper, experiments were carried out in a recirculating water channel over the range of Reynolds number 6000aspect ratios (0.3≤L/D≤2.0) were shown and the results were discussed in depth. Conversely to what would be expected for cylinders with very low aspect ratio, the results showed large motions in the transverse direction with maximum amplitudes around 1.5 diameters for cylinders with L/D=2.0, despite being smaller when the aspect ratio is reduced. Moreover, the response amplitudes presented high values around 0.4 diameters in the in-line direction. In fact, the large transverse motions were related to a strong coupling with the in-line responses, visibly identified in the plots of nondimensional frequency, as well as by the trajectories in the XY-plane, Lissajous figures, particularly in the case of m⁎=1.00 and L/D=2.0, when 8-shape trajectories were clearly observed. The case of m⁎=1.00 deserves more attention because of its smaller amplitude compared to the cases with the same aspect ratio and a larger mass ratio. This counter-intuitive behavior seems to be related to the energy transferring process from the steady stream to the oscillatory hydroelastic system. Finally, it is noteworthy that the characteristic of the “Strouhal-like” number decreases when the aspect ratio decreases, as also observed in previous works available in the literature, most of them for stationary cylinders.

Characterization of turbulent jets from high-aspect-ratio rectangular nozzles

Turbulent free jets issuing from rectangular slots with various high aspect ratios (15-120) are characterized. The centerline mean and rms velocities are measured using hot-wire anemometry over a downstream distance of up to 160 slot heights at a slot-height-based Reynolds number of 10000. Experimental results suggest that a rectangular jet with sufficiently high aspect ratio (> 15) may be distinguished between three flow zones: an initial quasi-plane-jet zone, a transition zone, and a final quasi-axisymmetric-jet zone. In the quasi-plane-jet zone, the turbulent velocity field is statistically similar, but not identical, to those of a plane jet. (c) 2005 American Institute of Physics.

Capillary network models for transport in packed beds: Considerations of pore aspect ratio

The conventional analysis for the estimation of the tortuosity factor for transport in porous media is modified here to account for the effect of pore aspect ratio. Structural models of the porous medium are also constructed for calculating the aspect ratio as a function of porosity. Comparison of the model predictions with the extensive data of Currie (1960) for the effective diffusivity of hydrogen in packed beds shows good agreement with a network model of randomly oriented intersecting pores for porosities upto about 50 percent, which is the region of practical interest. The predictions based on this network model are also found to be in better agreement with the data of Currie than earlier expressions developed for unconsolidated and grainy media.

The intuitive basis of implicature: relevance theoretic implicitness versus gricean implying

The notion of implicature was first introduced by Paul Grice (1967, 1989), who defined it essentially as what is communicated less what is said. This definition contributed in part to the proliferation of a large number of different species of implicature by neo-Griceans. Relevance theorists have responded to this by proposing a shift back to the distinction between "explicit" & "implicit" meaning (corresponding to "explicature" & "implicature," respectively). However, they appear to have pared down the concept of implicature too much, ignoring phenomena that may be better treated as implicatures in their overgeneralization of the concept of explicature. These problems have their roots in the fact that explicit & implicit meaning intuitively overlap & thus do not provide a suitable basis for distinguishing implicature from other types of pragmatic phenomena. An alternative conceptualization of implicature based on the concept of "implying" with which Grice originally associated his notion of implicature is thus proposed. From this definition, it emerges that implicature constitutes something else inferred by the addressee that is not literally said by the speaker. Instead, it is meant in addition to what the speaker literally says & is consequently defeasible like all other types of pragmatic phenomena. 1 Figure, 60 References. Adapted from the source document

Applying complex network theory to the understanding of high-aspect-ratio carbon-filled composites

This work demonstrates that the theoretical framework of complex networks typically used to study systems such as social networks or the World Wide Web can be also applied to material science, allowing deeper understanding of fundamental physical relationships. In particular, through the application of the network theory to carbon nanotubes or vapour-grown carbon nanofiber composites, by mapping fillers to vertices and edges to the gap between fillers, the percolation threshold has been predicted and a formula that relates the composite conductance to the network disorder has been obtained. The theoretical arguments are validated by experimental results from the literature.

The influence of matrix mediated hopping conductivity, filler concentration, aspect ratio and orientation on the electrical response of carbon nanotube/polymer nanocomposites

A model to simulate the conductivity of carbon nanotube/polymer nanocomposites is presented. The proposed model is based on hopping between the fillers. A parameter related to the influence of the matrix in the overall composite conductivity is defined. It is demonstrated that increasing the aspect ratio of the fillers will increase the conductivity. Finally, it is demonstrated that the alignment of the filler rods parallel to the measurement direction results in higher conductivity values, in agreement with results from recent experimental work.

Aspect-oriented domain analysis

Dissertação de Mestrado em Engenharia Informática