An example of cognitive obstacles in advanced integration: the case of scalar line integrals

Cognitive obstacles that arise in the teaching and learning of scalar line integrals, derived from cognitive aids provided to students when first learning about integration of single variable functions are described. A discussion of how and why the obstacles cause students problems is presented and possible strategies to overcome the obstacles are outlined.

Sistema de reserves hoteleres on-line, basat en el protocol de comunicació OTA

L’origen d’aquest projecte neix en la necessitat de crear un sistema de reserves hoteleres on-line integral i amb connectivitat amb altres sistemes de reserves. S'ha optat pel protocol de comunicació OTA(Open Travel Alliance), es tracta d'un protocol de comunicació XML ideat per empreses del sector turístic dels Estats Units per la necessitat comuna d’unes especificacions tècniques que permetessin la comunicació electrònica de la informació

A model of road effect using line integrals and a test of the performance of two new road indices using the distribution of small mammals in an Atlantic Forest landscape

Effects of roads on wildlife and its habitat have been measured using metrics, such as the nearest road distance, road density, and effective mesh size. In this work we introduce two new indices: (1) Integral Road Effect (IRE), which measured the sum effects of points in a road at a fixed point in the forest; and (2) Average Value of the Infinitesimal Road Effect (AVIRE), which measured the average of the effects of roads at this point. IRE is formally defined as the line integral of a special function (the infinitesimal road effect) along the curves that model the roads, whereas AVIRE is the quotient of IRE by the length of the roads. Combining tools of ArcGIS software with a numerical algorithm, we calculated these and other road and habitat cover indices in a sample of points in a human-modified landscape in the Brazilian Atlantic Forest, where data on the abundance of two groups of small mammals (forest specialists and habitat generalists) were collected in the field. We then compared through the Akaike Information Criterion (AIC) a set of candidate regression models to explain the variation in small mammal abundance, including models with our two new road indices (AVIRE and IRE) or models with other road effect indices (nearest road distance, mesh size, and road density), and reference models (containing only habitat indices, or only the intercept without the effect of any variable). Compared to other road effect indices, AVIRE showed the best performance to explain abundance of forest specialist species, whereas the nearest road distance obtained the best performance to generalist species. AVIRE and habitat together were included in the best model for both small mammal groups, that is, higher abundance of specialist and generalist small mammals occurred where there is lower average road effect (less AVIRE) and more habitat. Moreover, AVIRE was not significantly correlated with habitat cover of specialists and generalists differing from the other road effect indices, except mesh size, which allows for separating the effect of roads from the effect of habitat on small mammal communities. We suggest that the proposed indices and GIS procedures could also be useful to describe other spatial ecological phenomena, such as edge effect in habitat fragments. (C) 2012 Elsevier B.V. All rights reserved.

Line Integrals and Work in Thermodynamics

This paper considers line integration in the context of elementary thermodynamics, ending with irreversible to reversible work integrations (employing, in part, L'Hopital's rule).

The hydrodynamic and capture/retention performance of a gross pollutant trap

This research shows that gross pollutant traps (GPTs) continue to play an important role in preventing visible street waste—gross pollutants—from contaminating the environment. The demand for these GPTs calls for stringent quality control and this research provides a foundation to rigorously examine the devices. A novel and comprehensive testing approach to examine a dry sump GPT was developed. The GPT is designed with internal screens to capture gross pollutants—organic matter and anthropogenic litter. This device has not been previously investigated. Apart from the review of GPTs and gross pollutant data, the testing approach includes four additional aspects to this research, which are: field work and an historical overview of street waste/stormwater pollution, calibration of equipment, hydrodynamic studies and gross pollutant capture/retention investigations. This work is the first comprehensive investigation of its kind and provides valuable practical information for the current research and any future work pertaining to the operations of GPTs and management of street waste in the urban environment. Gross pollutant traps—including patented and registered designs developed by industry—have specific internal configurations and hydrodynamic separation characteristics which demand individual testing and performance assessments. Stormwater devices are usually evaluated by environmental protection agencies (EPAs), professional bodies and water research centres. In the USA, the American Society of Civil Engineers (ASCE) and the Environmental Water Resource Institute (EWRI) are examples of professional and research organisations actively involved in these evaluation/verification programs. These programs largely rely on field evaluations alone that are limited in scope, mainly for cost and logistical reasons. In Australia, evaluation/verification programs of new devices in the stormwater industry are not well established. The current limitations in the evaluation methodologies of GPTs have been addressed in this research by establishing a new testing approach. This approach uses a combination of physical and theoretical models to examine in detail the hydrodynamic and capture/retention characteristics of the GPT. The physical model consisted of a 50% scale model GPT rig with screen blockages varying from 0 to 100%. This rig was placed in a 20 m flume and various inlet and outflow operating conditions were modelled on observations made during the field monitoring of GPTs. Due to infrequent cleaning, the retaining screens inside the GPTs were often observed to be blocked with organic matter. Blocked screens can radically change the hydrodynamic and gross pollutant capture/retention characteristics of a GPT as shown from this research. This research involved the use of equipment, such as acoustic Doppler velocimeters (ADVs) and dye concentration (Komori) probes, which were deployed for the first time in a dry sump GPT. Hence, it was necessary to rigorously evaluate the capability and performance of these devices, particularly in the case of the custom made Komori probes, about which little was known. The evaluation revealed that the Komori probes have a frequency response of up to 100 Hz —which is dependent upon fluid velocities—and this was adequate to measure the relevant fluctuations of dye introduced into the GPT flow domain. The outcome of this evaluation resulted in establishing methodologies for the hydrodynamic measurements and gross pollutant capture/retention experiments. The hydrodynamic measurements consisted of point-based acoustic Doppler velocimeter (ADV) measurements, flow field particle image velocimetry (PIV) capture, head loss experiments and computational fluid dynamics (CFD) simulation. The gross pollutant capture/retention experiments included the use of anthropogenic litter components, tracer dye and custom modified artificial gross pollutants. Anthropogenic litter was limited to tin cans, bottle caps and plastic bags, while the artificial pollutants consisted of 40 mm spheres with a range of four buoyancies. The hydrodynamic results led to the definition of global and local flow features. The gross pollutant capture/retention results showed that when the internal retaining screens are fully blocked, the capture/retention performance of the GPT rapidly deteriorates. The overall results showed that the GPT will operate efficiently until at least 70% of the screens are blocked, particularly at high flow rates. This important finding indicates that cleaning operations could be more effectively planned when the GPT capture/retention performance deteriorates. At lower flow rates, the capture/retention performance trends were reversed. There is little difference in the poor capture/retention performance between a fully blocked GPT and a partially filled or empty GPT with 100% screen blockages. The results also revealed that the GPT is designed with an efficient high flow bypass system to avoid upstream blockages. The capture/retention performance of the GPT at medium to high inlet flow rates is close to maximum efficiency (100%). With regard to the design appraisal of the GPT, a raised inlet offers a better capture/retention performance, particularly at lower flow rates. Further design appraisals of the GPT are recommended.

Developments in texture-based vector field visualisation techniques

Vector field visualisation is one of the classic sub-fields of scientific data visualisation. The need for effective visualisation of flow data arises in many scientific domains ranging from medical sciences to aerodynamics. Though there has been much research on the topic, the question of how to communicate flow information effectively in real, practical situations is still largely an unsolved problem. This is particularly true for complex 3D flows. In this presentation we give a brief introduction and background to vector field visualisation and comment on the effectiveness of the most common solutions. We will then give some examples of current development on texture-based techniques, and given practical examples of their use in CFD research and hydrodynamic applications.

Visualisation of complex flows using texture-based techniques

Complex flow datasets are often difficult to represent in detail using traditional vector visualisation techniques such as arrow plots and streamlines. This is particularly true when the flow regime changes in time. Texture-based techniques, which are based on the advection of dense textures, are novel techniques for visualising such flows (i.e., complex dynamics and time-dependent). In this paper, we review two popular texture-based techniques and their application to flow datasets sourced from real research projects. The texture-based techniques investigated were Line Integral Convolution (LIC), and Image-Based Flow Visualisation (IBFV). We evaluated these techniques and in this paper report on their visualisation effectiveness (when compared with traditional techniques), their ease of implementation, and their computational overhead.

Visualisation of complex flows using texture-based techniques

Detailed representations of complex flow datasets are often difficult to generate using traditional vector visualisation techniques such as arrow plots and streamlines. This is particularly true when the flow regime changes in time. Texture-based techniques, which are based on the advection of dense textures, are novel techniques for visualising such flows. We review two popular texture based techniques and their application to flow datasets sourced from active research projects. The techniques investigated were Line integral convolution (LIC) [1], and Image based flow visualisation (IBFV) [18]. We evaluated these and report on their effectiveness from a visualisation perspective. We also report on their ease of implementation and computational overheads.

Visualising experimental flow fields through a stormwater gross pollutant trap

Abstract An experimental dataset representing a typical flow field in a stormwater gross pollutant trap (GPT) was visualised. A technique was developed to apply the image-based flow visualisation (IBFV) algorithm to the raw dataset. Particle image velocimetry (PIV) software was previously used to capture the flow field data by tracking neutrally buoyant particles with a high speed camera. The dataset consisted of scattered 2D point velocity vectors and the IBFV visualisation facilitates flow feature characterisation within the GPT. The flow features played a pivotal role in understanding stormwater pollutant capture and retention behaviour within the GPT. It was found that the IBFV animations revealed otherwise unnoticed flow features and experimental artefacts. For example, a circular tracer marker in the IBFV program visually highlighted streamlines to investigate the possible flow paths of pollutants entering the GPT. The investigated flow paths were compared with the behaviour of pollutants monitored during experiments.

The partition of unity finite element method for elastic wave propagation in Reissner-Mindlin plates

This paper reports a numerical method for modelling the elastic wave propagation in plates. The method is based on the partition of unity approach, in which the approximate spectral properties of the infinite dimensional system are embedded within the space of a conventional finite element method through a consistent technique of waveform enrichment. The technique is general, such that it can be applied to the Lagrangian family of finite elements with specific waveform enrichment schemes, depending on the dominant modes of wave propagation in the physical system. A four-noded element for the Reissner-indlin plate is derived in this paper, which is free of shear locking. Such a locking-free property is achieved by removing the transverse displacement degrees of freedom from the element nodal variables and by recovering the same through a line integral and a weak constraint in the frequency domain. As a result, the frequency-dependent stiffness matrix and the mass matrix are obtained, which capture the higher frequency response with even coarse meshes, accurately. The steps involved in the numerical implementation of such element are discussed in details. Numerical studies on the performance of the proposed element are reported by considering a number of cases, which show very good accuracy and low computational cost. Copyright (C)006 John Wiley & Sons, Ltd.

Far-field analysis of axially symmetric three-dimensional directional cloaks.

Axisymmetric radiating and scattering structures whose rotational invariance is broken by non-axisymmetric excitations present an important class of problems in electromagnetics. For such problems, a cylindrical wave decomposition formalism can be used to efficiently obtain numerical solutions to the full-wave frequency-domain problem. Often, the far-field, or Fraunhofer region is of particular interest in scattering cross-section and radiation pattern calculations; yet, it is usually impractical to compute full-wave solutions for this region. Here, we propose a generalization of the Stratton-Chu far-field integral adapted for 2.5D formalism. The integration over a closed, axially symmetric surface is analytically reduced to a line integral on a meridional plane. We benchmark this computational technique by comparing it with analytical Mie solutions for a plasmonic nanoparticle, and apply it to the design of a three-dimensional polarization-insensitive cloak.

La formación on-line : una mirada integral sobre el e-learning, b-learning...

Se ofrecen el instrumento para los profesionales y las organizaciones que quieran analizar y profundizar en la formación on-line. Este tipo de formación supone la toma de decisiones sobre multitud de aspectos vinculados a la impartición, implica la creación y la coordinación de equipos multiprofesionales, y la generación de procesos y circuitos internos. Se basa en la experiencia docente de sus autores.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.