Search results for "equation"
showing 10 items of 4219 documents
DORA algorithm for network flow models with improved stability and convergence properties
2001
A new methodology for the solution of shallow water equations is applied for the computation of the unsteady-state flow in an urban drainage network. The inertial terms are neglected in the momentum equations and the solution is decoupled into one kinematic and one diffusive component. After a short presentation of the DORA (Double ORder Approximation) methodology in the case of a single open channel, the new methodology is applied to the case of a sewer network. The transition from partial to full section and vice versa is treated without the help of the Preissmann approximation. The algorithm also allows the computation of the diffusive component in the case of vertical topographic discon…
Tractional Motion Machines: Tangent-Managing Planar Mechanisms as Analog Computers and Educational Artifacts
2012
Concrete and virtual machines play a central role in the both Unconventional Computing (machines as computers) and in Math Education (influence of artifacts on reaching/producing abstract thought). Here we will examine some fallouts in these fields for the Tractional Motion Machines, planar mechanisms based on some devices used to plot the solutions of differential equations by the management of the tangent since the late 17th century.
A Method of Three-Dimensional Visualization of Molecular Processes of Apoptosis
2014
Apoptosis or programmed cell death plays an important role in many physiological states and diseases. Detection of apoptotic cells, tracing the development of apoptosis, drug development and regulation of apoptosis are an important parts of basic research in medicine. A large number of models have been developed that are based on the differential equations of the chemical kinetics, and can be expressed in a uniform notation using some XML-based languages, such as SBML and CellML. We describe the CellML and the simulation environment OpenCell herein. These tools can display models schematically and output results in the form of graphs showing time dependencies of component concentrations. Ho…
Estimation of brain connectivity through Artificial Neural Networks
2019
Among different methods available for estimating brain connectivity from electroencephalographic signals (EEG), those based on MVAR models have proved to be flexible and accurate. They rely on the solution of linear equations that can be pursued through artificial neural networks (ANNs) used as MVAR model. However, when few data samples are available, there is a lack of accuracy in estimating MVAR parameters due to the collinearity between regressors. Moreover, the assessment procedure is also affected by the lack of data points. The mathematical solution to these problems is represented by penalized regression methods based on l 1 norm, that can reduce collinearity by means of variable sel…
Experimental validation for spectrum cartography using adaptive multi-kernels
2017
This paper validates the functionality of an algorithm for spectrum cartography, generating a radio environment map (REM) using adaptive radial basis functions (RBF) based on a limited number of measurements. The power at all locations is estimated as a linear combination of different RBFs without assuming any prior information about either power spectral densities (PSD) of the transmitters or their locations. The RBFs are represented as centroids at optimized locations, using machine learning to jointly optimize their positions, weights and Gaussian decaying parameters. Optimization is performed using expectation maximization with a least squares loss function and a quadratic regularizer. …
Design and Investigation of a Touch Gesture for Dividing in a Virtual Manipulative Model for Equation-solving
2020
AbstractPhysical models for equation solving typically lack feedback regarding their appropriate use. Such feedback is possible in virtual environments and could be implemented in hybrid models. Based on an epistemological analysis, this article presents a touch gesture as a way for users to signal they want to divide both sides of an equation and a design for feedback on the use of this so-called ‘division gesture’. The design is investigated by contrasting a case study, in which students used an app with the division gesture, with a preparatory study where students had to perform corresponding actions on physical manipulatives. This investigation revealed insight into feedback functions, …
Specifications of model development
2016
Chapter 4 goes into detail with the specifications of the model and model validation. Why Partial Least Squares (PLS), a structural equation modelling approach, is chosen as the method for model testing is explained in section 4.1, while 4.2 describes the survey conducted to collect data for model testing. Section 4.3 goes into detail with the PLS approach, its theoretical background and its application to the research question, before section 4.4 outlines the necessary operationalisation of the constructs introduced in chapter 3.
Designing an Experimental Research Using the Finite Element Analysis Method
2019
In order to study the impact of cutting parameters on the cutting process, several research methods can be used. The first method generally used to understand the cutting process is the experiment from which clear and precise results are obtained. However, experiments can be very costly and time-consuming. The work piece material can be damaged, the processing centre can be busy and people have to spend a lot of time observing the process and recording the data. The objective of this paper is to design an experimental research using the finite element method. In this respect, an orthogonal cutting pattern will be established using this method. This involves determining the type, the method …
Numerical experiments with a parallel fast direct elliptic solver on Cray T3E
1997
A parallel fast direct O(N log N) solver is shortly described for linear systems with separable block tridiagonal matrices. A good parallel scalability of the proposed method is demonstrated on a Cray T3E parallel computer using MPI in communication. Also, the sequential performance is compared with the well-known BLKTRI-implementation of the generalized. cyclic reduction method using a single processor of Cray T3E.
Macroscopic equations of motion for two-phase flow in porous media
1998
The established macroscopic equations of motion for two phase immiscible displacement in porous media are known to be physically incomplete because they do not contain the surface tension and surface areas governing capillary phenomena. Therefore a more general system of macroscopic equations is derived here which incorporates the spatiotemporal variation of interfacial energies. These equations are based on the theory of mixtures in macroscopic continuum mechanics. They include wetting phenomena through surface tensions instead of the traditional use of capillary pressure functions. Relative permeabilities can be identified in this approach which exhibit a complex dependence on the state v…