A unified error analysis for spatial discretizations of wave-type equations with applications to dynamic boundary conditions

This thesis provides a unified framework for the error analysis of non-conforming space discretizations of linear wave equations in time-domain, which can be cast as symmetric hyperbolic systems or second-order wave equations. Such problems can be written as first-order evolution equations in Hilbert spaces with linear monotone operators. We employ semigroup theory for the well-posedness analysis and to obtain stability estimates for the space discretizations. To compare the finite dimensional approximations with the original solution, we use the concept of a lift from the discrete to the continuous space. Time integration with the Crank–Nicolson method is analyzed. In this framework, we derive a priori error bounds for the abstract space semi-discretization in terms of interpolation and discretization errors. These error bounds yield previously unkown convergence rates for isoparametric finite element discretizations of wave equations with dynamic boundary conditions in smooth domains. Moreover, our results allow to consider already investigated space discretizations in a unified way. Here it successfully reproduces known error bounds. Among the examples which we dicuss in this thesis are discontinuous Galerkin discretizations of Maxwell’s equations and finite elements with mass lumping for the scalar wave equation

Front-tracking finite element methods for a void electro-stress migration problem

Continued research in electronic engineering technology has led to a miniaturisation of integrated circuits. Further reduction in the dimensions of the interconnects is impeded by the presence of small cracks or voids. Subject to high current and elastic stress, voids tend to drift and change shape in the interconnect, leading to a potential mechanical failure of the system. This thesis investigates the temporal evolution of voids moving along conductors, in the presence of surface diffusion, electric loading and elastic stress. We simulate a bulk-interface coupled system, with a moving interface governed by a fourth-order geometric evolution equation and a bulk where the electric potential and the displacement field are computed. We first give a general overview about geometric evolution equations, which define the motion of a hypersurface by prescribing its normal velocity in terms of geometric quantities. We briefly describe the three main approaches that have been proposed in the literature to solve numerically this class of equations, namely parametric approach, level set approach and phase field approach. We then present in detail two methods from the parametric approach category for the void electro-stress migration problem. We first introduce an unfitted method, where bulk and interface grids are totally independent, i.e. no topological compatibility between the two grids has to be enforced over time. We then discuss a fitted method, where the interface grid is at all times part of the boundary of the bulk grid. A detailed analysis, in terms of existence and uniqueness of the finite element solutions, experimental order of convergence (when the exact solution to the free boundary problem is known) and coupling operations (e.g., smoothing/remeshing of the grids, intersection between elements of the two grids), is carried out for both approaches. Several numerical simulations, both two- and three-dimensional, are performed in order to test the accuracy of the methods.Open Acces

Modes of Representation, the Epistemic Subject and Developmental Word Association Phenomena

This study was devised to investigate the developmental syntagmaticparadigmatic word association shift. In syntagmatic associations the stimulus and associative response are of different grammatical form classes and appear to be grammatically continuous, as response may follow stimulus in an utterance (e.g. cat-meows). These are the predominant responses of children before the ages of six to eight. Older children and adults shift to making paradigmatic associations in which stimulus and response are from the same form class and may be substituted for one another in an utterance (e.g. cat-dog). This shift was explained in terms of underlying symbolic mediational processes and the epistemic subject, the child’s interpretation of the unstated task demands of the word association test. The central hypotheses were: 1. The syntagmatic-paradigmatic shift occurs because younger children use verbally-evoked images to generate their word associations and so produce syntagmatic responses. Older children, on the other hand, rely less on verbally-evoked images and more on knowledge of unstated task demands to generate their word associations. Older children can accomplish this because they have acquired explicit or potentially articulated knowledge of hierarchic semantic organization (abbreviated HSO) of words (e.g. cats and dogs are animals), which younger children have only tacit, unarticulated knowledge of. On the basis of other studies (e.g. Mansfield, 1977; Steinberg & Anderson, 1975) it was assumed that all age groups have comparable implicit knowledge of hierarchic semantic organization and that therefore this would not play a significant role in the shift to paradigmatic responding. 2. The ability to change deliberately the mode of representation (i.e. imaginal or linguistic) through which word association responses are mediated depends on the acquisition of two kinds of metaknowledge: a) metalinguistic knowledge and b) explicit knowledge of imagery. To test these hypotheses, twenty kindergarteners, twenty second graders and ten college students were presented with 48 words, consisting of high and low imagery nouns, verbs and adjectives under five different word association instruction conditions: 1) the standard firstword ; 2) paradigmatic, in which Ss were trained to give an association which could substitute for the stimulus in a sentence; 3) syntagmatic in which Ss were trained to give an association which together with the stimulus would complete a phrase; 4) imagery, in which the subject was asked to obtain a picture of the stimulus word in her head before responding and 5) time delay, which required that the subject wait three seconds before responding. The purpose of this last condition was to determine whether the delay in responding was responsible for a possible increased frequency of syntagmatic associations in the imagery condition. One half the kindergarteners and second graders also received: 1) two convergent measures of metalinguistic knowledge, which tap the child\u27s understanding of words as arbitrary, interchangeable units; 2) two convergent measures of explicit knowledge of imagery, which tap the child\u27s understanding of the distinction between (a) images and words and (b) images and objects; 3) the hierarchic semantic organization and 4) word-word relationship tasks. The latter two tasks respectively tap the child\u27s tacit and explicit understanding of the hierarchic semantic organization of words. A control group consisted of the remaining ten kindergarten and second grade children who received only the five word association tests. The purpose of this control group was to determine if administration of the metalinguistic and other cognitive tasks influenced subsequent word association responding. The results showed that there appears to be a developmental progression in the way children approach the word association task. First, very young children seem to produce responses based only on the phonological form of the word; i.e., they produce clang responses, which rhyme with the stimulus, or negated responses, generated through an negation rule which consists of prefixing not or un to the phonological form of the stimulus word to produce a response. Later, children begin to consider the meaning of the stimulus word. At the start, this may be confined to considering the imagery which the stimulus word evokes. Evidence indicates that stimulus imagery mediates the generation of syntagmatic associations. Gradually, as tacitly known hierarchic semantic organization becomes more filled-in,* and the child gains explicit access to it, it is possible for her to produce paradigmatic responses. But in order to do so spontaneously, she must also understand that words are arbitrary, manipulable units. On the other hand, if she is explicitly directed to produce paradigmatic responses, she will be able to do so, as long as she has explicit access to a filled-in hierarchic semantic structure. Metalinguistic knowledge does not play a role in this case since the explicit directions replace its function as an aid to the spontaneous production of paradigmatic responses. * As determined by absolute number of correct responses

A computational-based drug development framework.

Tse, Ching Man.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (p. 188-200).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.viChapter 1 --- Introduction --- p.1Chapter 1.1 --- Obtain information on drug targets --- p.3Chapter 1.2 --- Drug Design --- p.5Chapter 1.3 --- Interface for interaction --- p.9Chapter 1.4 --- Summary --- p.10Chapter 2 --- Background Study --- p.12Chapter 2.1 --- Protein Function Prediction --- p.16Chapter 2.2 --- Drug Design --- p.37Chapter 2.3 --- Visualisation and Interaction in Biomedic --- p.44Chapter 3 --- Overview --- p.48Chapter 3.1 --- Protein prediction using secondary structure analysis --- p.52Chapter 3.2 --- Knowledge-driven ligand design --- p.55Chapter 3.3 --- Interactive interface in virtual reality --- p.57Chapter 4 --- Protein Function Prediction --- p.60Chapter 4.1 --- Introduction --- p.61Chapter 4.1.1 --- Motivation --- p.61Chapter 4.1.2 --- Objective --- p.62Chapter 4.1.3 --- Overview --- p.63Chapter 4.2 --- Methods and Design --- p.66Chapter 4.2.1 --- Feature Cell --- p.68Chapter 4.2.2 --- Heterogeneous Vector --- p.71Chapter 4.2.3 --- Feature Cell Similarity --- p.75Chapter 4.2.4 --- Heterogeneous Vector Similarity --- p.79Chapter 4.3 --- Experiments --- p.85Chapter 4.3.1 --- Data Preparation --- p.85Chapter 4.3.2 --- Experimental Methods --- p.87Chapter 4.4 --- Results --- p.97Chapter 4.4.1 --- Scalability --- p.97Chapter 4.4.2 --- Cluster Quality --- p.99Chapter 4.4.3 --- Classification Quality --- p.102Chapter 4.5 --- Discussion --- p.103Chapter 4.6 --- Conclusion --- p.104Chapter 5 --- Drug Design --- p.106Chapter 5.1 --- Introduction --- p.107Chapter 5.1.1 --- Motivation --- p.107Chapter 5.1.2 --- Objective --- p.109Chapter 5.1.3 --- Overview --- p.109Chapter 5.2 --- Methods --- p.111Chapter 5.2.1 --- Fragment Joining --- p.115Chapter 5.2.2 --- Genetic Operators --- p.116Chapter 5.2.3 --- Post-Processing --- p.124Chapter 5.3 --- Experiments --- p.128Chapter 5.3.1 --- Data Preparation --- p.129Chapter 5.3.2 --- Experimental Methods --- p.132Chapter 5.4 --- Results --- p.134Chapter 5.4.1 --- Binding Pose --- p.134Chapter 5.4.2 --- Free Energy and Molecular Weight --- p.137Chapter 5.4.3 --- Execution Time --- p.138Chapter 5.4.4 --- Handling Phosphorus --- p.138Chapter 5.5 --- Discussions --- p.139Chapter 5.6 --- Conclusion --- p.140Chapter 6 --- Interface in Virtual Reality --- p.142Chapter 6.1 --- Introduction --- p.143Chapter 6.1.1 --- Motivation --- p.143Chapter 6.1.2 --- Objective --- p.145Chapter 6.1.3 --- Overview --- p.145Chapter 6.2 --- Methods and Design --- p.146Chapter 6.2.1 --- Hybrid Drug Synthesis --- p.147Chapter 6.2.2 --- Interactive Interface in Virtual Reality --- p.154Chapter 6.3 --- Experiments and Results --- p.171Chapter 6.3.1 --- Data Preparation --- p.171Chapter 6.3.2 --- Experimental Settings --- p.172Chapter 6.3.3 --- Results --- p.173Chapter 6.4 --- Discussions --- p.176Chapter 6.5 --- Conclusions --- p.179Chapter 7 --- Conclusion --- p.180A Glossary --- p.184Bibliography --- p.18

GiD 2008. 4th Conference on advances and applications of GiD

The extended use of simulation programs has leaned on the advances in user-friendly interfaces and in the capability to generate meshes for any generic complex geometry. More than ten years of development have made Gid grow to become one of the more popular pre ans postprocessing systems at international level. The constant dialogue between the GiD development team and the users has guided the development of giD to cover the pre-post needs of many disciplines in science and engineering. Following gthis philosophy, the biannual GiD Conference has become an important forum for discussion and interchange of experiences among the GiD community. This monograph includes the contributions of the participants to the fourth edition of the GiD Conference held in the island of Ibiza from 8-9 May 2008