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Search Results: 1 - 10 of 23693 matches for " Paul Libbrecht "
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Escaping the Trap of too Precise Topic Queries
Paul Libbrecht
Computer Science , 2013,
Abstract: At the very center of digital mathematics libraries lie controlled vocabularies which qualify the {\it topic} of the documents. These topics are used when submitting a document to a digital mathematics library and to perform searches in a library. The latter are refined by the use of these topics as they allow a precise classification of the mathematics area this document addresses. However, there is a major risk that users employ too precise topics to specify their queries: they may be employing a topic that is only "close-by" but missing to match the right resource. We call this the {\it topic trap}. Indeed, since 2009, this issue has appeared frequently on the i2geo.net platform. Other mathematics portals experience the same phenomenon. An approach to solve this issue is to introduce tolerance in the way queries are understood by the user. In particular, the approach of including fuzzy matches but this introduces noise which may prevent the user of understanding the function of the search engine. In this paper, we propose a way to escape the topic trap by employing the navigation between related topics and the count of search results for each topic. This supports the user in that search for close-by topics is a click away from a previous search. This approach was realized with the i2geo search engine and is described in detail where the relation of being {\it related} is computed by employing textual analysis of the definitions of the concepts fetched from the Wikipedia encyclopedia.
Notations Around the World: Census and Exploitation
Paul Libbrecht
Computer Science , 2010,
Abstract: Mathematical notations around the world are diverse. Not as much as requiring computing machines' makers to adapt to each culture, but as much as to disorient a person landing on a web-page with a text in mathematics. In order to understand better this diversity, we are building a census of notations: it should allow any content creator or mathematician to grasp which mathematical notation is used in which language and culture. The census is built collaboratively, collected in pages with a given semantic and presenting observations of the widespread notations being used in existing materials by a graphical extract. We contend that our approach should dissipate the fallacies found here and there about the notations in "other cultures" so that a better understanding of the cultures can be realized. The exploitation of the census in the math-bridge project is also presented: this project aims at taking learners "where they are in their math-knowledge" and bring them to a level ready to start engineering studies. The census serves as definitive reference for the transformation elements that generate the rendering of formul{\ae} in web-browsers.
Understanding the Learners' Actions when using Mathematics Learning Tools
Paul Libbrecht,Sandra Rebholz,Daniel Herding,Wolfgang Müller,Felix Tscheulin
Computer Science , 2012, DOI: 10.1007/978-3-642-31374-5
Abstract: The use of computer-based mathematics tools is widespread in learning. Depending on the way that these tools assess the learner's solution paths, one can distinguish between automatic assessment tools and semi-automatic assessment tools. Automatic assessment tools directly provide all feedback necessary to the learners, while semi-automatic assessment tools involve the teachers as part the assessment process. They are provided with as much information as possible on the learners' interactions with the tool. How can the teachers know how the learning tools were used and which intermediate steps led to a solution? How can the teachers respond to a learner's question that arises while using a computer tool? Little is available to answer this beyond interacting directly with the computer and performing a few manipulations to understand the tools' state. This paper presents SMALA, a web-based logging architecture that addresses these problems by recording, analyzing and representing user actions. While respecting the learner's privacy, the SMALA architecture supports the teachers by offering fine-grained representations of the learners' activities as well as overviews of the progress of a classroom.
Quantitative Modeling of Faceted Ice Crystal Growth from Water Vapor Using Cellular Automata
Kenneth G. Libbrecht
Journal of Computational Methods in Physics , 2013, DOI: 10.1155/2013/174806
Abstract: We describe a numerical model of faceted crystal growth using a cellular automata method. The model was developed for investigating the diffusion-limited growth of ice crystals from water vapor, when the surface boundary conditions are determined primarily by strongly anisotropic molecular attachment kinetics. We restricted our model to cylindrically symmetric crystal growth with relatively simple growth morphologies, as this was sufficient for making quantitative comparisons between models and ice growth experiments. Overall this numerical model appears to reproduce ice growth behavior with reasonable fidelity over a wide range of conditions. More generally, the model could easily be adapted for other material systems, and the cellular automata technique appears well suited for investigating crystal growth dynamics when strongly anisotropic surface attachment kinetics yields faceted growth morphologies. 1. Introduction The formation of crystalline structures during solidification yields a remarkable variety of morphological behaviors, resulting from the often subtle interplay of nonequilibrium physical processes over a range of length scales. In many cases, seemingly small changes in surface molecular structure and dynamics at the nanoscale can produce large morphological changes at all scales. Some examples include free dendritic growth from the solidification of melts, where small anisotropies in the interfacial surface energy govern the overall characteristics of the growth morphologies [1, 2], whisker growth from the vapor phase initiated by single screw dislocations and other effects [3], the formation of porous aligned structures from directional freezing of composite materials [4], and a range of other pattern formation systems [5, 6]. Since controlling crystalline structure formation during solidification has application in many areas of materials science, much effort has been directed toward better understanding the underlying physical processes and their interactions. We have been exploring the growth of ice crystals from water vapor in an inert background gas as a case study of how complex faceted structures emerge in diffusion-limited growth. Although this is a relatively simple monomolecular physical system, ice crystals exhibit columnar and plate-like growth behaviors that depend strongly on temperature, and much of the phenomenology of their growth remains poorly understood [7–9]. Ice has also become something of a standard test system for investigating numerical methods of faceted crystal growth [10, 11]. A better understanding of ice
Aerodynamical Effects in Snow Crystal Growth
K. G. Libbrecht
Physics , 2009,
Abstract: We review several aspects of aerodynamics that affect the growth, morphology, and symmetry of snow crystals. We derive quantitative estimates for aerodynamical forces that orient falling snow crystals, estimate how air flow around snow crystals affects their growth rates (the ventilation effect), and examine how the combination of orientation and growth modification can stabilize or destabilize different growth behaviors. Special attention is given to the formation of triangular snow crystals, since it appears that aerodynamical effects are responsible for producing this unusual morphology, both in nature and in the laboratory.
Identification of a Novel "Fishbone" Structure in the Dendritic Growth of Columnar Ice Crystals
Kenneth G. Libbrecht
Physics , 2009,
Abstract: Ice crystals growing in highly supersaturated air at temperatures near -5 C exhibit a distinctive, nonplanar dendritic morphology that has not been previously documented or explained. We examine this structure and identify its most prominent features in relation to the ice crystal lattice. Developing a full 3D numerical model that reproduces this robust morphology will be an interesting challenge in understanding diffusion-limited crystal growth in the presence of highly anisotropic surface attachment kinetics.
Observations of an Impurity-driven Hysteresis Behavior in Ice Crystal Growth at Low Pressure
Kenneth G. Libbrecht
Physics , 2008,
Abstract: We describe observations of a novel hysteresis behavior in the growth of ice crystals under near-vacuum conditions. Above a threshold supersaturation, we find that the ice growth rate often exhibits a sudden increase that we attribute to an impurity-driven growth instability. We examine possible mechanisms for this instability, which can be used to produce clean, faceted ice surfaces.
Physically Derived Rulesfor Simulating Faceted Crystal Growth using Cellular Automata
Kenneth G. Libbrecht
Physics , 2008,
Abstract: We derive a set of algorithms for simulating the diffusion-limited growth of faceted crystals using local cellular automata. This technique has been shown to work well in reproducing realistic crystal morphologies, and the present work provides a more rigorous physical foundation that connects the numerical code to the physics of attachment kinetics and diffusion dynamics. We then apply these algorithms to examine a novel morphological transition in the growth of thin plate-like crystals.
Crystal Growth in the Presence of Surface Melting and Impurities: An Explanation of Snow Crystal Growth Morphologies
Kenneth G. Libbrecht
Physics , 2008,
Abstract: We examine the molecular dynamics of crystal growth in the presence of surface melting and surface impurities, and from this propose a detailed microscopic model for the growth of ice from the vapor phase. Our model naturally accounts for many aspects of the experimental data that are otherwise difficult to explain, and it suggests a variety of measurements that can provide further confirmation. Although additional work is needed to refine these ideas, we believe that the combined influences of surface melting and impurities provide a viable solution to the 60-year-old mystery of why snow crystal morphologies vary so dramatically with temperature.
An Improved Apparatus For Measuring the Growth of Ice Crystals from Water Vapor
Kenneth G. Libbrecht
Physics , 2011,
Abstract: We describe an apparatus designed for obtaining precise measurements of the growth rates of ice crystals from water vapor over a range of experimental conditions. Our aim is to produce clean, high-quality test crystals in a well controlled environment for investigating the detailed molecular dynamics that controls the basic physics of ice crystal growth. In this paper we describe the nucleation and initial growth of test crystals, their transport and selection into a experimental chamber, the creation of a stable and controllable supersaturation, hardware and calibration issues, and the crystal measurement via direct imaging and broad-band interferometry.
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