| 1. |
- Bernhoff, Niclas, 1971-, et al.
(author)
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Discrete Velocity Models for Mixtures Without Nonphysical Collision Invariants
- 2016
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In: Journal of statistical physics. - New York : Springer. - 0022-4715 .- 1572-9613. ; 165:2, s. 434-453
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Journal article (peer-reviewed)abstract
- An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. It is a well-known fact that DVMs can also have extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and so without spurious ones, is called normal. For binary mixtures also the concept of supernormal DVMs was introduced, meaning that in addition to the DVM being normal, the restriction of the DVM to any single species also is normal. Here we introduce generalizations of this concept to DVMs for multicomponent mixtures. We also present some general algorithms for constructing such models and give some concrete examples of such constructions. One of our main results is that for any given number of species, and any given rational mass ratios we can construct a supernormal DVM. The DVMs are constructed in such a way that for half-space problems, as the Milne and Kramers problems, but also nonlinear ones, we obtain similar structures as for the classical discrete Boltzmann equation for one species, and therefore we can apply obtained results for the classical Boltzmann equation.
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| 2. |
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| 3. |
- Bobylev, Alexander, 1947-, et al.
(author)
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Symmetric extensions of normal discrete velocity models
- 2012. - 1
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In: 28th International Symposium on Rarefied Gas Dynamics 2012. - : American Institute of Physics (AIP). - 9780735411159 ; , s. 254-261
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Conference paper (peer-reviewed)abstract
- In this paper we discuss a general problem related to spurious conservation laws for discrete velocity models (DVMs) of the classical (elastic) Boltzmann equation. Models with spurious conservation laws appeared already at the early stage of the development of discrete kinetic theory. The well-known theorem of uniqueness of collision invariants for the continuous velocity space very often does not hold for a set of discrete velocities. In our previous works we considered the general problem of the construction of normal DVMs, we found a general algorithm for the construction of all such models and presented a complete classification of normal DVMs with small number n of velocities (n<11). Even if we have a general method to classify all normal discrete kinetic models (and in particular DVMs), the existing method is relatively slow and the amount of possible cases to check increases rapidly with n. We remarked that many of our normal DVMs appear to be axially symmetric. In this paper we consider a connection between symmetric transformations and normal DVMs. We first develop a new inductive method that, starting with a given normal DVM, leads by symmetric extensions to a new normal DVM. This method can produce very fast many new normal DVMs with larger number of velocities, showing that the class of normal DVMs contains a large subclass of symmetric models. We finally apply the method to several normal DVMs and construct new models that are not only normal, but also symmetric relatively to more and more axes. We hope that such symmetric velocitysets can be used for DSMC methods of solving Boltzmann equation.
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| 4. |
- Brandl, Matthias, et al.
(author)
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Narrative Didactics in Mathematics Education : Results from a University Geometry Course
- 2023
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In: Open Education Studies. - : De Gruyter Open. - 2544-7831. ; 5:1
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Journal article (peer-reviewed)abstract
- In a Swedish second semester course on Euclidean and non-Euclidean geometry in mathematics education at Karlstad University, a bridging teaching strategy comprising elements from Mathematics, Didactics, History, Literature, and Technology was applied by using the concept of Narrative Didactics and Digital Interactive Mathematical Maps developed by the Professorship for Didactics of Mathematics at the University of Passau, Germany. The complete assessment of the teaching strategy comprised both an evaluation of the technological and the narrative didactical scaffolding and was partly analysed previously concerning especially the technology acceptance aspect, while here we broaden and deepen the evaluation analysis of the application of narrative didactic elements. Regarding the latter, at the end of the course, students were asked to formulate a short historical-oriented narrative motivation for a school topic of own choice with the help of information provided by the timeline of the Mathematical Map. A representative example of these art-combining products is presented and evaluated according to elements of narrative didactics. Results indicate a fruitful, promising, and synergetic connection between different fields of Science, Technology, Engineering, the Arts, and Mathematics that can lead to a richer and more sustainable learning process in mathematics lessons both at university and school level.
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| 5. |
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| 6. |
- Brunström, Mats, 1960-, et al.
(author)
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Computer-aided assessment based on dynamic mathematics investigations
- 2020
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In: Proceedings of the Tenth ERME Topic Conference (ETC 10) on Mathematics Education in the Digital Age (MEDA), 16-18 September 2020 in Linz, Austria. - Linz, Austria.
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Conference paper (peer-reviewed)abstract
- In the poster, we will present a planned study focusing on the design of DMS tasks and elaborated feedback within a CAA system. The study will be conducted in a first year engineering mathematics course during autumn 2020.
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| 7. |
- Brunström, Mats, 1960-, et al.
(author)
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Designing for a combined use of a dynamic mathematics software environment and a computer-aided assessment system
- 2022
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In: Proceedings of the Twelfth Congress of the European Research Society in Mathematics Education (CERME12). - : ERME.
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Conference paper (peer-reviewed)abstract
- This paper reports on a pilot study with the focus on (re)design of a digitized task environment utilizing two types of technology – a dynamic mathematics software and a computer-aided assessment system. The data consist of responses from 256 first year engineering students, taking their first Calculus course, on two different types of task. The results are discussed in relation to (re)design of tasks as well as possible feedback design options to enable a formative assessment approach.
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| 8. |
- Fahlgren, Maria, 1966-, et al.
(author)
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Designing tasks and feedback utilizing a combination of a dynamic mathematics software and a computer-aided assessment system
- 2022
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In: Proceedings of the 15th International Conference on Technology in Mathematics Teaching (ICTMT 15). - Aarhus : Danish School of Education, Aarhus Unviersity. - 9788775075256 ; , s. 272-279
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Conference paper (peer-reviewed)abstract
- This paper reports on the planning of a design-based research (DBR) study, where the main aim is to develop principles in designing technology-enhanced learning environment utilizing a combination of a dynamic mathematics software (DMS) and a computer-aided assessment (CAA) system. The focus is on the design of tasks and automated feedback of high quality so as to enhance first year engineering students’ engagement in and conceptual understanding of mathematical contents. The paper outlines the rationale for the project and highlights theoretical aspects that will be considered in the study. Moreover, some findings from a pilot study that will inform the first cycle of the DBR study are presented.
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| 9. |
- Fahlgren, Maria, 1966-, et al.
(author)
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Prospective teachers designing tasks for dynamic geometry environments
- 2022
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In: Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME 12). - Bozen-Bolzano : Free University of Bozen-Bolzano. - 9791221025378
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Conference paper (peer-reviewed)abstract
- The paper examines the quality of digitized tasks designed by 10 (small) groups of prospective upper secondary school teachers as part of a geometry course assignment. The results indicate that a small instructional intervention, addressing the planning and implementation of tasks in digitized task environments as well as how to stimulate students to make mathematical generalizations, led to a relatively high proportion (8 out of 10) of high-quality tasks designed by the prospective teachers.
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| 10. |
- Fallaha, Maarouf, et al.
(author)
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Delivering Round-the-Clock Study Support in Mathematics Courses to Engineering Students Using Discord: An Experience Report
- 2024
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Conference paper (peer-reviewed)abstract
- In this paper, the authors aim to share insights gained from a pilot project on self-studies in mathematics courses for engineering students. We propose an innovative approach to tackle the challenges faced by engineering students, including managing academic workload, stress, and time constraints, namely we re-design a Discord platform as a dynamic resource where students can partake in discussions, request guidance on course material, join study groups, and obtain personalized assistance from experienced assistants. This independent resource is not integrated into any specific curriculum and it is available to all engineering students belonging to our university that are in need of help for their mathematics courses, This approach has demonstrated a significant positive impact on engineering education by enhancing student engagement, reducing isolation, and improving academic performance. The findings highlight the potential for teaching assistants to facilitate effective learning experiences through interactions on the user-friendly and freely accessible Discord platform.
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