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  • 1.
    Bernhoff, Niclas
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Vinerean, Mirela
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Discrete Velocity Models for Mixtures Without Nonphysical Collision Invariants2016In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 165, no 2, p. 434-453Article in journal (Refereed)
    Abstract [en]

    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.
    Bobylev, Alexander
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Vinerean (Bernhoff), Mirela
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Symmetric extensions of normal discrete velocity models2012In: 28th International Symposium on Rarefied Gas Dynamics 2012 / [ed] Michel Mareschal, Andrés Santos, American Institute of Physics (AIP), 2012, 1, Vol. 1501, no 1, p. 254-261Conference paper (Refereed)
    Abstract [en]

    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.

  • 3.
    Bobylev, Alexander
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Vinerean (Bernhoff), Mirela
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Windfäll, Åsa
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Discrete velocity models of the Boltzmann equation and conservation laws2010In: Kinetic and Related Models, ISSN 1937-5093, E-ISSN 1937-5077, Vol. 3, no 1, p. 35-58Article in journal (Refereed)
  • 4.
    Bobylev, Alexander
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Vinerean-Bernhoff, Mirela
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Construction and Classification of Discrete Kinetic Models without Spurious Invariants2007In: Riv. Mat. Univ. Parma (7) 7 (2007), pp.1-80, Vol. 7Article in journal (Refereed)
  • 5.
    Bobylev, Alexander
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Vinerean-Bernhoff, Mirela
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Construction of Discrete Kinetic Models with Given Invariants2008In: Journal of Statistical PhysicsArticle in journal (Refereed)
  • 6.
    Bobylev, Alexander
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Vinerean-Bernhoff, Mirela
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Discrete Kinetic Models and Conservation Laws2006In: Modelling and Numerics of Kinetic Dissipative Systems, L. Pareschi and G. Russo and G. Toscani, eds., Nova Science Publishers, 2006, pp. 147-162, Nova Science , 2006Chapter in book (Other academic)
  • 7.
    Bobylev, Alexander
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Vinerean-Bernhoff, Mirela
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    General Methods of the Construction of Discrete Kinetic Models with Given Conservation Laws2007Conference paper (Refereed)
    Abstract [en]

    In the present work we consider the general problem of the construction of discrete kinetic models (DKMs) with given conservation laws. This problem was first stated by R. Gatignol [1] in connection with discrete models of the Boltzmann equation (BE), when it became clear that the velocity discretization can lead to equations with spurious conservation laws (not linear combinations of physical invariants). The problem has been addressed in the last decade by several authors, in particular by Cercignani, Bobylev, Vedenyapin, and Cornille. Even though a practical criterion for the non-existence of spurious conservation laws has been devised [2], and a method for enlarging existing physical models by new velocity points without adding non-physical invariants has been proposed [3], a general algorithm for the construction of all normal (physical) discrete models with assigned conservation laws, in any dimension and for any number of points, is still lacking in the literature. We develop such a general algorithm in the present work.

    We introduce the most general class of discrete kinetic models and obtain a general method for the construction and classification of normal DKMs. In particular, it is proved that for any given dimension d 2 and for any sufficiently large number N of velocities (for example, N 6 for the planar case d = 2) there exists just a finite number of distinct (non-equivalent) classes of DKMs. We apply the general method in the particular cases of discrete velocity models (DVMs) of the inelastic BE and elastic BE. In the first case, we show that all normal models can be explicitly described. In the second case, we give a complete classification of normal models up to 9 velocities and show that the extension method [3], does not lead to all normal DVMs.

    Using our general approach to DKMs and our results on normal DVMs for a single gas, we develop a method for the construction of the most natural (from physical point of view) subclass of normal DVMs for binary gas mixtures. We call such models supernormal models (SNMs) (they have the property that by isolating the velocities of one-kind particles of the single gases involved in the mixture, the corresponding discrete models for a single gas are also normal models). We apply this method and obtain SNMs with up to 20 velocities and their spectrum of mass ratio.

    Finally, we develop a new method that can lead, by symmetric transformations, from a given normal DVM to extended normal DVMs.



    ACKNOWLEDGEMENTS. The support by the grant 2003-5357 from Swedish Research Council for both authors is gratefully acknowledged.



    REFERENCES

    [1] R. Gatignol, Théorie Cinétique des Gaz à Répartition Discrète de Vitesses, Springer-Verlag, New-York, 1975

    [2] V. V. Vedenyapin, Y. N. Orlov, Teoret. and Math. Phys., 121, 1516-1523 (1999)

    [3] A. V. Bobylev, C. Cercignani, J. Statist. Phys., 97, 677-686 (1999)

  • 8.
    Brandl, Matthias
    et al.
    University of Passau, Germany.
    Vinerean-Bernhoff, Mirela
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Narrative Didactics in Mathematics Education: Results from a University Geometry Course2023In: Open Education Studies, ISSN 2544-7831, Vol. 5, no 1, article id 20220186Article in journal (Refereed)
    Abstract [en]

    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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  • 9.
    Brunström, Mats
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Karlstad University, Faculty of Health, Science and Technology (starting 2013), Science, Mathematics and Engineering Education Research.
    Fahlgren, Maria
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Karlstad University, Faculty of Health, Science and Technology (starting 2013), Science, Mathematics and Engineering Education Research.
    Vinerean, Mirela
    Karlstad University, Faculty of Technology and Science, Department of Mathematics. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Wondmagegne, Yosief
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Designing for a combined use of a dynamic mathematics software environment and a computer-aided assessment system2022In: Proceedings of the Twelfth Congress of the European Research Society in Mathematics Education (CERME12) / [ed] J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferrettti, ERME , 2022Conference paper (Refereed)
    Abstract [en]

    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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  • 10.
    Brunström, Mats
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Karlstad University, Faculty of Health, Science and Technology (starting 2013), Science, Mathematics and Engineering Education Research.
    Fahlgren, Maria
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Karlstad University, Faculty of Health, Science and Technology (starting 2013), Science, Mathematics and Engineering Education Research.
    Vinerean-Bernhoff, Mirela
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Wondmagegne, Yosief
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Computer-aided assessment based on dynamic mathematics investigations2020In: Proceedings of the Tenth ERME Topic Conference (ETC 10) on Mathematics Education in the Digital Age (MEDA), 16-18 September 2020 in Linz, Austria / [ed] A. Donevska-Todorova, E. Faggiano, J. Trgalová, Z. Lavicza, R. Weinhandl, A. Clark-Wilson, & H.-G. Weigand, Linz, Austria, 2020Conference paper (Refereed)
    Abstract [en]

    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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  • 11.
    Brunström, Mats
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Mossberg, Eva
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Vinerean-Bernhoff, Mirela
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    An exploratory approach to engineering mathematics using GeoGebra2016Conference paper (Other academic)
  • 12.
    Fahlgren, Maria
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Science, Mathematics and Engineering Education Research. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Brunström, Mats
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Science, Mathematics and Engineering Education Research. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Vinerean-Bernhoff, Mirela
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Wondmagegne, Yosief
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Designing tasks and feedback utilizing a combination of a dynamic mathematics software and a computer-aided assessment system2022In: Proceedings of the 15th International Conference on Technology in Mathematics Teaching (ICTMT 15) / [ed] U.T. Jankvist, R. Elicer, A. Clark-Wilson, H.-G. Weigand, & M. Thomsen, Aarhus: Danish School of Education, Aarhus Unviersity , 2022, p. 272-279Conference paper (Refereed)
    Abstract [en]

    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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  • 13.
    Fahlgren, Maria
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Szabo, Attila
    Stockholm University.
    Vinerean-Bernhoff, Mirela
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Prospective teachers designing tasks for dynamic geometry environments2022In: Proceedings of the Twelfth Congress of the European Research Society in Mathematics Education (CERME12) / [ed] J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferrettti, ERME , 2022, article id hal-03747493Conference paper (Refereed)
    Abstract [en]

    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.

  • 14.
    Mellroth, Elisabet
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Vinerean-Bernhoff, Mirela
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Boström, Mattias
    Karlstad kommun.
    Liljekvist, Yvonne
    Karlstad University, Faculty of Arts and Social Sciences (starting 2013), Department of Educational Studies (from 2013).
    Differentiated instruction using learning management systems in upper secondary school and university level: A research proposal2019In: Including the highly gifted and creative students: Current ideas and future directions.: Proceedings of the 11th International conference on mathematics creativity and giftedness. / [ed] Marianne Nolte, Münster: Verlag für wissenschaftliche Texte und Medien , 2019, p. 378-380Conference paper (Refereed)
    Abstract [en]

    There is a need to develop an infrastructure to support and maintain teaching that both challenge all students at their knowledge level and open up the possibility to applying mathematical knowledge in innovative and creative ways. Learning management systems (LMS) are widely used throughout the Swedish school system. However, recent studies shows that few teachers use this resource for teaching development, i.e., using LMS as an instrument to improve forthcoming lessons. In this poster a research proposal is outlined. The aim is to explore how LMS can be used as an instrument for differentiated instruction throughout the intertwined processes of planning, teaching, studying, follow up and assessment.

  • 15.
    Przybilla, Johannes
    et al.
    University of Passau, Germany.
    Brandl, Matthias
    University of Passau, Germany.
    Vinerean, Mirela
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Karlstad University, Faculty of Health, Science and Technology (starting 2013), Science, Mathematics and Engineering Education Research.
    Liljekvist, Yvonne
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Karlstad University, Faculty of Arts and Social Sciences (starting 2013), Department of Educational Studies (from 2013). Karlstad University, Faculty of Health, Science and Technology (starting 2013), Science, Mathematics and Engineering Education Research.
    Interactive Mathematical Maps: A contextualized way of meaningful Learning2021In: Bringing Nordic mathematics education into the future. Papers from NORMA 20, Preceedings of Norma 20, The ninth Nordic Conference on Mathematics Education, Oslo, 2021 / [ed] Nortvedt, G. A.; Buchholtz, N. F.; Fauskanger, J.; Hreinsdóttir, F.; Hähkiöniemi, M.; Jesse, B. E.; Kurvits, J.; Liljekvist, Y.; Misfeldt, M.; Naalsund, M.; Nilsen, H. K.; Pálsdóttir, G.; Portaankorva-Koivisto, P.; Radišić, J.; Virman, O. and Werneberg, 2021, p. 209-216Conference paper (Refereed)
    Abstract [en]

    Student teachers are often not able to link mathematical school and university contents. This problem results in the “double discontinuity” that goes back to Klein (1924)[1], which manifests itself in a lack of understanding and significance of university contents on the part of future teachers. Based on modern learning psychology we assume that this issue can be overcome by defragmentation – a thematically meaningful arrangement – of knowledge. For this purpose, we present a "dynamic interactive mathematical map" which should enable "meaningful learning" in the sense of Ausubel (1963) [2]. By giving the learners the possibility to retrace the formation of mathematical subjects in conjunction with the presentation of similar concepts, understanding is deepened and ultimately transfer of learning is facilitated. We also present one of the tentative studies connected with the map.

     [1] “The first ‘discontinuity’ concerns the well-known problems of transition which students face as they enter university. The second ‘discontinuity’ concerns those […] which return to school as teachers and the (difficult) transfer of academic knowledge gained at university to relevant knowledge for a teacher.” (Winsløw & Grønbæk, 2013, p. 2)[2] Ausubel (1963) shaped the term “meaningful learning”, which declares that learning is only meaningful (contrasted to rote learning), when connected to past learnings and many different contexts. 

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  • 16.
    Przybilla, Johannes
    et al.
    University of Passau, GER.
    Vinerean-Bernhoff, Mirela
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Brandl, Matthias
    University of Passau, GER.
    Liljekvist, Yvonne
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Karlstad University, Faculty of Health, Science and Technology (starting 2013), Science, Mathematics and Engineering Education Research.
    Rooms of Learning: A conceptual framework for student-centered teaching development in a digital era2021Report (Refereed)
    Abstract [en]

    In the context of teaching, there is often a clash of different generation cohorts, which have different attitudes to and skills in digital media and corresponding ways of teaching and learning, respectively. The current COVID19 situation works as an intensifying lens and shows the problems occurring in this context even more clearly. Many mathematics teachers feel urged to move away from the instruction- and lecture-centered teaching style and many universities are upgrading digitally, thus creating the conditions for innovative teaching.  

    Considering the change in learning theories and education curricula, we offer a general model called “Rooms of Learning” as a quick-to-see-and-interpret framework for the pre- and post-analysis of course design. It is backed by subject didactical frameworks that focus on interactions between the main actors involved in learning.  

    As starting points, we use the basic needs of today’s learners for autonomy, relatedness, and competence as well as the requirements of the present information society. Focusing on different levels of the learners’ autonomy, as the key factor for building up mathematical competence and life-long learning, we illustrate our practice-oriented model by analyzing different course layouts. Herein the strength of the model is demonstrated, as commonalities of the modern course designs successfully applied today are revealed. It suggests, when designing a course, care should be taken to ensure that the defined Peer teaching room and Self-studies room are given enough space.

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  • 17.
    Szabo, Attila
    et al.
    Stockholm university.
    Vinerean, Mirela
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Fahlgren, Maria
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Karlstad University, Faculty of Health, Science and Technology (starting 2013), Science, Mathematics and Engineering Education Research.
    Surveying prospective teachers’ conceptions of GeoGebra when constructing mathematical activities for pupils2020In: Proceedings of the 10th ERME Topic Conference (ETC 10) on Mathematics Education in the Digital Age (MEDA), 16-18 September 2020 in Linz, Austria / [ed] A. Donevska-Todorova; E. Faggiano, J. Trgalová; Z. Lavicza; R. Weinhandl; A. Clark-Wilson and H.-G. Weigand, 2020Conference paper (Refereed)
    Abstract [en]

    In this poster, we present an ongoing study about prospective mathematics teachers' conceptions about the relationship between mathematics, problem-solving and GeoGebra. The context of our study is a curriculum reform in Sweden that emphasizes the use of digital tools in mathematics education. In that respect, we will investigate prospective upper-secondary teachers´ conceptions when participating in a geometry course at the university level. During the course, participants will construct mathematical activities for pupils by using GeoGebra.

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  • 18.
    Vinerean, Mirela Cristina
    Karlstad University, Division for Engineering Sciences, Physics and Mathematics.
    Discrete Kinetic Models and Conservation Laws2005Doctoral thesis, monograph (Other academic)
    Abstract [en]

    Classical kinetic theory of gases is based on the Boltzmann equation (BE) which describes the evolution of a system of particles undergoing collisions preserving mass, momentum and energy. Discretization methods have been developed on the idea of replacing the original BE by a finite set of nonlinear hyperbolic PDEs corresponding to the densities linked to a suitable finite set of velocities. One open problem related to the discrete BE is the construction of normal (fulfilling only physical conservation laws) discrete velocity models (DVMs). In many papers on DVMs, authors postulate from the beginning that a finite velocity space with such "good" properties is given, and after this step, they study the discrete BE. Our aim is not to study the equations for DVMs, but to discuss all possible choices of finite phase spaces (sets) satisfying this type of "good" restrictions.

    We start by introducing the most general class of discrete kinetic models (DKMs) and then, develop a general method for the construction and classification of normal DKMs. We apply this method in the particular cases of DVMs of the inelastic BE (where we show that all normal models can be explicitly described) and elastic BE (where we give a complete classification of normal models up to 9 velocities). Using our general approach to DKMs and our results on normal DVMs for a single gas, we develop a method for the construction of the most natural (from physical point of view) subclass of normal DVMs for binary gas mixtures. We call such models supernormal models (SNMs). We apply this method and obtain SNMs with up to 20 velocities and their spectrum of mass ratio. Finally, we develop a new method that can lead, by symmetric transformations, from a given normal DVM to extended normal DVMs. Many new normal models can be constructed in this way, and we give some examples to illustrate this.

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  • 19.
    Vinerean, Mirela
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Windfäll, Åsa
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Bobylev, Alexander
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Construction of Normal Discrete Velocity Models of the Boltzmann Equation2010In: Nuovo cimento della societa italiana de fisica. C, Geophysics and space physics, ISSN 1124-1896, E-ISSN 1826-9885, Vol. 33, no 1, p. 257-264Article in journal (Refereed)
  • 20.
    Vinerean-Bernhoff, Mirela
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Classification of Normal Discrete Kinetic Models2004Licentiate thesis, monograph (Other academic)
    Abstract [en]

    In many interesting papers on discrete velocity models (DVMs), authors postulate from the beginning that the finite velocity space with "good" properties is given and only after this step they study the Discrete Boltzmann Equation. Contrary to this approach, our aim is not to study the equation, but to discuss all possible choices of finite phase spaces (sets) satisfying this type of "good" restrictions. Due to the velocity discretization it is well known that it is possible to have DVMs with "spurious" summational invariants (conservation laws which are not linear combinations of physical invariants). Our purpose is to give a method for constructing normal models (without spurious invariants) and to classify all normal plane models with small number of velocities (which usually appear in applications). On the first step we describe DKMs as algebraic systems. We introduce for this an abstract discrete model (ADM) which is defined by a matrix of reactions (the same as for the concrete model). This matrix contains as rows all vectors of reactions describing the "jump" from a pre-reaction state to a new reaction state. The conservation laws corresponding to the many-particle system are uniquely determined by the ADM and do not depend on the concrete realization. We find the restrictions on ADM and then we give a general method of constructing concrete normal models (using the results on ADMs). Having the general algorithm, we consider in more detail, the particular cases of models with mass and momentum conservation (inelastic lattice gases with pair collisions) and models with mass, momentum and energy conservation (elastic lattice gases with pair collisions).

  • 21.
    Vinerean-Bernhoff, Mirela
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    On the construction of normal discrete kinetic models2005Conference paper (Other (popular science, discussion, etc.))
  • 22.
    Vinerean-Bernhoff, Mirela
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Fahlgren, Maria
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Szabo, Attila
    Stockholm University, Sweden.
    Sriraman, Bharath
    University of Montana Missoula, USA.
    Prospective teachers constructing dynamic geometry activities for gifted pupils: Connections between the frameworks of Krutetskii and van Hiele2022In: Gifted Education International, ISSN 0261-4294, E-ISSN 2047-9077, Vol. 38, no 2, p. 273-294Article in journal (Refereed)
    Abstract [en]

    The Swedish educational system has, so far, accorded little attention to the development of gifted pupils. Moreover, up to date, no Swedish studies have investigated teacher education from the perspective of mathematically gifted pupils. Our study is based on an instructional intervention, aimed to introduce the notion of giftedness in mathematics and to prepare prospective teachers (PTs) for the needs of the gifted. The data consists of 10 dynamic geometry software activities, constructed by 24 PTs. We investigated the constructed activities for their qualitative aspects, according to two frameworks: Krutetskii’s framework for mathematical giftedness and van Hiele’s model of geometrical thinking. The results indicate that nine of the 10 activities have the potential to address pivotal abilities of mathematically gifted pupils. In another aspect, the analysis suggests that Krutetskii’s holistic description of mathematical giftedness does not strictly correspond with the discrete levels of geometrical thinking proposed by van Hiele.

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  • 23.
    Vinerean-Bernhoff, Mirela
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Liljekvist, Yvonne
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Bengu, Elif
    Abdullah Gül University, Turkiye.
    “Literally I Grew Up” Secondary–Tertiary Transition in Mathematics for Engineering Students beyond the Purely Cognitive Aspects2023In: Open Education Studies, ISSN 25447831, Vol. 5, no 1, article id 20220184Article in journal (Refereed)
    Abstract [en]

    High dropout rates in the first year of undergraduate studies are an expression of the secondary–tertiary transition problem and they seem to be particularly high in those degree programs where specialized mathematics courses are taught in the first year of study. Research shows that students’ difficulties during the transition period cannot be reduced to purely cognitive factors. In this article, we address the secondary–tertiary transition problem in mathematics for engineering students. Based on a questionnaire with focus beyond the purely cognitive aspects, a comparison of the transition problem at three European mid-sized universities is carried out, to identify common challenges and difficulties, as well as differences. The questionnaire concentrates on the four dimensions (personal, organizational, content related, and social) and corresponding critical requirements for a successful transition described in Trautwein, C., & Bosse, E. (2017). The first year in higher education – critical requirements from the student perspective. Higher Education, 73, 371–387. A group of 308 first-year engineering students partook in the study. In the presentation, we highlight students’ perceptions regarding the transition, changes, and challenges they experienced under the above-mentioned four dimensions and discuss similarities and differences between countries.

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