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  • 1. Aaboud, M
    et al.
    Kastanas, Konstatinos A.
    KTH, School of Engineering Sciences (SCI), Physics, Particle and Astroparticle Physics.
    Lund-Jensen, Bengt
    KTH, School of Engineering Sciences (SCI), Physics, Particle and Astroparticle Physics.
    Sidebo, P. Edvin
    KTH, School of Engineering Sciences (SCI), Physics, Particle and Astroparticle Physics.
    Strandberg, Jonas
    KTH, School of Engineering Sciences (SCI), Physics, Particle and Astroparticle Physics.
    Zwalinski, L.
    et al.,
    Jet reconstruction and performance using particle flow with the ATLAS Detector2017In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 77, no 7, article id 466Article in journal (Refereed)
    Abstract [en]

    This paper describes the implementation and performance of a particle flow algorithm applied to 20.2 fb- 1 of ATLAS data from 8 TeV proton–proton collisions in Run 1 of the LHC. The algorithm removes calorimeter energy deposits due to charged hadrons from consideration during jet reconstruction, instead using measurements of their momenta from the inner tracker. This improves the accuracy of the charged-hadron measurement, while retaining the calorimeter measurements of neutral-particle energies. The paper places emphasis on how this is achieved, while minimising double-counting of charged-hadron signals between the inner tracker and calorimeter. The performance of particle flow jets, formed from the ensemble of signals from the calorimeter and the inner tracker, is compared to that of jets reconstructed from calorimeter energy deposits alone, demonstrating improvements in resolution and pile-up stability.

  • 2.
    Airey, John
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics, Physics Didactics.
    Linder, Cedric
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics, Physics Didactics.
    Language and the Experience of Learning University Physics in Sweden2006In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 27, no 3, p. 553-560Article in journal (Refereed)
    Abstract [en]

    This qualitative study explores the relationship between the lecturing language (English or Swedish) and the related learning experiences of 22 undergraduate physics students at two Swedish universities. Students attended lectures in both English and Swedish as part of their regular undergraduate programme. These lectures were videotaped and students were then interviewed about their learning experiences using selected excerpts of the video in a process of stimulated recall. The study finds that although the students initially report no difference in their experience of learning physics when taught in Swedish or English, there are in fact some important differences which become apparent during stimulated recall. The pedagogical implications of these differences are discussed.

  • 3. Anderson, D
    et al.
    Desaix, Mats
    University of Borås, Faculty of Textiles, Engineering and Business.
    Introduction to direct variational and moment methods and an application to the Child–Langmuir law2015In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 36, no 6Article in journal (Refereed)
    Abstract [en]

    A short introduction is given of direct variational methods and its relation to Galerkin and moment methods, all flexible and powerful approaches for finding approximate solutions of difficult physical equations. A pedagogical application of moment methods is given to the physically and technically important Child–Langmuir law in electron physics. The analysis is shown to provide simple, yet accurate, approximate solutions of the two-dimensional problem (a problem which does not allow an exact analytical solution) and illustrates the usefulness and the power of moment methods.

  • 4.
    Anderson, Dan
    et al.
    Chalmers .
    Desaix, Mats
    University of Borås, Faculty of Textiles, Engineering and Business.
    Approximate solution of a Thomas-Fermi model equation for bulk self-gravitating stellar objects in two dimensions2017In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 38, p. 1-8, article id 015406Article in journal (Refereed)
    Abstract [en]

    Direct variational methods are used to find simple approximate solutions of the Thomas–Fermi equations describing the properties of self-gravitating radially symmetric stellar objects both in the non-relativistic and ultra-relativistic cases. The approximate solutions are compared and shown to be in good agreement with exact and numerically obtained solutions.

  • 5.
    Aurell, Erik
    et al.
    RISE, Swedish ICT, SICS.
    Fanelli, Duccio
    Self-gravitating systems in a three-dimensional expanding universe2002In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404Article in journal (Refereed)
    Abstract [en]

    The non-linear evolution of one-dimensional perturbations in a three-dimensional expanding Universe is considered. A general Lagrangian scheme is derived, and compared to two previously introduced approximate models. These models are simulated with heap-based event-driven numerical procedure that allows for the study of large systems, averaged over many realisations of random initial conditions. One of the models is shown to be qualitatively, and, in some respects, concerning mass aggregation, quantitatively similar to the adhesion model.

  • 6.
    Björk, Gunnar
    KTH, School of Engineering Sciences (SCI), Applied Physics.
    Information gain when measuring an unknown qubit2018In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 39, no 1, article id 015403Article in journal (Refereed)
    Abstract [en]

    In quantum information the fundamental information-containing system is the qubit. A measurement of a single qubit can at most yield one classical bit. However, a dichotomous measurement of an unknown qubit will yield much less information about the qubit state. We use Bayesian inference to compute how much information one progressively gets by making sucessive, individual measurements on an ensemble of identically prepared qubits. Perhaps surprisingly, even if the measurements are arranged so that each measurement yields one classical bit, that is, the two possible measurement outcomes are a priori equiprobable, it takes almost a handful of measurements before one has gained one bit of information about the gradually concentrated qubit probability density. We also show that by following a strategy that reaps the maximum information per measurement, we are led to a mutually unbiased basis as our measurement bases. This is a pleasing, although not entirely surprising, result.

  • 7.
    Dunnett, K.
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Gorman, M. N.
    Aberystwyth Univ, Dept Phys, Aberystwyth SY23 3BZ, Ceredigion, Wales..
    Bartlett, P. A.
    UCL, Dept Phys & Astron, Gower St, London WC1E 6BT, England..
    Assessing first-year undergraduate physics students' laboratory practices: seeking to encourage research behaviours2019In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 40, no 1, article id 015702Article in journal (Refereed)
    Abstract [en]

    Encouraging positive inquiry-focused behaviours within the constraints of a physics teaching laboratory environment can be challenging. Here, we report on an implementation, the 'working grade' ( w-grade), designed to directly assess aspects of students' laboratory practice with the aim of encouraging first-year undergraduate students to look beyond the concept of a correct outcome' to a physics experiment. The w-grade is composed of the five aspects of group work, querying, exploration, attitude and progress which are each marked on a 0, 1, 2, 3 scale. The initial implementation is presented in full as well as a second, simpler variant. The w-grade emphasises and directly rewards inquiry behaviours and students were much more willing to explore the experiments than in previous years.

  • 8.
    Dunnett, Kirsty
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University College London, United Kingdom.
    Gorman, M. N.
    Bartlett, P. A.
    Assessing first-year undergraduate physics students' laboratory practices: seeking to encourage research behaviours2019In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 40, no 1, article id 015702Article in journal (Refereed)
    Abstract [en]

    Encouraging positive inquiry-focused behaviours within the constraints of a physics teaching laboratory environment can be challenging. Here, we report on an implementation, the 'working grade' ( w-grade), designed to directly assess aspects of students' laboratory practice with the aim of encouraging first-year undergraduate students to look beyond the concept of a correct outcome' to a physics experiment. The w-grade is composed of the five aspects of group work, querying, exploration, attitude and progress which are each marked on a 0, 1, 2, 3 scale. The initial implementation is presented in full as well as a second, simpler variant. The w-grade emphasises and directly rewards inquiry behaviours and students were much more willing to explore the experiments than in previous years.

  • 9.
    Enberg, R.
    et al.
    Ecole Polytechnique.
    Pire, B.
    Szymanowski, L.
    Transversity GPD in photo- and electroproduction of two vector mesons2006In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. C47, p. 87-94Article in journal (Refereed)
  • 10.
    Enberg, R.
    et al.
    Ecole Polytechnique.
    Pire, B.
    Szymanowski, L.
    Wallon, S.
    BFKL resummation effects in gamma* gamma* —> rho rho2006In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. C45, p. 759-769Article in journal (Refereed)
  • 11.
    Essen, Hanno
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Sten, Johan C-E
    A new look at the pushing force of an electromagnetic wave on a classical charged particle2015In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 36, no 5, article id 055029Article in journal (Refereed)
    Abstract [en]

    The interaction between a plane wave and a classical charged particle is reviewed in this paper. A matrix formulation is used to derive the relativistic motion of the particle due to the Lorentz force of a spatially homogeneous time-harmonic radiation field. The Landau-Lifshitz approach to the radiation damping force is then investigated for the same field. In conclusion only the radiation damping accelerates the particle in the direction of the Poynting vector for this type of field. The Lorentz force only leads to an extra constant drift velocity, plus oscillations with the frequency of the field.

  • 12.
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics.
    An exact formula for electromagnetic momentum in terms of the charge density and the Coulomb gauge vector potential2018In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 39, no 2, article id 025202Article in journal (Refereed)
    Abstract [en]

    The electromagnetic momentum p=1(4 pi c) integral E x BdV is sometimes approximated by p(0)=(1/c) integral rho AdV, where rho is the charge density and A is the Coulomb gauge vector potential. Here, we show that p(0) is the first term in an exact two-term expression p = p(0)+p(1) where the second term refers to radiation. When the charge density is zero, p = p(1) is the momentum of fields propagating in vacuum. In the presence of charged particles, however, p(0) normally dominates. We argue that p(0) is the natural formula for the electromagnetic momentum when radiation can be neglected. It is shown that this term may in fact be much larger than the purely mechanical contribution from mass times velocity.

  • 13.
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Comment on 'Modeling the magnetic dipole'2016In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 37, no 5, article id 058001Article in journal (Other academic)
    Abstract [en]

    The model which Seleznyova et al (2016 Eur. J. Phys. 37 025203) claim to consist of two oppositely charged magnetic monopoles is in fact a model of an infinitely thin solenoid.

  • 14.
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Electrodynamic model connecting superconductor response to magnetic field and to rotation2005In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 26, no 2, p. 279-285Article in journal (Refereed)
    Abstract [en]

    Theory and experiment on the London moment is reviewed. A simple mathematical model is motivated and then used to study the responses of a spherical superconductor to an external field and to rotation. It reveals a connection between perfect diamagnetism (Meissner effect) and the London moment. In the model neither of these are exact but the deviation from B = 0 internal field in the former and from B = (2mc/e)Omega in the latter case is described by the same dimensionless parameter. Apart from its pedagogical value the model might throw some light on the controversy surrounding the correction to the London moment.

  • 15.
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    From least action in electrodynamics to magnetomechanical energy-a review2009In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 30, no 3, p. 515-539Article, review/survey (Refereed)
    Abstract [en]

    The equations of motion for electromechanical systems are traced back to the fundamental Lagrangian of particles and electromagnetic fields, via the Darwin Lagrangian. When dissipative forces can be neglected the systems are conservative and one can study them in a Hamiltonian formalism. The central concepts of generalized capacitance and inductance coefficients are introduced and explained. The problem of gauge independence of self-inductance is considered. Our main interest is in magnetomechanics, i.e. the study of systems where there is exchange between mechanical and magnetic energy. This throws light on the concept of magnetic energy, which according to the literature has confusing and peculiar properties. We apply the theory to a few simple examples: the extension of a circular current loop, the force between parallel wires, interacting circular current loops and the rail gun. These show that the Hamiltonian, phase space, form of magnetic energy has the usual property that an equilibrium configuration corresponds to an energy minimum.

  • 16.
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Gravitationally bound ideal gas sphere in Newtonian and in Einsteinian gravity2014In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 35, no 6, p. 065003-Article in journal (Refereed)
    Abstract [en]

    The gravitational hydrostatic equilibrium of an isothermal ideal gas with pressure proportional to density is investigated. The system is known from the literature as the singular isothermal sphere since it has infinite central density and infinite total mass. In spite of these unphysical features the system is of pedagogical interest since it allows exact mathematical treatment both within Newtonian gravity and within general relativity. The difference between these two theories is nicely illustrated.

  • 17.
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Mechanics, cosmology and Mach's principle2013In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 34, no 1, p. 139-145Article in journal (Refereed)
    Abstract [en]

    It is pointed out that recent cosmological findings seem to support the view that the mass/energy distribution of the universe defines the Newtonian inertial frames, as originally suggested by Mach. The background concepts of inertial frame, Newton's second law and fictitious forces are clarified. A precise definition of Mach's principle is suggested. Then, an approximation to general relativity discovered by Einstein, Infeld and Hoffmann is used and it is found that this precise formulation of Mach's principle is realized provided the mass/energy density of the universe has a specific value. This value turns out to be twice the critical density. The implications of this approximate result are put into context.

  • 18.
    Essén, Hanno
    KTH, Superseded Departments, Mechanics.
    Note on the relativistic elastic head-on collision2002In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 23, no 5, p. 565-568Article in journal (Refereed)
    Abstract [en]

    A short, elegant, instructive, and explicit solution for the relativistic elastic head-on collision is presented. It uses the invariance of the relative speed and a suitable Lorentz transformation of the total momentum four-vector before and after the collision.

  • 19.
    Essén, Hanno
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Apazidis, Nicholas
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Turning points of the spherical pendulum and the golden ratio2009In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 30, no 2, p. 427-432Article in journal (Refereed)
    Abstract [en]

    We study the turning point problem of a spherical pendulum. The special cases of the simple pendulum and the conical pendulum are noted. For simple initial conditions the solution to this problem involves the golden ratio, also called the golden section, or the golden number. This number often appears in mathematics where you least expect it. To put our result in perspective we briefly discuss its relevance in physics.

  • 20.
    Essén, Hanno
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Nordmark, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics.
    A simple model for the falling cat problem2018In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 39, no 3, article id 035004Article in journal (Refereed)
    Abstract [en]

    We introduce a specific four-particle, four degree-of-freedom model and calculate the rotation that can be achieved by purely internal torques and forces, keeping the total angular momentum zero. We argue that the model qualitatively explains much of the ability of a cat to land on its feet even though released from rest upside down.

  • 21.
    Essén, Hanno
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Nordmark, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Static deformation of a heavy spring due to gravity and centrifugal force2010In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 31, no 3, p. 603-609Article in journal (Refereed)
    Abstract [en]

    The static equilibrium deformation of a heavy spring due to its own weight is calculated for two cases: first for a spring hanging in a constant gravitational field, and then for a spring which is at rest in a rotating system where it is stretched by the centrifugal force. Two different models are considered: first a discrete model assuming a finite number of point masses connected by springs of negligible weight, and then the continuum limit of this model. In the second case, the differential equation for the deformation is obtained by demanding that the potential energy is minimized. In this way a simple application of the variational calculus is obtained.

  • 22.
    Essén, Hanno
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Nordmark, Arne B.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Relativistic version of the Feynman-Dyson-Hughes derivation of the Lorentz force law and Maxwell's homogeneous equations2016In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 37, no 5, article id 055201Article in journal (Refereed)
    Abstract [en]

    The canonical Poisson bracket algebra of four-dimensional relativistic mechanics is used to derive the equation of motion for a charged particle, with the Lorentz force, and the homogeneous Maxwell equations.

  • 23. Fannon, James
    et al.
    Loiseau, Jean-Christophe
    Valluri, Prashant
    Bethune, Iain
    Naraigh, Lennon O.
    High-performance computational fluid dynamics: a custom-code approach2016In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 37, no 4, article id 045001Article in journal (Refereed)
    Abstract [en]

    We introduce a modified and simplified version of the pre-existing fully parallelized three-dimensional Navier-Stokes flow solver known as TPLS. We demonstrate how the simplified version can be used as a pedagogical tool for the study of computational fluid dynamics (CFDs) and parallel computing. TPLS is at its heart a two-phase flow solver, and uses calls to a range of external libraries to accelerate its performance. However, in the present context we narrow the focus of the study to basic hydrodynamics and parallel computing techniques, and the code is therefore simplified and modified to simulate pressure-driven single-phase flow in a channel, using only relatively simple Fortran 90 code with MPI parallelization, but no calls to any other external libraries. The modified code is analysed in order to both validate its accuracy and investigate its scalability up to 1000 CPU cores. Simulations are performed for several benchmark cases in pressure-driven channel flow, including a turbulent simulation, wherein the turbulence is incorporated via the large-eddy simulation technique. The work may be of use to advanced undergraduate and graduate students as an introductory study in CFDs, while also providing insight for those interested in more general aspects of high-performance computing.

  • 24.
    Fredlund, Tobias
    et al.
    Uppsala Univ, Sweden.
    Airey, John
    Linnaeus University, Faculty of Arts and Humanities, Department of Languages. Uppsala Univ, Sweden.
    Linder, Cedric
    Uppsala Univ, Sweden ; Univ Western Cape, South Africa.
    Enhancing the possibilities for learning: variation of disciplinary-relevant aspects in physics representations2015In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 36, no 5, article id 055001Article in journal (Refereed)
    Abstract [en]

    In this theoretical article we propose three factors that can enhance the possibilities for learning physics from representations, namely: (1) the identification of disciplinary-relevant aspects for a particular disciplinary task, such as solving a physics problem or explaining a phenomenon, (2) the selection of appropriate representations that showcase these disciplinary-relevant aspects, and (3) the creation of variation within the selected representations to help students notice these disciplinary-relevant aspects and the ways in which they are related to each other. An illustration of how these three factors can guide teachers in their efforts to promote physics learning is presented.

  • 25.
    Fredlund, Tobias
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Physics Didactics.
    Airey, John
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Physics Didactics.
    Linder, Cedric
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Physics Didactics.
    Enhancing the possibilities for learning: Variation of disciplinary-relevant aspects in physics representations2015In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 36, no 5, article id 055001Article in journal (Refereed)
    Abstract [en]

    In this theoretical article we propose three factors that can enhance the possibilities for learning physics from representations, namely: (1) the identification of disciplinary-relevant aspects for a particular disciplinary task, such as solving a physics problem or explaining a phenomenon, (2) the selection of appropriate representations that showcase these disciplinary-relevant aspects, and (3) the creation of variation within the selected representations to help students notice these disciplinary-relevant aspects and the ways in which they are related to each other. An illustration of how these three factors can guide teachers in their efforts to promote physics learning is presented.

  • 26.
    Fredlund, Tobias
    et al.
    Uppsala universitet, Fysikundervisningens didaktik.
    Airey, John
    Uppsala universitet, Fysikundervisningens didaktik.
    Linder, Cedric
    Uppsala universitet, Fysikundervisningens didaktik.
    Enhancing the possibilities for learning: Variation of disciplinary-relevant aspects in physics representations2015In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 36, no 5, article id 055001Article in journal (Refereed)
    Abstract [en]

    In this theoretical article we propose three factors that can enhance the possibilities for learning physics from representations, namely: (1) the identification of disciplinary-relevant aspects for a particular disciplinary task, such as solving a physics problem or explaining a phenomenon, (2) the selection of appropriate representations that showcase these disciplinary-relevant aspects, and (3) the creation of variation within the selected representations to help students notice these disciplinary-relevant aspects and the ways in which they are related to each other. An illustration of how these three factors can guide teachers in their efforts to promote physics learning is presented.

  • 27. Fredlund, Tobias
    et al.
    Airey, John
    Linnaeus University, Faculty of Humanities and Social Sciences, School of Language and Literature.
    Linder, Cedric
    Uppsala University.
    Exploring the role of physics representations: an illustrative example from students sharing knowledge about refraction2012In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 33, p. 657-666Article in journal (Refereed)
    Abstract [en]

    Research has shown that interactive engagement enhances student learning outcomes. A growing body of research suggests that the representations we use in physics are important in such learning environments. In this paper we draw on a number of sources in the literature to explore the role of representations in interactive engagement in physics. In particular we are interested in the potential for sharing disciplinary knowledge inherent in so-called persistent representations (such as equations, diagrams and graphs), which we use in physics.

    We use selected extracts from a case study, where a group of senior undergraduate physics students are asked to explain the phenomenon of refraction, to illustrate implications for interactive engagement. In this study the ray diagram that was initially introduced by the students did not appear to sufficiently support their interactive engagement. However, the introduction of a wavefront diagram quickly led their discussion to an agreed conclusion. 

    From our analysis we conclude that in interactive engagement it is important to choose appropriate persistent representations to coordinate the use of other representations such as speech and gestures. Pedagogical implications and future research are proposed. 

  • 28.
    Fredlund, Tobias
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Physics Didactics.
    Airey, John
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Physics Didactics.
    Linder, Cedric
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Physics Didactics.
    Exploring the role of physics representations: an illustrative example from students sharing knowledge about refraction2012In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 33, no 3, p. 657-666Article in journal (Refereed)
    Abstract [en]

    Research has shown that interactive engagement enhances student learning outcomes. A growing body of research suggests that the representations we use in physics are important in such learning environments. In this paper we draw on a number of sources in the literature to explore the role of representations in interactive engagement in physics. In particular we are interested in the potential for sharing disciplinary knowledge inherent in so-called persistent representations (such as equations, diagrams and graphs), which we use in physics. We use selected extracts from a case study, where a group of senior undergraduate physics students are asked to explain the phenomenon of refraction, to illustrate implications for interactive engagement. In this study the ray diagram that was initially introduced by the students did not appear to sufficiently support their interactive engagement. However, the introduction of a wavefront diagram quickly led their discussion to an agreed conclusion. From our analysis we conclude that in interactive engagement it is important to choose appropriate persistent representations to coordinate the use of other representations such as speech and gestures. Pedagogical implications and future research are proposed.

  • 29.
    Fredlund, Tobias
    et al.
    Uppsala universitet, Fysikundervisningens didaktik.
    Airey, John
    Uppsala universitet, Fysikundervisningens didaktik.
    Linder, Cedric
    Uppsala universitet, Fysikundervisningens didaktik.
    Exploring the role of physics representations: an illustrative example from students sharing knowledge about refraction2012In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 33, no 3, p. 657-666Article in journal (Refereed)
    Abstract [en]

    Research has shown that interactive engagement enhances student learning outcomes. A growing body of research suggests that the representations we use in physics are important in such learning environments. In this paper we draw on a number of sources in the literature to explore the role of representations in interactive engagement in physics. In particular we are interested in the potential for sharing disciplinary knowledge inherent in so-called persistent representations (such as equations, diagrams and graphs), which we use in physics. We use selected extracts from a case study, where a group of senior undergraduate physics students are asked to explain the phenomenon of refraction, to illustrate implications for interactive engagement. In this study the ray diagram that was initially introduced by the students did not appear to sufficiently support their interactive engagement. However, the introduction of a wavefront diagram quickly led their discussion to an agreed conclusion. From our analysis we conclude that in interactive engagement it is important to choose appropriate persistent representations to coordinate the use of other representations such as speech and gestures. Pedagogical implications and future research are proposed.

  • 30.
    Fredlund, Tobias
    et al.
    Uppsala Univ, Sweden.
    Linder, Cedric
    Uppsala Univ, Sweden ; Univ Western Cape, South Africa.
    Airey, John
    Linnaeus University, Faculty of Arts and Humanities, Department of Languages.
    Towards addressing transient learning challenges in undergraduate physics: An example from electrostatics2015In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 36, no 5, article id 055002Article in journal (Refereed)
    Abstract [en]

    In this article we characterize transient learning challenges as learning challenges that arise out of teaching situations rather than conflicts with prior knowledge. We propose that these learning challenges can be identified by paying careful attention to the representations that students produce. Once a transient learning challenge has been identified, teachers can create interventions to address it. By illustration, we argue that an appropriate way to design such interventions is to create variation around the disciplinary-relevant aspects associated with the transient learning challenge.

    References:

    Bowden J and Marton F 1998 The University of Learning: Beyond Quality and Competence in Higher Education (London: Kogan Page)

    Chen Z and Gladding G 2014 How to make a good animation: a grounded cognition model of how visual representation design affects the construction of abstract physics knowledge Phys. Rev. ST— Phys. Educ. Res. 10 010111

    Coppens P, De Cock M and Kautz C 2012 Student understanding of filters in analog electronics lab courses Proc. 40th Ann. Proc. SEFI Conf. (Thessaloniki, Greece)

    Cummings K 2011 A developmental history of physics education research The Second Committee Meeting on the Status, Contributions, and Future Directions of Discipline-Based Education Research (http://sites.nationalacademies.org/xpedio/groups/dbassesite/documents/webpage/ dbasse_072580.pdf)

    Domert D, Linder C and Ingerman Å 2005 Probability as a conceptual hurdle to understanding one- dimensional quantum scattering and tunnelling Eur. J. Phys. 26 47–59

    Driver R and Erickson G 1983 Theories-in-action: some theoretical and empirical issues in the study of students’ conceptual frameworks in science Stud. Sci. Educ. 10 37–60

    Fraser J M, Timan A L, Miller K, Dowd J E, Tucker L and Mazur E 2014 Teaching and physics education research: bridging the gap Rep. Prog. Phys. 77 1–17

    Fredlund, T, Airey, J and Linder, C (2012) Exploring the role of physics representations: an illustrative example from students sharing knowledge about refraction. Eur. J. Phys. 33, 657–66

    Fredlund, T, Airey, J and Linder, C (2015) Enhancing the possibilities for learning: variation of disciplinary-relevant aspects in physics representations. Eur. J. Phys. 36, 055001

    Hammer D 2000 Student resources for learning introductory physics Phys. Educ. Res., Am. J. Phys. Suppl. 68 52–9

    Helm H and Novak J D (ed) 1983 Proc. Int. Seminar on Misconceptions in Science and Mathematics (Ithaca, NY: Department of Education, Cornell University)

    Heron P R L and Hazelton R 2013 Interpreting students’ errors: examples from electrostatics Proc. ESERA 2013 (Nicosia, Cyprus) pp 82–9

    Ingerman Å, Berge M and Booth S 2009a Physics group work in a phenomenographic perspective— learning dynamics as the experience of variation and relevance Eur. J. Eng. Educ. 34 349–58

    Ingerman Å, Linder C and Marshall D 2009b The learners’ experience of variation: following students’ threads of learning physics in computer simulation sessions Instr. Sci. 37 273–92

    Khan Academy 2014 Electric potential at a point in space (www.khanacademy.org/test-prep/mcat/ physical-processes/electrostatics-1/v/electric-potential-at-a-point-in-space)

    Knight R D 2002 Five Easy Lessons: Strategies for Successful Physics Teaching (San Fransisco: Addison-Wesley)

    Marton F 2015 Necessary Conditions of Learning (New York: Routledge)

    Marton F and Booth S 1997 Learning and Awareness (Mahwah: Lawrence Erlbaum Associates)

    Marton F and Pang M F 2006 On some necessary conditions of learning J. Learn. Sci. 15 193–220

    Marton F and Tsui A B M 2004 Classroom Discourse and the Space of Learning (Mahwah: Lawrence Erlbaum Associates)

    McDermott L C 1991 Millikan lecture 1990: what we teach and what is learned–closing the gap Am. J. Phys. 59 301–15

    McDermott L C and Redish E F 1999 Resource letter PER-1: physics education research Am. J. Phys. 67 755–67

    McDermott L C and Shaffer P S 2002 Tutorials in Introductory Physics 1st edn (Upper Saddle River, NJ: Prentice-Hall)

    Nordling C and Österman J 2006 Physics Handbook: for Science and Engineering (Lund: Studentlitteratur)

    Planinic M 2006 Assessment of difficulties of some conceptual areas from electricity and magnetism using the conceptual survey of electricity and magnetism Am. J. Phys. 74 1143–8

    Prather E E, Rudolph A L, Brissenden G and Schlingman W M 2009 A national study assessing the teaching and learning of introductory astronomy: I. The effect of interactive instruction Am. J. Phys. 77 320–30

    Reif F 2008 Applying Cognitive Science to Education: Thinking and Learning in Scientific and Other Complex Domains (Cambridge: MIT Press)

    Reif F and Larkin J H 1991 Cognition in scientific and everyday domains: comparison and learning implications J. Res. Sci. Teach. 28 733–60

    Roth W-M and McGinn M K 1998 Inscriptions: toward a theory of representing as social practice Rev. Educ. Res. 68 35–59

    Sayre E C and Heckler A F 2009 Peaks and decays of student knowledge in an introductory E&M course Phys. Rev. ST—Phys. Educ. Res. 5 013101

    Tao P-K and Gunstone R F 1999 The process of conceptual change in force and motion during computer-supported physics instruction J. Res. Sci. Teach. 36 859–82

    Tuminaro J and Redish E F 2007 Elements of a cognitive model of physics problem solving: epistemic games Phys. Rev. ST—Phys. Educ. Res. 3 020201

    Viennot L 2001 Reasoning in Physics: the Part of Common Sense (Dordrecht: Kluwer Publishers) Young H D and Freedman R A 2004 University Physics with Modern Physics (San Francisco: Pearson)

  • 31.
    Fredlund, Tobias
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Physics Didactics.
    Linder, Cedric
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Physics Didactics.
    Airey, John
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Physics Didactics.
    Towards addressing transient learning challenges in undergraduate physics: An example from electrostatics2015In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 36, no 5, article id 055002Article in journal (Refereed)
    Abstract [en]

    In this article we characterize transient learning challenges as learning challenges that arise out of teaching situations rather than conflicts with prior knowledge. We propose that these learning challenges can be identified by paying careful attention to the representations that students produce. Once a transient learning challenge has been identified, teachers can create interventions to address it. By illustration, we argue that an appropriate way to design such interventions is to create variation around the disciplinary-relevant aspects associated with the transient learning challenge.

  • 32.
    Fredlund, Tobias
    et al.
    Uppsala universitet, Fysikundervisningens didaktik.
    Linder, Cedric
    Uppsala universitet, Fysikundervisningens didaktik.
    Airey, John
    Uppsala universitet, Fysikundervisningens didaktik.
    Towards addressing transient learning challenges in undergraduate physics: An example from electrostatics2015In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 36, no 5, article id 055002Article in journal (Refereed)
    Abstract [en]

    In this article we characterize transient learning challenges as learning challenges that arise out of teaching situations rather than conflicts with prior knowledge. We propose that these learning challenges can be identified by paying careful attention to the representations that students produce. Once a transient learning challenge has been identified, teachers can create interventions to address it. By illustration, we argue that an appropriate way to design such interventions is to create variation around the disciplinary-relevant aspects associated with the transient learning challenge.

  • 33.
    Johansson, Anders
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Physics Didactics.
    Undergraduate quantum mechanics: lost opportunities for engaging motivated students?2018In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 39, no 2, article id 025705Article in journal (Refereed)
    Abstract [en]

    Quantum mechanics is widely recognised as an important and difficult subject, and many studies have been published focusing on students' conceptual difficulties. However, the sociocultural aspects of studying such an emblematic subject have not been researched to any large extent. This study explores students' experiences of undergraduate quantum mechanics using qualitative analysis of semi-structured interview data. The results inform discussions about the teaching of quantum mechanics by adding a sociocultural dimension. Students pictured quantum mechanics as an intriguing subject that inspired them to study physics. The study environment they encountered when taking their first quantum mechanics course was however not always as inspiring as expected. Quantum mechanics instruction has commonly focused on the mathematical framework of quantum mechanics, and this kind of teaching was also what the interviewees had experienced. Two ways of handling the encounter with a traditional quantum mechanics course were identified in the interviews; either students accept the practice of studying quantum mechanics in a mathematical, exercise-centred way or they distance themselves from these practices and the subject. The students who responded by distancing themselves experienced a crisis and disappointment, where their experiences did not match the way they imagined themselves engaging with quantum mechanics. The implications of these findings are discussed in relation to efforts to reform the teaching of undergraduate quantum mechanics.

  • 34.
    Jääskeläinen, Markku
    et al.
    Dalarna University, School of Technology and Business Studies, Physics.
    Lagerkvist, Andreas
    Dalarna University, School of Technology and Business Studies, Mathematics.
    Why do they not answer and do they really learn?: A case study in analysing student response flows in introductory physics using an audience response system2017In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 38, no 4, article id 045705Article in journal (Refereed)
    Abstract [en]

    In this paper we investigate teaching with a classroom response system in introductory physics with emphasis on two issues. First, we discuss retention between question rounds and the reasons why students avoid answering the question a second time. A question with declining response rate was followed by a question addressing the student reasons for not answering. We find that there appear to be several reasons for the observed decline, and that the students need to be reminded. We argue that small drops are unimportant as the process appears to work despite the drops. Second, we discuss the dynamics of learning in a concept-sequence in electromagnetism, where a majority of the students, despite poor statistics in a first round, manage to answer a followup question correctly. In addition, we analyse the response times for both situations to connect with research on student reasoning on situations with misconception-like answers. From the combination of the answer flows and response time behaviours we find it plausible that conceptual learning occurred during the discussion phase.

  • 35.
    Linder, Cedric
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Physics Didactics.
    Book Review: Thinking in Physics: The Pleasure of Reasoning and Understanding2015In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 37, no 1, article id 019001Article, book review (Other academic)
  • 36.
    Lundqvist, Hans
    et al.
    Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Oncology, Radiology and Clinical Immunology.
    Lubberink, Mark
    Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Oncology, Radiology and Clinical Immunology.
    Tolmachev, Vladimir
    Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Oncology, Radiology and Clinical Immunology.
    Positron Emission Tomography1998In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 19, p. 537-552Article in journal (Refereed)
  • 37.
    Mörtsell, Edvard
    Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC). Stockholm University, Faculty of Science, Department of Physics.
    Cosmological histories from the Friedmann equation: the Universe as a particle2016In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 37, no 5, article id 055603Article in journal (Refereed)
    Abstract [en]

    In this note, we discuss how possible expansion histories of the Universe can be inferred in a simple way, for arbitrary energy contents. No new physical results are obtained, but the goal is rather to discuss an alternative way of writing the Friedmann equation in order to facilitate an intuitive understanding of the possible solutions; for students and researchers alike. As has been noted in passing by others, this specific form of the Friedmann equation allows us to view the universal expansion as a particle rolling along a frictionless track. Specific examples depicted include the current concordance cosmological model as well as a stable static universal model.

  • 38.
    Nordmark, Arne B.
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Essen, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    The comfortable roller coaster-on the shape of tracks with a constant normal force2010In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 31, no 6, p. 1307-1317Article in journal (Refereed)
    Abstract [en]

    A particle that moves along a smooth track in a vertical plane is influenced by two forces: gravity and normal force. The force experienced by roller coaster riders is the normal force, so a natural question to ask is, what shape of the track gives a normal force of constant magnitude? Here we solve this problem. It turns out that the solution is related to the Kepler problem; the trajectories in velocity space are conic sections.

  • 39.
    Nordmark, Arne B.
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Biomechanics.
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics.
    The skipping rope curve2007In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 28, no 2, p. 241-247Article in journal (Refereed)
    Abstract [en]

    The equilibrium of a flexible inextensible string, or chain, in the centrifugal force field of a rotating reference frame is investigated. It is assumed that the end points are fixed on the rotation axis. The shape of the curve, the skipping rope curve or troposkien, is given by the Jacobi elliptic function sn.

  • 40.
    Nordmark, Arne
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics.
    An impacting linear three body system2018In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 39, no 1, article id 015001Article in journal (Refereed)
    Abstract [en]

    We study a system of three identical bodies that can move freely on a horizontal track. Initially one body moves and two are at rest. The moving body impacts with one of the resting bodies which then impacts with the third and so on. The impacts are assumed to be characterised by a coefficient of restitution. We investigate the total number of impacts, the final velocities of the bodies, and the final energy of the system in terms of the initial velocity and the coefficient of restitution. The problem, which originates from mechanics textbooks, can be analysed as a discrete dynamical system with three degrees of freedom. The full solution is more subtle that one might expect.

  • 41.
    Nordmark, Arne
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Reply to Comment on 'An impacting linear three body system'2018In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 39, no 3, article id 038002Article in journal (Other academic)
  • 42.
    Ohlin, Kjell
    et al.
    Ohlin Labs, Sweden.
    Berggren, Karl-Fredrik
    Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics. Linköping University, Faculty of Science & Engineering.
    Patterns beyond Faraday waves: observation of parametric crossover from Faraday instabilities to the formation of vortex lattices in open dual fluid strata2016In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 37, no 4, p. 045803-Article in journal (Refereed)
    Abstract [en]

    Faraday first characterised the behaviour of a fluid in a container subjected to vertical periodic oscillations. His study pertaining to hydrodynamic instability, the Faraday instability, has catalysed a myriad of experimental, theoretical, and numerical studies shedding light on the mechanisms responsible for the transition of a system at rest to a new state of well-ordered vibrational patterns at fixed frequencies. Here we study dual strata in a shallow vessel containing distilled water and high-viscosity lubrication oil on top of it. At elevated driving power, beyond the Faraday instability, the top stratum is found to freeze into a rigid pattern with maxima and minima. At the same time there is a dynamic crossover into a new state in the form of a lattice of recirculating vortices in the lower layer containing the water. Instrumentation and the physics behind are analysed in a phenomenological way together with a basic heuristic modelling of the wave field. The study, which is based on relatively low-budget equipment, stems from related art projects that have evolved over the years. The study is of value within basic research as well as in education, especially as more advanced collective project work in e.g. engineering physics, where it invites further studies of pattern formation, the emergence of vortex lattices and complexity.

  • 43.
    Petersson, Tomas
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Hellsing, Bo
    Institutionen för fysik, Göteborgs Universitet.
    Detailed derivation of Gaussian orbital based matrix elements in electron structure calculations.2010In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 31, p. 37-46Article in journal (Refereed)
    Abstract [en]

    A detailed derivation of analytic solutions is presented for overlap, kinetic, nuclear attraction and electron repulsion integrals involving Cartesian Gaussian-type orbitals. It is demonstrated how s-type orbitals can be used to evaluate integrals with higher angular momentum via the properties of Hermite polynomials and differentiation with respect to non-integration variables.

  • 44.
    Ribberfors, Roland
    et al.
    Linköping University, Department of Physics, Chemistry and Biology. Linköping University, The Institute of Technology.
    Rietz, Andreas
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    A study of a rotating rod carrying a collar using Lagrange's equation of motion and varitional calculus2000In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 21, no 2, p. 151-157Article in journal (Other academic)
    Abstract [en]

    In this paper we use Lagrange's equation of motion to study a rotating rod carrying a collar. The focus is on how the shape of the rod affects the velocity of the collar. The calculus of variations is used to find the shape that gives the least time of travel along the rod.

  • 45. Rosenberg, C.-J.
    et al.
    Andersson, D.
    Desaix, Mats
    University of Borås, School of Engineering.
    Johannisson, P.
    Lisak, M.
    Diffusion of super-Gaussian profiles2007In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 28, no 1, p. 45-Article in journal (Refereed)
  • 46.
    Samuelsson, Leif
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    The radon indicator2005In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 26, no 6, p. 999-1006Article in journal (Refereed)
    Abstract [en]

    The radon indicator is an efficient instrument for measuring the radon daughter concentrations in a house or dwelling. Physics or environmental science students could build a radon indicator as a student project. Another possibility would be to use a radon indicator in a student investigation of radon levels in different houses. Finally the radon indicator is an excellent device for producing a radioactive source, free of charge, for the study of a-, ß- and ?-radiation. The half-life of the activity collected is approximately 40 min. The radon indicator makes use of an electrostatic method by which charged particles are drawn to a small aluminium plate with a high negative voltage (-5 kV), thus creating a strong electric field between the plate and a surrounding copper wire. The radioactivity on the plate is subsequently measured by a GM-counter and the result calculated in Bq m -3. The collecting time is just 5.5 min and therefore the instrument is only suitable for use in a short-time method for indicating the radon concentration. An improved diagram, ground-radon and/or wall-radon in houses, is presented on the basis of the author's measurements recorded with the radon indicator over many years. This diagram is very useful when discussing how to reduce radiation levels in homes. © 2005 IOP Publishing Ltd.

  • 47.
    Sten, Johan C-E
    et al.
    Univ Helsinki, Dept Math & Stat, Helsinki, Finland..
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics.
    On a tendency of the magnetic field to maximise its energy2019In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 40, no 3, article id 035202Article in journal (Refereed)
    Abstract [en]

    We show that a system of movable conductors in which constant currents are maintained will tend to maximise its magnetic energy. Even if it is not a new discovery, very few textbooks present this somewhat counterintuitive result. We outline the underlying theory using the basic laws of electrodynamics and discuss some illuminating examples, among them the law of attraction of parallel currents.

  • 48. Sun, Fei
    et al.
    He, Sailing
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering. Zhejiang University, China.
    Reversing the direction of space and inverse Doppler effect in positive refraction index media2017In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 38, no 1, article id 014003Article in journal (Refereed)
    Abstract [en]

    A negative refractive index medium, in which all spatial coordinates are reversed (i.e. a left-hand triplet is formed) by a spatial folding transformation, can create many novel electromagnetic phenomena, e.g. backward wave propagation, and inversed Doppler effect (IDE). In this study, we use coordinate rotation transformation to reverse only two spatial coordinates (e.g. x' and y'), while keeping z' unchanged. In this case, some novel phenomena, e.g. radiation-direction-reversing illusions and IDE, can be achieved in a free space region wrapped by the proposed shell without any negative refractive index medium, which is easier for experimental realization and future applications.

  • 49.
    Wang, Wenlong
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Diaz-Mendez, Rogelio
    KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Capdevila, Raudys
    Univ Politecn Valencia, Dept Appl Math, E-46022 Valencia, Spain..
    Solving the one-dimensional Ising chain via mathematical induction: an intuitive approach to the transfer matrix2019In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 40, no 6, article id 065102Article in journal (Refereed)
    Abstract [en]

    The aim of this work is to present a formulation to solve the one-dimensional Ising model using the elementary technique of mathematical induction. This formulation is physically clear and leads to the same partition function form as the transfer matrix method, which is a common subject in the introductory courses of statistical mechanics. In this way our formulation is a useful tool to complement the traditional more abstract transfer matrix method. The method can be straightforwardly generalised to other short-range chains, coupled chains and is also computationally friendly. These two approaches provide a more complete understanding of the system, and therefore our work can be of broad interest for undergraduate teaching in statistical mechanics.

  • 50.
    Wei, Yajun
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Solid State Physics.
    Zhai, Zhaohui
    Gunnarsson, Klas
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Solid State Physics.
    Svedlindh, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Solid State Physics.
    A guided enquiry approach to introduce basic concepts concerning magnetic hysteresis to minimize student misconceptions2014In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 35, no 6, p. 065015-Article in journal (Refereed)
    Abstract [en]

    Basic concepts concerning magnetic hysteresis are of vital importance in understanding magnetic materials. However, these concepts are often misinterpreted by many students and even textbooks. We summarize the most common misconceptions and present a new approach to help clarify these misconceptions and enhance students' understanding of the hysteresis loop. In this approach, students are required to perform an experiment and plot the measured magnetization values and thereby calculated demagnetizing field, internal field, and magnetic induction as functions of the applied field point by point on the same graph. The concepts of the various coercivity, remanence, saturation magnetization, and saturation induction will not be introduced until this stage. By plotting this graph, students are able to interlink all the preceding concepts and intuitively visualize the underlying physical relations between them.

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