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  • 1. Anderson, D.
    et al.
    Andersson, F.
    Andersson, Peter
    University of Borås, School of Engineering.
    Billander, A.
    Desaix, Mats
    University of Borås, School of Engineering.
    The optimal journey from A to B2008In: American Journal of Physics, ISSN 0002-9505, E-ISSN 1943-2909, Vol. 76, no 9, p. 863-866Article in journal (Refereed)
    Abstract [en]

    How fast can you comfortably travel between two points A and B? This question is formulated as a minimization problem of a functional where the discomfort is quantified in terms of the integral of the square of the acceleration between A and B. The problem is solved in terms of the corresponding Euler-Lagrange equation and approximately using a direct variational approach based on trial functions and Ritz optimization. The main purpose of the analysis is to introduce undergraduate students to variational calculus in an interesting and pedagogical way.

  • 2. 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.

  • 3. Anderson, D.
    et al.
    Desaix, Mats
    University of Borås, School of Engineering.
    Lisak, M.
    Rasch, J.
    Galerkin approach to approximate solutions of some nonlinear oscillator equations2010In: American Journal of Physics, ISSN 0002-9505, E-ISSN 1943-2909, Vol. 78, no 9, p. 920-924Article in journal (Refereed)
    Abstract [en]

    An analysis based on the Galerkin method is given of some nonlinear oscillator equations that have been analyzed by several other methods, including harmonic balance and direct variational methods. The present analysis is shown to provide simple yet accurate approximate solutions of these nonlinear equations and illustrates the usefulness and the power of the Galerkin method. (C) 2010 American Association of Physics Teachers.

  • 4.
    Anderson, D.
    et al.
    Chalmers University of Technology.
    Desaix, Mats
    University of Borås, Faculty of Textiles, Engineering and Business.
    Nyqvist, R.
    Chalmers University of Technology.
    The least uncomfortable journey from A to B2016In: American Journal of Physics, ISSN 0002-9505, E-ISSN 1943-2909, Vol. 84, no 9, p. 690-695Article in journal (Refereed)
    Abstract [en]

    A short introduction is given about direct variational methods and their relation to Galerkin and moment methods, all flexible and powerful approaches for finding approximate solutions to difficult physicalequations. An application of these methods is given in the form of the variational problem of minimizing the discomfort experienced during different journeys, between two fixed horizontal points while keeping the travel time constant. The analysis is shown to provide simple, yet accurate, approximate solutions of the problem and illustrates the usefulness and the power of direct variational and moment methods. It also demonstrates the problem of a priori assessing the accuracy of the approximate solutions and illustrates that the variational solution does not necessarily provide a more accurate solution than that obtained by moment methods.

  • 5.
    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.

  • 6.
    Bengtsson, Anders
    et al.
    University of Borås, School of Engineering.
    Arlebrink, Jim
    University of Borås, School of Engineering.
    Desaix, Mats
    University of Borås, School of Engineering.
    Försöksprojekt i matematik vid Ingenjörshögskolan i Borås2002Report (Other academic)
  • 7.
    Desaix, Mats
    et al.
    University of Borås, School of Engineering.
    Anderson, D
    Lisak, M
    Nonlinear Schrödinger Solitons with non-zero velocities emerging from real symmetric initial conditions2009Conference paper (Refereed)
    Abstract [en]

    Solutions of the nonlinear Schrodinger equation for initial conditions in the form of two separated sech-shaped in-phase pulsed,; are analyzed. It is found that; this initial condition, with appropriate amplitude, may give rise to, not; only stationary solitons, but also to symmetrically separating solitons, if the initial distance of separation is large enough. The condition for the generation of a separating soliton pair is derived from the Zakharov-Shabat eigenvalue problem using a variational approach.

  • 8.
    Desaix, Mats
    et al.
    University of Borås, School of Engineering.
    Andersson, Dan
    Lisak, Mietek
    Eigenvalues of the Zakharov-Shabat scattering problem for two separated sech-shaped pulses2008In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 372, no 14, p. 2386-2390Article in journal (Refereed)
  • 9. Rosenberg, C.-J.
    et al.
    Andersson, D.
    Desaix, Mats
    University of Borås, School of Engineering.
    Johannisson, P.
    Lisak, M.
    Analysis of the dynamics of high intensity Gaussian laser beams in nonlinear de-focusing Kerr media2007In: Optics Communications, ISSN 0030-4018, E-ISSN 1873-0310, Vol. 275, no 2, p. 458-463Article in journal (Refereed)
  • 10. 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)
  • 11. Rosenberg, C.-J.
    et al.
    Andersson, D.
    Desaix, Mats
    University of Borås, School of Engineering.
    Johannisson, P.
    Lisak, M.
    Evolution of optical pulses towards wave breaking in highly nonlinear fibres2007In: Optics Communications, ISSN 0030-4018, E-ISSN 1873-0310, Vol. 273, no 1, p. 272-277Article in journal (Refereed)
1 - 11 of 11
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