Change search
Link to record
Permanent link

Direct link
BETA
Desaix, Mats
Publications (10 of 11) Show all publications
Anderson, D. & Desaix, M. (2017). Approximate solution of a Thomas-Fermi model equation for bulk self-gravitating stellar objects in two dimensions. European journal of physics, 38, 1-8, Article ID 015406.
Open this publication in new window or tab >>Approximate solution of a Thomas-Fermi model equation for bulk self-gravitating stellar objects in two dimensions
2017 (English)In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 38, p. 1-8, article id 015406Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2017
Keywords
direct variational methods, Rayleigh–Ritz optimization procedure, Thomas–Fermi model equation
National Category
Fusion, Plasma and Space Physics Other Mathematics
Identifiers
urn:nbn:se:hb:diva-11201 (URN)10.1088/0143-0807/38/1/015406 (DOI)000390342400001 ()
Available from: 2016-12-07 Created: 2016-12-07 Last updated: 2018-11-28Bibliographically approved
Anderson, D., Desaix, M. & Nyqvist, R. (2016). The least uncomfortable journey from A to B. American Journal of Physics, 84(9), 690-695
Open this publication in new window or tab >>The least uncomfortable journey from A to B
2016 (English)In: American Journal of Physics, ISSN 0002-9505, E-ISSN 1943-2909, Vol. 84, no 9, p. 690-695Article in journal (Refereed) Published
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.

National Category
Engineering and Technology Other Physics Topics
Research subject
Resource Recovery
Identifiers
urn:nbn:se:hb:diva-10646 (URN)10.1119/1.4955151 (DOI)000383787100005 ()2-s2.0-84983661951 (Scopus ID)
Available from: 2016-09-02 Created: 2016-09-02 Last updated: 2018-11-30Bibliographically approved
Anderson, D. & Desaix, M. (2015). Introduction to direct variational and moment methods and an application to the Child–Langmuir law. European journal of physics, 36(6)
Open this publication in new window or tab >>Introduction to direct variational and moment methods and an application to the Child–Langmuir law
2015 (English)In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 36, no 6Article in journal (Refereed) Published
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.

Keywords
direct variational methods, moment methods, Child-Langmuir law
National Category
Mathematics
Identifiers
urn:nbn:se:hb:diva-769 (URN)10.1088/0143-0807/36/6/065032 (DOI)000366994700033 ()2-s2.0-84947288078 (Scopus ID)
Available from: 2015-09-17 Created: 2015-09-17 Last updated: 2018-11-30Bibliographically approved
Anderson, D., Desaix, M., Lisak, M. & Rasch, J. (2010). Galerkin approach to approximate solutions of some nonlinear oscillator equations. American Journal of Physics, 78(9), 920-924
Open this publication in new window or tab >>Galerkin approach to approximate solutions of some nonlinear oscillator equations
2010 (English)In: American Journal of Physics, ISSN 0002-9505, E-ISSN 1943-2909, Vol. 78, no 9, p. 920-924Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
American Association of Physics Teachers, 2010
Keywords
Matematik och teoretisk fysik
National Category
Mathematics
Identifiers
urn:nbn:se:hb:diva-2810 (URN)10.1119/1.3429974 (DOI)2320/6598 (Local ID)2320/6598 (Archive number)2320/6598 (OAI)
Available from: 2015-11-13 Created: 2015-11-13 Last updated: 2017-09-06Bibliographically approved
Desaix, M., Anderson, D. & Lisak, M. (2009). Nonlinear Schrödinger Solitons with non-zero velocities emerging from real symmetric initial conditions. In: : . Paper presented at MMWP08 - The third International Conference on Mathematical Modelling of Wave Phenomena, June 9-13, 2008, Växjö University, Sweden. American Institute of Physics
Open this publication in new window or tab >>Nonlinear Schrödinger Solitons with non-zero velocities emerging from real symmetric initial conditions
2009 (English)Conference paper, Published 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.

Place, publisher, year, edition, pages
American Institute of Physics, 2009
Keywords
zakhariv-shabat, variational methods, eigenvalue problem, Matematik och teoretisk fysik
National Category
Other Physics Topics
Identifiers
urn:nbn:se:hb:diva-6151 (URN)2320/5021 (Local ID)978-0-7354-0643-8 (ISBN)2320/5021 (Archive number)2320/5021 (OAI)
Conference
MMWP08 - The third International Conference on Mathematical Modelling of Wave Phenomena, June 9-13, 2008, Växjö University, Sweden
Available from: 2015-12-22 Created: 2015-12-22 Last updated: 2017-05-02Bibliographically approved
Desaix, M., Andersson, D. & Lisak, M. (2008). Eigenvalues of the Zakharov-Shabat scattering problem for two separated sech-shaped pulses. Physics Letters A, 372(14), 2386-2390
Open this publication in new window or tab >>Eigenvalues of the Zakharov-Shabat scattering problem for two separated sech-shaped pulses
2008 (English)In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 372, no 14, p. 2386-2390Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Elsevier BV, 2008
Keywords
zakharov-shabat, separating solitons, Matematik och teoretisk fysik
National Category
Mathematics
Identifiers
urn:nbn:se:hb:diva-2411 (URN)10.1016/j.physleta.2007.11.060 (DOI)2320/3562 (Local ID)2320/3562 (Archive number)2320/3562 (OAI)
Available from: 2015-11-13 Created: 2015-11-13 Last updated: 2017-09-06Bibliographically approved
Anderson, D., Andersson, F., Andersson, P., Billander, A. & Desaix, M. (2008). The optimal journey from A to B. American Journal of Physics, 76(9), 863-866
Open this publication in new window or tab >>The optimal journey from A to B
Show others...
2008 (English)In: American Journal of Physics, ISSN 0002-9505, E-ISSN 1943-2909, Vol. 76, no 9, p. 863-866Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
American Association of Physics Teachers, 2008
Keywords
variational calculus, ritz optimization, undergraduate students, Matematik och teoretisk fysik
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:hb:diva-2428 (URN)10.1119/1.2929673 (DOI)000259275900013 ()2-s2.0-51749094830 (Scopus ID)2320/3929 (Local ID)2320/3929 (Archive number)2320/3929 (OAI)
Available from: 2015-11-13 Created: 2015-11-13 Last updated: 2017-05-04Bibliographically approved
Rosenberg, C.-J., Andersson, D., Desaix, M., Johannisson, P. & Lisak, M. (2007). Analysis of the dynamics of high intensity Gaussian laser beams in nonlinear de-focusing Kerr media. Optics Communications, 275(2), 458-463
Open this publication in new window or tab >>Analysis of the dynamics of high intensity Gaussian laser beams in nonlinear de-focusing Kerr media
Show others...
2007 (English)In: Optics Communications, ISSN 0030-4018, E-ISSN 1873-0310, Vol. 275, no 2, p. 458-463Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Elsevier BV, 2007
Keywords
Matematik och teoretisk fysik
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:hb:diva-2145 (URN)10.1016/j.optcom.2007.03.054 (DOI)2320/2151 (Local ID)2320/2151 (Archive number)2320/2151 (OAI)
Available from: 2015-11-13 Created: 2015-11-13 Last updated: 2017-12-01Bibliographically approved
Rosenberg, C.-J., Andersson, D., Desaix, M., Johannisson, P. & Lisak, M. (2007). Diffusion of super-Gaussian profiles. European journal of physics, 28(1), 45
Open this publication in new window or tab >>Diffusion of super-Gaussian profiles
Show others...
2007 (English)In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 28, no 1, p. 45-Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Institute of Physics Publishing, Bristol, BS1 6BE, United Kingdom, 2007
Keywords
Matematik och teoretisk fysik
National Category
Physical Sciences
Identifiers
urn:nbn:se:hb:diva-2143 (URN)10.1088/0143-0807/28/1/005 (DOI)2320/2149 (Local ID)2320/2149 (Archive number)2320/2149 (OAI)
Available from: 2015-11-13 Created: 2015-11-13 Last updated: 2017-12-01Bibliographically approved
Rosenberg, C.-J., Andersson, D., Desaix, M., Johannisson, P. & Lisak, M. (2007). Evolution of optical pulses towards wave breaking in highly nonlinear fibres. Optics Communications, 273(1), 272-277
Open this publication in new window or tab >>Evolution of optical pulses towards wave breaking in highly nonlinear fibres
Show others...
2007 (English)In: Optics Communications, ISSN 0030-4018, E-ISSN 1873-0310, Vol. 273, no 1, p. 272-277Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Elsevier BV, 2007
Keywords
Matematik och teoretisk fysik
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:hb:diva-2144 (URN)10.1016/j.optcom.2006.12.037 (DOI)2320/2150 (Local ID)2320/2150 (Archive number)2320/2150 (OAI)
Available from: 2015-11-13 Created: 2015-11-13 Last updated: 2017-12-01Bibliographically approved
Organisations

Search in DiVA

Show all publications