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Abdullaev, F., Ögren, M. & Sørensen, M.-P. (2019). Collective dynamics of Fermi-Bose mixtures with an oscillating scattering length. Physical Review A. Atomic, Molecular, and Optical Physics, 99(3), Article ID 033614.
Open this publication in new window or tab >>Collective dynamics of Fermi-Bose mixtures with an oscillating scattering length
2019 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 99, no 3, article id 033614Article in journal (Refereed) Published
Abstract [en]

Collective oscillations of superfluid mixtures of ultra cold fermionic and bosonic atoms are investigated while varying the fermion-boson scattering length. We study the dynamics with respect to excited center of mass modes and breathing modes in the mixture. Parametric resonances are also analyzed when the scattering length varies periodically in time, by comparing partial differential equation (PDE) models and ordinary differential equation (ODE) models for the dynamics. An application to the recent experiment with fermionic Li-6 and bosonic Li-7 atoms, which approximately have the same masses, is discussed.

Place, publisher, year, edition, pages
American Physical Society, 2019
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:oru:diva-73269 (URN)10.1103/PhysRevA.99.033614 (DOI)000461899100005 ()2-s2.0-85063301819 (Scopus ID)
Note

Funding Agency:

Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq-Brasil) 

Available from: 2019-03-22 Created: 2019-03-22 Last updated: 2019-04-04Bibliographically approved
Gulliksson, M., Ögren, M., Oleynik, A. & Zhang, Y. (2019). Damped Dynamical Systems for Solving Equations and Optimization Problems. In: Bharath Sriraman (Ed.), Handbook of the Mathematics of the Arts and Sciences: . Springer
Open this publication in new window or tab >>Damped Dynamical Systems for Solving Equations and Optimization Problems
2019 (English)In: Handbook of the Mathematics of the Arts and Sciences / [ed] Bharath Sriraman, Springer , 2019Chapter in book (Other academic)
Abstract [en]

We present an approach for solving optimization problems with or without constrains which we call Dynamical Functional Particle Method (DFMP). The method consists of formulating the optimization problem as a second order damped dynamical system and then applying symplectic method to solve it numerically. In the first part of the chapter, we give an overview of the method and provide necessary mathematical background. We show that DFPM is a stable, efficient, and given the optimal choice of parameters, competitive method. Optimal parameters are derived for linear systems of equations, linear least squares, and linear eigenvalue problems. A framework for solving nonlinear problems is developed and numerically tested. In the second part, we adopt the method to several important applications such as image analysis, inverse problems for partial differential equations, and quantum physics.  At the end, we present open problems and share some ideas of future work on generalized (nonlinear) eigenvalue problems, handling constraints with reflection, global optimization, and nonlinear ill-posed problems.

Place, publisher, year, edition, pages
Springer, 2019
Keywords
Optimization, damped dynamical systems, convex problems, eigenvalue problems, image analysis, inverse problems, quantum physics, Schrödinger equation
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:oru:diva-71881 (URN)10.1007/978-3-319-70658-0 (DOI)978-3-319-70658-0 (ISBN)
Available from: 2019-01-29 Created: 2019-01-29 Last updated: 2019-04-01Bibliographically approved
Roussou, A., Smyrnakis, I., Magiropoulos, M., Efremidis, N., Kavoulakis, G., Sandin, P., . . . Gulliksson, M. (2018). Excitation spectrum of a mixture of two Bose gases confined in a ring potential with interaction asymmetry. New Journal of Physics, 20, Article ID 045006.
Open this publication in new window or tab >>Excitation spectrum of a mixture of two Bose gases confined in a ring potential with interaction asymmetry
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2018 (English)In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 20, article id 045006Article in journal (Refereed) Published
Abstract [en]

We study the rotational properties of a two-component Bose-Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the many-body Hamiltonian. We demonstrate that the angular momentum may be given to the system either via single-particle, or "collective" excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion relation is determined via collective excitation. The corresponding many-body state, which, in addition to the interaction energy minimizes also the kinetic energy, is dictated by elementary number theory.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2018
Keywords
Bose-Einstein condensation; mixtures; superfluidity; vector solitons
National Category
Computational Mathematics Atom and Molecular Physics and Optics Condensed Matter Physics
Research subject
Physics; Mathematics
Identifiers
urn:nbn:se:oru:diva-65601 (URN)10.1088/1367-2630/aab599 (DOI)000430345700001 ()
Available from: 2018-03-09 Created: 2018-03-09 Last updated: 2018-05-02Bibliographically approved
Ögren, M. (2018). Övningsuppgifter, Ellära för civilingenjörer. Örebro: Örebro universitet
Open this publication in new window or tab >>Övningsuppgifter, Ellära för civilingenjörer
2018 (Swedish)Book (Other academic)
Place, publisher, year, edition, pages
Örebro: Örebro universitet, 2018
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Physics
Identifiers
urn:nbn:se:oru:diva-71882 (URN)
Available from: 2019-01-29 Created: 2019-01-29 Last updated: 2019-02-01Bibliographically approved
Sandin, P., Ögren, M., Gulliksson, M., Smyrnakis, J., Magiropoulos, M. & Kavoulakis, G. M. (2017). Dimensional reduction in Bose-Einstein condensed clouds of atoms confined in tight potentials of any geometry and any interaction strength. Physical Review E, 95(1), Article ID 012142.
Open this publication in new window or tab >>Dimensional reduction in Bose-Einstein condensed clouds of atoms confined in tight potentials of any geometry and any interaction strength
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2017 (English)In: Physical Review E, ISSN 2470-0045, Vol. 95, no 1, article id 012142Article in journal (Refereed) Published
Abstract [en]

Motivated by numerous experiments on Bose-Einstein condensed atoms which have been performed in tight trapping potentials of various geometries (elongated and/or toroidal/annular), we develop a general method which allows us to reduce the corresponding three-dimensional Gross-Pitaevskii equation for the order parameter into an effectively one-dimensional equation, taking into account the interactions (i.e., treating the width of the transverse profile variationally) and the curvature of the trapping potential. As an application of our model we consider atoms which rotate in a toroidal trapping potential. We evaluate the state of lowest energy for a fixed value of the angular momentum within various approximations of the effectively one-dimensional model and compare our results with the full solution of the three-dimensional problem, thus getting evidence for the accuracy of our model.

Place, publisher, year, edition, pages
American Physical Society, 2017
National Category
Computational Mathematics Condensed Matter Physics
Research subject
Mathematics; Physics
Identifiers
urn:nbn:se:oru:diva-54302 (URN)10.1103/PhysRevE.95.012142 (DOI)000400777500008 ()28208309 (PubMedID)2-s2.0-85010341455 (Scopus ID)
Note

Funding Agency:

Örebro University, School of Science and Technology  RR 2015/2016 

Available from: 2017-01-07 Created: 2017-01-07 Last updated: 2018-07-30Bibliographically approved
Ögren, M., Abdullaev, F. & Konotop, V. (2017). Solitons in a 𝒫𝒯-symmetric 𝜒(2) coupler [Letter to the editor]. Optics Letters, 42(20), 4079-4082
Open this publication in new window or tab >>Solitons in a 𝒫𝒯-symmetric 𝜒(2) coupler
2017 (English)In: Optics Letters, ISSN 0146-9592, E-ISSN 1539-4794, Vol. 42, no 20, p. 4079-4082Article in journal, Letter (Refereed) Published
Abstract [en]

We consider the existence and stability of solitons in a 𝜒(2) coupler. Both the fundamental and second harmonics (SHs) undergo gain in one of the coupler cores and are absorbed in the other one. The gain and loss are balanced, creating a parity-time (𝒫𝒯) symmetric configuration. We present two types of families of 𝒫𝒯-symmetric solitons having equal and different profiles of the fundamental and SHs. It is shown that the gain and loss can stabilize solitons. The interaction of stable solitons is shown. In the cascading limit, the model is reduced to the 𝒫𝒯-symmetric coupler with effective Kerr-type nonlinearity and the balanced nonlinear gain and loss.

Place, publisher, year, edition, pages
Optical Society of America, 2017
Keywords
solitons, PT-symmetri, optical coupler, guided waves, propagation
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:oru:diva-61268 (URN)10.1364/OL.42.004079 (DOI)000412916200011 ()29028018 (PubMedID)2-s2.0-85031289752 (Scopus ID)
Note

Funding Agency:

International Islamic University Malaysia (IIUM)  FRGS 16-014-0513

Available from: 2017-10-05 Created: 2017-10-05 Last updated: 2017-11-07Bibliographically approved
Sørensen, M. P., Falsig Pedersen, N. & Ögren, M. (2017). The dynamics of magnetic vortices in type II superconductors with pinning sites studied by the time dependent Ginzburg–Landau model. Physica. C, Superconductivity, 533, 40-43
Open this publication in new window or tab >>The dynamics of magnetic vortices in type II superconductors with pinning sites studied by the time dependent Ginzburg–Landau model
2017 (English)In: Physica. C, Superconductivity, ISSN 0921-4534, E-ISSN 1873-2143, Vol. 533, p. 40-43Article in journal (Refereed) Published
Abstract [en]

We investigate the dynamics of magnetic vortices in type II superconductors with normal state pinning sites using the Ginzburg–Landau equations. Simulation results demonstrate hopping of vortices between pinning sites, influenced by external magnetic fields and external currents. The system is highly nonlinear and the vortices show complex nonlinear dynamical behaviour.

Place, publisher, year, edition, pages
Amsterdam: Elsevier, 2017
Keywords
Ginzburg–Landau equations, Type II superconductivity, Vortices, Pinning sites
National Category
Condensed Matter Physics Computational Mathematics Nano Technology Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Physics
Identifiers
urn:nbn:se:oru:diva-51656 (URN)10.1016/j.physc.2016.08.001 (DOI)000395954100006 ()2-s2.0-84994314576 (Scopus ID)
Note

Funding Agency:

EU Horizon (COST) program Nanoscale Superconductivity: Novel Functionalities through Optimized Confinement of Condensate and Fields (NanoSC-COST)  MP1201

Available from: 2016-08-13 Created: 2016-08-13 Last updated: 2017-11-28Bibliographically approved
Ögren, M., Nyström, M. & Jarodzka, H. (2017). There’s more to the multimedia effect than meets the eye: is seeing pictures believing?. Instructional science, 45(2), 263-287
Open this publication in new window or tab >>There’s more to the multimedia effect than meets the eye: is seeing pictures believing?
2017 (English)In: Instructional science, ISSN 0020-4277, E-ISSN 1573-1952, Vol. 45, no 2, p. 263-287Article in journal (Refereed) Published
Abstract [en]

Textbooks in applied mathematics often use graphs to explain the meaning of formulae, even though their benefit is still not fully explored. To test processes underlying this assumed multimedia effect we collected performance scores, eye movements, and think-aloud protocols from students solving problems in vector calculus with and without graphs. Results showed no overall multimedia effect, but instead an effect to confirm statements that were accompanied by graphs, irrespective of whether these statements were true or false. Eye movement and verbal data shed light on this surprising finding. Students looked proportionally less at the text and the problem statement when a graph was present. Moreover, they experienced more mental effort with the graph, as indicated by more silent pauses in thinking aloud. Hence, students actively processed the graphs. This, however, was not sufficient. Further analysis revealed that the more students looked at the statement, the better they performed. Thus, in the multimedia condition the graph drew students’ attention and cognitive capacities away from focusing on the statement. A good alternative strategy in the multimedia condition was to frequently look between graph and problem statement, and thus to integrate their information. In conclusion, graphs influence where students look and what they process, and may even mislead them into believing accompanying information. Thus, teachers and textbook designers should be very critical on when to use graphs and carefully consider how the graphs are integrated with other parts of the problem.

Place, publisher, year, edition, pages
Springer Netherlands, 2017
Keywords
Multimedia effect, Eye tracking, Verbal data, Mathematics education, Science education
National Category
Didactics Other Mathematics Educational Sciences Psychology
Research subject
Physics; Mathematics
Identifiers
urn:nbn:se:oru:diva-53277 (URN)10.1007/s11251-016-9397-6 (DOI)000397984900007 ()2-s2.0-84991387594 (Scopus ID)
Note

Funding Agency:

Sveriges läromedelsförfattares förbund (SLFF)

Available from: 2016-10-26 Created: 2016-10-26 Last updated: 2017-10-18Bibliographically approved
Lockby, A., Sandin, P., Ögren, M. & Gulliksson, M. (2016). Finding Stationary Solutions of PDEs with Constraints using Damped Dynamical Systems. In: Comsol Conference 2016: . Paper presented at Comsol Conference 2016, Münich, Germany, October 12-14 2016.
Open this publication in new window or tab >>Finding Stationary Solutions of PDEs with Constraints using Damped Dynamical Systems
2016 (English)In: Comsol Conference 2016, 2016Conference paper, Published paper (Refereed)
Abstract [en]

The dynamical functional particle method(DFPM) is a method for solving equations, e.g. PDEs, using a second order damped dynamical system. We show how the method can be extended to include constraints both explicitly as global constraints and adding the constraints as additional damped dynamical equations. These methods are implemented in Comsol and we show numerical tests for finding the stationary solution of a nonlinear heat equation with and without constraints (global and dynamical). The results show that DFPM is a very general and robust way of solving PDEs and it should be of interest to implement the approach more generally in Comsol.

Keywords
PDE, constraints, dynamical system
National Category
Computational Mathematics
Research subject
Mathematics; Physics
Identifiers
urn:nbn:se:oru:diva-53278 (URN)
Conference
Comsol Conference 2016, Münich, Germany, October 12-14 2016
Projects
Metoder för att lösa ekvationer med andra ordningens dämpade dynamiska system
Available from: 2016-10-26 Created: 2016-10-26 Last updated: 2017-10-18Bibliographically approved
Sandin, P., Ögren, M. & Gulliksson, M. (2016). Numerical solution of the stationary multicomponent nonlinear Schrodinger equation with a constraint on the angular momentum. Physical Review E, 93(3), Article ID 033301.
Open this publication in new window or tab >>Numerical solution of the stationary multicomponent nonlinear Schrodinger equation with a constraint on the angular momentum
2016 (English)In: Physical Review E, ISSN 2470-0045, Vol. 93, no 3, article id 033301Article in journal (Refereed) Published
Abstract [en]

We formulate a damped oscillating particle method to solve the stationary nonlinear Schrodinger equation (NLSE). The ground-state solutions are found by a converging damped oscillating evolution equation that can be discretized with symplectic numerical techniques. The method is demonstrated for three different cases: for the single-component NLSE with an attractive self-interaction, for the single-component NLSE with a repulsive self-interaction and a constraint on the angular momentum, and for the two-component NLSE with a constraint on the total angular momentum. We reproduce the so-called yrast curve for the single-component case, described in [A. D. Jackson et al., Europhys. Lett. 95, 30002 (2011)], and produce for the first time an analogous curve for the two-component NLSE. The numerical results are compared with analytic solutions and competing numerical methods. Our method is well suited to handle a large class of equations and can easily be adapted to further constraints and components.

Place, publisher, year, edition, pages
American Physical Society, 2016
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:oru:diva-49550 (URN)10.1103/PhysRevE.93.033301 (DOI)000371415500006 ()2-s2.0-84960942930 (Scopus ID)
Note

Funding Agencies:

Örebro University, School of Science and Technology

RR

Available from: 2016-03-29 Created: 2016-03-29 Last updated: 2018-07-10Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-2630-7479

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