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  • 1.
    Alhulaimi, Bassemah
    et al.
    Dalhousie University, Halifax, Canada .
    Coley, Alan
    Dalhousie University, Halifax, Canada .
    Sandin, Patrik
    Dalhousie University, Halifax, Canada; Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Potsdam, Germany.
    Anisotropic Einstein-aether cosmological models2013In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 54, no 4Article in journal (Refereed)
    Abstract [en]

    We investigate a class of spatially anisotropic cosmological models in Einstein-aether theory with a scalar field in which the self-interaction potential depends on the timelike aether vector field through the expansion and shear scalars. We derive the evolution equations in terms of expansion-normalized variables, which reduce to a dynamical system. We study the local stability of the equilibrium points of the dynamical system corresponding to physically realistic solutions, and find that there are always ranges of values of the parameters of the models for which there exists an inflationary attractor. © 2013 AIP Publishing LLC.

  • 2.
    Coley, Alan A.
    et al.
    Department of Mathematics and Statistics, Dalhousie University, Halifax NS, Canada.
    Leon, Genly
    Instituto de Física, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile.
    Sandin, Patrik
    Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Potsdam, Germany.
    Latta, Joey
    Department of Mathematics and Statistics, Dalhousie University, Halifax NS, Canada.
    Spherically symmetric Einstein-aether perfect fluid models2015In: Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, E-ISSN 1475-7516, no 12, article id 010Article in journal (Refereed)
    Abstract [en]

    We investigate spherically symmetric cosmological models in Einstein-act her theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic in homogeneous cosmological models and astrophysical objects with values for the parameters which are consistent. with current constraints. In particular, we consider dust models in (beta-) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs models using, appropriate bounded normalized variables. We then analyse these models, with special emphasis on the future asymptotic behaviour for different values of the parameters. Finally, we investigate static models for a mixture of a (necessarily non-tilted) perfect fluid with a barotropic equations of state and a scalar field.

  • 3.
    Lockby, Andreas
    et al.
    School of Science and Technology, Örebro University, Örebro, Sweden..
    Sandin, Patrik
    Örebro University, School of Science and Technology.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Finding Stationary Solutions of PDEs with Constraints using Damped Dynamical Systems2016In: Comsol Conference 2016, 2016Conference 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.

  • 4.
    Roussou, Alexandra
    et al.
    Department of Applied Mathematics, University of Crete, Heraklion, Greece.
    Smyrnakis, Ioannis
    Technological Education Institute of Crete, Heraklion, Greece.
    Magiropoulos, Manolis
    Technological Education Institute of Crete, Heraklion, Greece.
    Efremidis, Nikolaos
    Department of Applied Mathematics, University of Crete, Heraklion, Greece.
    Kavoulakis, Georgios
    Technological Education Institute of Crete, Heraklion, Greece.
    Sandin, Patrik
    Örebro University, School of Science and Technology.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Excitation spectrum of a mixture of two Bose gases confined in a ring potential with interaction asymmetry2018In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 20, article id 045006Article in journal (Refereed)
    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.

  • 5.
    Sandin, Patrik
    et al.
    Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Potsdam, Germany; Dalhousie University, Halifax, Canada.
    Alhulaimi, Bassemah
    Dalhousie University, Halifax, Canada.
    Coley, Alan
    Dalhousie University, Halifax, Canada.
    Stability of Einstein-aether cosmological models2013In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 87, no 4Article in journal (Refereed)
    Abstract [en]

    We use a dynamical systems analysis to investigate the future behavior of Einstein-Aether cosmological models with a scalar field coupling to the expansion of the aether and a noninteracting perfect fluid. The stability of the equilibrium solutions are analyzed, and the results are compared with the standard inflationary cosmological solutions and previously studied cosmological Einstein-aether models. © 2013 American Physical Society.

  • 6.
    Sandin, Patrik
    et al.
    Örebro University, School of Science and Technology.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology. Sch Sci & Technol, Univ Örebro, Örebro, Sweden.
    Numerical solution of the stationary multicomponent nonlinear Schrodinger equation with a constraint on the angular momentum2016In: Physical Review E, ISSN 2470-0045, Vol. 93, no 3, article id 033301Article in journal (Refereed)
    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.

  • 7.
    Sandin, Patrik
    et al.
    Örebro University, School of Science and Technology.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Smyrnakis, J.
    Technological Education Institute of Crete, Heraklion, Greece.
    Magiropoulos, M.
    Technological Education Institute of Crete, Heraklion, Greece.
    Kavoulakis, G. M.
    Technological Education Institute of Crete, Heraklion, Greece.
    Dimensional reduction in Bose-Einstein condensed clouds of atoms confined in tight potentials of any geometry and any interaction strength2017In: Physical Review E, ISSN 2470-0045, Vol. 95, no 1, article id 012142Article in journal (Refereed)
    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.

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