The Experts below are selected from a list of 51 Experts worldwide ranked by ideXlab platform
J. Alberto Montero - One of the best experts on this subject based on the ideXlab platform.
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Vortices for a Rotating Toroidal Bose–Einstein Condensate
Archive for Rational Mechanics and Analysis, 2008Co-Authors: Stan Alama, Lia Bronsard, J. Alberto MonteroAbstract:We construct local minimizers of the Gross–Pitaevskii energy, introduced to model Bose–Einstein condensates (BEC) in the Thomas–Fermi regime which are subject to a uniform rotation. Our sample domain is taken to be a solid Torus of Revolution in $${\mathbb{R}}^3$$ with starshaped cross-section. We show that for angular speeds ω_ε = O (|ln ε|) there exist local minimizers of the energy which exhibit vortices, for small enough values of the parameter ε . These vortices concentrate at one or several planar arcs (represented by integer multiplicity rectifiable currents) which minimize a line energy, obtained as a Γ-limit of the Gross–Pitaevskii functional. The location of these limiting vortex lines can be described under certain geometrical hypotheses on the cross-sections of the Torus.
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Vortices for a Rotating Toroidal Bose–Einstein Condensate
Archive for Rational Mechanics and Analysis, 2007Co-Authors: Stan Alama, Lia Bronsard, J. Alberto MonteroAbstract:We construct local minimizers of the Gross–Pitaevskii energy, introduced to model Bose–Einstein condensates (BEC) in the Thomas–Fermi regime which are subject to a uniform rotation. Our sample domain is taken to be a solid Torus of Revolution in \({\mathbb{R}}^3\) with starshaped cross-section. We show that for angular speeds ωe = O(|ln e|) there exist local minimizers of the energy which exhibit vortices, for small enough values of the parameter e. These vortices concentrate at one or several planar arcs (represented by integer multiplicity rectifiable currents) which minimize a line energy, obtained as a Γ-limit of the Gross–Pitaevskii functional. The location of these limiting vortex lines can be described under certain geometrical hypotheses on the cross-sections of the Torus.
Stan Alama - One of the best experts on this subject based on the ideXlab platform.
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Vortices for a Rotating Toroidal Bose–Einstein Condensate
Archive for Rational Mechanics and Analysis, 2008Co-Authors: Stan Alama, Lia Bronsard, J. Alberto MonteroAbstract:We construct local minimizers of the Gross–Pitaevskii energy, introduced to model Bose–Einstein condensates (BEC) in the Thomas–Fermi regime which are subject to a uniform rotation. Our sample domain is taken to be a solid Torus of Revolution in $${\mathbb{R}}^3$$ with starshaped cross-section. We show that for angular speeds ω_ε = O (|ln ε|) there exist local minimizers of the energy which exhibit vortices, for small enough values of the parameter ε . These vortices concentrate at one or several planar arcs (represented by integer multiplicity rectifiable currents) which minimize a line energy, obtained as a Γ-limit of the Gross–Pitaevskii functional. The location of these limiting vortex lines can be described under certain geometrical hypotheses on the cross-sections of the Torus.
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Vortices for a Rotating Toroidal Bose–Einstein Condensate
Archive for Rational Mechanics and Analysis, 2007Co-Authors: Stan Alama, Lia Bronsard, J. Alberto MonteroAbstract:We construct local minimizers of the Gross–Pitaevskii energy, introduced to model Bose–Einstein condensates (BEC) in the Thomas–Fermi regime which are subject to a uniform rotation. Our sample domain is taken to be a solid Torus of Revolution in \({\mathbb{R}}^3\) with starshaped cross-section. We show that for angular speeds ωe = O(|ln e|) there exist local minimizers of the energy which exhibit vortices, for small enough values of the parameter e. These vortices concentrate at one or several planar arcs (represented by integer multiplicity rectifiable currents) which minimize a line energy, obtained as a Γ-limit of the Gross–Pitaevskii functional. The location of these limiting vortex lines can be described under certain geometrical hypotheses on the cross-sections of the Torus.
Lia Bronsard - One of the best experts on this subject based on the ideXlab platform.
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Vortices for a Rotating Toroidal Bose–Einstein Condensate
Archive for Rational Mechanics and Analysis, 2008Co-Authors: Stan Alama, Lia Bronsard, J. Alberto MonteroAbstract:We construct local minimizers of the Gross–Pitaevskii energy, introduced to model Bose–Einstein condensates (BEC) in the Thomas–Fermi regime which are subject to a uniform rotation. Our sample domain is taken to be a solid Torus of Revolution in $${\mathbb{R}}^3$$ with starshaped cross-section. We show that for angular speeds ω_ε = O (|ln ε|) there exist local minimizers of the energy which exhibit vortices, for small enough values of the parameter ε . These vortices concentrate at one or several planar arcs (represented by integer multiplicity rectifiable currents) which minimize a line energy, obtained as a Γ-limit of the Gross–Pitaevskii functional. The location of these limiting vortex lines can be described under certain geometrical hypotheses on the cross-sections of the Torus.
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Vortices for a Rotating Toroidal Bose–Einstein Condensate
Archive for Rational Mechanics and Analysis, 2007Co-Authors: Stan Alama, Lia Bronsard, J. Alberto MonteroAbstract:We construct local minimizers of the Gross–Pitaevskii energy, introduced to model Bose–Einstein condensates (BEC) in the Thomas–Fermi regime which are subject to a uniform rotation. Our sample domain is taken to be a solid Torus of Revolution in \({\mathbb{R}}^3\) with starshaped cross-section. We show that for angular speeds ωe = O(|ln e|) there exist local minimizers of the energy which exhibit vortices, for small enough values of the parameter e. These vortices concentrate at one or several planar arcs (represented by integer multiplicity rectifiable currents) which minimize a line energy, obtained as a Γ-limit of the Gross–Pitaevskii functional. The location of these limiting vortex lines can be described under certain geometrical hypotheses on the cross-sections of the Torus.
D. S. Timonina - One of the best experts on this subject based on the ideXlab platform.
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Topological classification of integrable geodesic flows in a potential field on the Torus of Revolution
Lobachevskii Journal of Mathematics, 2017Co-Authors: D. S. TimoninaAbstract:A Liouville classification of integrable Hamiltonian systems which are the geodesic flows on 2-dimensional Torus of Revolution in a invariant potential field in the case of linear integral is obtained. This classification is obtained using the Fomenko–Zieschang invariant (marked molecules) of investigated systems. All types of bifurcation curves are described. Also a classification of singularities of the system solutions is obtained.
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Liouville classification of integrable geodesic flows on a Torus of Revolution in a potential field
Moscow University Mathematics Bulletin, 2017Co-Authors: D. S. TimoninaAbstract:A Liouville classification of integrable Hamiltonian systems being geodesic flows on a twodimensional Torus of Revolution in an invariant potential field is obtained in the case of linear integral. This classification is obtained using the Fomenko–Zieschang invariant (so called marked molecules) of the systems under consideration. All types of bifurcation curves are described. A classification of singularities of the system solutions is also obtained.
Clémence Labrousse - One of the best experts on this subject based on the ideXlab platform.
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Polynomial growth of volume of balls for zero-entropy geodesic systems
Nonlinearity, 2012Co-Authors: Clémence LabrousseAbstract:The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we use two numerical conjugacy invariants, the {\em strong polynomial entropy $h_{pol}$} and the {\em weak polynomial entropy $h_{pol}^*$}. Both are infinite when the topological entropy is positive and they satisfy $h_{pol}^*\leq h_{pol}$. We first prove that the growth rate of the volume of balls is bounded above by means of the strong polynomial entropy and we show that for the flat Torus this inequality becomes an equality. We then study the explicit example of the Torus of Revolution for which we can give an exact asymptotic equivalent of the growth rate of volume of balls, which we relate to the weak polynomial entropy.