4,511 research outputs found
Bose-Einstein condensate: critical velocities and energy diagrams in the Thomas-Fermi regime
For a Bose-Einstein condensate placed in a rotating trap and confined in the
z axis, we set a framework of study for the Gross-Pitaevskii energy in the
Thomas Fermi regime. We investigate an asymptotic development of the energy,
the critical velocities of nucleation of vortices with respect to a small
parameter \ep and the location of vortices. The limit \ep going to zero
corresponds to the Thomas Fermi regime. The non-dimensionalized energy is
similar to the Ginzburg-Landau energy for superconductors in the high-kappa
high-field limit and our estimates rely on techniques developed for this latter
problem. We also take the advantage of this similarity to develop a numerical
algorithm for computing the Bose-Einstein vortices. Numerical results and
energy diagrams are presented.Comment: 10pages 9 figure
Modelling and Simulations of Multi-component Lipid Membranes and Open Membranes via Diffusive Interface Approaches
In this paper, phase field models are developed for multi-component vesicle
membranes with different lipid compositions and membranes with free boundary.
These models are used to simulate the deformation of membranes under the
elastic bending energy and the line tension energy with prescribed volume and
surface area constraints. By comparing our numerical simulations with recent
experiments, it is demonstrated that the phase field models can capture the
rich phenomena associated with the membrane transformation, thus it offers
great functionality in the simulation and modeling of multicomponent membranes
The Universal Property of the Entropy Sum of Black Holes in All Dimensions
It is proposed by Cvetic et al [Phys. Rev. Lett. 106 (2011) 121301] that the
product of all horizon areas for general rotating multi-change black holes has
universal expressions independent of the mass. When we consider the product of
all horizon entropies, however, the mass will be present in some cases, while
another new universal property [JHEP 1401 (2014) 031] is preserved, which is
more general and says that the sum of all horizon entropies depends only on the
coupling constants of the theory and the topology of the black hole. The
property has been studied in limited dimensions and the generalization in
arbitrary dimensions is not straight-forward. In this Letter, we prove a useful
formula, which makes it possible to investigate this conjectured universality
in arbitrary dimensions for the maximally symmetric black holes in general
Lovelock gravity and gravity. We also propose an approach to compute the
entropy sum of general Kerr-(anti-)de-Sitter black holes in arbitrary
dimensions. In all these cases, we prove that the entropy sum only depends on
the coupling constants and the topology of the black hole.Comment: 16 pages,no figures;v2: 17 pages, references added, minor
corrections/modifications; v3: 16 pages, added references, correct some
expressons, added equation (16) to make the context more clear, to appear in
PL
Nonlocal criteria for compactness in the space of vector fields
This work presents a set of sufficient conditions that guarantee a compact
inclusion in the function space of vector fields defined on a domain that
is either a bounded domain in or itself. The
criteria are nonlocal and are given with respect to nonlocal interaction
kernels that may not be necessarily radially symmetric. Moreover, these
criteria for vector fields are also different from those given for scalar
fields in that the conditions are based on nonlocal interactions involving only
parts of the components of the vector fields
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