98,317 research outputs found
Norm minima in certain Siegel leaves
In this paper we shall illustrate that each polytopal moment-angle complex
can be understood as the intersection of the minima of corresponding Siegel
leaves and the unit sphere, with respect to the maximum norm. Consequently, an
alternative proof of a rigidity theorem of Bosio and Meersseman is obtained; as
piecewise linear manifolds, polytopal real moment-angle complexes can be
smoothed in a natural way.Comment: 21 page
A Holographic P-wave Superconductor Model
We study a holographic p-wave superconductor model in a four dimensional
Einstein-Maxwell-complex vector field theory with a negative cosmological
constant. The complex vector field is charged under the Maxwell field. We solve
the full coupled equations of motion of the system and find black hole
solutions with the vector hair. The vector hairy black hole solutions are dual
to a thermal state with the U(1) symmetry as well as the spatial rotational
symmetry breaking spontaneously. Depending on two parameters, the mass and
charge of the vector field, we find a rich phase structure: zeroth order, first
order and second order phase transitions can happen in this model. We also find
"retrograde condensation" in which the hairy black hole solution exists only
for the temperatures above a critical value with the free energy much larger
than the black hole without hair. We construct the phase diagram for this
system in terms of the temperature and charge of the vector field.Comment: v3: 26 pages, 15 figures, references added, extra arguments added, to
appear in JHE
Numerical Regularized Moment Method of Arbitrary Order for Boltzmann-BGK Equation
We introduce a numerical method for solving Grad's moment equations or
regularized moment equations for arbitrary order of moments. In our algorithm,
we do not need explicitly the moment equations. As an instead, we directly
start from the Boltzmann equation and perform Grad's moment method \cite{Grad}
and the regularization technique \cite{Struchtrup2003} numerically. We define a
conservative projection operator and propose a fast implementation which makes
it convenient to add up two distributions and provides more efficient flux
calculations compared with the classic method using explicit expressions of
flux functions. For the collision term, the BGK model is adopted so that the
production step can be done trivially based on the Hermite expansion. Extensive
numerical examples for one- and two-dimensional problems are presented.
Convergence in moments can be validated by the numerical results for different
number of moments.Comment: 33 pages, 13 figure
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