19,897 research outputs found
Lattice Boltzmann Model for The Volume-Averaged Navier-Stokes Equations
A numerical method, based on the discrete lattice Boltzmann equation, is
presented for solving the volume-averaged Navier-Stokes equations. With a
modified equilibrium distribution and an additional forcing term, the
volume-averaged Navier-Stokes equations can be recovered from the lattice
Boltzmann equation in the limit of small Mach number by the Chapman-Enskog
analysis and Taylor expansion. Due to its advantages such as explicit solver
and inherent parallelism, the method appears to be more competitive with
traditional numerical techniques. Numerical simulations show that the proposed
model can accurately reproduce both the linear and nonlinear drag effects of
porosity in the fluid flow through porous media.Comment: 9 pages, 2 figure
Model-Based Method for Social Network Clustering
We propose a simple mixed membership model for social network clustering in
this note. A flexible function is adopted to measure affinities among a set of
entities in a social network. The model not only allows each entity in the
network to possess more than one membership, but also provides accurate
statistical inference about network structure. We estimate the membership
parameters by using an MCMC algorithm. We evaluate the performance of the
proposed algorithm by applying our model to two empirical social network data,
the Zachary club data and the bottlenose dolphin network data. We also conduct
some numerical studies for different types of simulated networks for assessing
the effectiveness of our algorithm. In the end, some concluding remarks and
future work are addressed briefly
Exact results for Wilson loops in orbifold ABJM theory
We investigate the exact results for circular 1/4 and 1/2 BPS Wilson loops in
the super Chern-Simons-matter theory that could be
obtained by orbifolding Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. The
partition function of the orbifold ABJM theory has been
computed previously in the literature. In this paper, we re-derive it using a
slightly different method. We calculate the vacuum expectation values of the
circular 1/4 BPS Wilson loops in fundamental representation and of circular 1/2
BPS Wilson loops in arbitrary representations. We use both the saddle point
approach and Fermi gas approach. The results for Wilson loops are in accord
with the available gravity results.Comment: V1, 19 pages, 1 figure; V2, 24 pages, 1 figure, general
representations added; V3, 26 pages, no figure, published versio
Novel BPS Wilson loops in three-dimensional quiver Chern-Simons-matter theories
We show that generic three-dimensional quiver super
Chern-Simons-matter theories admit Bogomol'nyi-Prasad-Sommerfield (BPS)
Drukker-Trancanelli (DT) type Wilson loops. We investigate both Wilson loops
along timelike infinite straight lines in Minkowski spacetime and circular
Wilson loops in Euclidean space. In Aharnoy-Bergman-Jafferis-Maldacena theory,
we find that generic BPS DT type Wilson loops preserve the same number of
supersymmetries as Gaiotto-Yin type Wilson loops. There are several free
parameters for generic BPS DT type Wilson loops in the construction, and
supersymmetry enhancement for Wilson loops happens for special values of the
parameters.Comment: V1, 5 pages; V2, 13 pages, circular Wilson loops added, published
versio
BPS Wilson loops in Minkowski spacetime and Euclidean space
We give evidence that spacelike BPS Wilson loops do not exist in Minkowski
spacetime. We show that spacelike Wilson loops in Minkowski spacetime cannot
preserve any supersymmetries, in super Yang-Mills
theory, super Chern-Simons-matter theory, and
Aharony-Bergman-Jafferis-Maldacena theory. We not only show
this using infinite straight lines and circles as examples, but also we give
proofs for general curves. We attribute this to the conflicts of reality
conditions of the spinors. However, spacelike Wilson loops do exist in
Euclidean space. There are both BPS Wilson loops along infinite straight lines
and circular BPS Wilson loops. This is because the reality conditions of the
spinors are lost after Wick rotation. The result is reasonable in view of the
AdS/CFT correspondence.Comment: V1, 19 pages, no figure; V2, 25 pages, typos corrected and proofs for
general curves added thanks to the careful reading and valuable suggestions
of the anonymous referee, version to appear in EPJC; V3, 25 pages, published
versio
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