9,265 research outputs found
The Generalized Point-Vortex Problem and Rotating Solutions to the Gross-Pitaevskii Equation on Surfaces of Revolution
We study the generalized point-vortex problem and the Gross-Pitaevskii
equation on surfaces of revolution. We find rotating periodic solutions to the
generalized point-vortex problem, which have two two rings of equally
spaced vortices with degrees . In particular we prove the existence of
such solutions when the surface is longitudinally symmetric. Then we seek a
rotating solution to the Gross-Pitaevskii equation having vortices that follow
those of the point-vortex flow for sufficiently small
Instability of Ginzburg-Landau Vortices on Manifolds
We investigate two settings of Ginzburg-Landau posed on a manifold where
vortices are unstable. The first is an instability result for critical points
with vortices of the Ginzburg-Landau energy posed on a simply connected,
compact, closed 2-manifold. The second is a vortex annihilation result for the
Ginzburg-Landau heat flow posed on certain surfaces of revolution with
boundary
Observation of vortex-antivortex pairing in decaying 2D turbulence of a superfluid gas
In a two-dimensional (2D) classical fluid, a large-scale flow structure
emerges out of turbulence, which is known as the inverse energy cascade where
energy flows from small to large length scales. An interesting question is
whether this phenomenon can occur in a superfluid, which is inviscid and
irrotational by nature. Atomic Bose-Einstein condensates (BECs) of highly
oblate geometry provide an experimental venue for studying 2D superfluid
turbulence, but their full investigation has been hindered due to a lack of the
circulation sign information of individual quantum vortices in a turbulent
sample. Here, we demonstrate a vortex sign detection method by using Bragg
scattering, and we investigate decaying turbulence in a highly oblate BEC at
low temperatures, with our lowest being , where is the
superfluid critical temperature. We observe that weak spatial pairing between
vortices and antivortices develops in the turbulent BEC, which corresponds to
the vortex-dipole gas regime predicted for high dissipation. Our results
provide a direct quantitative marker for the survey of various 2D turbulence
regimes in the BEC system.Comment: 8 pages, 8 figure
VIGAN: Missing View Imputation with Generative Adversarial Networks
In an era when big data are becoming the norm, there is less concern with the
quantity but more with the quality and completeness of the data. In many
disciplines, data are collected from heterogeneous sources, resulting in
multi-view or multi-modal datasets. The missing data problem has been
challenging to address in multi-view data analysis. Especially, when certain
samples miss an entire view of data, it creates the missing view problem.
Classic multiple imputations or matrix completion methods are hardly effective
here when no information can be based on in the specific view to impute data
for such samples. The commonly-used simple method of removing samples with a
missing view can dramatically reduce sample size, thus diminishing the
statistical power of a subsequent analysis. In this paper, we propose a novel
approach for view imputation via generative adversarial networks (GANs), which
we name by VIGAN. This approach first treats each view as a separate domain and
identifies domain-to-domain mappings via a GAN using randomly-sampled data from
each view, and then employs a multi-modal denoising autoencoder (DAE) to
reconstruct the missing view from the GAN outputs based on paired data across
the views. Then, by optimizing the GAN and DAE jointly, our model enables the
knowledge integration for domain mappings and view correspondences to
effectively recover the missing view. Empirical results on benchmark datasets
validate the VIGAN approach by comparing against the state of the art. The
evaluation of VIGAN in a genetic study of substance use disorders further
proves the effectiveness and usability of this approach in life science.Comment: 10 pages, 8 figures, conferenc
Meta-stable Supersymmetry Breaking in an N=1 Perturbed Seiberg-Witten Theory
In this contribution, we discuss the possibility of meta-stable supersymmetry
(SUSY) breaking vacua in a perturbed Seiberg-Witten theory with
Fayet-Iliopoulos (FI) term. We found meta-stable SUSY breaking vacua at the
degenerated dyon and monopole singular points in the moduli space at the
nonperturbative level.Comment: Submitted for the SUSY08 proceedings, 3 pages, 4 figures, references
added, minor change
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