4,896 research outputs found
Special Lagrangians, stable bundles and mean curvature flow
We make a conjecture about mean curvature flow of Lagrangian submanifolds of
Calabi-Yau manifolds, expanding on \cite{Th}. We give new results about the
stability condition, and propose a Jordan-H\"older-type decomposition of
(special) Lagrangians. The main results are the uniqueness of special
Lagrangians in hamiltonian deformation classes of Lagrangians, under mild
conditions, and a proof of the conjecture in some cases with symmetry: mean
curvature flow converging to Shapere-Vafa's examples of SLags.Comment: 36 pages, 4 figures. Minor referee's correction
Decomposing feature-level variation with Covariate Gaussian Process Latent Variable Models
The interpretation of complex high-dimensional data typically requires the
use of dimensionality reduction techniques to extract explanatory
low-dimensional representations. However, in many real-world problems these
representations may not be sufficient to aid interpretation on their own, and
it would be desirable to interpret the model in terms of the original features
themselves. Our goal is to characterise how feature-level variation depends on
latent low-dimensional representations, external covariates, and non-linear
interactions between the two. In this paper, we propose to achieve this through
a structured kernel decomposition in a hybrid Gaussian Process model which we
call the Covariate Gaussian Process Latent Variable Model (c-GPLVM). We
demonstrate the utility of our model on simulated examples and applications in
disease progression modelling from high-dimensional gene expression data in the
presence of additional phenotypes. In each setting we show how the c-GPLVM can
extract low-dimensional structures from high-dimensional data sets whilst
allowing a breakdown of feature-level variability that is not present in other
commonly used dimensionality reduction approaches
Positivity of Quasilocal Mass
Motivated by the important work of Brown adn York on quasilocal energy, we
propose definitions of quasilocal energy and momentum surface energy of a
spacelike 2-surface with positive intrinsic curvature in a spacetime. We show
that the quasilocal energy of the boundary of a compact spacelike hypersurface
which satisfies the local energy condition is strictly positive unless the
spacetime is flat along the spacelike hypersurface.Comment: 4 pages; final published versio
Parallel Mean Curvature Surfaces in Symmetric Spaces
We present a reduction of codimension theorem for surfaces with parallel mean
curvature in symmetric spaces
Elevated temperature crack growth
Critical gas turbine engine hot section components such as blades, vanes, and combustor liners tend to develop minute cracks during early stages of operations. The ability of currently available path-independent (P-I) integrals to correlate fatigue crack propagation under conditions that simulate the turbojet engine combustor liner environment was determined. To date, an appropriate specimen design and a crack displacement measurement method were determined. Alloy 718 was selected as the analog material based on its ability to simulate high temperature behavior at lower temperatures in order to facilitate experimental measurements. Available P-I integrals were reviewed and the best approaches are being programmed into a finite element post processor for eventual comparison with experimental data. The experimental data will include cyclic crack growth tests under thermomechanical conditions, and, additionally, thermal gradients
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