38,865 research outputs found
Hydrodynamic Flows on Curved Surfaces: Spectral Numerical Methods for Radial Manifold Shapes
We formulate hydrodynamic equations and spectrally accurate numerical methods
for investigating the role of geometry in flows within two-dimensional fluid
interfaces. To achieve numerical approximations having high precision and level
of symmetry for radial manifold shapes, we develop spectral Galerkin methods
based on hyperinterpolation with Lebedev quadratures for -projection to
spherical harmonics. We demonstrate our methods by investigating hydrodynamic
responses as the surface geometry is varied. Relative to the case of a sphere,
we find significant changes can occur in the observed hydrodynamic flow
responses as exhibited by quantitative and topological transitions in the
structure of the flow. We present numerical results based on the
Rayleigh-Dissipation principle to gain further insights into these flow
responses. We investigate the roles played by the geometry especially
concerning the positive and negative Gaussian curvature of the interface. We
provide general approaches for taking geometric effects into account for
investigations of hydrodynamic phenomena within curved fluid interfaces.Comment: 14 figure
EEG-Based User Reaction Time Estimation Using Riemannian Geometry Features
Riemannian geometry has been successfully used in many brain-computer
interface (BCI) classification problems and demonstrated superior performance.
In this paper, for the first time, it is applied to BCI regression problems, an
important category of BCI applications. More specifically, we propose a new
feature extraction approach for Electroencephalogram (EEG) based BCI regression
problems: a spatial filter is first used to increase the signal quality of the
EEG trials and also to reduce the dimensionality of the covariance matrices,
and then Riemannian tangent space features are extracted. We validate the
performance of the proposed approach in reaction time estimation from EEG
signals measured in a large-scale sustained-attention psychomotor vigilance
task, and show that compared with the traditional powerband features, the
tangent space features can reduce the root mean square estimation error by
4.30-8.30%, and increase the estimation correlation coefficient by 6.59-11.13%.Comment: arXiv admin note: text overlap with arXiv:1702.0291
Motion of a droplet for the mass-conserving stochastic Allen-Cahn equation
We study the stochastic mass-conserving Allen-Cahn equation posed on a
bounded two-dimensional domain with additive spatially smooth space-time noise.
This equation associated with a small positive parameter describes the
stochastic motion of a small almost semicircular droplet attached to domain's
boundary and moving towards a point of locally maximum curvature. We apply
It\^o calculus to derive the stochastic dynamics of the droplet by utilizing
the approximately invariant manifold introduced by Alikakos, Chen and Fusco for
the deterministic problem. In the stochastic case depending on the scaling, the
motion is driven by the change in the curvature of the boundary and the
stochastic forcing. Moreover, under the assumption of a sufficiently small
noise strength, we establish stochastic stability of a neighborhood of the
manifold of droplets in and , which means that with overwhelming
probability the solution stays close to the manifold for very long time-scales
Stochastic filtering via L2 projection on mixture manifolds with computer algorithms and numerical examples
We examine some differential geometric approaches to finding approximate
solutions to the continuous time nonlinear filtering problem. Our primary focus
is a new projection method for the optimal filter infinite dimensional
Stochastic Partial Differential Equation (SPDE), based on the direct L2 metric
and on a family of normal mixtures. We compare this method to earlier
projection methods based on the Hellinger distance/Fisher metric and
exponential families, and we compare the L2 mixture projection filter with a
particle method with the same number of parameters, using the Levy metric. We
prove that for a simple choice of the mixture manifold the L2 mixture
projection filter coincides with a Galerkin method, whereas for more general
mixture manifolds the equivalence does not hold and the L2 mixture filter is
more general. We study particular systems that may illustrate the advantages of
this new filter over other algorithms when comparing outputs with the optimal
filter. We finally consider a specific software design that is suited for a
numerically efficient implementation of this filter and provide numerical
examples.Comment: Updated and expanded version published in the Journal reference
below. Preprint updates: January 2016 (v3) added projection of Zakai Equation
and difference with projection of Kushner-Stratonovich (section 4.1). August
2014 (v2) added Galerkin equivalence proof (Section 5) to the March 2013 (v1)
versio
Cryogenic propellant management: Integration of design, performance and operational requirements
The integration of the design features of the Shuttle elements into a cryogenic propellant management system is described. The implementation and verification of the design/operational changes resulting from design deficiencies and/or element incompatibilities encountered subsequent to the critical design reviews are emphasized. Major topics include: subsystem designs to provide liquid oxygen (LO2) tank pressure stabilization, LO2 facility vent for ice prevention, liquid hydrogen (LH2) feedline high point bleed, pogo suppression on the Space Shuttle Main Engine (SSME), LO2 low level cutoff, Orbiter/engine propellant dump, and LO2 main feedline helium injection for geyser prevention
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