17,498 research outputs found
mfEGRA: Multifidelity Efficient Global Reliability Analysis through Active Learning for Failure Boundary Location
This paper develops mfEGRA, a multifidelity active learning method using
data-driven adaptively refined surrogates for failure boundary location in
reliability analysis. This work addresses the issue of prohibitive cost of
reliability analysis using Monte Carlo sampling for expensive-to-evaluate
high-fidelity models by using cheaper-to-evaluate approximations of the
high-fidelity model. The method builds on the Efficient Global Reliability
Analysis (EGRA) method, which is a surrogate-based method that uses adaptive
sampling for refining Gaussian process surrogates for failure boundary location
using a single-fidelity model. Our method introduces a two-stage adaptive
sampling criterion that uses a multifidelity Gaussian process surrogate to
leverage multiple information sources with different fidelities. The method
combines expected feasibility criterion from EGRA with one-step lookahead
information gain to refine the surrogate around the failure boundary. The
computational savings from mfEGRA depends on the discrepancy between the
different models, and the relative cost of evaluating the different models as
compared to the high-fidelity model. We show that accurate estimation of
reliability using mfEGRA leads to computational savings of 46% for an
analytic multimodal test problem and 24% for a three-dimensional acoustic horn
problem, when compared to single-fidelity EGRA. We also show the effect of
using a priori drawn Monte Carlo samples in the implementation for the acoustic
horn problem, where mfEGRA leads to computational savings of 45% for the
three-dimensional case and 48% for a rarer event four-dimensional case as
compared to single-fidelity EGRA
Abrasion of flat rotating shapes
We report on the erosion of flat linoleum "pebbles" under steady rotation in
a slurry of abrasive grit. To quantify shape as a function of time, we develop
a general method in which the pebble is photographed from multiple angles with
respect to the grid of pixels in a digital camera. This reduces digitization
noise, and allows the local curvature of the contour to be computed with a
controllable degree of uncertainty. Several shape descriptors are then employed
to follow the evolution of different initial shapes toward a circle, where
abrasion halts. The results are in good quantitative agreement with a simple
model, where we propose that points along the contour move radially inward in
proportion to the product of the radius and the derivative of radius with
respect to angle
Local correlation functional for electrons in two dimensions
We derive a local approximation for the correlation energy in two-dimensional
electronic systems. In the derivation we follow the scheme originally developed
by Colle and Salvetti for three dimensions, and consider a Gaussian
approximation for the pair density. Then, we introduce an ad-hoc modification
which better accounts for both the long-range correlation, and the
kinetic-energy contribution to the correlation energy. The resulting functional
is local, and depends parametrically on the number of electrons in the system.
We apply this functional to the homogeneous electron gas and to a set of
two-dimensional quantum dots covering a wide range of electron densities and
thus various amounts of correlation. In all test cases we find an excellent
agreement between our results and the exact correlation energies. Our
correlation functional has a form that is simple and straightforward to
implement, but broadly outperforms the commonly used local-density
approximation
Scattering from Solutions of Star Polymers
We calculate the scattering intensity of dilute and semi-dilute solutions of
star polymers. The star conformation is described by a model introduced by
Daoud and Cotton. In this model, a single star is regarded as a spherical
region of a semi-dilute polymer solution with a local, position dependent
screening length. For high enough concentrations, the outer sections of the
arms overlap and build a semi-dilute solution (a sea of blobs) where the inner
parts of the actual stars are embedded. The scattering function is evaluated
following a method introduced by Auvray and de Gennes. In the dilute regime
there are three regions in the scattering function: the Guinier region (low
wave vectors, q R << 1) from where the radius of the star can be extracted; the
intermediate region (1 << q R << f^(2/5)) that carries the signature of the
form factor of a star with f arms: I(q) ~ q^(-10/3); and a high wavevector zone
(q R >> f^(2/5)) where the local swollen structure of the polymers gives rise
to the usual q^(-5/3) decay. In the semi-dilute regime the different stars
interact strongly, and the scattered intensity acquires two new features: a
liquid peak that develops at a reciprocal position corresponding to the
star-star distances; and a new large wavevector contribution of the form
q^(-5/3) originating from the sea of blobs.Comment: REVTeX, 12 pages, 4 eps figure
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