4,378 research outputs found
Semilinear geometric optics with boundary amplification
We study weakly stable semilinear hyperbolic boundary value problems with
highly oscillatory data. Here weak stability means that exponentially growing
modes are absent, but the so-called uniform Lopatinskii condition fails at some
boundary frequency in the hyperbolic region. As a consequence of this
degeneracy there is an amplification phenomenon: outgoing waves of amplitude
O(\eps^2) and wavelength \eps give rise to reflected waves of amplitude
O(\eps), so the overall solution has amplitude O(\eps). Moreover, the
reflecting waves emanate from a radiating wave that propagates in the boundary
along a characteristic of the Lopatinskii determinant. An approximate solution
that displays the qualitative behavior just described is constructed by solving
suitable profile equations that exhibit a loss of derivatives, so we solve the
profile equations by a Nash-Moser iteration. The exact solution is constructed
by solving an associated singular problem involving singular derivatives of the
form \partial_{x'}+\beta\frac{\partial_{\theta_0}}{\eps}, being the
tangential variables with respect to the boundary. Tame estimates for the
linearization of that problem are proved using a first-order calculus of
singular pseudodifferential operators constructed in the companion article
\cite{CGW2}. These estimates exhibit a loss of one singular derivative and
force us to construct the exact solution by a separate Nash-Moser iteration.
The same estimates are used in the error analysis, which shows that the exact
and approximate solutions are close in on a fixed time interval
independent of the (small) wavelength \eps. The approach using singular
systems allows us to avoid constructing high order expansions and making small
divisor assumptions
A comparative study of two stochastic mode reduction methods
We present a comparative study of two methods for the reduction of the
dimensionality of a system of ordinary differential equations that exhibits
time-scale separation. Both methods lead to a reduced system of stochastic
differential equations. The novel feature of these methods is that they allow
the use, in the reduced system, of higher order terms in the resolved
variables. The first method, proposed by Majda, Timofeyev and Vanden-Eijnden,
is based on an asymptotic strategy developed by Kurtz. The second method is a
short-memory approximation of the Mori-Zwanzig projection formalism of
irreversible statistical mechanics, as proposed by Chorin, Hald and Kupferman.
We present conditions under which the reduced models arising from the two
methods should have similar predictive ability. We apply the two methods to
test cases that satisfy these conditions. The form of the reduced models and
the numerical simulations show that the two methods have similar predictive
ability as expected.Comment: 35 pages, 6 figures. Under review in Physica
The refined inviscid stability condition and cellular instability of viscous shock waves
Combining work of Serre and Zumbrun, Benzoni-Gavage, Serre, and Zumbrun, and
Texier and Zumbrun, we propose as a mechanism for the onset of cellular
instability of viscous shock and detonation waves in a finite-cross-section
duct the violation of the refined planar stability condition of Zumbrun--Serre,
a viscous correction of the inviscid planar stability condition of Majda. More
precisely, we show for a model problem involving flow in a rectangular duct
with artificial periodic boundary conditions that transition to
multidimensional instability through violation of the refined stability
condition of planar viscous shock waves on the whole space generically implies
for a duct of sufficiently large cross-section a cascade of Hopf bifurcations
involving more and more complicated cellular instabilities.
The refined condition is numerically calculable as described in
Benzoni-Gavage--Serre-Zumbrun
Modeling of flexible surfaces: A preliminary study
The one-dimensional classical scalar string equation which involves linearization about a horizontal reference or equilibrium position is derived. We then derive a model for small motion about a nonhorizontal reference. The implications of our findings to modeling of flexible antenna surfaces such as that in the Maypole Hoop/Column antenna are discussed
Optimizing Face Recognition Using PCA
Principle Component Analysis PCA is a classical feature extraction and data
representation technique widely used in pattern recognition. It is one of the
most successful techniques in face recognition. But it has drawback of high
computational especially for big size database. This paper conducts a study to
optimize the time complexity of PCA (eigenfaces) that does not affects the
recognition performance. The authors minimize the participated eigenvectors
which consequently decreases the computational time. A comparison is done to
compare the differences between the recognition time in the original algorithm
and in the enhanced algorithm. The performance of the original and the enhanced
proposed algorithm is tested on face94 face database. Experimental results show
that the recognition time is reduced by 35% by applying our proposed enhanced
algorithm. DET Curves are used to illustrate the experimental results.Comment: 9 page
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