12,588 research outputs found
From discretization to regularization of composite discontinuous functions
Discontinuities between distinct regions, described by different equation sets, cause difficulties for PDE/ODE solvers. We present a new algorithm that eliminates integrator discontinuities through regularizing discontinuities. First, the algorithm determines the optimum switch point between two functions spanning adjacent or overlapping domains. The optimum switch point is determined by searching for a “jump point” that minimizes a discontinuity between adjacent/overlapping functions. Then, discontinuity is resolved using an interpolating polynomial that joins the two discontinuous functions.
This approach eliminates the need for conventional integrators to either discretize and then link discontinuities through generating interpolating polynomials based on state variables or to reinitialize state variables when discontinuities are detected in an ODE/DAE system. In contrast to conventional approaches that handle discontinuities at the state variable level only, the new approach tackles discontinuity at both state variable and the constitutive equations level. Thus, this approach eliminates errors associated with interpolating polynomials generated at a state variable level for discontinuities occurring in the constitutive equations.
Computer memory space requirements for this approach exponentially increase with the dimension of the discontinuous function hence there will be limitations for functions with relatively high dimensions. Memory availability continues to increase with price decreasing so this is not expected to be a major limitation
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
Harmonic density interpolation methods for high-order evaluation of Laplace layer potentials in 2D and 3D
We present an effective harmonic density interpolation method for the
numerical evaluation of singular and nearly singular Laplace boundary integral
operators and layer potentials in two and three spatial dimensions. The method
relies on the use of Green's third identity and local Taylor-like
interpolations of density functions in terms of harmonic polynomials. The
proposed technique effectively regularizes the singularities present in
boundary integral operators and layer potentials, and recasts the latter in
terms of integrands that are bounded or even more regular, depending on the
order of the density interpolation. The resulting boundary integrals can then
be easily, accurately, and inexpensively evaluated by means of standard
quadrature rules. A variety of numerical examples demonstrate the effectiveness
of the technique when used in conjunction with the classical trapezoidal rule
(to integrate over smooth curves) in two-dimensions, and with a Chebyshev-type
quadrature rule (to integrate over surfaces given as unions of non-overlapping
quadrilateral patches) in three-dimensions
Quantitative analysis of the reconstruction performance of interpolants
The analysis presented provides a quantitative measure of the reconstruction or interpolation performance of linear, shift-invariant interpolants. The performance criterion is the mean square error of the difference between the sampled and reconstructed functions. The analysis is applicable to reconstruction algorithms used in image processing and to many types of splines used in numerical analysis and computer graphics. When formulated in the frequency domain, the mean square error clearly separates the contribution of the interpolation method from the contribution of the sampled data. The equations provide a rational basis for selecting an optimal interpolant; that is, one which minimizes the mean square error. The analysis has been applied to a selection of frequently used data splines and reconstruction algorithms: parametric cubic and quintic Hermite splines, exponential and nu splines (including the special case of the cubic spline), parametric cubic convolution, Keys' fourth-order cubic, and a cubic with a discontinuous first derivative. The emphasis in this paper is on the image-dependent case in which no a priori knowledge of the frequency spectrum of the sampled function is assumed
Decuplet Baryon Structure from Lattice QCD
The electromagnetic properties of the SU(3)-flavor baryon decuplet are
examined within a lattice simulation of quenched QCD. Electric charge radii,
magnetic moments, and magnetic radii are extracted from the E0 and M1 form
factors. Preliminary results for the E2 and M3 moments are presented giving the
first model independent insight to the shape of the quark distribution in the
baryon ground state. As in our octet baryon analysis, the lattice results give
evidence of spin-dependent forces and mass effects in the electromagnetic
properties. The quark charge distribution radii indicate these effects act in
opposing directions. Some baryon dependence of the effective quark magnetic
moments is seen. However, this dependence in decuplet baryons is more subtle
than that for octet baryons. Of particular interest are the lattice predictions
for the magnetic moments of and for which new recent
experimental measurements are available. The lattice prediction of the
ratio appears larger than the experimental ratio, while the
lattice prediction for the magnetic moment ratio is in good
agreement with the experimental ratio.Comment: RevTeX manuscript, 34 pages plus 21 figures (available upon request
Twist solitons in complex macromolecules: from DNA to polyethylene
DNA torsion dynamics is essential in the transcription process; simple models
for it have been proposed by several authors, in particular Yakushevich (Y
model). These are strongly related to models of DNA separation dynamics such as
the one first proposed by Peyrard and Bishop (and developed by Dauxois, Barbi,
Cocco and Monasson among others), but support topological solitons. We recently
developed a ``composite'' version of the Y model, in which the sugar-phosphate
group and the base are described by separate degrees of freedom. This at the
same time fits experimental data better than the simple Y model, and shows
dynamical phenomena, which are of interest beyond DNA dynamics. Of particular
relevance are the mechanism for selecting the speed of solitons by tuning the
physical parameters of the non linear medium and the hierarchal separation of
the relevant degrees of freedom in ``master'' and ``slave''. These mechanisms
apply not only do DNA, but also to more general macromolecules, as we show
concretely by considering polyethylene.Comment: New version substantially longer, with new applications to
Polyethylene. To appear in "International Journal of Non-Linear Mechanics
Precision Electromagnetic Structure of Octet Baryons in the Chiral Regime
The electromagnetic properties of the baryon octet are calculated in quenched
QCD on a 20^3 x 40 lattice with a lattice spacing of 0.128 fm using the
fat-link irrelevant clover (FLIC) fermion action. FLIC fermions enable
simulations to be performed efficiently at quark masses as low as 300 MeV. By
combining FLIC fermions with an improved-conserved vector current, we ensure
that discretisation errors occur only at O(a^2) while maintaining current
conservation. Magnetic moments and electric and magnetic radii are extracted
from the electric and magnetic form factors for each individual quark sector.
From these, the corresponding baryon properties are constructed. Our results
are compared extensively with the predictions of quenched chiral perturbation
theory. We detect substantial curvature and environment sensitivity of the
quark contributions to electric charge radii and magnetic moments in the low
quark mass region. Furthermore, our quenched QCD simulation results are in
accord with the leading non-analytic behaviour of quenched chiral perturbation
theory, suggesting that the sum of higher-order terms makes only a small
contribution to chiral curvature.Comment: 29 pages, 33 figures, 20 table
Onboard multichannel demultiplexer/demodulator
An investigation performed for NASA LeRC by COMSAT Labs, of a digitally implemented on-board demultiplexer/demodulator able to process a mix of uplink carriers of differing bandwidths and center frequencies and programmable in orbit to accommodate variations in traffic flow is reported. The processor accepts high speed samples of the signal carried in a wideband satellite transponder channel, processes these as a composite to determine the signal spectrum, filters the result into individual channels that carry modulated carriers and demodulate these to recover their digital baseband content. The processor is implemented by using forward and inverse pipeline Fast Fourier Transformation techniques. The recovered carriers are then demodulated using a single digitally implemented demodulator that processes all of the modulated carriers. The effort has determined the feasibility of the concept with multiple TDMA carriers, identified critical path technologies, and assessed the potential of developing these technologies to a level capable of supporting a practical, cost effective on-board implementation. The result is a flexible, high speed, digitally implemented Fast Fourier Transform (FFT) bulk demultiplexer/demodulator
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