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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

On the fractional Laplacian of variable order

We present a novel definition of variable-order fractional Laplacian on R n based on a natural generalization of the standard Riesz potential. Our definition holds for values of the fractional parameter spanning the entire open set (0, n/2). We then discuss some properties of the fractional Poisson’s equation involving this operator and we compute the corresponding Green’s function, for which we provide some instructive examples for specific problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1971

Eigenvalues of the Laplacian of a graph

Let G be a finite undirected graph with no loops or multiple edges. The Laplacian matrix of G, Delta(G), is defined by Delta sub ii = degree of vertex i and Delta sub ij = -1 if there is an edge between vertex i and vertex j. The structure of the graph G is related to the eigenvalues of Delta(G); in particular, it is proved that all the eigenvalues of Delta(G) are nonnegative, less than or equal to the number of vertices, and less than or equal to twice the maximum vertex degree. Precise conditions for equality are given.

Anderson, W. N., Jr.↗
NASA NTRS1981

Orbital inclination of Iapetus and the rotation of the Laplacian plane

This paper explores the possibility that the orbit of Iapetus, with its relatively large inclination but small eccentricity, was generated by a rapid dispersal of a gaseous circumplanetary disk, assumed to be the progenitor of the satellite system. The orientation of the local Laplacian plane is shown to be a sensitive function of the disk's structure. Modification of the disk on a time scale comparable to the precession of the orbit's nodal line can produce a large inclination from one that is initially zero, while leaving the eccentricity unchanged. This time scale is of the same order of magnitude as the viscous evolution time scale for a fully turbulent disk. Hence, Iapetus need not be a captured satellite to account for its curious orbital signature.

Ward, W. R.↗
NASA NTRS1982

The computation of Laplacian smoothing splines with examples

Laplacian smoothing splines (LSS) are presented as generalizations of graduation, cubic and thin plate splines. The method of generalized cross validation (GCV) to choose the smoothing parameter is described. The GCV is used in the algorithm for the computation of LSS's. An outline of a computer program which implements this algorithm is presented along with a description of the use of the program. Examples in one, two and three dimensions demonstrate how to obtain estimates of function values with confidence intervals and estimates of first and second derivatives. Probability plots are used as a diagnostic tool to check for model inadequacy.

Wendelberger, J. G.↗
NASA NTRS1984

The Laplacian resonance and tidal dissipation

The Laplacian resonance amongst Io, Europa, and Ganymede was examined, taking into account tidal dissipation in Jupiter, Io and Europa. In equilibrium, it is not possible to neglect dissipation in Europa nor the torques of Jupiter on Europa and Ganymede. A formal calculation was made on the assumption that the tidal torques and the torques in orbit-orbit resonance reached an equilibrium such that the rates of decrease of the mean motions of the satellites are in the ratios 4:2:1. Q(j)/k(j)=167 Q(1)/k(1), Q(2)/k(2) = 0.44 Q(1)/K(1), where Q denotes the quality at the body's frequency of rotation, k its second degree Love number and the subscripts J, 1 and 2 denote Jupiter, Io, and Europa. The Q(J) found is at Jupiter's frequency of rotation. The rate of tidal dissipation in Europa comes to 1/5 that of Io. Such a low value of Q(2)/K(2) is plausible if dissipation in both Io and Europa is due to tidal friction in fluid against underlying and overlying solid layers.

Cook, A. F.↗
NASA NTRS1984

Permutation codes for the Laplacian source

Permutation codes for the Laplacian source are developed. The performance of these codes is evaluated and compared with other quantizers and the rate-distortion function. It is shown that there is a bit-rate region in which the permutation codes outperform certain single-sample quantizers.

Townes, S. A.↗
NASA NTRS1989

Structural stereo matching of Laplacian-of-Gaussian contour segments for 3D perception

The stereo correspondence problem is solved using Laplacian-of-Gaussian zero-crossing contours as a source of primitives for structural stereopsis, as opposed to traditional point-based algorithms. Up to 74 percent matching of candidate zero crossing points are being achieved on 240 x 246 images at small scales and large ranges of disparity, without coarse-to-fine tracking and without precise knowledge of the epipolar geometry. This approach should prove particularly useful in recovering the epipolar geometry automatically for stereo pairs for which it is unavailable a priori. Such situations occur in the extraction of terrain models from stereo aerial photographs.

Boyer, K. L.↗
NASA NTRS1997

The Path Resistance Method for Bounding the Smallest Nontrivial Eigenvalue of a Laplacian

We introduce the path resistance method for lower bounds on the smallest nontrivial eigenvalue of the Laplacian matrix of a graph. The method is based on viewing the graph in terms of electrical circuits; it uses clique embeddings to produce lower bounds on lambda(sub 2) and star embeddings to produce lower bounds on the smallest Rayleigh quotient when there is a zero Dirichlet boundary condition. The method assigns priorities to the paths in the embedding; we show that, for an unweighted tree T, using uniform priorities for a clique embedding produces a lower bound on lambda(sub 2) that is off by at most an 0(log diameter(T)) factor. We show that the best bounds this method can produce for clique embeddings are the same as for a related method that uses clique embeddings and edge lengths to produce bounds.

Guattery, Stephen↗
DOE OSTI2015

Evaluating the Potential of a Laplacian Linear Solver.

A new approach for solving Laplacian linear systems proposed by Kelner et al. involves the random sampling and update of fundamental cycles in a graph. We evaluate the performance of this approach on a variety of real world graphs. We examine di erent ways to choose the set of cycles and their sequence of updates with the goal of providing more exibility and potential parallelism. We propose a parallel model of the Kelner et al. method for evaluating potential parallelism concerned with minimizing the span of edges updated at every iteration. We provide experimental results comparing the potential parallelism of the fundamental cycle basis and the extended basis. Our preliminary experiments show that choosing a non-fundamental set of cycles can save signi cant work compared to a fundamental cycle basis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

On the Existence of Regular Global Attractor for p-Laplacian Evolution Equation

In this study, we consider the nonlinear evolution equation of parabolic type u{sub t}−div(|∇u|{sup p−2}∇u)+f(u)=g. We analyze the long time dynamics (in the sense of global attractors) under very general conditions on the nonlinearity f. Since we do not assume any polynomial growth condition on it, the main difficulty arises at first in the proof of well-posedness. In fact, the very first contribution to this problem is a pioneering paper (Efendiev and Ôtano, Differ Int Equ 20:1201–1209, 2007) where the well-posedness result has been shown by exploiting the technique from the theory of maximal monotone operators. However, from some physical aspects, to obtain the solution in variational sense might be demanding which requires limiting procedure on the approximate solutions. In this work, we are interested in variational (weak) solution. The critical issue in the proof of well-posedness is to deal with the limiting procedure on f which is overcome utilizing the weak convergence tecniques in Orlicz spaces (Geredeli and Khanmamedov, Commun Pure Appl Anal 12:735–754, 2013; Krasnosel’skiĭ and Rutickiĭ, Convex functions and Orlicz spaces, 1961). Then, proving the existence of the global attractors in L{sup 2}(Ω) and in more regular space W{sub 0}{sup 1,p}(Ω), we show that they coincide. In addition, if f is monotone and g=0, we give an explicit estimate of the decay rate to zero of the solution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗