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Showing 1 to 20 of 46 for “"spherical harmonics"”.
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Fast multipole acceleration of periodic Green's function using spherical harmonics and Ewald summation
In this thesis, we present a fast multipole algorithm (FMA) for solving a periodic scattering problem using method of moments (MOM). The difference between the standard integral equations (EFIE and MFIE) and the ones used for periodic geometry is the use of periodic Green's function (PGF) over …
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From the Harmony of the Spheres to Spherical Harmonics : The Potential of Wave-Based Morphogenetic Processes for Musical and Architectural Composition
… the radical changes undergone by the notion of harmonics since Fourier’s and Helmoltz’s seminal works, allow to cast a completely new light on the music/architecture relationship. It opens new paths for design and composition strategies in architecture, with direct transferability to music …
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Lagrangian Points and Jacobi Constants for a Class of Asteroids
… gravity fields, namely, multiple-body and spherical harmonics modeling. Computation of gravity potential serves as a first step to determine equilibrium points called Lagrangian points for a spacecraft orbiting as an asteroid. Further, Jacobi analysis is carried out to determine …
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Fock's representation for molecular orbitals
… space the eigen-functions are the R<sub>4</sub> spherical harmonics and that the eigenvalues are determined only by the principal quantum number n. In this chapter we note that if his method is applied to the 2-dimensional Kepler problem in momentum space, the eigenfunctions are the R<sub>3</sub> …
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Vector occluders: an empirical approximation for rendering global illumination effects in real-time
… representation for PRT data. “Cpherical harmonics” (CH) are introduced as an alternative to spherical harmonics, by substituting the Chebyshev polynomial in the place of the Legendre polynomial as the orthogonal polynomial in the spherical harmonics definition. We show that CH can be used …
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Analysis of crystallographic texture information by the hyperspherical harmonic expansion
… as a linear combination of the generalized spherical harmonics. Since the use of generalized spherical harmonics requires that orientations be described by sets of Euler angles, the field of texture analysis suffers from the inherent limitations of Euler angles. These include difficulty of …
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Approximation and Integration on Compact Subsets of Euclidean Space
… Theorem and Taylors Theorem. In addition, spherical harmonics, the Laplacian, Hilbert spaces and linear projections are considered with respect to the unit sphere. An example of distributing points equally on a sphere is illustrated and a covering theorem for a unit sphere is proved.
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EXTERIOR REGULARIZED HARMONIC AND HARMONIC FUNCTIONS
… exactly certain well-known results on Laplace's spherical harmonics in classical mathematical physics.
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Time dependence of nonlinear flow dynamics of near hard sphere suspensions
… and the resulting scattering was expanded using spherical harmonics. The coefficients of the spherical harmonics are successfully used to predict the stress response of the microstructure under steady shear, and, for the first time, for near hard sphere suspensions, under oscillatory shear.
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Natural and perturbed dynamics about Trojan bodies
… gravitational potential is formulated using spherical harmonics, the coefficients describing the physical properties of the body. An analytical, arbitrary degree, perturbation theory, assuming the spherical harmonics of the body as known, is derived. This result generalizes to arbitrary …
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Using power spectra to look for anisotropies in ultra-high energy cosmic ray distributions
… I will be using the method of calculating spherical harmonics coefficients to analyze the data. The method of using these angular power spectra is an attempt to provide a common language for model builders and experimentalists. Anisotropies of any size are easily detected using these …
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Autonomous optimal trajectory design employing convex optimization for powered descent on an asteroid
… high fidelity gravity model employed was the 2x2 spherical harmonics model assuming a perfect triaxial ellipsoid and placement of the coordinate frame at the asteroid's center of mass and aligned with the semi-major axes. The spherical harmonics model is not valid inside the Brillouin sphere and …
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ILLUMINATION RECOVERY FROM IMAGES WITH CAST SHADOWS
… represented by a combination of low frequency spherical harmonics, and a small number of directional sources. Therefore, the illumination of the scene can be recovered by summing the spherical harmonic lighting and a small number of directional light sources. To demonstrate the effectiveness of …
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HEAD MOTION EVALUATION AND CORRECTION IN MAGNETOENCEPHALOGRAPHY
… This route uses oblate/prolate spheroidal harmonics in place of the spherical harmonics expansion and preserves the simplicity of the translation and rotation transformations of the spherical harmonic functions. The preservation is achieved via forward and inverse spherical to spheroidal …
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Even Parity Perturbations of the Janis-Newman-Winicour Singularity
… to the metric can be decomposed using tensor spherical harmonics and Fourier decomposition, and are further reduced by gauge transformations. By calculating the Einstein field equations and the divergence of the stress-energy tensor, one obtains 8 independent radial equations for the …
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Improving Generative Models for 3D Molecular Structures
… “Symphony: SymmetryEquivariant Point-Centered Spherical Harmonics for 3D Molecule Generation" [13] authored by Ameya Daigavane, Song Kim, Mario Geiger and Tess Smidt, and published at the International Conference on Learning Representations (ICLR), 2024.
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Observing Wave Propagation of a Float Serve on a Volleyball
… surface. We first solve the wave equation with spherical coordinates using separation of variables. For our model, we study the wave equation restricted to a sphere and describe it solutions, which are known as spherical harmonics. By using the software \emph{Matlab}, we are able to implement …
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Nonlinear acceleration methods for even-parity neutron transport
… into the application in a full three-dimensional spherical-harmonics even-parity transport code. Once moved into the nonlinear solution scheme, the implicit coupling of the convergence accelerated transport method into codes for other physics can be done seamlessly, providing an efficient, fully …
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Feature extraction from millimetre wave radar images
… terrain types cluster in the eigenspace of these spherical harmonics. Segmentation then follows from the clustering properties of pixels within this multidimensional eigenspace and classification from the locations of the clusters.
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