14,512 research outputs found
Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification
We present an efficient method for classifying the morphology of the
intersection curve of two quadrics (QSIC) in PR3, 3D real projective space;
here, the term morphology is used in a broad sense to mean the shape,
topological, and algebraic properties of a QSIC, including singularity,
reducibility, the number of connected components, and the degree of each
irreducible component, etc. There are in total 35 different QSIC morphologies
with non-degenerate quadric pencils. For each of these 35 QSIC morphologies,
through a detailed study of the eigenvalue curve and the index function jump we
establish a characterizing algebraic condition expressed in terms of the Segre
characteristics and the signature sequence of a quadric pencil. We show how to
compute a signature sequence with rational arithmetic so as to determine the
morphology of the intersection curve of any two given quadrics. Two immediate
applications of our results are the robust topological classification of QSIC
in computing B-rep surface representation in solid modeling and the derivation
of algebraic conditions for collision detection of quadric primitives
Dynamic simulation of hydrodynamically interacting suspensions
A general method for computing the hydrodynamic interactions among an infinite suspension of particles, under the condition of vanishingly small particle Reynolds number, is presented. The method follows the procedure developed by O'Brien (1979) for constructing absolutely convergent expressions for particle interactions. For use in dynamic simulation, the convergence of these expressions is accelerated by application of the Ewald summation technique. The resulting hydrodynamic mobility and/or resistance matrices correctly include all far-field non-convergent interactions. Near-field lubrication interactions are incorporated into the resistance matrix using the technique developed by Durlofsky, Brady & Bossis (1987). The method is rigorous, accurate and computationally efficient, and forms the basis of the Stokesian-dynamics simulation method. The method is completely general and allows such diverse suspension problems as self-diffusion, sedimentation, rheology and flow in porous media to be treated within the same formulation for any microstructural arrangement of particles. The accuracy of the Stokesian-dynamics method is illustrated by comparing with the known exact results for spatially periodic suspensions
Dielectric resonances in disordered media
Binary disordered systems are usually obtained by mixing two ingredients in
variable proportions: conductor and insulator, or conductor and
super-conductor. and are naturally modeled by regular bi-dimensional or
tri-dimensional lattices, on which sites or bonds are chosen randomly with
given probabilities. In this article, we calculate the impedance of the
composite by two independent methods: the so-called spectral method, which
diagonalises Kirchhoff's Laws via a Green function formalism, and the Exact
Numerical Renormalization method (ENR). These methods are applied to mixtures
of resistors and capacitors (R-C systems), simulating e.g. ionic
conductor-insulator systems, and to composites consituted of resistive
inductances and capacitors (LR-C systems), representing metal inclusions in a
dielectric bulk. The frequency dependent impedances of the latter composites
present very intricate structures in the vicinity of the percolation threshold.
We analyse the LR-C behavior of compounds formed by the inclusion of small
conducting clusters (``-legged animals'') in a dielectric medium. We
investigate in particular their absorption spectra who present a pattern of
sharp lines at very specific frequencies of the incident electromagnetic field,
the goal being to identify the signature of each animal. This enables us to
make suggestions of how to build compounds with specific absorption or
transmission properties in a given frequency domain.Comment: 10 pages, 6 figures, LaTeX document class EP
Extension of the Finite Integration Technique including dynamic mesh refinement and its application to self-consistent beam dynamics simulations
An extension of the framework of the Finite Integration Technique (FIT)
including dynamic and adaptive mesh refinement is presented. After recalling
the standard formulation of the FIT, the proposed mesh adaptation procedure is
described. Besides the linear interpolation approach, a novel interpolation
technique based on specialized spline functions for approximating the discrete
electromagnetic field solution during mesh adaptation is introduced. The
standard FIT on a fixed mesh and the new adaptive approach are applied to a
simulation test case with known analytical solution. The numerical accuracy of
the two methods are shown to be comparable. The dynamic mesh approach is,
however, much more efficient. This is also demonstrated for the full scale
modeling of the complete RF gun at the Photo Injector Test Facility DESY
Zeuthen (PITZ) on a single computer. Results of a detailed design study
addressing the effects of individual components of the gun onto the beam
emittance using a fully self-consistent approach are presented.Comment: 33 pages, 14 figures, 4 table
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