Search results for "Geometry"
showing 10 items of 4487 documents
Two -methods to generate Bézier surfaces from the boundary
2009
Two methods to generate tensor-product Bezier surface patches from their boundary curves and with tangent conditions along them are presented. The first one is based on the tetraharmonic equation: we show the existence and uniqueness of the solution of @D^4x->=0 with prescribed boundary and adjacent to the boundary control points of a nxn Bezier surface. The second one is based on the nonhomogeneous biharmonic equation @D^2x->=p, where p could be understood as a vectorial load adapted to the C^1-boundary conditions.
Conversion d'un carreau de Bézier rationnel biquadratique en un carreau de cyclide de Dupin quartique
2006
Dupin cyclides were introduced in 1822 by the French mathematician C-P. Dupin. They are algebraic surfaces of degree 3 or 4. The set of geometric properties of these surfaces has encouraged an increasing interest in using them for geometric modeling. A couple of algorithmes is already developed to convert a Dupin cyclide patch into a rational biquadratic Bezier patch. In this paper, we consider the inverse problem: we investigate the conditions of convertibility of a Bezier patch into a Dupin cyclide one, and we present a conversion algorithm to compute the parameters of a Dupin cyclide with the boundary of the patch that corresponds to the given Bezier patch.
Bézier surfaces of minimal area: The Dirichlet approach
2004
The Plateau-Bezier problem consists in finding the Bezier surface with minimal area from among all Bezier surfaces with prescribed border. An approximation to the solution of the Plateau-Bezier problem is obtained by replacing the area functional with the Dirichlet functional. Some comparisons between Dirichlet extremals and Bezier surfaces obtained by the use of masks related with minimal surfaces are studied.
Index-based triangulation method for efficient generation of large three-dimensional ultrasonic C-scans
2018
The demand for high-speed ultrasonic scanning of large and complex components is driven by a desire to reduce production bottlenecks during the non-destructive evaluation (NDE) of critical parts. Emerging systems (including robotic inspection) allow for the collection of large volumes of data in short time spans, compared to existing inspection systems. To maximise throughput, it is crucial that the reconstructed inspection datasets are generated and evaluated rapidly without loss of detail. This requires new data visualisation and analysis tools capable of mapping complex geometries while guaranteeing full coverage. This paper presents an entirely new approach for the visualisation of thre…
Infinitesimal Hilbertianity of Locally CAT(κ)-Spaces
2021
We show that, given a metric space (Y,d)(Y,d) of curvature bounded from above in the sense of Alexandrov, and a positive Radon measure μμ on YY giving finite mass to bounded sets, the resulting metric measure space (Y,d,μ)(Y,d,μ) is infinitesimally Hilbertian, i.e. the Sobolev space W1,2(Y,d,μ)W1,2(Y,d,μ) is a Hilbert space. The result is obtained by constructing an isometric embedding of the ‘abstract and analytical’ space of derivations into the ‘concrete and geometrical’ bundle whose fibre at x∈Yx∈Y is the tangent cone at x of YY. The conclusion then follows from the fact that for every x∈Yx∈Y such a cone is a CAT(0)CAT(0) space and, as such, has a Hilbert-like structure. peerReviewed
Tensile behaviour of anti-symmetric CFRP composite
2011
Abstract This paper addresses the response of a 17-ply anti-symmetric carbon/epoxy composite subjected to uniaxial tensile loading. Hashin ply damage model is adopted to describe the damage behaviour of the plies, whereas damage initiation and progression of the interfaces are characterised by mixed-mode cohesive damage model. Force-displacement curves obtained numerically and experimentally show good agreement. Results show that all laminae and interfaces experience the damage except laminae with 0o fibre. In addition, damage is concentrated at the tab and central regions of the tensile specimen. Edge delamination is observed in all interfaces.
Measurement and interpretation of the $W$-pair cross-section in $e^+e^-$ interactions at 161 GeV
1997
In 1996 LEP ran at a centre-of-mass energy of 161~GeV, just above the threshold of W-pair production. DELPHI accumulated data corresponding to an integrated luminosity of $9.93 {\mathrm{~pb^{-1}}}$, and observed 29 events that are considered as candidates for W-pair production. From these, a cross-section for the doubly resonant $e^+e^-\to\mathrm{WW}$ process of $3.67~^{+0.97}_{-0.85} \pm 0.19{\mathrm{~pb}}$ has been measured. Within the Standard Model, this cross-section corresponds to a mass of the W-boson of ${\mathrm{80.40~\pm~0.44~(stat.)~\pm~0.09~(syst.) ~\pm 0.03~(LEP)~GeV}}/c^2$. Alternatively, if $m_{\mathrm{W}}$ is held fixed at its current value determined by other experiments, t…
Spectroscopic, crystal structural, theoretical and biological studies of phenylacetohydrazide Schiff base derivatives and their copper complexes
2020
Two phenylacetohydrazide Schiff base derivatives: N’-(1-(2-hydroxyphenyl)ethylidene)-2-phenylacetohydrazide, HL1, and N’-((1-hydroxynaphthalen-2-yl)methylene)-2-phenylacetohydrazide, HL2, were synthesized. HL1 dimerizes in presence of HCl, probably via radical mechanism to give (2,2’-((1E)-hydrazine-1,2-diylidenebis(ethan-1-yl-1-ylidene))diphenol (DIM). Thermal reactions of Cu(II) ions with the two Schiff base ligands resulted in formation of the binuclear complexes [(CuL1)2] and [(CuL2)2]. The stoichiometry and structures of the reported compounds were investigated by several spectroscopic and analytical techniques. The structure of the HL1 ligand and its complex [(CuL1)2] as well as the D…
Quantum interference and the time-dependent radiation of nanojunctions
2021
Using the recently developed time-dependent Landauer-B\"uttiker formalism and Jefimenko's retarded solutions to the Maxwell equations, we show how to compute the time-dependent electromagnetic field produced by the charge and current densities in nanojunctions out of equilibrium. We then apply this formalism to a benzene ring junction, and show that geometry-dependent quantum interference effects can be used to control the magnetic field in the vicinity of the molecule. Then, treating the molecular junction as a quantum emitter, we demonstrate clear signatures of the local molecular geometry in the non-local radiated power.