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Otimização da asfericidade de superfícies refratoras conicodais

Pereira, Wiliam Gonzaga
Fonte: Universidade Estadual Paulista (UNESP) Publicador: Universidade Estadual Paulista (UNESP)
Tipo: Dissertação de Mestrado Formato: 113 f. : il.
POR
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Pós-graduação em Física - FEG; A topografia de uma superfície refratora é importante para a geração de uma imagem com boa definição. Para objetos puntuais localizados sobre o eixo ótico, efeitos de aberração esférica tornam-se relevantes quando estamos modelando raios não paraxiais. O uso de superfícies asféricas permite reduzir tais imperfeições. No entanto, a determinação exata da asfericidade não é trivial, pois depende da altura de incidência do raio, bem como da posição do objeto. Esta dissertação objetivou otimizar a asfericidade de superfícies refratoras visando a minimização da aberração esférica. Para isso, descrevemos as superfícies através da equação de um conicóide e empregamos o Princípio de Fermat para modelar a propagação de raios. Desenvolvemos um modelo analítico para determinar a posição da imagem para um objeto axial e a partir daí realizamos simulações numéricas para otimizar as asfericidades. Os resultados mostram que para raios não paraxiais, superfícies esféricas e parabólicas não são adequadas. O parâmetro de asfericidade depende fortemente da posição do objeto, porém fracamente da altura h com que raio de luz incide na superfície refratora. Dentro dos limites de validade da aproximação paraxial...

Highly aspherical silica nanoshells by templating tubular liposomes

Tan, Grace; Xu, Peng; He, Jibao; Lawson, Louise; McPherson, Gary L.; John, Vijay T.
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 01/07/2009 EN
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A dual-lipid liposome system consisting of a phospholipid and a skin ceramide extruded though a 100 nm membrane yields novel tubular and helical liposomes. These liposomes were used as templates to generate highly aspherical silica nanocapsules with length to diameter aspect ratios exceeding 10. Many of these nanocapsules have the morphology of a bulbous end attached to a long tip, mimicking microneedles attached to a reservoir. The fidelity of helical liposomes is transcribed to the silicas and the long tips indicate helically entwined left-handed silica structures. The silica coating is expected to protect and stabilize the internal contents of the liposomes, as well as enable surface functionalization for applications in drug or targeted delivery.

Set Voronoi diagrams of 3D assemblies of aspherical particles

Schaller, Fabian M.; Kapfer, Sebastian C.; Evans, Myfanwy E.; Hoffmann, Matthias J.F.; Aste, Tomaso; Saadatfar, Mohammad; Mecke, Klaus; Delaney, Gary W.; Schröder-Turk, Gerd E.
Fonte: Taylor & Francis Publicador: Taylor & Francis
Tipo: Artigo de Revista Científica Formato: 24 pages
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Several approaches to quantitative local structure characterization for particulate assemblies, such as structural glasses or jammed packings, use the partition of space provided by the Voronoi diagram. The conventional construction for spherical mono-disperse particles, by which the Voronoi cell of a particle is that of its centre point, cannot be applied to configurations of aspherical or polydisperse particles. Here, we discuss the construction of a Set Voronoi diagram for configurations of aspherical particles in three-dimensional space. The Set Voronoi cell of a given particle is composed of all points in space that are closer to the surface (as opposed to the centre) of the given particle than to the surface of any other; this definition reduces to the conventional Voronoi diagram for the case of mono-disperse spheres. An algorithm for the computation of the Set Voronoi diagram for convex particles is described, as a special case of a Voronoi-based medial axis algorithm, based on a triangulation of the particles’ bounding surfaces. This algorithm is further improved by a pre-processing step based on morphological erosion, which improves the quality of the approximation and circumvents the problems associated with small degrees of particle–particle overlap that may be caused by experimental noise or soft potentials. As an application...

A new method for aspherical surface fitting with large-volume datasets

EL HAYEK, Nadim; NOUIRA, Hichem; ANWER, Nabil; GIBARU, Olivier; DAMAK, Mohamed
Fonte: Elsevier Publicador: Elsevier
EN_US
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In the framework of form characterization of aspherical surfaces, European National Metrology Institutes (NMIs) have been developing ultra-high precision machines having the ability to measure aspherical lenses with an uncertainty of few tens of nanometers. The fitting of the acquired aspherical datasets onto their corresponding theoretical model should be achieved at the same level of precision. In this article, three fitting algorithms are investigated: the Limited memory-Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), the Levenberg–Marquardt (LM) and one variant of the Iterative Closest Point (ICP). They are assessed based on their capacities to converge relatively fast to achieve a nanometric level of accuracy, to manage a large volume of data and to be robust to the position of the data with respect to the model. Nev-ertheless, the algorithms are first evaluated on simulated datasets and their performances are studied. The comparison of these algorithms is extended on measured datasets of an aspherical lens. The results validate the newly used method for the fitting of aspherical surfaces and reveal that it is well adapted, faster and less complex than the LM or ICP methods.; EMRP

Comparison of tactile and chromatic confocal measurements of aspherical lenses for form metrology

EL HAYEK, Nadim; NOUIRA, Hichem; ANWER, Nabil; DAMAK, Mohamed; GIBARU, Olivier
Fonte: Arts et Métiers ParisTech Publicador: Arts et Métiers ParisTech
EN_US
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Both contact and non-contact probes are often used in dimensional metrology applications, especially for roughness, form and surface profile measurements. To perform such kind of measurements with a nanometer level of accuracy, LNE (French National Metrology Institute (NMI)) has developed a high precision profilometer traceable to the SI meter definition. The architecture of the machine contains a short and stable metrology frame dissociated from the supporting frame. It perfectly respects Abbe principle. The metrology loop incorporates three Renishaw laser interferometers and is equipped either with a chromatic confocal probe or a tactile probe to achieve measurements at the nanometric level of uncertainty. The machine allows the in-situ calibration of the probes by means of a differential laser interferometer considered as a reference. In this paper, both the architecture and the operation of the LNE’s high precision profilometer are detailed. A brief comparison of the behavior of the chromatic confocal and tactile probes is presented. Optical and tactile scans of an aspherical surface are performed and the large number of data are processed using the L-BFGS (Limited memory-Broyden-Fletcher-Goldfarb-Shanno) algorithm. Fitting results are compared with respect to the evaluated residual errors which reflect the form defects of the surface.; EMRP

Topological rigidity for non-aspherical manifolds

Kreck, Matthias; Lueck, Wolfgang
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/09/2005
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The Borel Conjecture predicts that closed aspherical manifolds are topological rigid. We want to investigate when a non-aspherical oriented connected closed manifold M is topological rigid in the following sense. If f: N --> M is an orientation preserving homotopy equivalence with a closed oriented manifold as target, then there is an orientation preserving homeomorphism h: N --> M such that h and f induce up to conjugation the same maps on the fundamental groups. We call such manifolds Borel manifolds. We give partial answers to this questions for S^k x S^d, for sphere bundles over aspherical closed manifolds of dimension less or equal to 3 and for 3-manifolds with torsionfree fundamental groups. We show that this rigidity is inherited under connected sums in dimensions greater or equal to 5. We also classify manifolds of dimension 5 or 6 whose fundamental group is the one of a surface and whose second homotopy group is trivial.; Comment: 35 pages

$S^2$-bundles over 2-orbifolds

Hillman, Jonathan A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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Let $M$ be a closed 4-manifold with $\pi_2(M)\cong{Z}$. Then $M$ is homotopy equivalent to either $CP^2$, or the total space of an orbifold bundle with general fibre $S^2$ over a 2-orbifold $B$, or the total space of an $RP^2$-bundle over an aspherical surface. If $\pi=\pi_1(M)\not=1$ there are at most two such bundle spaces with given action $u:\pi\to{Aut}(\pi_2(M))$. The bundle space has the geometry $\mathbb{S}^2\times\mathbb{E}^2$ (if $\chi(M)=0$) or $\mathbb{S}^2\times\mathbb{H}^2$ (if $\chi(M)<0$), except when $B$ is orientable and $\pi$ is generated by involutions, in which case the action is unique and there is one non-geometric orbifold bundle.; Comment: We have completed the determination of which $S^2$-orbifold bundles are geometric, and also computed the second Wu class for each such manifold. Further minor changes have been made (principally to the section on surgery) in the second revision

Modelling of aspherical nebulae. I. A quick pseudo-3D photoionization code

Morisset, C.; Stasinska, G.; Pena, M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 03/03/2005
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We describe a pseudo-3D photoionization code, NEBU_3D and its associated visualization tool, VIS_NEB3D, which are able to easily and rapidly treat a wide variety of nebular geometries, by combining models obtained with a 1D photoionization code. The only requirement for the code to work is that the ionization source is uniqu e and not extended. It is applicable as long as the diffuse ionizing radiation f ield is not dominant and strongly inhomogeneous. As examples of the capabilities of these new tools, we consider two very differ ent theoretical cases. One is that of a high excitation planetary nebula that ha s an ellipsoidal shape with two polar density knots. The other one is that of a blister HII region, for which we have also constructed a spherical model (the sp herical impostor) which has exactly the same Hbeta surface brightness distrib ution as the blister model and the same ionizing star. These two examples warn against preconceived ideas when interpreting spectroscop ic and imaging data of HII regions and planetary nebulae. The tools NEBU_3D and VIS_NEB3D, which will be made publicly available in the future, should facilitat e the performance of numerical experiments, to yield a better understanding of t he physics of aspherical ionized nebulae.; Comment: 11 pages...

Immersions of Surfaces into Aspherical 3-Manifolds

Nowik, Tahl
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/10/2005
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We study finite order invariants of null-homotopic immersions of a closed orientable surface into an aspherical orientable 3-manifold. We give the foundational constructions, and classify all order one invariants.

The Structure of the Homunculus. III. Forming a Disk and Bipolar Lobes in a Rotating Surface Explosion

Smith, Nathan; Townsend, Richard H. D.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 21/05/2007
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We present a semi-analytic model for shaping the nebula around eta Carinae that accounts for the simultaneous production of bipolar lobes and an equatorial disk through a rotating surface explosion. Material is launched normal to the surface of an oblate rotating star with an initial kick velocity that scales approximately with the local escape speed. Thereafter, ejecta follow ballistic orbital trajectories, feeling only a central force corresponding to a radiatively reduced gravity. Our model is conceptually similar to the wind-compressed disk model of Bjorkman & Cassinelli, but we modify it to an explosion instead of a steady line-driven wind, we include a rotationally-distorted star, and we treat the dynamics somewhat differently. Continuum-driving avoids the disk inhibition that normally operates in line-driven winds. Our model provides a simple method by which rotating hot stars can simultaneously produce intrinsically bipolar and equatorial mass ejections, without an aspherical environment or magnetic fields. Although motivated by eta Carinae, the model may have generic application to other LBVs, B[e] stars, or SN1987A's nebula. When near-Eddington radiative driving is less influential, our model generalizes to produce bipolar morphologies without disks...

NEBU_3D: A fast pseudo-3D photoionization code for aspherical planetary nebulae and HII regions

Morisset, C.; Stasinska, G.; Pena, M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/09/2005
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25.94%
We describe a pseudo-3D photoionization code, NEBU_3D and its associated visualization tool, VIS_NEB3D, which are able to easily and rapidly treat a wide variety of nebular geometries, by combining models obtained with a 1D photoionization code. We also present a tool, VELNEB_3D, which can be applied to the results of 1D or 3D photoionization codes to generate emission line profiles, position-velocity maps and 3D maps in any emission line by assuming an arbitrary velocity field. As examples of the capabilities of these new tools, we consider three very different theoretical cases. The first one is a blister HII region, for which we have also constructed a spherical model (the spherical impostor) which has exactly the same Hbeta surface brightness distribution as the blister model and the same ionizing star. The second example shows how complex line profiles can be obtained even with a simple expansion law if the nebula is bipolar and the slit slightly off-center. The third example shows different ways to produce line profiles that could be attributed to a turbulent velocity field while there is no turbulence in the model.; Comment: Proceeding of the Planetary Nebulae as Astronomical Tools, Gdansk, 2005

Preplanetary Nebulae: An HST Imaging Survey and a New Morphological Classification System

Sahai, Raghvendra; Morris, Mark; Contreras, Carmen Sánchez; Claussen, Mark
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 31/07/2007
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Using the Hubble Space Telescope (HST), we have carried out a survey of candidate preplanetary nebulae (PPNs). We report here our discoveries of objects having well-resolved geometrical structures, and use the large sample of PPNs now imaged with HST (including previously studied objects in this class) to devise a comprehensive morphological classification system for this category of objects. The wide variety of aspherical morphologies which we have found for PPNs are qualitatively similar to those found for young planetary nebulae in previous surveys. We also find prominent halos surrounding the central aspherical shapes in many of our objects -- these are direct signatures of the undisturbed circumstellar envelopes of the progenitor AGB stars. Although the majority of these have surface-brightness distributions consistent with a constant mass-loss rate with a constant expansion velocity, there are also examples of objects with varying mass-loss rates. As in our surveys of young planetary nebulae (PNs), we find no round PPNs. The similarities in morphologies between our survey objects and young PNs supports the view that the former are the progenitors of aspherical planetary nebulae, and that the onset of aspherical structure begins during the PPN phase (or earlier). Thus...

Crystallization of hard aspherical particles

Miller, William L.; Bozorgui, Behnaz; Cacciuto, Angelo
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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We use numerical simulations to study the crystallization of monodisperse systems of hard aspherical particles. We find that particle shape and crystallizability can be easily related to each other when particles are characterized in terms of two simple and experimentally accessible order parameters: one based on the particle surface-to-volume ratio, and the other on the angular distribution of the perturbations away from the ideal spherical shape. We present a phase diagram obtained by exploring the crystallizability of 487 different particle shapes across the two-order-parameter spectrum. Finally, we consider the physical properties of the crystalline structures accessible to aspherical particles, and discuss limits and relevance of our results.; Comment: 4 pages, 3 figures. Published in the Journal of Chemical Physics.

Sections of surface bundles

Hillman, Jonathan A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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A bundle with base $B$ and fibre $F$ aspherical closed surfaces has a section if and only if the action $:\pi_1(B)\to{Out}(\pi_1(F))$ factors through $Aut(\pi_1(F))$ and a cohomology class is 0. We simplify and make more explicit the latter condition. We also show that the transgression $d^2_{2,0}$ in the homology LHS spectral sequence of a central extension is evaluation of the extension class. Examples with hyperbolic fibre and no section (based on ideas of Endo) added.; Comment: Some new background material. Section on flat fibred case rewritten. In v3, details of Endo's example corrected and commentary added to final section on questions

Aspherical gravitational monopoles

Connes, Alain; Damour, Thibault; Fayet, Pierre
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 21/11/1996
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We show how to construct non-spherically-symmetric extended bodies of uniform density behaving exactly as pointlike masses. These ``gravitational monopoles'' have the following equivalent properties: (i) they generate, outside them, a spherically-symmetric gravitational potential $M/|x - x_O|$; (ii) their interaction energy with an external gravitational potential $U(x)$ is $- M U(x_O)$; and (iii) all their multipole moments (of order $l \geq 1$) with respect to their center of mass $O$ vanish identically. The method applies for any number of space dimensions. The free parameters entering the construction are: (1) an arbitrary surface $\Sigma$ bounding a connected open subset $\Omega$ of $R^3$; (2) the arbitrary choice of the center of mass $O$ within $\Omega$; and (3) the total volume of the body. An extension of the method allows one to construct homogeneous bodies which are gravitationally equivalent (in the sense of having exactly the same multipole moments) to any given body.; Comment: 55 pages, Latex , submitted to Nucl.Phys.B

Four-manifolds, geometries and knots

Hillman, Jonathan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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The goal of this book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of such manifolds and knots. The first chapter is purely algebraic. The rest of the book may be divided into three parts: general results on homotopy and surgery (Chapters 2-6), geometries and geometric decompositions (Chapters 7-13), and 2-knots (Chapters 14-18). In many cases the Euler characteristic, fundamental group and Stiefel-Whitney classes together form a complete system of invariants for the homotopy type of such manifolds, and the possible values of the invariants can be described explicitly. The strongest results are characterizations of manifolds which fibre homotopically over S^1 or an aspherical surface (up to homotopy equivalence) and infrasolvmanifolds (up to homeomorphism). As a consequence 2-knots whose groups are poly-Z are determined up to Gluck reconstruction and change of orientations by their groups alone. This book arose out of two earlier books "2-Knots and their Groups" and "The Algebraic Characterization of Geometric 4-Manifolds", published by Cambridge University Press for the Australian Mathematical Society and for the London Mathematical Society...

The stable moduli space of flat connections over a surface

Ramras, Daniel A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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26.12%
We compute the homotopy type of the moduli space of flat, unitary connections over aspherical surfaces, after stabilizing with respect to the rank of the underlying bundle. Over the orientable surface M^g, we show that this space has the homotopy type of the infinite symmetric product of M^g, generalizing a well-known fact for the torus. Over a non-orientable surface, we show that this space is homotopy equivalent to a disjoint union of two tori, whose common dimension corresponds to the rank of the first (co)homology group of the surface. Similar calculations are provided for products of surfaces, and show a close analogy with the Quillen-Lichtenbaum conjectures in algebraic K-theory. The proofs utilize Tyler Lawson's work in deformation K-theory, and rely heavily on Yang-Mills theory and gauge theory.; Comment: 40 pages. V2: Expanded Section 5.2; updated references; various minor revisions. Submitted version. V3: various proofs simplified, esp. in Sections 3, 5.2, and 6. This version includes many revisions based on a referee's comments, especially in Section 6. V4: proof of Lemma 5.7 corrected, other minor revisions. To appear in Trans. AMS

Towards a dynamical interpretation of Hamiltonian spectral invariants on surfaces

Humilière, Vincent; Roux, Frédéric Le; Seyfaddini, Sobhan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 12/02/2015
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Inspired by Le Calvez' theory of transverse foliations for dynamical systems of surfaces, we introduce a dynamical invariant, denoted by N, for Hamiltonians of any surface other than the sphere. When the surface is the plane or is closed and aspherical, we prove that on the set of autonomous Hamiltonians this invariant coincides with the spectral invariants constructed by Viterbo on the plane and Schwarz on closed and aspherical surfaces. Along the way, we obtain several results of independent interest: We show that a formal spectral invariant, satisfying a minimal set of axioms, must coincide with N on autonomous Hamiltonians thus establishing a certain uniqueness result for spectral invariants, we obtain a "Max Formula" for spectral invariants on aspherical manifolds, give a very simple description of the Entov-Polterovich quasi-state on aspherical surfaces and characterize the heavy and super-heavy subsets of such surfaces.; Comment: 94 pages, 16 figures, 7 footnotes

Applications of controlled surgery in dimension 4: Examples

Hegenbarth, Friedrich; Repovš, Dušan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/08/2006
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25.94%
The validity of Freedman's disk theorem is known to depend only on the fundamental group. It was conjectured that it fails for nonabelian free fundamental groups. If this were true then surgery theory would work in dimension four. Recently, Krushkal and Lee proved a surprising result that surgery theory works for a large special class of 4-manifolds with free nonabelian fundamental groups. The goal of this paper is to show that this also holds for other fundamental groups which are not known to be good, and that it is best understood using controlled surgery theory of Pedersen--Quinn--Ranicki. We consider some examples of 4-manifolds which have the fundamental group either of a closed aspherical surface or of a 3-dimensional knot space. A more general theorem is stated in the appendix.

Spherical aberration correction using aspheric surfaces with an analytic-numerical method

Vázquez-Montiel,S.; García-Liévanos,O.
Fonte: Sociedad Mexicana de Física Publicador: Sociedad Mexicana de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/06/2013 EN
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36.09%
This method is a discrete case of the E. Wolf method for the design of an aspheric surface. Using the proposed method, the designer can select how many points (x, y) there will be on the entrance pupil at which the spherical aberration will be zero, by using the aspheric coefficients as degrees of freedom. For fitting the coordinates that correct the spherical aberration to an aspheric surface we solve a system of equations of the first degree. An optimisation procedure is not required because we use equations without approximations and with exact ray tracing. We obtained diffraction limited optical systems faster than the commercial programs.