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## Otimização da asfericidade de superfícies refratoras conicodais

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...

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## Highly aspherical silica nanoshells by templating tubular liposomes

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.

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## Set Voronoi diagrams of 3D assemblies of aspherical particles

Fonte: Taylor & Francis
Publicador: Taylor & Francis

Tipo: Artigo de Revista Científica
Formato: 24 pages

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#set Voronoi diagram#ellipsoid packings#random close packing#aspherical particles#medial axes and surfaces#Area Voronoi diagram#navigation map#skeleton by zone of influence

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...

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

Fonte: Elsevier
Publicador: Elsevier

EN_US

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#aspherical surface fitting#form metrology#large data#Sciences de l'ingénieur: Mécanique: Génie mécanique#Sciences de l'ingénieur: Optique / photonique

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

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

Fonte: Arts et Métiers ParisTech
Publicador: Arts et Métiers ParisTech

EN_US

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#Aspherical surface#Chromatic confocal probe#Form metrology#L-BFGS method#Profilometer#Tactile probe#Sciences de l'ingénieur: Mécanique: Génie mécanique#Sciences de l'ingénieur: Mécanique: Mécanique des matériaux#Sciences de l'ingénieur: Mécanique: Mécanique des solides

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

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## Topological rigidity for non-aspherical manifolds

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

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## $S^2$-bundles over 2-orbifolds

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

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

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...

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## Immersions of Surfaces into Aspherical 3-Manifolds

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.

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

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...

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/09/2005

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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. 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

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

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...

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## Crystallization of hard aspherical particles

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.

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## Sections of surface bundles

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

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## Aspherical gravitational monopoles

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

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## Four-manifolds, geometries and knots

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...

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## The stable moduli space of flat connections over a surface

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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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

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## Towards a dynamical interpretation of Hamiltonian spectral invariants on surfaces

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

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## Applications of controlled surgery in dimension 4: Examples

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/08/2006

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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.

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

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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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.

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