Search results for "Torus"
showing 10 items of 100 documents
Periodic measures and partially hyperbolic homoclinic classes
2019
In this paper, we give a precise meaning to the following fact, and we prove it: $C^1$-open and densely, all the non-hyperbolic ergodic measures generated by a robust cycle are approximated by periodic measures. We apply our technique to the global setting of partially hyperbolic diffeomorphisms with one dimensional center. When both strong stable and unstable foliations are minimal, we get that the closure of the set of ergodic measures is the union of two convex sets corresponding to the two possible $s$-indices; these two convex sets intersect along the closure of the set of non-hyperbolic ergodic measures. That is the case for robustly transitive perturbation of the time one map of a tr…
Dupin cyclide blends between non-natural quadrics of revolution and concrete shape modeling applications
2014
Abstract In this work, we focus on the blending of two quadrics of revolution by two patches of Dupin cyclides. We propose an algorithm for the blending of non-natural quadrics of revolution by decomposing the blending operation into two complementary sub-blendings, each of which is a Dupin cyclide-based blending between one of the two quadrics and a circular cylinder, thus enabling the direct computation of the two Dupin cyclide patches and offering better flexibility for shape composition. Our approach uses rational quadric Bezier curves to model the relevant arcs of the principal circles of Dupin cyclides. It is quite general and we have successfully used it for the blending of several n…
Anomalous Anosov flows revisited
2017
This paper is devoted to higher dimensional Anosov flows and consists of two parts. In the first part, we investigate fiberwise Anosov flows on affine torus bundles which fiber over 3-dimensional Anosov flows. We provide a dichotomy result for such flows --- they are either suspensions of Anosov diffeomorphisms or the stable and unstable distributions have equal dimensions. In the second part, we give a new surgery type construction of Anosov flows, which yields non-transitive Anosov flows in all odd dimensions.
Functions of One Variable
2019
A classical result of Fatou gives that every bounded holomorphic function on the disc has radial limits for almost every point in the torus, and the limit function belongs to the Hardy space H_\infty of the torus. This property is no longer true when we consider vector-valued functions. The Banach spaces X for which this property is satisfied are said to have the analytic Radon-Nikodym property (ARNP). Some important equivalent reformulations of ARNP are studied in this chapter. Among others, X has ARNP if and only if each X-valued H_p- function f on the disc has radial limits almost everywhere on the torus (and not only H_\infty-functions). Even more, in this case each such f has non-tange…
NUMERICAL IMPLEMENTATION OF A K.A.M. ALGORITHM
1993
We discuss a numerical implementation of a K.A.M. algorithm to determine invariant tori, for systems that are quadratic in the action variables. The method has the advantage that the iteration procedure does not produce higher order terms in the actions, allowing thus a systematic control of the convergence.
Renormalization-group analysis for the transition to chaos in Hamiltonian systems
2002
Abstract We study the stability of Hamiltonian systems in classical mechanics with two degrees of freedom by renormalization-group methods. One of the key mechanisms of the transition to chaos is the break-up of invariant tori, which plays an essential role in the large scale and long-term behavior. The aim is to determine the threshold of break-up of invariant tori and its mechanism. The idea is to construct a renormalization transformation as a canonical change of coordinates, which deals with the dominant resonances leading to qualitative changes in the dynamics. Numerical results show that this transformation is an efficient tool for the determination of the threshold of the break-up of…
Beyond the triangle and uniqueness relations: non-zeta counterterms at large $N$ from positive knots
1997
Counterterms that are not reducible to ζn are generated by 3F2 hypergeometric series arising from diagrams for which triangle and uniqueness relations furnish insufficient data. Irreducible double sums, corresponding to the torus knots (4, 3) = 819 and (5, 3) = 10124, are found in anomalous dimensions at O(1/N 3) in the large-N limit, which we compute analytically up to terms of level 11, corresponding to 11 loops for 4-dimensional field theories and 12 loops for 2-dimensional theories. High-precision numerical results are obtained up to 24 loops and used in Pade resummations of e-expansions, which are compared with analytical results in 3 dimensions. The O(1/N 3) results entail knots gener…
Flexible Spare Core Placement in Torus Topology based NoCs and its validation on an FPGA
2021
In the nano-scale era, Network-on-Chip (NoC) interconnection paradigm has gained importance to abide by the communication challenges in Chip Multi-Processors (CMPs). With increased integration density on CMPs, NoC components namely cores, routers, and links are susceptible to failures. Therefore, to improve system reliability, there is a need for efficient fault-tolerant techniques that mitigate permanent faults in NoC based CMPs. There exists several fault-tolerant techniques that address the permanent faults in application cores while placing the spare cores onto NoC topologies. However, these techniques are limited to Mesh topology based NoCs. There are few approaches that have realized …
Localized surface plasmons on a torus in the nonretarded approximation
2005
International audience; The dispersion relations and field patterns of the localized surface plasmons of a torus are derived analytically in toroidal coordinates in the nonretarded approximation. Numerical calculations are provided in order to identify the conditions under which a toroidal nanostructure supports a significant magnetic dipole moment at optical frequencies.
Optical absorption of torus-shaped metal nanoparticles in the visible range
2007
Received 22 November 2007; published 19 December 2007We theoretically and experimentally investigated the optical response of a thin metal nanotorus in the visiblerange. The close formulas describing the extinction cross sections of a torus are obtained in the nonretardedapproximation. We demonstrate a good agreement between numerical simulations and experimental data. Ourfindings show that the main resonance is highly sensitive to the external medium and the geometrical param-eters of the particle.DOI: 10.1103/PhysRevB.76.245422 PACS number s : 78.67.Bf, 73.20.Mf, 78.20.Ci