The Experts below are selected from a list of 183 Experts worldwide ranked by ideXlab platform
Radu Ignat - One of the best experts on this subject based on the ideXlab platform.
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Two-dimensional unit-length Vector Fields of vanishing divergence
Journal of Functional Analysis, 2012Co-Authors: Radu IgnatAbstract:Abstract We prove the following regularity result: any two-dimensional unit-length divergence-Free Vector Field belonging to W 1 / p , p ( p ∈ [ 1 , 2 ] ) is locally Lipschitz except at a locally finite number of vortex-point singularities. We also prove approximation results for such Vector Fields: the dense sets are formed either by unit-length divergence-Free Vector Fields that are smooth except at a finite number of points and the approximation result holds in the W loc 1 , q -topology ( 1 ⩽ q 2 ), or by everywhere smooth unit-length Vector Fields (not necessarily divergence-Free) and the approximation result holds in a weaker topology.
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Two-dimensional unit-length Vector Fields of vanishing divergence
2011Co-Authors: Radu IgnatAbstract:We prove the following regularity result: any two-dimensional unit-length divergence-Free Vector Field belonging to $H^{1/2}$ (or $W^{1,1}$) is locally Lipschitz except at a locally finite number of vortices. We also prove approximation results for such Vector Fields: the dense sets are formed either by unit-length divergence-Free Vector Fields that are smooth except at a finite number of points and the approximation result holds in the $W_{loc}^{1,p}$-topology ($1\leq p
Manseob Lee - One of the best experts on this subject based on the ideXlab platform.
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Continuum-wise expansiveness for non-conservative or conservative systems
Chaos Solitons & Fractals, 2016Co-Authors: Manseob LeeAbstract:Abstract In this paper, we show that a non-conservative Vector Field is robustly continuum-wise expansive if and only if it satisfies both Axiom A and the quasi-transversality condition. Moreover, a conservative Vector Field (divergence-Free Vector Field, Hamiltonian system) is robustly continuum-wise expansive if and only if it is Anosov.
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Measure expansivity for C1-conservative systems
Chaos Solitons & Fractals, 2015Co-Authors: Jiweon Ahn, Manseob LeeAbstract:Abstract In this paper, we introduce the notion of measure expansivity for volume preserving diffeomorphisms and divergence Free Vector Fields. We prove that the following three theorems. (1) The C 1 -interior of measure expansive volume preserving diffeomorphism is Anosov. (2) A C 1 -generic volume preserving diffeomorphism is Anosov. (3) The C 1 -interior of measure expansive divergence Free Vector Field is Anosov.
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Divergence-Free Vector Fields with inverse shadowing
Advances in Difference Equations, 2013Co-Authors: Keonhee Lee, Manseob LeeAbstract:We show that if a divergence-Free Vector Field has the -stably orbital inverse shadowing property with respect to the class of continuous methods , then the Vector Field is Anosov. The results extend the work of Bessa and Rocha (J. Differ. Equ. 250:3960-3966, 2011). MSC:37C10, 37C27, 37C50.
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Divergence-Free Vector Fields with orbital shadowing
Advances in Difference Equations, 2013Co-Authors: Manseob LeeAbstract:We show that a divergence-Free Vector Field belongs to the C 1 -interior of the set of divergence-Free Vector Fields satisfying the orbital shadowing property when the Vector Field is Anosov. MSC: 37C10; 37C50; 37D20
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Orbital shadowing property for generic divergence-Free Vector Fields
Chaos Solitons & Fractals, 2013Co-Authors: Manseob LeeAbstract:Abstract We show that C 1 -generically, if a divergence-Free Vector Field has the orbital shadowing property then the Vector Field is Anosov.
Célia Ferreira - One of the best experts on this subject based on the ideXlab platform.
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Stability properties of divergence-Free Vector Fields
Dynamical Systems, 2012Co-Authors: Célia FerreiraAbstract:A divergence-Free Vector Field satisfies the star property if any divergence-Free Vector Field in some C 1-neighbourhood has all singularities and all closed orbits hyperbolic. In this article, we prove that any divergence-Free Vector Field defined on a Riemannian manifold and satisfying the star property is Anosov. It is also shown that a C 1-structurally stable divergence-Free Vector Field is Anosov. Moreover, we prove that any divergence-Free Vector Field can be C 1-approximated by an Anosov divergence-Free Vector Field, or else by a divergence-Free Vector Field exhibiting a heterodimensional cycle.
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Shadowing, expansiveness and stability of divergence-Free Vector Fields
arXiv: Dynamical Systems, 2010Co-Authors: Célia FerreiraAbstract:Let X be a divergence-Free Vector Field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions: 1. X is in the C1-interior of the set of expansive divergence-Free Vector Fields. 2. X is in the C1-interior of the set of divergence-Free Vector Fields which satisfy the shadowing property. 3. X is in the C1-interior of the set of divergence-Free Vector Fields which satisfy the Lipschitz shadowing property. 4. X has no singularities and X is Anosov.
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Stability properties of divergence-Free Vector Fields
arXiv: Dynamical Systems, 2010Co-Authors: Célia FerreiraAbstract:A divergence-Free Vector Field satisfies the star property if any divergence-Free Vector Field in some C1-neighborhood has all singularities and all periodic orbits hyperbolic. In this paper we prove that any divergence-Free Vector Field defined on a Riemannian manifold and satisfying the star property is Anosov. It is also shown that a C1-structurally stable divergenceFree Vector Field can be approximated by an Anosov divergence-Free Vector Field. Moreover, we prove that any divergence-Free Vector Field can be C1-approximated by an Anosov divergence-Free Vector Field, or else by a divergence-Free Vector Field exhibiting a heterodimensional cycle.
Yunbo He - One of the best experts on this subject based on the ideXlab platform.
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Triangular Model Registration Algorithm Through Differential Topological Singularity Points by Helmholtz-Hodge Decomposition
IEEE Access, 2019Co-Authors: Dongqing Wu, Zhengtao Xiao, Lanyu Zhang, Yun Chen, Hui Tang, Xin Chen, Yunbo HeAbstract:Iterative closest point algorithms suffer from non-convergence and local minima when dealing with cloud points with a different sampling density. Alternative global or semi-global registration algorithms may suffer from efficiency problem. This paper proposes a new registration algorithm through the differential topological singularity points (DTSP) based on the Helmholtz-Hodge decomposition (HHD), which is called DTSP-ICP method. The DTSP-ICP method contains two algorithms. First, the curvature gradient Fields on surfaces are decomposed by the HHD into three orthogonal parts: divergence-Free Vector Field, curl-Free Vector Field, and a harmonic Vector Field, and then the DTSP algorithm is used to extract the differential topological singularity points in the curl-Free Vector Field. Second, the ICP algorithm is utilized to register the singularity points into one aligned model. The singularity points represent the feature of the whole model, and the DTSP algorithm is designed to capture the nature of the differential topological structure of a mesh model. Through the singularity alignment, the DTSP-ICP method, therefore, possesses better performance in triangular model registration. The experimental results show that independent of sampling schemes, the proposed DTSP-ICP method can maintain convergence and robustness in cases where other alignment algorithms including the ICP alone are unstable. Moreover, this DTSP-ICP method can avoid the local errors of model registration based on Euclidean distance and overcome the computation insufficiencies observed in other global or semi-global registration publications. Finally, we demonstrate the significance of the DTSP-ICP algorithm's advantages on a variety of challenging models through result comparison with that of two other typical methods.
Ajit P. Yoganathan - One of the best experts on this subject based on the ideXlab platform.
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a divergence Free Vector Field model for imaging applications
International Symposium on Biomedical Imaging, 2009Co-Authors: Oskar Skrinjar, Arnaud Bistoquet, John N. Oshinski, Kartik S. Sundareswaran, David H. Frakes, Ajit P. YoganathanAbstract:Biological soft and fluid tissues, due to the high percentage of water, are nearly incompressible and consequently their velocity Fields are nearly divergence-Free. The two most commonly used types of Vector Field representation are piece-wise continuous representations, which are used in the finite element method (FEM), and discrete representations, which are used in the finite difference method (FDM). In both FEM and FDM frameworks divergence-Free Vector Fields are approximated, i.e. they are not exactly divergence-Free and both representation types require a relatively large number of degrees Freedom. We showed that a continuous, divergence-Free Vector Field model can effectively represent myocardial and blood velocity with a relatively small number of degrees of Freedom. The divergence-Free model consistently outperformed the thin plate spline model in simulations and applications with real data. The same model can be used with other incompressible solids and fluids.
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ISBI - A divergence-Free Vector Field model for imaging applications
2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2009Co-Authors: Oskar Skrinjar, Arnaud Bistoquet, John N. Oshinski, Kartik S. Sundareswaran, David H. Frakes, Ajit P. YoganathanAbstract:Biological soft and fluid tissues, due to the high percentage of water, are nearly incompressible and consequently their velocity Fields are nearly divergence-Free. The two most commonly used types of Vector Field representation are piece-wise continuous representations, which are used in the finite element method (FEM), and discrete representations, which are used in the finite difference method (FDM). In both FEM and FDM frameworks divergence-Free Vector Fields are approximated, i.e. they are not exactly divergence-Free and both representation types require a relatively large number of degrees Freedom. We showed that a continuous, divergence-Free Vector Field model can effectively represent myocardial and blood velocity with a relatively small number of degrees of Freedom. The divergence-Free model consistently outperformed the thin plate spline model in simulations and applications with real data. The same model can be used with other incompressible solids and fluids.
