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NavierStokes, fluid dynamics, and image and video inpainting
 Proc. IEEE Computer Vision and Pattern Recognition (CVPR
, 2001
"... Image inpainting involves filling in part of an image or video using information from the surrounding area. Applications include the restoration of damaged photographs and movies and the removal of selected objects. In this paper, we introduce a class of automated methods for digital inpainting. The ..."
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Cited by 167 (18 self)
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on the NavierStokes equations for fluid dynamics, which has the immediate advantage of welldeveloped theoretical and numerical results. This is a new approach for introducing ideas from computational fluid dynamics into problems in computer vision and image analysis.
On the Finite Element Analysis of Shells and their Full Interaction with NavierStokes Fluid Flows
"... Our objective is to present an oveliew of some of our latest research and developments in the finite element analysis of shells, NavierStokes fluid flows and the fulI interactions of these flows with general shell structures. In the area of shell analysis, we have studied some generic physical beha ..."
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Our objective is to present an oveliew of some of our latest research and developments in the finite element analysis of shells, NavierStokes fluid flows and the fulI interactions of these flows with general shell structures. In the area of shell analysis, we have studied some generic physical
THE ROLE OF SE(d)REDUCTION FOR SWIMMING IN STOKES AND NAVIERSTOKES FLUIDS
"... Abstract. Steady swimming appears both periodic and stable. These characteristics are the very definition of limit cycles, and so we ask “Can we view swimming as a limit cycle? ” In this paper we will not be able to answer this question in full. However, we shall find that reduction by SE(d)symmet ..."
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Abstract. Steady swimming appears both periodic and stable. These characteristics are the very definition of limit cycles, and so we ask “Can we view swimming as a limit cycle? ” In this paper we will not be able to answer this question in full. However, we shall find that reduction by SE(d)symmetry brings us closer. Upon performing reduction by symmetry, we will find a stable fixed point which corresponds to a motionless body in stagnant water. We will then speculate on the existence of periodic orbits which are “approximately ” limit cycles in the reduced system. When we lift these periodic orbits from the reduced phase space, we obtain dynamically robust relatively periodic orbits wherein each period is related to the previous by an SE(d) phase. Clearly, an SE(d) phase consisting of nonzero translation and identity rotation means directional swimming, while nontrivial rotations correspond to turning with a constant turning radius. 1.
Operatorsplitting and Lagrange multiplier domain decomposition methods for numerical simulation of two coupled Navier–Stokes fluids
 Int. J. Appl. Math. Comput. Sci
, 2006
"... We present a numerical simulation of two coupled NavierStokes flows, using operatorsplitting and optimizationbased nonoverlapping domain decomposition methods. The model problem consists of two NavierStokes fluids coupled, through a common interface, by a nonlinear transmission condition. Numeri ..."
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Cited by 3 (0 self)
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We present a numerical simulation of two coupled NavierStokes flows, using operatorsplitting and optimizationbased nonoverlapping domain decomposition methods. The model problem consists of two NavierStokes fluids coupled, through a common interface, by a nonlinear transmission condition
Connection Between Kinetic Energy And Vorticity Blowup in 3D NavierStokes Fluid.
, 906
"... Abstract: In this paper the author formulates and proves a theorem that relates smoothness of kinetic energy and smoothness of vorticity in a 3D NavierStokes fluid. Setting velocity and vorticity boundary conditions, a direct relation arises between kinetic energy and the squared Euclidean norm of ..."
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Abstract: In this paper the author formulates and proves a theorem that relates smoothness of kinetic energy and smoothness of vorticity in a 3D NavierStokes fluid. Setting velocity and vorticity boundary conditions, a direct relation arises between kinetic energy and the squared Euclidean norm
A diffusion tensor imaging tractography algorithm based on navierstokes fluid mechanics
 IEEE Transactions on Medical Imaging
"... We introduce a method for estimating regional connectivity in diffusion tensor magnetic resonance imaging (DTMRI) based on a fluid mechanics model. We customize the NavierStokes equations to include information from the diffusion tensor and simulate an artificial fluid flow. The velocity vector ..."
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Cited by 9 (1 self)
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We introduce a method for estimating regional connectivity in diffusion tensor magnetic resonance imaging (DTMRI) based on a fluid mechanics model. We customize the NavierStokes equations to include information from the diffusion tensor and simulate an artificial fluid flow. The velocity vector
Recurrent motions in the nonautonomous NavierStokes system, Discrete Contin
 Dyn. Syst. B
"... Abstract. We prove the existence of recurrent or Poisson stable motions in the NavierStokes fluid system under recurrent or Poisson stable forcing, respectively. We use an approach based on nonautonomous dynamical systems ideas. ..."
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Cited by 4 (3 self)
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Abstract. We prove the existence of recurrent or Poisson stable motions in the NavierStokes fluid system under recurrent or Poisson stable forcing, respectively. We use an approach based on nonautonomous dynamical systems ideas.
From NavierStokes to Einstein
, 2011
"... We show by explicit construction that for every solution of the incompressible NavierStokes equation in p + 1 dimensions, there is a uniquely associated “dual ” solution of the vacuum Einstein equations in p + 2 dimensions. The dual geometry has an intrinsically flat timelike boundary segment Σc wh ..."
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Cited by 1 (0 self)
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whose extrinsic curvature is given by the stress tensor of the NavierStokes fluid. We consider a “nearhorizon” limit in which Σc becomes highly accelerated. The nearhorizon expansion in gravity is shown to be mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Einstein
Existence of timeperiodic solutions to the NavierStokes equations around a moving body
 Pac. J. Math
"... We demonstrate the existence of timeperiodic motions of an incompressible Navier–Stokes fluid subject to a timeperiodic body force, occupying the region exterior to a body that performs a periodic rigid motion of same period. 1. ..."
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Cited by 6 (1 self)
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We demonstrate the existence of timeperiodic motions of an incompressible Navier–Stokes fluid subject to a timeperiodic body force, occupying the region exterior to a body that performs a periodic rigid motion of same period. 1.
Results 1  10
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