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Peter Constantin - One of the best experts on this subject based on the ideXlab platform.
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an eulerian Lagrangian Approach to the navier stokes equations
Communications in Mathematical Physics, 2001Co-Authors: Peter ConstantinAbstract:We present a formulation of the incompressible viscous Navier–Stokes equation based on a generalization of the inviscid Weber formula, in terms of a diffusive “back-to-labels” map and a virtual velocity. We derive a generalization of the inviscid Cauchy formula and obtain certain bounds for the objects introduced.
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an eulerian Lagrangian Approach to the navier stokes equations
arXiv: Analysis of PDEs, 2000Co-Authors: Peter ConstantinAbstract:This work presents an Approach to the Navier-Stokes equations that is phrased in unbiased Eulerian coordinates, yet describes objects that have Lagrangian significance: particle paths, their dispersion and diffusion. The commutator between Lagrangian and Eulerian derivatives plays an important role in the Navier-Stokes equations: it contributes a singular perturbation to the Euler equations, in addition to the Laplacian. Bounds for the Lagrangian displacements, their first and second derivatives are obtained without assumptions. Some of these rigorous bounds can be interpreted in terms of the heuristic Richardson law of pair dispersion in turbulent flows.
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an eulerian Lagrangian Approach for incompressible fluids local theory
arXiv: Analysis of PDEs, 2000Co-Authors: Peter ConstantinAbstract:We present a local existence result for the three dimensional incompressible Euler equations. The solution is constructed using a formulation of the equations as an active vector system in Eulerian coordinates. The formulation employs the inverse of the Lagrangian path map (the "back-to-labels" map) and its Eulerian gradient. We express sufficient conditions for regularity in terms of this gradient.
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an eulerian Lagrangian Approach for incompressible fluids local theory
Journal of the American Mathematical Society, 2000Co-Authors: Peter ConstantinAbstract:We study a formulation of the incompressible Euler equations in terms of the inverse Lagrangian map. In this formulation the equations become a first order advective nonlinear system of partial differential equations.
Jose Wudka - One of the best experts on this subject based on the ideXlab platform.
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effective Lagrangian Approach to neutrinoless double beta decay and neutrino masses
Journal of High Energy Physics, 2012Co-Authors: Francisco Del Aguila, Alberto Aparici, Subhaditya Bhattacharya, Arcadi Santamaria, Jose WudkaAbstract:Neutrinoless double beta (0νββ) decay can in general produce electrons of either chirality, in contrast with the minimal Standard Model (SM) extension with only the addition of the Weinberg operator, which predicts two left-handed electrons in the final state. We classify the lepton number violating (LNV) effective operators with two leptons of either chirality but no quarks, ordered according to the magnitude of their contribution to 0νββ decay. We point out that, for each of the three chirality assignments, e L e L , e L e R and e R e R , there is only one LNV operator of the corresponding type to lowest order, and these have dimensions 5, 7 and 9, respectively. Neutrino masses are always induced by these extra operators but can be delayed to one or two loops, depending on the number of RH leptons entering in the operator. Then, the comparison of the 0νββ decay rate and neutrino masses should indicate the effective scenario at work, which confronted with the LHC searches should also eventually decide on the specific model elected by nature. We also list the SM additions generating these operators upon integration of the heavy modes, and discuss simple realistic examples of renormalizable theories for each case.
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effective Lagrangian Approach to neutrinoless double beta decay and neutrino masses
arXiv: High Energy Physics - Phenomenology, 2012Co-Authors: Francisco Del Aguila, Alberto Aparici, Subhaditya Bhattacharya, Arcadi Santamaria, Jose WudkaAbstract:Neutrinoless double beta ($0\nu\beta\beta$) decay can in general produce electrons of either chirality, in contrast with the minimal Standard Model (SM) extension with only the addition of the Weinberg operator, which predicts two left-handed electrons in the final state. We classify the lepton number violating (LNV) effective operators with two leptons of either chirality but no quarks, ordered according to the magnitude of their contribution to \znbb decay. We point out that, for each of the three chirality assignments, $e_Le_L, e_Le_R$ and $e_Re_R$, there is only one LNV operator of the corresponding type to lowest order, and these have dimensions 5, 7 and 9, respectively. Neutrino masses are always induced by these extra operators but can be delayed to one or two loops, depending on the number of RH leptons entering in the operator. Then, the comparison of the $0\nu\beta\beta$ decay rate and neutrino masses should indicate the effective scenario at work, which confronted with the LHC searches should also eventually decide on the specific model elected by nature. We also list the SM additions generating these operators upon integration of the heavy modes, and discuss simple realistic examples of renormalizable theories for each case.
David Sarrut - One of the best experts on this subject based on the ideXlab platform.
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construction of 4d ct motion model using deformable registration comparison of eulerian and Lagrangian Approaches
49th Annual Meeting American Association of Physicists in Medicine AAPM, 2007Co-Authors: V Boldea, G Sharp, Steve B Jiang, David SarrutAbstract:Purpose: To analyze and compare two motion models constructed from 4D-CT using deformable registration using two different computation Approaches : Eulerian and Lagrangian. Method and Material : Accurate motion modeling within the lung is an important consideration in different clinical applications. We consider 4D-CT scans for three patients treated in radiotherapy for lung cancer. 4D-CTs were acquired using a 4-slice fan-beam CT scanner (GE Light speed QX/i ; GE Heathcare Technologies, Waukesha, WI),and a respiratory surrogate (Real-time Position Management ; Varian Medical Systems, Palo Alto,CA). Two motion models were constructed from vector fields computed with demons algorithm with Gaussian regularization. We used also a image pre-treatment method, a priori lung density modification, to handle this limitation of the demons algorithm. The first model, obtained with the Eulerian Approach, uses small deformation estimations between successive phases of the 4D-CT. The second model, obtained with the Lagrangian Approach, was generated by estimation of larger deformations between the end-exhale phase and all other states. The models were validated and compared using consistency (symmetry and transitivity)and accuracy (based on landmark points) metrics. Results : Mean values of accuracy were on the order of the image resolution and comparable to inter-observer variability (1.9mm), with slightly better results for the Lagrangian Approach : 2.3mm vs. 2.6mm. The differences were not statistically significant for consistency. Conclusions : The results of this study suggest that the Lagrangian Approach is more appropriate to use for generating a 4D-CT motion model with deformable registration. In on going works, lung and GTV contours are used in order to conclude on the superiority of on emotion model over the other for an automatic contour propagation tool, and for lung physiological information computation and analysis.
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mo d l100j 08 construction of 4d ct motion model using deformable registration comparison of eulerian and Lagrangian Approaches
Medical Physics, 2007Co-Authors: V Boldea, G Sharp, Steve B Jiang, David SarrutAbstract:Purpose: To analyze and compare two motion models constructed from 4D‐CT using deformable registration using two different computation Approaches: Eulerian and Lagrangian.Method and Material: Accurate motion modeling within the lung is an important consideration in different clinical applications. We consider 4D‐CT scans for three patients treated in radiotherapy for lungcancer. 4D‐CTs were acquired using a 4‐slice fan‐beam CT scanner (GE Lightspeed QX/i; GE Heathcare Technologies, Waukesha, WI), and a respiratory surrogate (Real‐time Position Management; Varian Medical Systems, Palo Alto, CA). Two motion models were constructed from vector fields computed with demons algorithm with Gaussian regularization. We used also a image pre‐treatment method, a priori lung density modification, to handle this limitation of the demons algorithm. The first model, obtained with the Eulerian Approach, uses small deformation estimations between successive phases of the 4D‐CT. The second model, obtained with the Lagrangian Approach, was generated by estimation of larger deformations between the end‐exhale phase and all other states. The models were validated and compared using consistency (symmetry and transitivity) and accuracy (based on landmark points) metrics. Results: Mean values of accuracy were on the order of the image resolution and comparable to inter‐observer variability (1.9 mm), with slightly better results for the Lagrangian Approach: 2.3 mm vs. 2.6 mm. The differences were not statistically significant for consistency.Conclusions: The results of this study suggest that the Lagrangian Approach is more appropriate to use for generating a 4D‐CT motion model with deformable registration. In ongoing works, lung and GTV contours are used in order to conclude on the superiority of one motion model over the other for an automatic contour propagation tool, and for lung physiological information computation and analysis.
Jerry L Prince - One of the best experts on this subject based on the ideXlab platform.
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a hybrid eulerian Lagrangian Approach for thickness correspondence and gridding of annular tissues
IEEE Transactions on Image Processing, 2007Co-Authors: Kelvin R Rocha, Anthony Yezzi, Jerry L PrinceAbstract:We present a novel Approach to efficiently compute thickness, correspondence, and gridding of tissues between two simply connected boundaries. The solution of Laplace's equation within the tissue region provides a harmonic function whose gradient flow determines the correspondence trajectories going from one boundary to the other. The proposed method uses and expands upon two recently introduced techniques in order to compute thickness and correspondences based on these trajectories. Pairs of partial differential equations are efficiently computed within an Eulerian framework and combined with a Lagrangian Approach so that correspondences trajectories are partially constructed when necessary. Examples are presented in order to compare the performance of this method with those of the pure Lagrangian and pure Eulerian Approaches. Results show that the proposed technique takes advantage of both the speed of the Eulerian Approach and the accuracy of the Lagrangian Approach
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a hybrid eulerian Lagrangian Approach for thickness correspondence and gridding of annular tissues
International Conference on Computer Vision, 2005Co-Authors: Kelvin R Rocha, Anthony Yezzi, Jerry L PrinceAbstract:We present a novel Approach to efficiently compute thickness, correspondence, and gridding of tissues between two simply connected boundaries. The solution of Laplace’s equation within the tissue region provides a harmonic function whose gradient flow determines the correspondence trajectories going from one boundary to the other. The proposed method uses and expands upon two recently introduced techniques in order to compute thickness and correspondences based on these trajectories. Pairs of partial differential equations (PDEs) are efficiently computed within an Eulerian framework and combined with a Lagrangian Approach so that correspondences trajectories are partially constructed when necessary. Results show that the proposed technique takes advantage of both the speed of the Eulerian PDE Approach and the accuracy of the Lagrangian Approach.
Mannque Rho - One of the best experts on this subject based on the ideXlab platform.
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chiral Lagrangian Approach to exchange vector currents in nuclei
Nuclear Physics, 1996Co-Authors: Tae-sun Park, Dong-pil Min, Mannque RhoAbstract:Abstract Nuclear exchange vector currents applicable to any finite nucleus are calculated up to one-loop order (corresponding to next-to-next-to-leading order) in chiral perturbation theory. As an illustration of the power of the Approach, we apply the formalism to the classic nuclear process n + p → d + γ at thermal energy. The exchange current correction comes out to be (4.5 ± 0.3) % in amplitude giving a predicted cross section σ = (334 ± 3) mb in excellent agreement with the experimental value (334.2 ± 0.5) mb. Together with the axial charge transitions computed previously, this result provides strong support for the power of chiral Lagrangians in nuclear physics. Certain aspects pertinent to heavy nuclei are also discussed. A by-product of our results is an open problem only partially addressed in the paper in the application of the chiral Lagrangian Approach to nuclear processes that has to do with giving a physical meaning to the short-range correlations that play an important role in nuclei.
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Chiral Lagrangian Approach to Exchange Vector Currents in Nuclei
Nuclear Physics A, 1996Co-Authors: Tae-sun Park, Dong-pil Min, Mannque RhoAbstract:Exchange vector currents are calculated up to one-loop order (corresponding to next-to-next-to-leading order) in chiral perturbation theory. As an illustration of the power of the Approach, we apply the formalism to the classic nuclear process $n+p\rightarrow d +\gamma$ at thermal energy. The exchange current correction comes out to be $(4.5 \pm 0.3)$ \% in amplitude giving a predicted cross section $\sigma= (334\pm 3)\ {\mbox mb}$ in excellent agreement with the experimental value $(334.2\pm 0.5)\ {\mbox mb}$. Together with the axial charge transitions computed previously, this result provides a strong support for the power of chiral Lagrangians in nuclear physics. As a by-product of our results, we suggest an open problem in the application of chiral Lagrangian Approach to nuclear processes that has to do with giving a physical meaning to the short-range correlations that play an important role in nuclei.
