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Jean Marie Buchlin - One of the best experts on this subject based on the ideXlab platform.

  • multi scale proper orthogonal decomposition of Complex Fluid flows
    Journal of Fluid Mechanics, 2019
    Co-Authors: M. A. Mendez, M. Balabane, Jean Marie Buchlin
    Abstract:

    Data-driven decompositions are becoming essential tools in Fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low-order models of Complex phenomena. In this work, we analyse the main limits of two popular decompositions, namely the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as multi-scale proper orthogonal decomposition (mPOD) and combines multi-resolution analysis (MRA) with a standard POD. Using MRA, the mPOD splits the correlation matrix into the contribution of different scales, retaining non-overlapping portions of the correlation spectra; using the standard POD, the mPOD extracts the optimal basis from each scale. After introducing a matrix factorization framework for data-driven decompositions, the MRA is formulated via one- and two-dimensional filter banks for the dataset and the correlation matrix respectively. The validation of the mPOD, and a comparison with the discrete Fourier transform (DFT), DMD and POD are provided in three test cases. These include a synthetic test case, a numerical simulation of a nonlinear advection–diffusion problem and an experimental dataset obtained by the time-resolved particle image velocimetry (TR-PIV) of an impinging gas jet. For each of these examples, the decompositions are compared in terms of convergence, feature detection capabilities and time–frequency localization.

  • multi scale proper orthogonal decomposition of Complex Fluid flows
    arXiv: Fluid Dynamics, 2018
    Co-Authors: M. A. Mendez, M. Balabane, Jean Marie Buchlin
    Abstract:

    Data-driven decompositions are becoming essential tools in Fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low order models of Complex phenomena. In this work, we analyze the main limits of two popular decompositions, namely the Proper Orthogonal Decomposition (POD) and the Dynamic Mode Decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as Multiscale Proper Orthogonal Decomposition (mPOD) and combines Multiresolution Analysis (MRA) with a standard POD. Using MRA, the mPOD splits the correlation matrix into the contribution of different scales, retaining non-overlapping portions of the correlation spectra; using the standard POD, the mPOD extracts the optimal basis from each scale. After introducing a matrix factorization framework for data-driven decompositions, the MRA is formulated via 1D and 2D filter banks for the dataset and the correlation matrix respectively. The validation of the mPOD, and a comparison with the Discrete Fourier Transform (DFT), DMD and POD are provided in three test cases. These include a synthetic test case, a numerical simulation of a nonlinear advection-diffusion problem, and an experimental dataset obtained by the Time-Resolved Particle Image Velocimetry (TR-PIV) of an impinging gas jet. For each of these examples, the decompositions are compared in terms of convergence, feature detection capabilities, and time-frequency localization.

Jeanbaptiste Salmon - One of the best experts on this subject based on the ideXlab platform.

  • steady and out of equilibrium phase diagram of a Complex Fluid at the nanolitre scale combining microevaporation confocal raman imaging and small angle x ray scattering
    Lab on a Chip, 2013
    Co-Authors: L Daubersies, Jacques Leng, Jeanbaptiste Salmon
    Abstract:

    We engineered specific microFluidic devices based on the pervaporation of water through a PDMS membrane, to formulate continuous and steady concentration gradients of a binary aqueous molecular mixture at the nanolitre scale. In the case of a model Complex Fluid (a triblock copolymer solution), we demonstrate that such a steady gradient crosses the phase diagram from pure water up to a succession of highly viscous mesophases. We then performed in situ spatially resolved measurements (confocal spectroscopy and small-angle X-ray scattering) to quantitatively measure the concentration profile and to determine the microstructure of the different textures. Within a single microFluidic channel, we thus screen quantitatively and continuously the phase diagram of a Complex Fluid. Beside, as such a gradient corresponds to an out-of-equilibrium regime, we also extract from the concentration measurement a precise estimate of the collective diffusion coefficient of the mixture as a function of the concentration. In the present case of the triblock copolymer, this transport coefficient features discontinuities at some phase boundaries, which have never been observed before.

  • confined drying of a Complex Fluid drop phase diagram activity and mutual diffusion coefficient
    Soft Matter, 2012
    Co-Authors: L Daubersies, Jacques Leng, Jeanbaptiste Salmon
    Abstract:

    We describe a drying setup where a liquid drop of a molecular mixture is confined between two circular plates and left to evaporate in a controlled manner. The direct observation of the drying kinetics in such a confined geometry, which includes the measurement of the volume of the drop against time and the monitoring of a series of nucleation events, permits the reconstruction of a rough phase diagram for the case of an aqueous triblock copolymer solution. Accurate estimations of the phase boundaries are obtained thanks to spatially-resolved Raman spectroscopic measurements of the temporal evolution of the solute concentration field within the drop. The comparison of such measurements with a theoretical model describing the drying kinetics of binary mixtures [L. Daubersies and J. B. Salmon, Phys. Rev. E, 2011, 84, 031406] yields estimations of the activity of the solution and of its mutual diffusion coefficient against the solute concentration.

M. A. Mendez - One of the best experts on this subject based on the ideXlab platform.

  • multi scale proper orthogonal decomposition of Complex Fluid flows
    Journal of Fluid Mechanics, 2019
    Co-Authors: M. A. Mendez, M. Balabane, Jean Marie Buchlin
    Abstract:

    Data-driven decompositions are becoming essential tools in Fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low-order models of Complex phenomena. In this work, we analyse the main limits of two popular decompositions, namely the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as multi-scale proper orthogonal decomposition (mPOD) and combines multi-resolution analysis (MRA) with a standard POD. Using MRA, the mPOD splits the correlation matrix into the contribution of different scales, retaining non-overlapping portions of the correlation spectra; using the standard POD, the mPOD extracts the optimal basis from each scale. After introducing a matrix factorization framework for data-driven decompositions, the MRA is formulated via one- and two-dimensional filter banks for the dataset and the correlation matrix respectively. The validation of the mPOD, and a comparison with the discrete Fourier transform (DFT), DMD and POD are provided in three test cases. These include a synthetic test case, a numerical simulation of a nonlinear advection–diffusion problem and an experimental dataset obtained by the time-resolved particle image velocimetry (TR-PIV) of an impinging gas jet. For each of these examples, the decompositions are compared in terms of convergence, feature detection capabilities and time–frequency localization.

  • multi scale proper orthogonal decomposition of Complex Fluid flows
    arXiv: Fluid Dynamics, 2018
    Co-Authors: M. A. Mendez, M. Balabane, Jean Marie Buchlin
    Abstract:

    Data-driven decompositions are becoming essential tools in Fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low order models of Complex phenomena. In this work, we analyze the main limits of two popular decompositions, namely the Proper Orthogonal Decomposition (POD) and the Dynamic Mode Decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as Multiscale Proper Orthogonal Decomposition (mPOD) and combines Multiresolution Analysis (MRA) with a standard POD. Using MRA, the mPOD splits the correlation matrix into the contribution of different scales, retaining non-overlapping portions of the correlation spectra; using the standard POD, the mPOD extracts the optimal basis from each scale. After introducing a matrix factorization framework for data-driven decompositions, the MRA is formulated via 1D and 2D filter banks for the dataset and the correlation matrix respectively. The validation of the mPOD, and a comparison with the Discrete Fourier Transform (DFT), DMD and POD are provided in three test cases. These include a synthetic test case, a numerical simulation of a nonlinear advection-diffusion problem, and an experimental dataset obtained by the Time-Resolved Particle Image Velocimetry (TR-PIV) of an impinging gas jet. For each of these examples, the decompositions are compared in terms of convergence, feature detection capabilities, and time-frequency localization.

Ting Zhang - One of the best experts on this subject based on the ideXlab platform.

  • global small solutions to a Complex Fluid model in three dimensional
    Archive for Rational Mechanics and Analysis, 2015
    Co-Authors: Fanghua Lin, Ting Zhang
    Abstract:

    In this paper, we provide a much simplified proof of the main result in Lin and Zhang (Commun Pure Appl Math 67: 531–580, 2014) concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a three dimensional incompressible Complex Fluid model under the assumption that the initial data are close to some equilibrium states. Besides the classical energy method, the interpolating inequalities and the algebraic structure of the equations coming from the incompressibility of the Fluid are crucial in our arguments. We combine the energy estimates with the L∞ estimates for time slices to deduce the key L1 in time estimates. The latter is responsible for the global in time existence.

  • global small solutions to a Complex Fluid model in 3d
    arXiv: Analysis of PDEs, 2014
    Co-Authors: Fanghua Lin, Ting Zhang
    Abstract:

    In this paper, we provide a much simplified proof of the main result in [Lin and Zhang, Comm. Pure Appl. Math.,67(2014), 531--580] concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a 3D incompressible Complex Fluid model under the assumption that the initial data are close to some equilibrium states. Beside the classical energy method, the interpolating inequalities and the algebraic structure of the equations coming from the incompressibility of the Fluid are crucial in our arguments. We combine the energy estimates with the $L^\infty$ estimates for time slices to deduce the key $L^1$ in time estimates. The latter is responsible for the global in time existence.

L Daubersies - One of the best experts on this subject based on the ideXlab platform.

  • steady and out of equilibrium phase diagram of a Complex Fluid at the nanolitre scale combining microevaporation confocal raman imaging and small angle x ray scattering
    Lab on a Chip, 2013
    Co-Authors: L Daubersies, Jacques Leng, Jeanbaptiste Salmon
    Abstract:

    We engineered specific microFluidic devices based on the pervaporation of water through a PDMS membrane, to formulate continuous and steady concentration gradients of a binary aqueous molecular mixture at the nanolitre scale. In the case of a model Complex Fluid (a triblock copolymer solution), we demonstrate that such a steady gradient crosses the phase diagram from pure water up to a succession of highly viscous mesophases. We then performed in situ spatially resolved measurements (confocal spectroscopy and small-angle X-ray scattering) to quantitatively measure the concentration profile and to determine the microstructure of the different textures. Within a single microFluidic channel, we thus screen quantitatively and continuously the phase diagram of a Complex Fluid. Beside, as such a gradient corresponds to an out-of-equilibrium regime, we also extract from the concentration measurement a precise estimate of the collective diffusion coefficient of the mixture as a function of the concentration. In the present case of the triblock copolymer, this transport coefficient features discontinuities at some phase boundaries, which have never been observed before.

  • confined drying of a Complex Fluid drop phase diagram activity and mutual diffusion coefficient
    Soft Matter, 2012
    Co-Authors: L Daubersies, Jacques Leng, Jeanbaptiste Salmon
    Abstract:

    We describe a drying setup where a liquid drop of a molecular mixture is confined between two circular plates and left to evaporate in a controlled manner. The direct observation of the drying kinetics in such a confined geometry, which includes the measurement of the volume of the drop against time and the monitoring of a series of nucleation events, permits the reconstruction of a rough phase diagram for the case of an aqueous triblock copolymer solution. Accurate estimations of the phase boundaries are obtained thanks to spatially-resolved Raman spectroscopic measurements of the temporal evolution of the solute concentration field within the drop. The comparison of such measurements with a theoretical model describing the drying kinetics of binary mixtures [L. Daubersies and J. B. Salmon, Phys. Rev. E, 2011, 84, 031406] yields estimations of the activity of the solution and of its mutual diffusion coefficient against the solute concentration.