The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Yongxiang Huang - One of the best experts on this subject based on the ideXlab platform.
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Arbitrary Order hilbert spectral analysis for time series possessing scaling statistics comparison study with detrended fluctuation analysis and wavelet leaders
Physical Review E, 2011Co-Authors: Yongxiang Huang, Francois G Schmitt, Jeanpierre Hermand, Yves Gagne, Yuanyuan LiuAbstract:In this paper we present an extended version of Hilbert-Huang transform, namely Arbitrary-Order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space. We first show numerically that due to a nonlinear distortion, traditional methods require high-Order harmonic components to represent nonlinear processes, except for the Hilbert-based method. This will lead to an artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus the power law, if it exists, is contaminated. We then compare the Hilbert method with structure functions (SF), detrended fluctuation analysis (DFA), and wavelet leader (WL) by analyzing fractional Brownian motion and synthesized multifractal time series. For the former simulation, we find that all methods provide comparable results. For the latter simulation, we perform simulations with an intermittent parameter μ=0.15. We find that the SF underestimates scaling exponent when q>3. The Hilbert method provides a slight underestimation when q>5. However, both DFA and WL overestimate the scaling exponents when q>5. It seems that Hilbert and DFA methods provide better singularity spectra than SF and WL. We finally apply all methods to a passive scalar (temperature) data obtained from a jet experiment with a Taylor's microscale Reynolds number Reλ 250. Due to the presence of strong ramp-cliff structures, the SF fails to detect the power law behavior. For the traditional method, the ramp-cliff structure causes a serious artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus DFA and WL underestimate the scaling exponents. However, the Hilbert method provides scaling exponents ξθ(q) quite close to the one for longitudinal velocity, indicating a less intermittent passive scalar field than what was believed before. © 2011 American Physical Society.
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analysis of daily river flow fluctuations using empirical mode decomposition and Arbitrary Order hilbert spectral analysis
Journal of Hydrology, 2009Co-Authors: Yongxiang Huang, Francois G Schmitt, Yulu LiuAbstract:In this paper we presented the analysis of two long time series of daily river flow data, 32 years recorded in the Seine river (France), and 25 years recorded in the Wimereux river (Wimereux, France). We applied a scale based decomposition method, namely Empirical Mode Decomposition (EMD), on these time series. The data were decomposed into several Intrinsic Mode Functions (IMF). The mean frequency of each IMF mode indicated that the EMD method acts as a filter bank. Furthermore, the cross-correlation between these IMF modes from Seine river and Wimereux river demonstrated correlation among the large scale IMF modes, which indicates that both rivers are likely to be influenced by the same events maritime climate event of Northern France. As a confirmation we found that the large scale parts have the same evolution trend. We finally applied Arbitrary Order Hilbert spectral analysis, a new technique coming from turbulence studies and time series analysis, on the flow discharge of Seine river. This new method provides an amplitude-frequency representation of the original time series, giving a joint pdf $p(\omega,\mathcal{A})$. When marginal moments of the amplitude are computed, one obtains an intermittency study in the frequency space. Applied to river flow discharge data from the Seine river, this shows the scaling range and characterizes the intermittent fluctuations over the range of scales from 4.5 to 60 days, between synoptic and intraseasonal scales.
Francois G Schmitt - One of the best experts on this subject based on the ideXlab platform.
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Multifractal description of wind power fluctuations using Arbitrary Order Hilbert spectral analysis
Physica A, 2013Co-Authors: Rudy Calif, Francois G Schmitt, Yue HuangAbstract:The objectives are to study and model the aggregate wind power fluctuations dynamics in the multifractal framework. We present here the analysis of aggregate power output sampled at 1 Hz during three years. We decompose the data into several Intrinsic Mode Functions (IMFs) using Empirical Mode Decomposition (EMD). We use a new approach, Arbitrary Order Hilbert spectral analysis, a combination of the EMD approach with Hilbert spectral analysis (or Hilbert-Huang Transform) and the classical structure-function analysis to extract the scaling exponents or multifractal spectrum ζ(q)ζ(q): this function provides a full characterization of a process at all intensities and all scales. The application of both methods, i.e. structure-function and Arbitrary-Order Hilbert spectral analyses, gives similar results indicating that the aggregate power output from a wind farm, possesses intermittent and multifractal properties. In Order to check this result, we generate stochastic simulations of a Multifractal Random Walk (MRW) using a log-normal stochastic equation. We show that the simulation results are fully compatible with the experimental results
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Arbitrary Order hilbert spectral analysis for time series possessing scaling statistics comparison study with detrended fluctuation analysis and wavelet leaders
Physical Review E, 2011Co-Authors: Yongxiang Huang, Francois G Schmitt, Jeanpierre Hermand, Yves Gagne, Yuanyuan LiuAbstract:In this paper we present an extended version of Hilbert-Huang transform, namely Arbitrary-Order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space. We first show numerically that due to a nonlinear distortion, traditional methods require high-Order harmonic components to represent nonlinear processes, except for the Hilbert-based method. This will lead to an artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus the power law, if it exists, is contaminated. We then compare the Hilbert method with structure functions (SF), detrended fluctuation analysis (DFA), and wavelet leader (WL) by analyzing fractional Brownian motion and synthesized multifractal time series. For the former simulation, we find that all methods provide comparable results. For the latter simulation, we perform simulations with an intermittent parameter μ=0.15. We find that the SF underestimates scaling exponent when q>3. The Hilbert method provides a slight underestimation when q>5. However, both DFA and WL overestimate the scaling exponents when q>5. It seems that Hilbert and DFA methods provide better singularity spectra than SF and WL. We finally apply all methods to a passive scalar (temperature) data obtained from a jet experiment with a Taylor's microscale Reynolds number Reλ 250. Due to the presence of strong ramp-cliff structures, the SF fails to detect the power law behavior. For the traditional method, the ramp-cliff structure causes a serious artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus DFA and WL underestimate the scaling exponents. However, the Hilbert method provides scaling exponents ξθ(q) quite close to the one for longitudinal velocity, indicating a less intermittent passive scalar field than what was believed before. © 2011 American Physical Society.
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analysis of daily river flow fluctuations using empirical mode decomposition and Arbitrary Order hilbert spectral analysis
Journal of Hydrology, 2009Co-Authors: Yongxiang Huang, Francois G Schmitt, Yulu LiuAbstract:In this paper we presented the analysis of two long time series of daily river flow data, 32 years recorded in the Seine river (France), and 25 years recorded in the Wimereux river (Wimereux, France). We applied a scale based decomposition method, namely Empirical Mode Decomposition (EMD), on these time series. The data were decomposed into several Intrinsic Mode Functions (IMF). The mean frequency of each IMF mode indicated that the EMD method acts as a filter bank. Furthermore, the cross-correlation between these IMF modes from Seine river and Wimereux river demonstrated correlation among the large scale IMF modes, which indicates that both rivers are likely to be influenced by the same events maritime climate event of Northern France. As a confirmation we found that the large scale parts have the same evolution trend. We finally applied Arbitrary Order Hilbert spectral analysis, a new technique coming from turbulence studies and time series analysis, on the flow discharge of Seine river. This new method provides an amplitude-frequency representation of the original time series, giving a joint pdf $p(\omega,\mathcal{A})$. When marginal moments of the amplitude are computed, one obtains an intermittency study in the frequency space. Applied to river flow discharge data from the Seine river, this shows the scaling range and characterizes the intermittent fluctuations over the range of scales from 4.5 to 60 days, between synoptic and intraseasonal scales.
Huazhong Tang - One of the best experts on this subject based on the ideXlab platform.
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globally hyperbolic moment model of Arbitrary Order for the three dimensional special relativistic boltzmann equation with the anderson witting collision
Science China-mathematics, 2021Co-Authors: Yangyu Kuang, Huazhong TangAbstract:This paper continues to derive the globally hyperbolic moment model of Arbitrary Order for the three-dimensional special relativistic Boltzmann equation with the Anderson-Witting collision. The method is the model reduction by the operator projection. Finding an orthogonal basis of the weighted polynomial space is crucial and built on infinite families of the complicate relativistic Grad type orthogonal polynomials depending on a parameter and the real spherical harmonics instead of the irreducible tensors. We study the properties of those functions carefully, including their recurrence relations, their derivatives with respect to the independent variable and parameter, and the zeros of the orthogonal polynomials. Our moment model is proved to be globally hyperbolic and linearly stable. Moreover, the Lorentz-covariance and the quasi-one-dimensional case, the non-relativistic and ultra-relativistic limits are also studied.
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globally hyperbolic moment model of Arbitrary Order for one dimensional special relativistic boltzmann equation
Journal of Statistical Physics, 2017Co-Authors: Yangyu Kuang, Huazhong TangAbstract:This paper extends the model reduction method by the operator projection to the one-dimensional special relativistic Boltzmann equation. The derivation of Arbitrary Order globally hyperbolic moment system is built on our careful study of two families of the complicate Grad type orthogonal polynomials depending on a parameter. We derive their recurrence relations, calculate their derivatives with respect to the independent variable and parameter respectively, and study their zeros and coefficient matrices in the recurrence formulas. Some properties of the moment system are also proved. They include the eigenvalues and their bound as well as eigenvectors, hyperbolicity, characteristic fields, linear stability, and Lorentz covariance. A semi-implicit numerical scheme is presented to solve a Cauchy problem of our hyperbolic moment system in Order to verify the convergence behavior of the moment method. The results show that the solutions of our hyperbolic moment system converge to the solution of the special relativistic Boltzmann equation as the Order of the hyperbolic moment system increases.
Droniou Jérôme - One of the best experts on this subject based on the ideXlab platform.
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An Arbitrary-Order discrete de Rham complex on polyhedral meshes. Part II: Consistency
2021Co-Authors: Di Pietro, Daniele Antonio, Droniou JérômeAbstract:In this paper we prove a complete panel of consistency results for the discrete de Rham (DDR) complex introduced in the companion paper [D. A. Di Pietro and J. Droniou, An Arbitrary-Order discrete de Rham complex on polyhedral meshes. Part I: Exactness and Poincar\'e inequalities, 2021, submitted], including primal and adjoint consistency for the discrete vector calculus operators, and consistency of the corresponding potentials. The theoretical results are showcased by performing a full convergence analysis for a DDR approximation of a magnetostatics model. Numerical results on three-dimensional polyhedral meshes complete the exposition.Comment: This paper was merged with the previous "Part I", and both are now available as a single paper at arXiv:2101.0494
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An Arbitrary-Order discrete de Rham complex on polyhedral meshes: Exactness, Poincar\'e inequalities, and consistency
2021Co-Authors: Di Pietro, Daniele Antonio, Droniou JérômeAbstract:In this paper we present a novel Arbitrary-Order discrete de Rham (DDR) complex on general polyhedral meshes based on the decomposition of polynomial spaces into the ranges of vector calculus operators and complements linked to the spaces in the Koszul complex. The DDR complex is fully discrete, meaning that both the spaces and discrete calculus operators are replaced by discrete counterparts. We prove a complete panel of results for the analysis of discretisation schemes for partial differential equations based on this complex: exactness properties, uniform Poincar\'e inequalities, as well as primal and adjoint consistency. We also show how this DDR complex enables the design of a numerical scheme for a magnetostatics problem, and use the aforementioned results to prove stability and optimal error estimates for this scheme
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An Arbitrary-Order discrete de Rham complex on polyhedral meshes: Exactness, Poincar\'e inequalities, and consistency
'Springer Science and Business Media LLC', 2021Co-Authors: Di Pietro, Daniele Antonio, Droniou JérômeAbstract:In this paper we present a novel Arbitrary-Order discrete de Rham (DDR) complex on general polyhedral meshes based on the decomposition of polynomial spaces into ranges of vector calculus operators and complements linked to the spaces in the Koszul complex. The DDR complex is fully discrete, meaning that both the spaces and discrete calculus operators are replaced by discrete counterparts, and satisfies suitable exactness properties depending on the topology of the domain. In conjunction with bespoke discrete counterparts of $L^2$-products, it can be used to design schemes for partial differential equations that benefit from the exactness of the sequence but, unlike classical (e.g., Raviart--Thomas--N\'ed\'elec) finite elements, are nonconforming. We prove a complete panel of results for the analysis of such schemes: exactness properties, uniform Poincar\'e inequalities, as well as primal and adjoint consistency. We also show how this DDR complex enables the design of a numerical scheme for a magnetostatics problem, and use the aforementioned results to prove stability and optimal error estimates for this scheme
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An Arbitrary Order scheme on generic meshes for miscible displacements in porous media
'Society for Industrial & Applied Mathematics (SIAM)', 2019Co-Authors: Anderson Daniel, Droniou JérômeAbstract:We design, analyse and implement an Arbitrary Order scheme applicable to generic meshes for a coupled elliptic-parabolic PDE system describing miscible displacement in porous media. The discretisation is based on several adaptations of the Hybrid-High-Order (HHO) method due to Di Pietro et al. [Computational Methods in Applied Mathematics, 14(4), (2014)]. The equation governing the pressure is discretised using an adaptation of the HHO method for variable diffusion, while the discrete concentration equation is based on the HHO method for advection-diffusion-reaction problems combined with numerically stable flux reconstructions for the advective velocity that we have derived using the results of Cockburn et al. [ESAIM: Mathematical Modelling and Numerical Analysis, 50(3), (2016)]. We perform some rigorous analysis of the method to demonstrate its $L^2$ stability under the irregular data often presented by reservoir engineering problems and present several numerical tests to demonstrate the quality of the results that are produced by the proposed scheme
Yuanyuan Liu - One of the best experts on this subject based on the ideXlab platform.
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Arbitrary Order hilbert spectral analysis for time series possessing scaling statistics comparison study with detrended fluctuation analysis and wavelet leaders
Physical Review E, 2011Co-Authors: Yongxiang Huang, Francois G Schmitt, Jeanpierre Hermand, Yves Gagne, Yuanyuan LiuAbstract:In this paper we present an extended version of Hilbert-Huang transform, namely Arbitrary-Order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space. We first show numerically that due to a nonlinear distortion, traditional methods require high-Order harmonic components to represent nonlinear processes, except for the Hilbert-based method. This will lead to an artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus the power law, if it exists, is contaminated. We then compare the Hilbert method with structure functions (SF), detrended fluctuation analysis (DFA), and wavelet leader (WL) by analyzing fractional Brownian motion and synthesized multifractal time series. For the former simulation, we find that all methods provide comparable results. For the latter simulation, we perform simulations with an intermittent parameter μ=0.15. We find that the SF underestimates scaling exponent when q>3. The Hilbert method provides a slight underestimation when q>5. However, both DFA and WL overestimate the scaling exponents when q>5. It seems that Hilbert and DFA methods provide better singularity spectra than SF and WL. We finally apply all methods to a passive scalar (temperature) data obtained from a jet experiment with a Taylor's microscale Reynolds number Reλ 250. Due to the presence of strong ramp-cliff structures, the SF fails to detect the power law behavior. For the traditional method, the ramp-cliff structure causes a serious artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus DFA and WL underestimate the scaling exponents. However, the Hilbert method provides scaling exponents ξθ(q) quite close to the one for longitudinal velocity, indicating a less intermittent passive scalar field than what was believed before. © 2011 American Physical Society.