The Experts below are selected from a list of 30 Experts worldwide ranked by ideXlab platform
Chuong V Tran - One of the best experts on this subject based on the ideXlab platform.
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the number of degrees of freedom of three dimensional navier stokes turbulence
Physics of Fluids, 2009Co-Authors: Chuong V TranAbstract:In Kolmogorov’s phenomenological theory of turbulence, the energy spectrum in the inertial range scales with the wave number k as k−5/3 and extends up to a dissipation wave number kν, which is given in terms of the energy dissipation rate ϵ and viscosity ν by kν∝(ϵ/ν3)1/4. This result leads to Landau’s Heuristic Estimate for the number of degrees of freedom that scales as Re9/4, where Re is the Reynolds number. Here we consider the possibility of establishing a quantitative basis for these results from first principles. In particular, we examine the extent to which they can be derived from the three-dimensional Navier–Stokes system, making use of Kolmogorov’s hypothesis of finite and viscosity-independent energy dissipation only. It is found that the Taylor microscale wave number kT (a close cousin of kν) can be expressed in the form kT≤CU/ν=(CU/‖u‖)1/2(ϵ/ν3)1/4. Here U and ‖u‖ are a “microscale” velocity and the root mean square velocity, respectively, and C≤1 is a dynamical parameter. This result can be...
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the number of degrees of freedom of three dimensional navier stokes turbulence
arXiv: Fluid Dynamics, 2009Co-Authors: Chuong V TranAbstract:In Kolmogorov's phenomenological theory of turbulence, the energy spectrum in the inertial range scales with the wave number $k$ as $k^{-5/3}$ and extends up to a dissipation wave number $k_\nu$, which is given in terms of the energy dissipation rate $\epsilon$ and viscosity $\nu$ by $k_\nu\propto(\epsilon/\nu^3)^{1/4}$. This result leads to Landau's Heuristic Estimate for the number of degrees of freedom that scales as $\Re^{9/4}$, where $\Re$ is the Reynolds number. Here we consider the possibility of establishing a quantitative basis for these results from first principles. In particular, we examine the extent to which they can be derived from the three-dimensional Navier--Stokes system, making use of Kolmogorov's hypothesis of finite and viscosity-independent energy dissipation only. It is found that the Taylor microscale wave number $k_T$ (a close cousin of $k_\nu$) can be expressed in the form $k_T \le CU/\nu = (CU/\norm{\u})^{1/2}(\epsilon/\nu^3)^{1/4}$. Here $U$ and $\norm{\u}$ are, respectively, a ``microscale'' velocity and the root mean square velocity, and $C\le1$ is a dynamical parameter. This result can be seen to be in line with Kolmogorov's prediction for $k_\nu$. Furthermore, it is shown that the minimum number of greatest Lyapunov exponents whose sum becomes negative does not exceed $\Re^{9/4}$, where $\Re$ is defined in terms of an average energy dissipation rate, the system length scale, and $\nu$. This result is in a remarkable agreement with the Landau Estimate, up to a presumably slight discrepancy between the conventional and the present energy dissipation rates used in the definition of $\Re$.
Volker Staemmler - One of the best experts on this subject based on the ideXlab platform.
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A Heuristic Estimate of molecular correlation energies using pair correlation energies of localized molecular orbitals
Theoretical Chemistry Accounts, 2019Co-Authors: Michael Böckers, Robert Franke, Volker StaemmlerAbstract:The biggest problem for the application of wavefunction-based quantum chemical ab initio methods is the calculation of the electronic correlation energy. Advanced methods such as coupled-cluster theory using iterative single and double excitations as well as perturbative triple excitations [CCSD(T)] are able to achieve an accuracy of ± 5 kJ/mol (‘chemical accuracy’) for small molecular systems, but become too time-consuming for routine applications to larger systems containing twenty or more heavy atoms. We propose a Heuristic approach for a rapid Estimate of correlation energies for larger molecules, based on parametrized pair correlation energies (PCEs) for localized molecular orbitals. Such PCEs were calculated for a training set of 112 small- and medium-sized neutral molecules from the G2/97 data set, using an approximate coupled-cluster method with single and double excitations (CCSD) and a basis set of quadruple zeta quality (def2-QZVP). The PCEs were then fitted to appropriate functional forms, taking into account the properties of the localized orbitals: type (lone pair, single bond, multiple bond), bond length, hybridization of the atoms involved in the bond, spatial extent, and distance between two orbitals. The ab initio results for the total correlation energies of the molecules in the training set could be reproduced within 1%. For most of the molecules in an extended test set containing also molecular ions a slightly lower accuracy of about 1% to 3% could be obtained.
Michael Böckers - One of the best experts on this subject based on the ideXlab platform.
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A Heuristic Estimate of molecular correlation energies using pair correlation energies of localized molecular orbitals
Theoretical Chemistry Accounts, 2019Co-Authors: Michael Böckers, Robert Franke, Volker StaemmlerAbstract:The biggest problem for the application of wavefunction-based quantum chemical ab initio methods is the calculation of the electronic correlation energy. Advanced methods such as coupled-cluster theory using iterative single and double excitations as well as perturbative triple excitations [CCSD(T)] are able to achieve an accuracy of ± 5 kJ/mol (‘chemical accuracy’) for small molecular systems, but become too time-consuming for routine applications to larger systems containing twenty or more heavy atoms. We propose a Heuristic approach for a rapid Estimate of correlation energies for larger molecules, based on parametrized pair correlation energies (PCEs) for localized molecular orbitals. Such PCEs were calculated for a training set of 112 small- and medium-sized neutral molecules from the G2/97 data set, using an approximate coupled-cluster method with single and double excitations (CCSD) and a basis set of quadruple zeta quality (def2-QZVP). The PCEs were then fitted to appropriate functional forms, taking into account the properties of the localized orbitals: type (lone pair, single bond, multiple bond), bond length, hybridization of the atoms involved in the bond, spatial extent, and distance between two orbitals. The ab initio results for the total correlation energies of the molecules in the training set could be reproduced within 1%. For most of the molecules in an extended test set containing also molecular ions a slightly lower accuracy of about 1% to 3% could be obtained.
Robert Franke - One of the best experts on this subject based on the ideXlab platform.
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A Heuristic Estimate of molecular correlation energies using pair correlation energies of localized molecular orbitals
Theoretical Chemistry Accounts, 2019Co-Authors: Michael Böckers, Robert Franke, Volker StaemmlerAbstract:The biggest problem for the application of wavefunction-based quantum chemical ab initio methods is the calculation of the electronic correlation energy. Advanced methods such as coupled-cluster theory using iterative single and double excitations as well as perturbative triple excitations [CCSD(T)] are able to achieve an accuracy of ± 5 kJ/mol (‘chemical accuracy’) for small molecular systems, but become too time-consuming for routine applications to larger systems containing twenty or more heavy atoms. We propose a Heuristic approach for a rapid Estimate of correlation energies for larger molecules, based on parametrized pair correlation energies (PCEs) for localized molecular orbitals. Such PCEs were calculated for a training set of 112 small- and medium-sized neutral molecules from the G2/97 data set, using an approximate coupled-cluster method with single and double excitations (CCSD) and a basis set of quadruple zeta quality (def2-QZVP). The PCEs were then fitted to appropriate functional forms, taking into account the properties of the localized orbitals: type (lone pair, single bond, multiple bond), bond length, hybridization of the atoms involved in the bond, spatial extent, and distance between two orbitals. The ab initio results for the total correlation energies of the molecules in the training set could be reproduced within 1%. For most of the molecules in an extended test set containing also molecular ions a slightly lower accuracy of about 1% to 3% could be obtained.
Li Zhongke - One of the best experts on this subject based on the ideXlab platform.
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fast approximation of geodesic based on Heuristic Estimate
International Conference on Computer Design, 2010Co-Authors: Ma Yaqi, Li ZhongkeAbstract:Geodesic computation is very important in various mesh processing techniques such as segmenting, re-meshing, parameterizing, navigating and editing. In this paper, we present a new method to quickly extract geodesic paths on 3D triangle meshes. Based on Heuristic Estimate and Dimas Martinez and Luiz Velho's evolving method, we generate an iterative process to obtain a good discrete geodesic approximation. It can handle convex and non-convex surfaces. Experiment results show that our method works very well both in efficiency and precision.