The Experts below are selected from a list of 42123 Experts worldwide ranked by ideXlab platform
Trygve Helgaker - One of the best experts on this subject based on the ideXlab platform.
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ground state densities from the rayleigh ritz Variation Principle and from density functional theory
Journal of Chemical Physics, 2015Co-Authors: Simen Kvaal, Trygve HelgakerAbstract:The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh-Ritz Variation Principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the Hohenberg-Kohn Variation Principle) is studied within the framework of convex conjugation, in a generic setting covering molecular systems, solid-state systems, and more. Having introduced admissible density functionals as functionals that produce the exact ground-state energy for a given external potential by minimizing over densities in the Hohenberg-Kohn Variation Principle, necessary and sufficient conditions on such functionals are established to ensure that the Rayleigh-Ritz ground-state densities and the Hohenberg-Kohn ground-state densities are identical. We apply the results to molecular systems in the Born-Oppenheimer approximation. For any given potential v ∈ L(3/2)(ℝ(3)) + L(∞)(ℝ(3)), we establish a one-to-one correspondence between the mixed ground-state densities of the Rayleigh-Ritz Variation Principle and the mixed ground-state densities of the Hohenberg-Kohn Variation Principle when the Lieb density-matrix constrained-search universal density functional is taken as the admissible functional. A similar one-to-one correspondence is established between the pure ground-state densities of the Rayleigh-Ritz Variation Principle and the pure ground-state densities obtained using the Hohenberg-Kohn Variation Principle with the Levy-Lieb pure-state constrained-search functional. In other words, all physical ground-state densities (pure or mixed) are recovered with these functionals and no false densities (i.e., minimizing densities that are not physical) exist. The importance of topology (i.e., choice of Banach space of densities and potentials) is emphasized and illustrated. The relevance of these results for current-density-functional theory is examined.
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ground state densities from the rayleigh ritz Variation Principle and from density functional theory
arXiv: Chemical Physics, 2015Co-Authors: Simen Kvaal, Trygve HelgakerAbstract:The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh--Ritz (RR) Variation Principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the Hohenberg--Kohn (HK) Variation Principle) is studied within the framework of convex conjugation, in a generic setting covering molecular systems, solid-state systems, and more. Having introduced admissible density functionals as functionals that produce the exact ground ground-state energy for a given external potential by minimizing over densities in the HK Variation Principle, necessary sufficient conditions on such functionals are established to ensure that the RR ground-state densities and the HK ground-state densities are identical. We apply the results to molecular systems in the BO-approximation. For any given potential $v \in L^{3/2}(\mathbb{R}^3) + L^{\infty}(\mathbb{R}^3)$, we establish a one-to-one correspondence between the mixed ground-state densities of the RR Variation Principle and the mixed ground-state densities of the HK Variation Principle when the Lieb density-matrix constrained-search universal density functional is taken as the admissible functional. A similar one-to-one correspondence is established between the pure ground-state densities of the RR Variation Principle and the pure ground-state densities obtained using the HK Variation Principle with the Levy--Lieb pure-state constrained-search functional. In other words, all physical ground-state densities (pure or mixed) are recovered with these functionals and no false densities (i.e., minimizing densities that are not physical) exist. The importance of topology (i.e., choice of Banach space of densities and potentials) is emphasized and illustrated. The relevance of these results for current-density-functional theory is examined.
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calculations of two photon absorption cross sections by means of density functional theory
Chemical Physics Letters, 2003Co-Authors: Yi Luo, Pawel Salek, Olav Vahtras, Jingdong Guo, Trygve Helgaker, Hans ÅgrenAbstract:We present density-functional theory and calculations for two-photon absorption spectra of molecules. The two-photon absorption cross sections are defined in terms of the single residues of the quadratic response function, which was recently derived for density-functional theory using the time-dependent Variation Principle and the quasi-energy ansatz. The cross-section dependence on different functionals, including the general gradient approximation and hybrid theory, is examined for a set of small molecules. The results of hybrid density-functional theory compare favorably with those from singles-and-doubles coupled-cluster response calculations.
Dewen Zhao - One of the best experts on this subject based on the ideXlab platform.
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analysis of vertical rolling using double parabolic model and stream function velocity field
The International Journal of Advanced Manufacturing Technology, 2016Co-Authors: Dianhua Zhang, Dewen ZhaoAbstract:Vertical rolling has been widely used in the roughing stand of hot strip rolling to improve the precision of slab width which influences the finished product quality significantly in actual production. Double parabolic dog-bone function model and corresponding velocity and strain rate fields are firstly proposed based on the incompressibility condition and stream function. They are successfully applied to three-dimensional vertical rolling. Using the first Variation Principle of rigid-plastic material, an analytical solution of slab total power functional in vertical rolling is obtained. Then, the shape parameters and the rolling force are received by minimizing the power functional. The error of shape and power parameters is within 4 % compared with finite element method (FEM) simulation’s result and less than 9.5 % compared with other models’ result.
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upper bound analysis of rolling force and dog bone shape via sine function model in vertical rolling
Journal of Materials Processing Technology, 2015Co-Authors: Dianhua Zhang, Dewen ZhaoAbstract:Abstract The control of the slab width in actual production is realized by the widely use of vertical rolling (edge rolling). According to the incompressibility condition, the sine function dog-bone model is firstly proposed in this paper for steady state deformation in vertical rolling with flat rolls combined with the actual conditions. Based on the first Variation Principle of rigid-plastic material, the variable upper bound integration method is used to integrate plastic deformation, shear and friction power terms. The upper bound solutions of rolling force and dog-bone shape are solved numerically, and this process is carried out using Matlab Optimization Toolbox by minimizing the total power functional. Results show that the rolling force increases and the dog-bone shape size become larger while engineering strain, initial thickness, or roll radius increases. The results obtained from sine function model are compared with those of experimental data in reference and FEM simulation, and a good agreement is found. The comparison shows that it is possible to determine the required optimum rolling force and dog-bone shape by using sine function model.
Andrei Gruzinov - One of the best experts on this subject based on the ideXlab platform.
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pulsar magnetospheres Variation Principle singularities and estimate of power
The Astrophysical Journal, 2006Co-Authors: Andrei GruzinovAbstract:We formulate a Variation Principle for the force-free magnetosphere of an inclined pulsar: + Ω M (where and M are electromagnetic energy and angular momentum and Ω is the angular velocity of the star) is stationary under isotopological Variations of the magnetic field and arbitrary Variations of the electric field. The Variation Principle gives the reason for the existence and proves the local stability of singular current layers along magnetic separatrices. Magnetic field lines of inclined pulsar magnetospheres lie on magnetic surfaces and do have magnetic separatrices. In the framework of the isotopological Variation Principle, inclined magnetospheres are expected to be simple deformations of the axisymmetric pulsar magnetosphere. A singular line should exist on the light cylinder, where the inner separatrix terminates and the outer separatrix emanates. The electromagnetic field should have an inverse square root singularity near the singular line inside the inner magnetic separatrix. The large-distance asymptotic solution is calculated and used to estimate the pulsar power, L ≈ c-3μ2Ω4 for spin-dipole inclinations 30°.
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Pulsar Magnetosphere: Variation Priciple, Singularities, Estimate of Power
The Astrophysical Journal, 2006Co-Authors: Andrei GruzinovAbstract:We formulate a Variation Principle for the force-free magnetosphere of an inclined pulsar: + Ω M (where and M are electromagnetic energy and angular momentum and Ω is the angular velocity of the star) is stationary under isotopological Variations of the magnetic field and arbitrary Variations of the electric field. The Variation Principle gives the reason for the existence and proves the local stability of singular current layers along magnetic separatrices. Magnetic field lines of inclined pulsar magnetospheres lie on magnetic surfaces and do have magnetic separatrices. In the framework of the isotopological Variation Principle, inclined magnetospheres are expected to be simple deformations of the axisymmetric pulsar magnetosphere. A singular line should exist on the light cylinder, where the inner separatrix terminates and the outer separatrix emanates. The electromagnetic field should have an inverse square root singularity near the singular line inside the inner magnetic separatrix. The large-distance asymptotic solution is calculated and used to estimate the pulsar power, L ≈ c-3μ2Ω4 for spin-dipole inclinations 30°.
Simen Kvaal - One of the best experts on this subject based on the ideXlab platform.
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ground state densities from the rayleigh ritz Variation Principle and from density functional theory
Journal of Chemical Physics, 2015Co-Authors: Simen Kvaal, Trygve HelgakerAbstract:The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh-Ritz Variation Principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the Hohenberg-Kohn Variation Principle) is studied within the framework of convex conjugation, in a generic setting covering molecular systems, solid-state systems, and more. Having introduced admissible density functionals as functionals that produce the exact ground-state energy for a given external potential by minimizing over densities in the Hohenberg-Kohn Variation Principle, necessary and sufficient conditions on such functionals are established to ensure that the Rayleigh-Ritz ground-state densities and the Hohenberg-Kohn ground-state densities are identical. We apply the results to molecular systems in the Born-Oppenheimer approximation. For any given potential v ∈ L(3/2)(ℝ(3)) + L(∞)(ℝ(3)), we establish a one-to-one correspondence between the mixed ground-state densities of the Rayleigh-Ritz Variation Principle and the mixed ground-state densities of the Hohenberg-Kohn Variation Principle when the Lieb density-matrix constrained-search universal density functional is taken as the admissible functional. A similar one-to-one correspondence is established between the pure ground-state densities of the Rayleigh-Ritz Variation Principle and the pure ground-state densities obtained using the Hohenberg-Kohn Variation Principle with the Levy-Lieb pure-state constrained-search functional. In other words, all physical ground-state densities (pure or mixed) are recovered with these functionals and no false densities (i.e., minimizing densities that are not physical) exist. The importance of topology (i.e., choice of Banach space of densities and potentials) is emphasized and illustrated. The relevance of these results for current-density-functional theory is examined.
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ground state densities from the rayleigh ritz Variation Principle and from density functional theory
arXiv: Chemical Physics, 2015Co-Authors: Simen Kvaal, Trygve HelgakerAbstract:The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh--Ritz (RR) Variation Principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the Hohenberg--Kohn (HK) Variation Principle) is studied within the framework of convex conjugation, in a generic setting covering molecular systems, solid-state systems, and more. Having introduced admissible density functionals as functionals that produce the exact ground ground-state energy for a given external potential by minimizing over densities in the HK Variation Principle, necessary sufficient conditions on such functionals are established to ensure that the RR ground-state densities and the HK ground-state densities are identical. We apply the results to molecular systems in the BO-approximation. For any given potential $v \in L^{3/2}(\mathbb{R}^3) + L^{\infty}(\mathbb{R}^3)$, we establish a one-to-one correspondence between the mixed ground-state densities of the RR Variation Principle and the mixed ground-state densities of the HK Variation Principle when the Lieb density-matrix constrained-search universal density functional is taken as the admissible functional. A similar one-to-one correspondence is established between the pure ground-state densities of the RR Variation Principle and the pure ground-state densities obtained using the HK Variation Principle with the Levy--Lieb pure-state constrained-search functional. In other words, all physical ground-state densities (pure or mixed) are recovered with these functionals and no false densities (i.e., minimizing densities that are not physical) exist. The importance of topology (i.e., choice of Banach space of densities and potentials) is emphasized and illustrated. The relevance of these results for current-density-functional theory is examined.
Dianhua Zhang - One of the best experts on this subject based on the ideXlab platform.
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analysis of vertical rolling using double parabolic model and stream function velocity field
The International Journal of Advanced Manufacturing Technology, 2016Co-Authors: Dianhua Zhang, Dewen ZhaoAbstract:Vertical rolling has been widely used in the roughing stand of hot strip rolling to improve the precision of slab width which influences the finished product quality significantly in actual production. Double parabolic dog-bone function model and corresponding velocity and strain rate fields are firstly proposed based on the incompressibility condition and stream function. They are successfully applied to three-dimensional vertical rolling. Using the first Variation Principle of rigid-plastic material, an analytical solution of slab total power functional in vertical rolling is obtained. Then, the shape parameters and the rolling force are received by minimizing the power functional. The error of shape and power parameters is within 4 % compared with finite element method (FEM) simulation’s result and less than 9.5 % compared with other models’ result.
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upper bound analysis of rolling force and dog bone shape via sine function model in vertical rolling
Journal of Materials Processing Technology, 2015Co-Authors: Dianhua Zhang, Dewen ZhaoAbstract:Abstract The control of the slab width in actual production is realized by the widely use of vertical rolling (edge rolling). According to the incompressibility condition, the sine function dog-bone model is firstly proposed in this paper for steady state deformation in vertical rolling with flat rolls combined with the actual conditions. Based on the first Variation Principle of rigid-plastic material, the variable upper bound integration method is used to integrate plastic deformation, shear and friction power terms. The upper bound solutions of rolling force and dog-bone shape are solved numerically, and this process is carried out using Matlab Optimization Toolbox by minimizing the total power functional. Results show that the rolling force increases and the dog-bone shape size become larger while engineering strain, initial thickness, or roll radius increases. The results obtained from sine function model are compared with those of experimental data in reference and FEM simulation, and a good agreement is found. The comparison shows that it is possible to determine the required optimum rolling force and dog-bone shape by using sine function model.
