The Experts below are selected from a list of 267 Experts worldwide ranked by ideXlab platform
Yunlong Xiao - One of the best experts on this subject based on the ideXlab platform.
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relativistic theory of nuclear spin Rotation Tensor with kinetically balanced Rotational london orbitals
Journal of Chemical Physics, 2014Co-Authors: Yunlong Xiao, Yong ZhangAbstract:Both kinetically balanced (KB) and kinetically unbalanced (KU) Rotational London orbitals (RLO) are proposed to resolve the slow basis set convergence in relativistic calculations of nuclear spin-Rotation (NSR) coupling Tensors of molecules containing heavy elements [Y. Xiao and W. Liu, J. Chem. Phys. 138, 134104 (2013)]. While they perform rather similarly, the KB-RLO Ansatz is clearly preferred as it ensures the correct nonrelativistic limit even with a finite basis. Moreover, it gives rise to the same “direct relativistic mapping” between nuclear magnetic resonance shielding and NSR coupling Tensors as that without using the London orbitals [Y. Xiao, Y. Zhang, and W. Liu, J. Chem. Theory Comput. 10, 600 (2014)].
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body fixed relativistic molecular hamiltonian and its application to nuclear spin Rotation Tensor linear molecules
Journal of Chemical Physics, 2013Co-Authors: Yunlong XiaoAbstract:The relativistic molecular Hamiltonian written in the body-fixed frame of reference is the basis for high-precision calculations of spectroscopic parameters involving nuclear vibrations and/or Rotations. Such a Hamiltonian that describes electrons fully relativistically and nuclei quasi-relativistically is just developed for semi-rigid nonlinear molecules [Y. Xiao and W. Liu, J. Chem. Phys. 138, 134104 (2013)]10.1063/1.4797496. Yet, the formulation should somewhat be revised for linear molecules thanks to some unusual features arising from the redundancy of the Rotation around the molecular axis. Nonetheless, the resulting isomorphic Hamiltonian is rather similar to that for nonlinear molecules. Consequently, the relativistic formulation of nuclear spin-Rotation (NSR) Tensor for linear molecules is very much the same as that for nonlinear molecules. So is the relativistic mapping between experimental NSR and NMR.
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body fixed relativistic molecular hamiltonian and its application to nuclear spin Rotation Tensor
Journal of Chemical Physics, 2013Co-Authors: Yunlong XiaoAbstract:A relativistic molecular Hamiltonian that describes electrons fully relativistically and nuclei quasi-relativistically is proposed and transformed from the laboratory to the body-fixed frame of reference. As a first application of the resulting body-fixed relativistic molecular Hamiltonian, the long anticipated relativistic theory of nuclear spin-Rotation (NSR) Tensor is formulated rigorously. A “relativistic mapping” between experimental NSR and NMR is further proposed, which is of great value in establishing high-precision absolute NMR shielding scales.
Peter J Attar - One of the best experts on this subject based on the ideXlab platform.
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some results for approximate strain and Rotation Tensor formulations in geometrically non linear reissner mindlin plate theory
International Journal of Non-linear Mechanics, 2008Co-Authors: Peter J AttarAbstract:Abstract Finite element deflection and stress results are presented for four flat plate configurations and are computed using kinematically approximate (Rotation Tensor, strain Tensor or both) non-linear Reissner–Mindlin plate models. The finite element model is based on a mixed variational principle and has both displacement and force field variables. High order interpolation of the field variables is possible through p-type discretization. Results for some of the higher order approximate models are given for what appears to be the first time. It is found that for the class of example problems examined, exact strain Tensor but approximate Rotation Tensor theories can significantly improve the solution over approximate strain Tensor models such as the von Karman and moderate Rotation models when moderate deflections/Rotations are present. However, for each of the problems examined (with the exception of a postbuckling problem) the von Karman and moderate Rotation model results compared favorably with the higher order models for deflection magnitudes which could be reasonably expected in typical aeroelastic configurations.
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Some results for approximate strain and Rotation Tensor formulations in geometrically non-linear Reissner–Mindlin plate theory
International Journal of Non-linear Mechanics, 2008Co-Authors: Peter J AttarAbstract:Abstract Finite element deflection and stress results are presented for four flat plate configurations and are computed using kinematically approximate (Rotation Tensor, strain Tensor or both) non-linear Reissner–Mindlin plate models. The finite element model is based on a mixed variational principle and has both displacement and force field variables. High order interpolation of the field variables is possible through p-type discretization. Results for some of the higher order approximate models are given for what appears to be the first time. It is found that for the class of example problems examined, exact strain Tensor but approximate Rotation Tensor theories can significantly improve the solution over approximate strain Tensor models such as the von Karman and moderate Rotation models when moderate deflections/Rotations are present. However, for each of the problems examined (with the exception of a postbuckling problem) the von Karman and moderate Rotation model results compared favorably with the higher order models for deflection magnitudes which could be reasonably expected in typical aeroelastic configurations.
Werner Wagner - One of the best experts on this subject based on the ideXlab platform.
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Multiplicative updating of the Rotation Tensor in the finite element analysis of rods and shells – a path independent approach
Computational Mechanics, 2003Co-Authors: Carlo Sansour, Werner WagnerAbstract:Rotation Tensors play a pre dominant role in many engineering applications. They exhibit a pronounced multiplicative structure, the various aspects of which must be dealt with carefully in order to arrive at a numerically efficient and physically sound treatment. A method of multiplicative updating of Rotations in the frame of finite element analysis of rods was suggested by Simo and Vu-Quoc which proved to be path-dependent, even in purely elastic problems, as observed by Jelenic and Crisfield. In this paper a path-independent treatment of Rotations is developed which proves to be numerically efficient, physically sound, and preserves the multiplicative structure of Rotations. In addition, a unified treatment of rod and shell theories is established which considers them from the point of view of Cosserat continua with same degrees of freedom. In the shell case, the formulation allows in a natural way for the inclusion of drill Rotations.
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multiplicative updating of the Rotation Tensor in the finite element analysis of rods and shells a path independent approach
Computational Mechanics, 2003Co-Authors: Carlo Sansour, Werner WagnerAbstract:Rotation Tensors play a pre dominant role in many engineering applications. They exhibit a pronounced multiplicative structure, the various aspects of which must be dealt with carefully in order to arrive at a numerically efficient and physically sound treatment. A method of multiplicative updating of Rotations in the frame of finite element analysis of rods was suggested by Simo and Vu-Quoc which proved to be path-dependent, even in purely elastic problems, as observed by Jelenic and Crisfield. In this paper a path-independent treatment of Rotations is developed which proves to be numerically efficient, physically sound, and preserves the multiplicative structure of Rotations. In addition, a unified treatment of rod and shell theories is established which considers them from the point of view of Cosserat continua with same degrees of freedom. In the shell case, the formulation allows in a natural way for the inclusion of drill Rotations.
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A finite Rotation shell theory with application to composite structures
Revue Européenne des Éléments Finis, 1995Co-Authors: Friedrich Gruttmann, Sven Klinkel, Werner WagnerAbstract:ABSTRACT In this paper we derive a finite element formulation for geometrical nonlinear shell structures. The formulation bases on a direct introduction of the isoparametric finite element formulation into the shell equations. The element allows the occurence of finite Rotations which are described by a Rotation Tensor. A layerwise linear elastic material model for composites is chosen. The consistent linearization of all equations leads to quadratic convergence behaviour within the nonlinear solution procedure. Examples show the applicability and effectivity of the developed element.
Carlo Sansour - One of the best experts on this subject based on the ideXlab platform.
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The modelling of fibre reorientation in soft tissue
Biomechanics and Modeling in Mechanobiology, 2009Co-Authors: Igor Karšaj, Carlo Sansour, Jurica SorićAbstract:In this paper, a hyperelastic and thermodynamically consistent model for soft tissue is developed that is able to describe the change of the initial orientation of the collagen fibres. Full numerical implementation is considered as well. The collagen architecture is assumed to reorient driven by a specific thermodynamical force. The anisotropy is described by a strain energy function, which is decomposed into a part related to the matrix and a part related to the fibres. The initial fibre orientation is defined by a structural Tensor, while the current orientation is described by a time-dependent structural Tensor, which results from the initial one by a Rotational transformation. The Rotation Tensor is obtained via an integration process of a rate Tensor, which depends on an adequately defined thermodynamical force. The integration is achieved via an exponential map algorithm, where it is shown that the Rotation is necessarily a two-parametric one. Efficiency of the proposed formulation is demonstrated using some numerical examples.
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Multiplicative updating of the Rotation Tensor in the finite element analysis of rods and shells – a path independent approach
Computational Mechanics, 2003Co-Authors: Carlo Sansour, Werner WagnerAbstract:Rotation Tensors play a pre dominant role in many engineering applications. They exhibit a pronounced multiplicative structure, the various aspects of which must be dealt with carefully in order to arrive at a numerically efficient and physically sound treatment. A method of multiplicative updating of Rotations in the frame of finite element analysis of rods was suggested by Simo and Vu-Quoc which proved to be path-dependent, even in purely elastic problems, as observed by Jelenic and Crisfield. In this paper a path-independent treatment of Rotations is developed which proves to be numerically efficient, physically sound, and preserves the multiplicative structure of Rotations. In addition, a unified treatment of rod and shell theories is established which considers them from the point of view of Cosserat continua with same degrees of freedom. In the shell case, the formulation allows in a natural way for the inclusion of drill Rotations.
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multiplicative updating of the Rotation Tensor in the finite element analysis of rods and shells a path independent approach
Computational Mechanics, 2003Co-Authors: Carlo Sansour, Werner WagnerAbstract:Rotation Tensors play a pre dominant role in many engineering applications. They exhibit a pronounced multiplicative structure, the various aspects of which must be dealt with carefully in order to arrive at a numerically efficient and physically sound treatment. A method of multiplicative updating of Rotations in the frame of finite element analysis of rods was suggested by Simo and Vu-Quoc which proved to be path-dependent, even in purely elastic problems, as observed by Jelenic and Crisfield. In this paper a path-independent treatment of Rotations is developed which proves to be numerically efficient, physically sound, and preserves the multiplicative structure of Rotations. In addition, a unified treatment of rod and shell theories is established which considers them from the point of view of Cosserat continua with same degrees of freedom. In the shell case, the formulation allows in a natural way for the inclusion of drill Rotations.
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a theory and finite element formulation of shells at finite deformations involving thickness change circumventing the use of a Rotation Tensor
Archive of Applied Mechanics, 1995Co-Authors: Carlo SansourAbstract:A nonlinear shell theory, including transverse strains perpendicular to the shell midsurface, as well as transverse shear strains, with exact description of the kinematical fields, is developed. The strain measures are derived by considering theGreen strain Tensor of the three-dimensional shell body. A quadratic displacement field over the shell thickness is considered. Altogether seven kinematical fields are incorporated in the formulation. The kinematics of the shell normal is described by means of a difference vector, avoiding the use of a Rotation Tensor and resulting in a configuration space, where the structure of a linear vector space is preserved. In the case of linear constitutive equations, a possible consistent reduction to six degrees of freedom is discussed. The finite element formulation is based on a hybrid variational principle. The accuracy of the theory and its wide range of applicability is demonstrated by several examples. Comparison with results based on shell theories formulated by means of a Rotation Tensor are included.
Sergio S. Gomez - One of the best experts on this subject based on the ideXlab platform.
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toward an absolute nmr shielding scale using the spin Rotation Tensor within a relativistic framework
Physical Chemistry Chemical Physics, 2016Co-Authors: Agustin I Aucar, Sergio S. Gomez, C G Giribet, Gustavo A AucarAbstract:One of the most influential articles showing the best way to get the absolute values of NMR magnetic shieldings, σ (non-measurables) from both accurate measurements and theoretical calculations, was published a long time ago by Flygare. His model was shown to break down when heavy atoms are involved. This fact motivated the development of new theories of nuclear spin-Rotation (SR) Tensors, which consider electronic relativistic effects. One was published recently by some of us. In this article we take another step further and propose three different models that generalize Flygare's model. All of them are written using four-component relativistic expressions, though the two-component relativistic SO-S term also appears in one. The first clues for these developments were built from the relationship among σ and the SR Tensors within the two-component relativistic LRESC model. Besides, we had to introduce a few other well defined assumptions: (i) relativistic corrections must be included in a way to best reproduce the relationship among the (e–e) term (called “paramagnetic” within the non-relativistic domain) of σ and its equivalent part of the SR Tensor, (ii) as happens in Flygare's rule, the shielding of free atoms shall be included to improve accuracy. In the highest accurate model, a new term known as Spin–orbit due to spin, SO-S (in this mechanism the spin-Zeeman Hamiltonian replaces the orbital-Zeeman Hamiltonian), is included. We show the results of the application of those models to halogen containing linear molecules.
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breit interaction effects in relativistic theory of the nuclear spin Rotation Tensor
Journal of Chemical Physics, 2013Co-Authors: Agustin I Aucar, Sergio S. Gomez, C G Giribet, Martin Ruiz C De AzuaAbstract:In this work, relativistic effects on the nuclear spin-Rotation (SR) Tensor originated in the electron-nucleus and electron-electron Breit interactions are analysed. To this end, four-component numerical calculations were carried out in model systems HX (X=H,F,Cl,Br,I). The electron-nucleus Breit interaction couples the electrons and nuclei dynamics giving rise to a purely relativistic contribution to the SR Tensor. Its leading order in 1/c is of the same value as that of relativistic corrections on the usual second order expression of the SR Tensor considered in previous work [I. A. Aucar, S. S. Gomez, J. I. Melo, C. G. Giribet, and M. C. Ruiz de Azua, J. Chem. Phys. 138, 134107 (2013)]10.1063/1.4796461, and therefore it is absolutely necessary to establish its relative importance. For the sake of completeness, the corresponding effect originating in the electron-electron Breit interaction is also considered. It is verified that in all cases these Breit interactions yield only very small corrections to t...
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Theoretical study of the nuclear spin-molecular Rotation coupling for relativistic electrons and non-relativistic nuclei
Journal of Chemical Physics, 2012Co-Authors: Ignacio Agustín Aucar, Sergio S. Gomez, Martín C. Ruiz De Azúa, Claudia G. GiribetAbstract:A theoretical study of the relation between the relativistic formulation of the nuclear magnetic shielding and spin-Rotation Tensors is presented. To this end a theoretical expression of the relativistic spin-Rotation Tensor is formulated, considering a molecular Hamiltonian of relativistic electrons and non-relativistic nuclei. Molecular Rotation effects are introduced considering the terms of the Born-Oppenheimer decomposition, which couple the electrons and nuclei dynamics. The loss of the simple relation linking both spectral parameters in the non-relativistic formulation is further analyzed carrying out a perturbative expansion of relativistic effects by means of the linear response within the elimination of the small component approach. It is concluded that relativistic effects on the spin-Rotation Tensor are less important than those of the nuclear magnetic shielding Tensor.
