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Kenichi Matsuyanagi - One of the best experts on this subject based on the ideXlab platform.
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adiabatic selfconsistent collective coordinate method for large amplitude collective motion in nuclei with pairing correlations
Progress of Theoretical Physics, 2000Co-Authors: Masayuki Matsuo, Takashi Nakatsukasa, Kenichi MatsuyanagiAbstract:An adiabatic approximation to the selfconsistent collective coordinate method is Formulated in order to describe large amplitude collective motions in nuclei with pairing correlations on the basis of the time-dependent Hartree-Fock-Bogoliubov equations of motion. The basic equations are presented in a local Harmonic Form which can be solved in a manner similar to that of the quasiparticle RPA equations. The Formalism guarantees the conservation of nucleon number expectation values. An extension to the multi-dimensional case is also discussed.
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adiabatic selfconsistent collective coordinate method for large amplitude collective motion in superconducting nuclei
arXiv: Nuclear Theory, 2000Co-Authors: Masayuki Matsuo, Takashi Nakatsukasa, Kenichi MatsuyanagiAbstract:An adiabatic approximation to the selfconsistent collective coordinate method is Formulated in order to describe large amplitude collective motions in superconducting nuclei on the basis of the time-dependent Hartree-Fock-Bogoliubov equations of motion. The basic equations are presented in a local Harmonic Form which can be solved in a similar way as the quasiparticle RPA equations. The Formalism guarantees the conservation of nucleon number expectation values. An extension to the multi-dimensional case is also discussed.
Tornabene F. - One of the best experts on this subject based on the ideXlab platform.
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Analytical and semi-analytical 3D shell models for composite structures
Instituto Superior Técnico Lisbon Portugal, 2019Co-Authors: Torre R., Brischetto S., Tornabene F.Abstract:This paper focuses on the mechanical analysis of multi-layered composite and sandwich plates and shells when subjected to several static loads. Two different 3D models are compared in order to show the advantages of both the methods and their respective limits. Both the 3D models consider the same mixed curvilinear and orthogonal coordinate system and the same 3D equilibrium equations written for spherical shells. The use of this coordinate system allows the equations to be reduced to those for plates and cylindrical shells with the advantage of a unique and comprehensive Formulation, which automatically adapts to the considered geometry. Plates and shells are considered as simply supported imposing a Harmonic Form for the displacements, the stresses and the loads. This feature allows the 3D equilibrium equations to be analytically solved in the in-plane directions positioned in the mean reference surface and to be converted into partial differential equations in the thickness direction z. The system of partial differential equations is, then, analytically solved in the thickness direction by the first model, defined as 3D EM, which employs the Exponential Matrix (EM) technique. The computational cost is significantly reduced by means of the second model, referred to as 3D GDQ, which uses the Generalized Differential Quadrature (GDQ) method in place of the Exponential Matrix method. A layerwise approach is employed by both the models: the system of partial differential equation is solved using an appropriate number of mathematical layers in 3D EM model and the Chebyshev-Gauss-Lobatto grid distribution in 3D GDQ model. The considered geometries can be loaded on the top and bottom surfaces in different directions. A transverse normal load or transverse shear loads can be applied on the top and/or bottom external surfaces. All the proposed benchmarks show that the analytical model (3D EM) and the semi-analytical one (3D GDQ) are in agreement, with coinciding results for different material and lamination schemes, geometries and dimensions, thickness ratios and loads. The approximation introduced by the use of the GDQ method does not give any noticeable effect on the accuracy of the results when the points are distributed across the domain using a stable and accurate grid. The results will be proposed in terms of displacement, strain and stress amplitudes through the thickness direction. Both the models are able to show the typical zigzag Form of displacements in multi-layered anisotropic structures. The equilibrium and compatibility conditions are also satisfied when transverse shear/normal stresses and displacements are continuous at each layer interface, respectively. Furthermore, transverse normal and transverse shear stresses exactly satisfy the boundary loading conditions on top and bottom external surfaces
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Cylindrical bending in composite structures by means of analytical and numerical 2D/3D shell models
A.J.M Ferreira H. Hu (Editors), 2019Co-Authors: Torre R., Brischetto S., Tornabene F.Abstract:A comparison between a 3D exact shell solution and 2D numerical approaches is proposed in the present paper with a specific focus on the free vibrations of multi-layered composite plates and shells. The validation of new plate and shell structural models is often carried out imposing the cylindrical bending conditions. The reference 3D model here employed is developed using an orthogonal and mixed curvilinear coordinate system. The equilibrium equations are proposed for spherical shells, and they can easily degenerate in those for cylindrical shells, cylinders and plates. In the free vibration analysis, the analytical solution of the system can be obtained using a Harmonic Form for the displacements by imposing arbitrary half-wave numbers in both the in-plane directions. This Harmonic Formulation automatically leads to simply supported boundary conditions. The cylindrical bending can be easily studied imposing that one of the two half-wave numbers is equal zero. The numerical solutions of the problem are obtained using different 2D models. A classical 2D Finite Element (FE) model and a 2D Generalized Differential Quadrature (GDQ) method are compared with the 3D analytical reference solution. The 2D FE model uses a refined mesh based on Quad8 elements in the framework of a commercial finite element code. The 2D GDQ model solves the problem using a non-uniForm Chebyshev-Gauss-Lobatto grid and they are based on refined 2D kinematic assumptions. The proposed benchmarks show that both the 2D numerical models (FE and GDQ ones) are able to provide almost all the natural frequencies of the investigated shells with a significant precision. The 3D model obtains all the vibration modes with a single run where all the edges are simply supported. However, both the 2D models can miss some modes when the simply supported boundary conditions are applied to all the edges in a no coherent way. Some of these modes are cylindrical bending modes and they can be recovered by opportunely modifying the boundary conditions in 2D numerical models. In the case of plates and cylinders, all the missing frequencies can be obtained imposing the simply supported conditions only for the edges parallel to the direction with zero half-wave number and using the free boundary conditions for the other two parallel sides. When a cylindrical shell panel is considered, the modes with zero half-wave number in the curvilinear direction cannot be obtained because the cylindrical bending conditions cannot be imposed. In the case of cylindrical bending modes, it has been observed that the 2D numerical solutions converge to the 3D exact model when the length of the simply supported sides increases in order to reduce the boundary effects corresponding to the free edges
Amitesh Maiti - One of the best experts on this subject based on the ideXlab platform.
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A coarse-grained model for PETN crystals A coarse-grained model for PETN crystals
2020Co-Authors: Richard Gee, Amitesh MaitiAbstract:Abstract Using the energetic material Pentaerythritol Tetranitrate (PETN) as a specific example of molecular crystal, we describe the development of a simple coarse-graining procedure by grouping several atoms or whole functional groups into single charge-neutral beads. As compared to fully atomistic calculations the coarse-grained model speeds up simulations by more than two orders of magnitude. Yet, by adjusting only two parameters in the coarse-grained interaction, the model accurately predicts the lattice constants, sublimation energy, pressure-volume curve up to P=10 GPa, and energetically the most stable facets. Computed surface and desorption energies, bulk modulus, and equilibrium morphology are reported as well. 2 Molecular crystals are becoming increasingly important in numerous applications ranging from drugs, pigments, agrochemicals, dyes, optoelectronic materials, and energetic materials used in detonation devices. Better utilization of such materials warrants a good understanding of the morphological properties of the crystals, as well as the response of exposed surfaces to external factors like temperature, impurities, solvent, and so on. With the availability of sophisticated inter-atomic interactions or force fields, parameterized primarily for organic molecules, it is becoming increasingly possible to study the surface kinetics and the morphological evolution of such materials at the atomic level via classical molecular mechanics However, typical molecules in such materials are uncharged and non-polar, and all the important dynamics is governed by weak inter-molecular interactions of short spatial range, while a significant part of atomistic molecular dynamics (MD) gets consumed in computing both intra-molecular and Coulombic energies and forces. One way to overcome this inefficiency is to coarse-grain a group of atoms into single charge-neutral "beads". The resulting decrease in the intra-molecular degrees of freedom and the absence of long-ranged electrostatics can significantly increase computational speed, while fewer inter-molecular interaction parameters can make it easier to fit select experimental parameters of interest for specific materials systems. In this Letter we consider the energetic material Pentaerythritol Tetranitrate (PETN), and develop a simple coarse-grained interaction potential for use in MD or Monte Carlo simulations. As compared with fully atomistic calculations the coarse-grained potential is found to be more than 100 times faster. The fitting of a single length and a single energy term in the nonbond interaction yields not only accurate lattice constants, but several other properties, including sublimation energy, and pressure-volume (P-V) curve with excellent accuracy as compared to room-temperature experimental measurements. Additional quantities, i.e., dominant facets in the equilibrium morphology are also in agreement with existing experimental literature. imposed symmetry constraints such a coarse-grained crystal, upon energy minimization (with a coarse-3 grained interaction potential described below), relaxes into a configuration with body-centered-tetragonal symmetry. In other words, although our initially constructed coarse-grained crystal is not constrained to any specific symmetry, the relaxed structure conForms to the symmetry: c b a ≠ = , and γ β α = = = 90º [3]. As for interactions between the coarse-grained beads, only a minimal set is considered: (1) the intramolecular A-B bond interaction, chosen to be of the Harmonic Form: and (2) the B-B nonbond interaction, chosen to be in the 12-6 Lennard-Jones Form Note that this later interaction is operative between both intra-molecular and inter-molecular B-beads, i.e., the 1-3 interactions are explicitly included. The intermolecular interactions, represented solely by the B-B nonbond term govern most physical properties of interest for this system (vibrational properties were not of interest in this study). With only two nonbond parameters BB D and BB σ at our disposal, we could aim at accurately fitting two experimental quantities. With the room-temperature lattice constant a (9.38 Å) [2] and the room-temperature heat of sublimation . It is interesting to note that by adjusting only two parameters in the coarse-grained interaction we obtain accurate values for all lattice constants, the sublimation energy, and even the P-V curve up to P=10 GPa, as compared with room-temperature experimental data. Compared to experiment, the coarse-grained results are as good as or even better than fully atomistic COMPASS results. Only the room-temperature bulk modulus is underestimated by ~15-20 %. However, it should be noted that even the experimental value of bulk modulus is a highly sensitive function of the low-pressure (< 0.5 GPa) P-V data. Comparing the room-temperature results of Finally, with the aim of explaining recent experimental data on the evolution of crystal size and surface features as a function of temperature, we compute the desorption energies (at T = 0) of various molecular sites on the most exposed facet of PETN crystallites, i.e., the {110} family of planes. More specifically, we look at a molecule on the top of a defect-free flat surface, a molecule in the top layer of a flat surface, and 5 molecules on two different types of steps, i.e., one running along the <001> direction, and the other running along the <1 1 0> direction. Along the <001> steps, the PETN molecules are arranged in a straight line. For such steps we compute the desorption energy of a molecule belonging to a straight step, and that of a molecule at a step-kink (i.e. corner). The <1 1 0> steps, on the other hand, have a zigzag arrangement of molecules, and each site is almost like a kink. Results listed in In summary, we demonstrate that for crystals of uncharged non-polar molecules like PETN, it is possible to reproduce a large number of structural, energetic, and thermodynamic properties using only a few parameters describing nonbond interactions of groups of atoms. These simplifications not only speed up calculations by more than two orders of magnitude as compared to fully atomistic calculations, but also expose the truly important interaction parameters governing the system properties. The resulting speed and accuracy should enable detailed exploration of kinetic, thermodynamic, and growth properties of such crystallites both from the melt as well as in the vapor phase. Acknowledgment: We would like to thank Alan Burnham for useful discussions. The work was perForme
Masayuki Matsuo - One of the best experts on this subject based on the ideXlab platform.
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adiabatic selfconsistent collective coordinate method for large amplitude collective motion in nuclei with pairing correlations
Progress of Theoretical Physics, 2000Co-Authors: Masayuki Matsuo, Takashi Nakatsukasa, Kenichi MatsuyanagiAbstract:An adiabatic approximation to the selfconsistent collective coordinate method is Formulated in order to describe large amplitude collective motions in nuclei with pairing correlations on the basis of the time-dependent Hartree-Fock-Bogoliubov equations of motion. The basic equations are presented in a local Harmonic Form which can be solved in a manner similar to that of the quasiparticle RPA equations. The Formalism guarantees the conservation of nucleon number expectation values. An extension to the multi-dimensional case is also discussed.
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adiabatic selfconsistent collective coordinate method for large amplitude collective motion in superconducting nuclei
arXiv: Nuclear Theory, 2000Co-Authors: Masayuki Matsuo, Takashi Nakatsukasa, Kenichi MatsuyanagiAbstract:An adiabatic approximation to the selfconsistent collective coordinate method is Formulated in order to describe large amplitude collective motions in superconducting nuclei on the basis of the time-dependent Hartree-Fock-Bogoliubov equations of motion. The basic equations are presented in a local Harmonic Form which can be solved in a similar way as the quasiparticle RPA equations. The Formalism guarantees the conservation of nucleon number expectation values. An extension to the multi-dimensional case is also discussed.
Torre R. - One of the best experts on this subject based on the ideXlab platform.
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Analytical and semi-analytical 3D shell models for composite structures
Instituto Superior Técnico Lisbon Portugal, 2019Co-Authors: Torre R., Brischetto S., Tornabene F.Abstract:This paper focuses on the mechanical analysis of multi-layered composite and sandwich plates and shells when subjected to several static loads. Two different 3D models are compared in order to show the advantages of both the methods and their respective limits. Both the 3D models consider the same mixed curvilinear and orthogonal coordinate system and the same 3D equilibrium equations written for spherical shells. The use of this coordinate system allows the equations to be reduced to those for plates and cylindrical shells with the advantage of a unique and comprehensive Formulation, which automatically adapts to the considered geometry. Plates and shells are considered as simply supported imposing a Harmonic Form for the displacements, the stresses and the loads. This feature allows the 3D equilibrium equations to be analytically solved in the in-plane directions positioned in the mean reference surface and to be converted into partial differential equations in the thickness direction z. The system of partial differential equations is, then, analytically solved in the thickness direction by the first model, defined as 3D EM, which employs the Exponential Matrix (EM) technique. The computational cost is significantly reduced by means of the second model, referred to as 3D GDQ, which uses the Generalized Differential Quadrature (GDQ) method in place of the Exponential Matrix method. A layerwise approach is employed by both the models: the system of partial differential equation is solved using an appropriate number of mathematical layers in 3D EM model and the Chebyshev-Gauss-Lobatto grid distribution in 3D GDQ model. The considered geometries can be loaded on the top and bottom surfaces in different directions. A transverse normal load or transverse shear loads can be applied on the top and/or bottom external surfaces. All the proposed benchmarks show that the analytical model (3D EM) and the semi-analytical one (3D GDQ) are in agreement, with coinciding results for different material and lamination schemes, geometries and dimensions, thickness ratios and loads. The approximation introduced by the use of the GDQ method does not give any noticeable effect on the accuracy of the results when the points are distributed across the domain using a stable and accurate grid. The results will be proposed in terms of displacement, strain and stress amplitudes through the thickness direction. Both the models are able to show the typical zigzag Form of displacements in multi-layered anisotropic structures. The equilibrium and compatibility conditions are also satisfied when transverse shear/normal stresses and displacements are continuous at each layer interface, respectively. Furthermore, transverse normal and transverse shear stresses exactly satisfy the boundary loading conditions on top and bottom external surfaces
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Cylindrical bending in composite structures by means of analytical and numerical 2D/3D shell models
A.J.M Ferreira H. Hu (Editors), 2019Co-Authors: Torre R., Brischetto S., Tornabene F.Abstract:A comparison between a 3D exact shell solution and 2D numerical approaches is proposed in the present paper with a specific focus on the free vibrations of multi-layered composite plates and shells. The validation of new plate and shell structural models is often carried out imposing the cylindrical bending conditions. The reference 3D model here employed is developed using an orthogonal and mixed curvilinear coordinate system. The equilibrium equations are proposed for spherical shells, and they can easily degenerate in those for cylindrical shells, cylinders and plates. In the free vibration analysis, the analytical solution of the system can be obtained using a Harmonic Form for the displacements by imposing arbitrary half-wave numbers in both the in-plane directions. This Harmonic Formulation automatically leads to simply supported boundary conditions. The cylindrical bending can be easily studied imposing that one of the two half-wave numbers is equal zero. The numerical solutions of the problem are obtained using different 2D models. A classical 2D Finite Element (FE) model and a 2D Generalized Differential Quadrature (GDQ) method are compared with the 3D analytical reference solution. The 2D FE model uses a refined mesh based on Quad8 elements in the framework of a commercial finite element code. The 2D GDQ model solves the problem using a non-uniForm Chebyshev-Gauss-Lobatto grid and they are based on refined 2D kinematic assumptions. The proposed benchmarks show that both the 2D numerical models (FE and GDQ ones) are able to provide almost all the natural frequencies of the investigated shells with a significant precision. The 3D model obtains all the vibration modes with a single run where all the edges are simply supported. However, both the 2D models can miss some modes when the simply supported boundary conditions are applied to all the edges in a no coherent way. Some of these modes are cylindrical bending modes and they can be recovered by opportunely modifying the boundary conditions in 2D numerical models. In the case of plates and cylinders, all the missing frequencies can be obtained imposing the simply supported conditions only for the edges parallel to the direction with zero half-wave number and using the free boundary conditions for the other two parallel sides. When a cylindrical shell panel is considered, the modes with zero half-wave number in the curvilinear direction cannot be obtained because the cylindrical bending conditions cannot be imposed. In the case of cylindrical bending modes, it has been observed that the 2D numerical solutions converge to the 3D exact model when the length of the simply supported sides increases in order to reduce the boundary effects corresponding to the free edges
