Orientation order parameters and effective conductivity of a 2-D solid with partially disordered array of circular inhomogeneities

2021 ◽  
pp. 108128652110243
Author(s):  
Volodymyr I Kushch ◽  
Igor Sevostianov
Keyword(s):  
Effective Conductivity ◽  
Cell Model ◽  
Structural Parameters ◽  
Quantitative Measure ◽  
Expansion Method ◽  
Multipole Expansion ◽  
Orientation Order ◽  
Multipole Expansion Method ◽  
Representative Unit Cell ◽  
Heterogeneous Solid

The paper focuses on the quantitative characterization of the microstructure of a two-dimensional heterogeneous solid with circular inhomogeneities that may vary from perfectly periodic arrangement to completely random one. This characterization is linked to the calculation of the effective conductivity of the material. The partially disordered system of disks is generated in the framework of the representative unit cell model using Metropolis algorithm. The orientation order metrics are taken as the structural parameters providing a quantitative measure of disorder, and their variation caused by the gradual disordering of the periodic system is assessed. The effective conductivity of the heterogeneous solid with partially disordered microstructure is evaluated by the multipole expansion method. It is shown that effective conductivity cannot be fully characterized by only one orientation order metric, and the required additional ones are identified.

scholarly journals Thermo-Viscoelastic Response of 3D Braided Composites Based on a Novel FsMsFE Method

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 271
Author(s):  
Jun-Jun Zhai ◽  
Xiang-Xia Kong ◽  
Lu-Chen Wang
Keyword(s):  
Finite Element ◽  
Cell Model ◽  
Structural Parameters ◽  
Thermal Relaxation ◽  
Viscoelastic Behavior ◽  
Unit Cell ◽  
Time Dependent ◽  
3D Braided Composites ◽  
Equivalent Time ◽  
Representative Unit Cell

A homogenization-based five-step multi-scale finite element (FsMsFE) simulation framework is developed to describe the time-temperature-dependent viscoelastic behavior of 3D braided four-directional composites. The current analysis was performed via three-scale finite element models, the fiber/matrix (microscopic) representative unit cell (RUC) model, the yarn/matrix (mesoscopic) representative unit cell model, and the macroscopic solid model with homogeneous property. Coupling the time-temperature equivalence principle, multi-phase finite element approach, Laplace transformation and Prony series fitting technology, the character of the stress relaxation behaviors at three scales subject to variation in temperature is investigated, and the equivalent time-dependent thermal expansion coefficients (TTEC), the equivalent time-dependent thermal relaxation modulus (TTRM) under micro-scale and meso-scale were predicted. Furthermore, the impacts of temperature, structural parameters and relaxation time on the time-dependent thermo-viscoelastic properties of 3D braided four-directional composites were studied.

scholarly journals On the Convergence of the Multipole Expansion Method

2021 ◽  
Vol 59 (5) ◽  
pp. 2473-2499
Author(s):  
Brian Fitzpatrick ◽  
Enzo De Sena ◽  
Toon van Waterschoot
Keyword(s):  
Expansion Method ◽  
Multipole Expansion ◽  
Multipole Expansion Method

scholarly journals Bonding modes of some labile Si compounds studied by charge density analysis

2014 ◽  
Vol 70 (a1) ◽  
pp. C1698-C1698
Author(s):  
Daisuke Hashizume
Keyword(s):  
Organic Molecules ◽  
Expansion Method ◽  
Multipole Expansion ◽  
Bond Critical Point ◽  
X Ray Diffraction ◽  
Density Distributions ◽  
Density Maps ◽  
Multipole Expansion Method ◽  
Density Analysis ◽  
Electron Donation

Some organic molecules containing Si atom(s) are very labile, even if the corresponding carbon analogs are very stable. To gain information on bonding modes of such compounds, we analyzed valence density distribution, which play critical roles in chemistry of molecule, by applying multipole expansion method. Very recently, an imine coordinated silacyclopropan-1-one, 1, has synthesized by Baceiredo, Kato and co-workers.[1] To clarify the bonding mode of 1, the electron density distributions of 1 and its precursor have analyzed by a multiple expansion method using single crystal X-ray diffraction data. As shown in static model density maps, bonding electrons of Si-C bonds distribute on the outside of the silacyclopropane ring (Si1-C1-C2 ring) (Fig. 1a) with largely extent, in compared with that of the precursor, indicating an in-plane pi-interaction on the Si1-C1 and Si1-C2 bonds. On the other hand, the C1-C2 bonding electrons distribute on the bond, and the bond critical point (BCP) is located on the inside of the three membered ring. In addition, the C1-C2 bonding electrons elongates inside the ring toward the Si1 atom, indicating electron donation from sigma(C1-C2)-bond to the Si1 (Fig. 1b). Consequently, these maps propose greater contribution of canonical structures in Fig. 1c.

scholarly journals Trapped modes around a row of circular cylinders in a channel

1999 ◽  
Vol 386 ◽  
pp. 259-279 ◽  
Author(s):  
T. UTSUNOMIYA ◽  
R. EATOCK TAYLOR
Keyword(s):  
Expansion Method ◽  
Wave Theory ◽  
Multipole Expansion ◽  
Circular Cylinders ◽  
Large Radius ◽  
Trapped Modes ◽  
Resonant Phenomenon ◽  
Trapped Mode ◽  
Linear Water Wave Theory ◽  
Multipole Expansion Method

Trapped modes around a row of bottom-mounted vertical circular cylinders in a channel are examined. The cylinders are identical, and their axes equally spaced in a plane perpendicular to the channel walls. The analysis has been made by employing the multipole expansion method under the assumption of linear water wave theory. At least the same number of trapped modes is shown to exist as the number of cylinders for both Neumann and Dirichlet trapped modes, with the exception that for cylinders having large radius the mode corresponding to the Dirichlet trapped mode for one cylinder will disappear. Close similarities between the Dirichlet trapped modes around a row of cylinders in a channel and the near-resonant phenomenon in the wave diffraction around a long array of cylinders in the open sea are discussed. An analogy with a mass–spring oscillating system is also presented.

X-ray Scattering Studies of Metalloproteins in Solution: a Quantitative Approach for Studying Molecular Conformations, a Quantitative Approach for Studying Molecular Conformations.

1997 ◽  
Vol 30 (5) ◽  
pp. 770-775 ◽  
Author(s):  
J. Günter Grossmann ◽  
S. S. Hasnain
Keyword(s):  
Conformational Changes ◽  
Structural Information ◽  
Expansion Method ◽  
Multipole Expansion ◽  
Quantitative Approach ◽  
Correct Treatment ◽  
Acta Cryst ◽  
Molecular Conformations ◽  
X Ray ◽  
Multipole Expansion Method

The model-independent approach based on the multipole expansion method using spherical harmonics [Stuhrmann (1970a). Acta Cryst. A26, 297–306] has been applied to obtain structural information on a variety of metalloproteins studied by synchrotron X-ray solution scattering. The method is applied to examples (nitrite reductase, transferrin and nitrogenase), not only with the view of comparing protein conformations in solution with those in the crystalline state, but also defining conformational changes and protein-protein interactions which are of functional importance. The shape restoration is found to be straightforward at low resolution (L≤ 3). For correct treatment using higher harmonics, overall molecular symmetry, if present, must be included in the multipole expansion.

Rapid and accurate calculation of small-angle scattering profiles using the golden ratio

2013 ◽  
Vol 46 (4) ◽  
pp. 1171-1177 ◽  
Author(s):  
Max C. Watson ◽  
Joseph E. Curtis
Keyword(s):  
Small Angle ◽  
Golden Ratio ◽  
Expansion Method ◽  
Multipole Expansion ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Approximation Technique ◽  
Scattering Intensity ◽  
Angle Scattering ◽  
Multipole Expansion Method

Calculating the scattering intensity of anN-atom system is a numerically exhaustingO(N2) task. A simple approximation technique that scales linearly with the number of atoms is presented. Using an exact expression for the scattering intensityI(q) at a given wavevectorq, the rotationally averaged intensityI(q) is computed by evaluatingI(q) in several scattering directions. The orientations of theqvectors are taken from a quasi-uniform spherical grid generated by the golden ratio. Using various biomolecules as examples, this technique is compared with an established multipole expansion method. For a given level of speed, the technique is more accurate than the multipole expansion for anisotropically shaped molecules, while comparable in accuracy for globular shapes. The processing time scales sub-linearly inNwhen the atoms are identical and lie on a lattice. The procedure is easily implemented and should accelerate the analysis of small-angle scattering data.

Sign in / Sign up

Export Citation Format

Share Document