scholarly journals Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub- and super-geometric analysis to Geometry-Independent Field approximaTion (GIFT)

2018 ◽  
Vol 114 (10) ◽  
pp. 1131-1159 ◽  
Author(s):  
Elena Atroshchenko ◽  
Satyendra Tomar ◽  
Gang Xu ◽  
Stéphane P.A. Bordas
Keyword(s):  
Isogeometric Analysis ◽  
Geometric Analysis ◽  
Field Approximation ◽  
Tight Coupling ◽  
Independent Field

scholarly journals Discrete Normal Vector Field Approximation via Time Scale Calculus

2020 ◽  
Vol 5 (1) ◽  
pp. 349-360
Author(s):  
Ömer Akgandüller ◽  
Sibel Paşalı Atmaca
Keyword(s):  
Time Scales ◽  
Vector Fields ◽  
Geometric Analysis ◽  
Field Approximation ◽  
Normal Vector ◽  
Normal Vector Field ◽  
Time Scale Calculus ◽  
Vertex Set ◽  
Rectangular Grids ◽  
Mimetic Discretization

AbstractThe theory of time scales calculus have long been a subject to many researchers from different disciplines. Beside the unification and the extension aspects of the theory, it emerge as a powerful tool for mimetic discretization process. In this study, we present a framework to find normal vector fields of discrete point sets in ℝ3 by using symmetric differential on time scales. A surface parameterized by the tensor product of two time scales can be analogously expressed as the vertex set of non-regular rectangular grids. If the time scales are dense, then the discrete grid structure vanishes. If the time scales are isolated, then the further geometric analysis can be executed by using symmetric dynamic differential. Moreover, we present an algorithmic procedure to determine the symmetric dynamic differential structure on the neighborhood of points in surfaces. Our results indicate that the method we present has good approximation to unit normal vector fields of parameterized surfaces rather than the Delaunay triangulation for some points.

scholarly journals Fast isogeometric boundary element method based on independent field approximation

2015 ◽  
Vol 284 ◽  
pp. 458-488 ◽  
Author(s):  
Benjamin Marussig ◽  
Jürgen Zechner ◽  
Gernot Beer ◽  
Thomas-Peter Fries
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Field Approximation ◽  
Independent Field ◽  
Element Method

Liquid crystalline ordering of paired helical filaments in neurofibrillary tangles of Alzheimer's disease

1986 ◽  
Vol 44 ◽  
pp. 348-349
Author(s):  
D.F. Clapin ◽  
V.J.A. Montpetit
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Neurofibrillary Tangles ◽  
Liquid Crystalline ◽  
Amyloid Fibrils ◽  
Geometric Analysis ◽  
Paired Helical Filaments ◽  
Microscopic Level ◽  
Light Microscopic Level ◽  
Regular Spacing

Alzheimer's disease is characterized by the accumulation of abnormal filamentous proteins. The most important of these are amyloid fibrils and paired helical filaments (PHF). PHF are located intraneuronally forming bundles called neurofibrillary tangles. The designation of these structures as "tangles" is appropriate at the light microscopic level. However, localized domains within individual tangles appear to demonstrate a regular spacing which may indicate a liquid crystalline phase. The purpose of this paper is to present a statistical geometric analysis of PHF packing.

Geometric analysis

1976 ◽  
Vol 55 (2) ◽  
pp. 67
Author(s):  
C.A. Gladman ◽  
R.A. Williams
Keyword(s):  
Geometric Analysis

Analysis of shear bands in slow granular flows using a frictional Cosserat model

2000 ◽  
Vol 627 ◽  
Author(s):  
Prabhu R. Nott ◽  
K. Kesava Rao ◽  
L. Srinivasa Mohan
Keyword(s):  
Scaling Laws ◽  
Shear Bands ◽  
Shear Layers ◽  
Theoretical Description ◽  
Field Variable ◽  
Cosserat Continuum ◽  
Momentum Balance ◽  
Rigid Plastic ◽  
Independent Field ◽  
Cosserat Model

ABSTRACTThe slow flow of granular materials is often marked by the existence of narrow shear layers, adjacent to large regions that suffer little or no deformation. This behaviour, in the regime where shear stress is generated primarily by the frictional interactions between grains, has so far eluded theoretical description. In this paper, we present a rigid-plastic frictional Cosserat model that captures thin shear layers by incorporating a microscopic length scale. We treat the granular medium as a Cosserat continuum, which allows the existence of localised couple stresses and, therefore, the possibility of an asymmetric stress tensor. In addition, the local rotation is an independent field variable and is not necessarily equal to the vorticity. The angular momentum balance, which is implicitly satisfied for a classical continuum, must now be solved in conjunction with the linear momentum balances. We extend the critical state model, used in soil plasticity, for a Cosserat continuum and obtain predictions for flow in plane and cylindrical Couette devices. The velocity profile predicted by our model is in qualitative agreement with available experimental data. In addition, our model can predict scaling laws for the shear layer thickness as a function of the Couette gap, which must be verified in future experiments. Most significantly, our model can determine the velocity field in viscometric flows, which classical plasticity-based model cannot.

The Determination of the Magnetoelectric Coupling Coefficient in Ferroelectric–Ferromagnetic Composite Based on PZT–Ferrite

2013 ◽  
Vol 58 (4) ◽  
pp. 1401-1403 ◽  
Author(s):  
J.A. Bartkowska ◽  
R. Zachariasz ◽  
D. Bochenek ◽  
J. Ilczuk
Keyword(s):  
Dielectric Permittivity ◽  
Coupling Coefficient ◽  
Mean Field ◽  
Field Approximation ◽  
Theoretical Description ◽  
Magnetoelectric Coupling ◽  
Mean Field Approximation ◽  
Dielectric Measurements ◽  
Temperature Dependences ◽  
Multiferroic Composite

Abstract In the present work, the magnetoelectric coupling coefficient, from the temperature dependences of the dielectric permittivity for the multiferroic composite was determined. The research material was ferroelectric-ferromagnetic composite on the based PZT and ferrite. We investigated the temperature dependences of the dielectric permittivity (") for the different frequency of measurement’s field. From the dielectric measurements we determined the temperature of phase transition from ferroelectric to paraelectric phase. For the theoretical description of the temperature dependence of the dielectric constant, the Hamiltonian of Alcantara, Gehring and Janssen was used. To investigate the dielectric properties of the multiferroic composite this Hamiltonian was expressed under the mean-field approximation. Based on dielectric measurements and theoretical considerations, the values of the magnetoelectric coupling coefficient were specified.

Magnetic Field Approximation in MR Tomography

PIERS Online ◽  
2007 ◽  
Vol 3 (8) ◽  
pp. 1250-1253
Author(s):  
Michal Hadinec ◽  
Pavel Fiala ◽  
Eva Kroutilova ◽  
M. Steinbauer ◽  
Karel Bartusek
Keyword(s):  
Magnetic Field ◽  
Field Approximation ◽  
Mr Tomography
Sign in / Sign up

Export Citation Format

Share Document