On the Wall Shear Stress Gradient in Fluid Dynamics

2015 ◽  
Vol 17 (3) ◽  
pp. 808-821 ◽  
Author(s):  
C. Cherubini ◽  
S. Filippi ◽  
A. Gizzi ◽  
M. G. C. Nestola
Keyword(s):  
Applied Sciences ◽  
Fluid Dynamics ◽  
Stress Gradient ◽  
Three Dimensional ◽  
Slow Motion ◽  
Directional Derivatives ◽  
Curved Surfaces ◽  
Curved Boundaries ◽  
Wall Shear Stress Gradient ◽  
Derivatives Of

AbstractThe gradient of the fluid stresses exerted on curved boundaries, conventionally computed in terms of directional derivatives of a tensor, is here analyzed by using the notion of intrinsic derivative which represents the geometrically appropriate tool for measuring tensor variations projected on curved surfaces. Relevant differences in the two approaches are found by using the classical Stokes analytical solution for the slow motion of a fluid over a fixed sphere and a numerically generated three dimensional dynamical scenario. Implications for theoretical fluid dynamics and for applied sciences are finally discussed.

Piezoelectric effect on the velocities of waves in an anisotropic piezo-poroelastic medium

2010 ◽  
Vol 466 (2119) ◽  
pp. 1977-1992 ◽  
Author(s):  
M. D. Sharma
Keyword(s):  
Phase Velocity ◽  
Velocity Vector ◽  
Plane Waves ◽  
Three Dimensional ◽  
Directional Derivatives ◽  
Poroelastic Medium ◽  
Arbitrary Phase ◽  
Phase Direction ◽  
Arbitrary Anisotropy ◽  
Derivatives Of

A mathematical model for mechanical and electrical dynamics in an anisotropic piezo-poroelastic (hereafter referred to as APP) medium is solved for three-dimensional propagation of harmonic plane waves. A system of modified Christoffel equations is derived to explain the existence and propagation of four waves in the medium of arbitrary anisotropy. This system is solved to calculate the phase velocities of four waves in an unbounded APP medium. Directional derivatives of phase velocity are derived analytically and are used to calculate the components of the ray velocity vector. A hypothetical numerical model is considered to compute the phase velocity for given (arbitrary) phase direction and then the ray velocity vector. Surfaces are plotted for the phase velocity and ray velocity of each wave in a saturated poroelastic medium in the absence/presence of piezoelectricity. The contributions of the piezoelectric activeness of the solid frame and pore-fluid to the phase and ray velocities are identified and analysed for each of the four waves in the medium.

Hemodynamic Simulations and Computer-Aided Designs of Graft-Artery Junctions

1997 ◽  
Vol 119 (3) ◽  
pp. 343-348 ◽  
Author(s):  
M. Lei ◽  
C. Kleinstreuer ◽  
J. P. Archie
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Vector Fields ◽  
Artery Bypass ◽  
Stress Gradient ◽  
Three Dimensional ◽  
Wall Shear Stress Gradient ◽  
Early Graft ◽  
Wall Shear ◽  
Hemodynamic Simulations

Severe occlusion of graft–artery junctions due to restenosis, e.g., excessive tissue overgrowth and renewed plaque formation, may occur within a few months or years after bypass surgery. Our hypothesis is that nonuniform hemodynamics, represented by large sustained wall shear stress gradients, trigger abnormal biological processes leading to rapid restenosis and hence early graft failure. In turn, this problem may be significantly mitigated by designing graft-artery bypass configurations for which the wall shear stress gradient (WSSG) is approximately zero and hence nearly uniform hemodynamics are achieved. Focusing on the distal end of several femoral artery bypass junctions, a validated finite volume code has been used to compute the transient three-dimensional velocity vector fields and its first and second surface derivatives in order to test the idea. Specifically, it is shown that the Taylor patch, which generates higher patency rates than standard end-to-side anastomoses, exhibits lower WSSG levels than standard configurations, and that further geometric design improvements reduce the WSSG in magnitude and local extent even more.

A Class of Novel Tetrahedron Elements with Curved Surfaces for Three-Dimensional Solid Mechanics Problems with Curved Boundaries

2019 ◽  
Vol 17 (04) ◽  
pp. 1950006
Author(s):  
C. Q. Wang ◽  
J. H. Yue ◽  
Ming Li
Keyword(s):  
Finite Element ◽  
Solid Mechanics ◽  
Three Dimensional ◽  
Curved Surfaces ◽  
Curved Boundaries ◽  
Hybrid Mesh ◽  
Curved Boundary ◽  
Flat Surfaces ◽  
Tetrahedral Elements ◽  
Hybrid Meshes

Linear tetrahedral elements with four nodes (Te4) are currently the simplest and most widely used ones in the finite element (FE) developed for solving three-dimensional (3D) mechanics problems. However, the standard Te4 element cannot be used to simulate accurately the 3D problems with curved boundaries because of the flat surfaces. In this paper, we develop a set of new elements having curved surfaces to properly simulate the curved boundaries. At the same time, additional nodes are put on the curved boundaries to improve the accuracy of the approximation. These novel elements are defined as five-noded, six-noded, and seven-noded tetrahedron elements (Te5, Te6, and Te7) according to the number of the nodes in one element. Based on the Te4 FE mesh, a hybrid mesh can be conveniently built for 3D problems with curved boundaries, in which the standard Te4 elements are used for the interior elements, and Te5, Te6, and Te7 elements are used for the curved boundary elements. Compared with the standard FEM using Te4 elements, our hybrid mesh can significantly improve the accuracy of the solutions at the curved boundaries. Several solid mechanics problems are studied using the hybrid meshes to validate the effectiveness of the present new elements.

Selectivity for three-dimensional contours and surfaces in the anterior intraparietal area

2012 ◽  
Vol 107 (3) ◽  
pp. 995-1008 ◽  
Author(s):  
Tom Theys ◽  
Siddharth Srivastava ◽  
Johannes van Loon ◽  
Jan Goffin ◽  
Peter Janssen
Keyword(s):  
Depth Profile ◽  
Three Dimensional ◽  
Vertical Axis ◽  
Visual Presentation ◽  
Neural Representation ◽  
Curved Surfaces ◽  
Visually Guided ◽  
Curved Boundaries ◽  
Object Depth ◽  
Neural Selectivity

The macaque anterior intraparietal area (AIP) is crucial for visually guided grasping. AIP neurons respond during the visual presentation of real-world objects and encode the depth profile of disparity-defined curved surfaces. We investigated the neural representation of curved surfaces in AIP using a stimulus-reduction approach. The stimuli consisted of three-dimensional (3-D) shapes curved along the horizontal axis, the vertical axis, or both the horizontal and the vertical axes of the shape. The depth profile was defined solely by binocular disparity that varied along either the boundary or the surface of the shape or along both the boundary and the surface of the shape. The majority of AIP neurons were selective for curved boundaries along the horizontal or the vertical axis, and neural selectivity emerged at short latencies. Stimuli in which disparity varied only along the surface of the shape (with zero disparity on the boundaries) evoked selectivity in a smaller proportion of AIP neurons and at considerably longer latencies. AIP neurons were not selective for 3-D surfaces composed of anticorrelated disparities. Thus the neural selectivity for object depth profile in AIP is present when only the boundary is curved in depth, but not for disparity in anticorrelated stereograms.

ANALYSIS OF THE GENERAL EQUATIONS OF THE TRANSVERSE VIBRATION OF A PIECEWISE UNIFORM VISCOELASTIC PLATE

2020 ◽  
Vol 7 (3) ◽  
pp. 52-56
Author(s):  
MMATMATISA JALILOV ◽  
◽  
RUSTAM RAKHIMOV ◽  
Keyword(s):  
Cross Section ◽  
Transverse Vibration ◽  
Three Dimensional ◽  
Viscoelastic Plate ◽  
Constant Thickness ◽  
Regional Problem ◽  
Rigid Contact ◽  
Under Construction ◽  
Derivatives Of ◽  
Theoretical Results

This article discusses the analysis of the general equations of the transverse vibration of a piecewise homogeneous viscoelastic plate obtained in the “Oscillation of inlayer plates of constant thickness” [1]. In the present work on the basis of a mathematical method, the approached theory of fluctuation of the two-layer plates, based on plate consideration as three dimensional body, on exact statement of a three dimensional mathematical regional problem of fluctuation is stood at the external efforts causing cross-section fluctuations. The general equations of fluctuations of piecewise homogeneous viscoelastic plates of the constant thickness, described in work [1], are difficult on structure and contain derivatives of any order on coordinates x, y and time t and consequently are not suitable for the decision of applied problems and carrying out of engineering calculations. For the decision of applied problems instead of the general equations it is expedient to use confidants who include this or that final order on derivatives. The classical equations of cross-section fluctuation of a plate contain derivatives not above 4th order, and for piecewise homogeneous or two-layer plates the elementary approached equation of fluctuation is the equation of the sixth order. On the basis of the analytical decision of a problem the general and approached decisions of a problem are under construction, are deduced the equation of fluctuation of piecewise homogeneous two-layer plates taking into account rigid contact on border between layers, and also taking into account mechanical and rheological properties of a material of a plate. The received theoretical results for the decision of dynamic problems of cross-section fluctuation of piecewise homogeneous two-layer plates of a constant thickness taking into account viscous properties of their material allow to count more precisely the is intense-deformed status of plates at non-stationary external loadings.

scholarly journals Stretchable micro-scale concentrator photovoltaic module with 15.4% efficiency for three-dimensional curved surfaces

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Daisuke Sato ◽  
Taizo Masuda ◽  
Kenji Araki ◽  
Masafumi Yamaguchi ◽  
Kenichi Okumura ◽  
...  
Keyword(s):  
Concentration Ratio ◽  
Power Conversion ◽  
Three Dimensional ◽  
Thin Film Solar Cells ◽  
Photovoltaic Module ◽  
Silicon Compound ◽  
Curved Surfaces ◽  
Power Sources ◽  
Micro Scale ◽  
Module Design

AbstractStretchable photovoltaics are emerging power sources for collapsible electronics, biomedical devices, and buildings and vehicles with curved surfaces. Development of stretchable photovoltaics are crucial to achieve rapid growth of the future photovoltaic market. However, owing to their rigidity, existing thin-film solar cells based predominantly on silicon, compound semiconductors, and perovskites are difficult to apply to 3D curved surfaces, which are potential real-world candidates. Herein, we present a stretchable micro-scale concentrator photovoltaic module with a geometrical concentration ratio of 3.5×. When perfectly fitted on a 3D curved surface with a sharp curvature, the prototype module achieves an outdoor power conversion efficiency of 15.4% and the daily generated electricity yield improves to a maximum of 190% relative to a non-concentration stretchable photovoltaic module. Thus, this module design enables high areal coverage on 3D curved surfaces, while generating a higher electricity yield in a limited installation area.

Numerical study of multi-dimensional hyperbolic telegraph equations arising in nuclear material science via an efficient local meshless method

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Imtiaz Ahmad ◽  
Aly R. Seadawy ◽  
Hijaz Ahmad ◽  
Phatiphat Thounthong ◽  
Fuzhang Wang
Keyword(s):  
Meshless Method ◽  
Material Science ◽  
Numerical Study ◽  
Research Work ◽  
Time Integration ◽  
Three Dimensional ◽  
Nuclear Material ◽  
Telegraph Equations ◽  
Model Equations ◽  
Derivatives Of

Abstract This research work is to study the numerical solution of three-dimensional second-order hyperbolic telegraph equations using an efficient local meshless method based on radial basis function (RBF). The model equations are used in nuclear material science and in the modeling of vibrations of structures. The explicit time integration technique is utilized to semi-discretize the model in the time direction whereas the space derivatives of the model are discretized by the proposed local meshless procedure based on multiquadric RBF. Numerical experiments are performed with the proposed numerical scheme for rectangular and non-rectangular computational domains. The proposed method solutions are converging quickly in comparison with the different existing numerical methods in the recent literature.

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