scholarly journals KOITER ESTIMATE REVISITED

2010 ◽  
Vol 20 (01) ◽  
pp. 1-42 ◽  
Author(s):  
MONIQUE DAUGE ◽  
ERWAN FAOU
Keyword(s):  
Energy Estimate ◽  
Three Dimensional ◽  
Two Dimensional ◽  
A Posteriori ◽  
Modeling Error ◽  
Dimensional Solution ◽  
Manifold With Boundary ◽  
Thickness Parameter ◽  
Posteriori Estimation ◽  
Heuristic Estimate

We prove a general adimensional energy estimate between the solution of the three-dimensional Lamé system on a thin clamped shell and a displacement reconstructed from the solution of the classical two-dimensional Koiter model. This estimate only involves the thickness parameter ε, constants attached to the mid-surface S, the two-dimensional energy of the solution of the Koiter model and "wavelengths" associated with this latter solution. This bound is in the same spirit as Koiter's heuristic estimate in Ref. 26 and can be viewed as an a posteriori estimation of the modeling error by means of the two-dimensional solution. It is general with respect to the geometry of the mid-surface S which is an arbitrary smooth manifold with boundary. Taking boundary layer terms into account, we prove that our estimates are sharp in the cases of plates and elliptic shells.

Three-Dimensional Axisymmetric Piezothermoelastic Solution of a Transversely Isotropic Piezoelectric Clamped Circular Plate

1998 ◽  
Vol 65 (1) ◽  
pp. 178-183 ◽  
Author(s):  
S. Kapuria ◽  
P. C. Dumir ◽  
S. Segupta
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Dimensional Solution ◽  
Infinite Systems ◽  
Finite Set ◽  
Thickness Parameter

Three-dimensional solution in terms of potential functions is presented for a transversely isotropic piezoelectric clamped circular plate subjected to axisymmetric ther-moelectromechanical load. The boundary conditions are satisfied using Fourier-Bessel expansions yielding two uncoupled infinite systems of algebraic equations for the arbitrary constants. These are solved to any desired degree of accuracy by truncating to finite set of equations. Results are presented to illustrate the effect of the thickness parameter. These would help assess two-dimensional theories of piezoelectric plates.

scholarly journals Visualization of CD2 interaction with LFA-3 and determination of the two-dimensional dissociation constant for adhesion receptors in a contact area.

1996 ◽  
Vol 132 (3) ◽  
pp. 465-474 ◽  
Author(s):  
M L Dustin ◽  
L M Ferguson ◽  
P Y Chan ◽  
T A Springer ◽  
D E Golan
Keyword(s):  
Contact Area ◽  
Dissociation Constants ◽  
Three Dimensional ◽  
Lateral Diffusion ◽  
Solution Phase ◽  
Phospholipid Bilayer ◽  
Cell Contact ◽  
Two Dimensional ◽  
Adhesion Receptors ◽  
Dimensional Solution

Many adhesion receptors have high three-dimensional dissociation constants (Kd) for counter-receptors compared to the KdS of receptors for soluble extracellular ligands such as cytokines and hormones. Interaction of the T lymphocyte adhesion receptor CD2 with its counter-receptor, LFA-3, has a high solution-phase Kd (16 microM at 37 degrees C), yet the CD2/LFA-3 interaction serves as an effective adhesion mechanism. We have studied the interaction of CD2 with LFA-3 in the contact area between Jurkat T lymphoblasts and planar phospholipid bilayers containing purified, fluorescently labeled LFA-3. Redistribution and lateral mobility of LFA-3 were measured in contact areas as functions of the initial LFA-3 surface density and of time after contact of the cells with the bilayers. LFA-3 accumulated at sites of contact with a half-time of approximately 15 min, consistent with the previously determined kinetics of adhesion strengthening. The two-dimensional Kd for the CD2/LFA-3 interaction was 21 molecules/microns 2, which is lower than the surface densities of CD2 on T cells and LFA-3 on most target or stimulator cells. Thus, formation of CD2/LFA-3 complexes should be highly favored in physiological interactions. Comparison of the two-dimensional (membrane-bound) and three-dimensional (solution-phase) KdS suggest that cell-cell contact favors CD2/LFA-3 interaction to a greater extent than that predicted by the three-dimensional Kd and the intermembrane distance at the site of contact. LFA-3 molecules in the contact site were capable of lateral diffusion in the plane of the phospholipid bilayer and did not appear to be irreversibly trapped in the contact area, consistent with a rapid off-rate. These data provide insights into the function of low affinity interactions in adhesion.

HIERARCHIC MODELS OF HELMHOLTZ PROBLEMS ON THIN DOMAINS

1998 ◽  
Vol 08 (01) ◽  
pp. 1-35 ◽  
Author(s):  
KLAUS GERDES ◽  
CHRISTOPH SCHWAB
Keyword(s):  
Three Dimensional ◽  
Posteriori Error ◽  
A Posteriori ◽  
Thin Domains ◽  
Modeling Error ◽  
Pollution Effects ◽  
A Posteriori Error ◽  
Error Estimators ◽  
Weighted Norms ◽  
Posteriori Error Estimators

The Helmholtz equation in a three-dimensional plate is approximated by a hierarchy of two-dimensional models. Computable a posteriori error estimators of the modeling error in exponentially weighted norms are derived, and sharp, computable estimates for their effectivity indices are also obtained. The necessity of including, besides polynomials, a certain number of trigonometric director functions into the Ansatz, in order to prevent pollution effects at high wave numbers is demonstrated both theoretically and computationally.

A Model for Heat Transfer From Embedded Blood Vessels in Two-Dimensional Tissue Preparations

1995 ◽  
Vol 117 (1) ◽  
pp. 64-73 ◽  
Author(s):  
Liang Zhu ◽  
Sheldon Weinbaum
Keyword(s):  
Heat Transfer ◽  
Blood Vessels ◽  
Three Dimensional ◽  
Tissue Preparation ◽  
Basic Solution ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Tissue Conductivity ◽  
Thermal Equilibration ◽  
Insight Into

Two-dimensional microvascular tissue preparations have been extensively used to study blood flow in the microcirculation, and, most recently, the mechanism of thermal equilibration between thermally significant countercurrent artery-vein pairs. In this paper, an approximate three-dimensional solution for the heat transfer from a periodic array of blood vessels in a tissue preparation of uniform thickness with surface convection is constructed using a newly derived fundamental solution for a Green’s function for this flow geometry. This approximate solution is exact when the ratio K′ of the blood to tissue conductivity is unity and a highly accurate approximation when K′ ≠ 1. This basic solution is applied to develop a model for the heat transfer from a countercurrent artery-vein pair in an exteriorized rat cremaster muscle preparation. The numerical results provide important new insight into the design of microvascular experiments in which the axial variation of the thermal equilibration in microvessels can be measured for the first time. The solutions also provide new insight into the design of fluted fins and microchips that are convectively cooled by internal pores.

scholarly journals Comparison of Two- and Three-Dimensional Flow Computations With Laser Anemometer Measurements in a Transonic Compressor Rotor

1983 ◽  
Vol 105 (3) ◽  
pp. 596-605 ◽  
Author(s):  
R. V. Chima ◽  
A. J. Strazisar
Keyword(s):  
Three Dimensional ◽  
Axial Compressor ◽  
Maximum Flow ◽  
Wave System ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Transonic Compressor ◽  
Function Solution ◽  
Compressor Rotor ◽  
Laser Anemometer

Two-and three-dimensional inviscid solutions for the flow within a transonic axial compressor rotor at design speed are compared to laser anemometer measurements at maximum flow and near stall operating points. Computational details of the two-dimensional axisymmetric stream function solution and the three-dimensional full Euler solution are described. Upstream of the rotor, the two and three-dimensional solutions for radial distribution of relative Mach number and total pressure agree well with the data. Within the bow wave system and the blade row, the axisymmetric two-dimensional solution shows only qualitative agreement with the data.

scholarly journals Comparison of Two and Three Dimensional Flow Computations With Laser Anemometer Measurements in a Transonic Compressor Rotor

1982 ◽  
Author(s):  
R. V. Chima ◽  
A. J. Strazisar
Keyword(s):  
Three Dimensional ◽  
Axial Compressor ◽  
Maximum Flow ◽  
Wave System ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Transonic Compressor ◽  
Function Solution ◽  
Compressor Rotor ◽  
Laser Anemometer

Two and three-dimensional inviscid solutions for the flow within a transonic axial compressor rotor at design speed are compared to laser anemometer measurements at maximum flow and near stall operating points. Computational details of the two-dimensional axisymmetric stream function solution and the three-dimensional full Euler solution are described. Upstream of rotor, the two-dimensional and three-dimensional solutions for radial distribution of relative Mach number and total pressure agree well with the data. Within the bow wave system and the blade row, the axisymmetric two-dimensional solution shows only qualitative agreement with the data.

Three-dimensional flow near a two-dimensional stagnation point

1967 ◽  
Vol 28 (1) ◽  
pp. 149-151 ◽  
Author(s):  
A. Davey ◽  
D. Schofield
Keyword(s):  
Boundary Layer ◽  
Numerical Solution ◽  
Stagnation Point ◽  
Incompressible Flow ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Dimensional Solution ◽  
Boundary Layer Equations ◽  
Viscous Incompressible Flow

This paper shows the existence of a three-dimensional solution of the boundary-layer equations of viscous incompressible flow in the immediate neighbourhood of a two-dimensional stagnation point of attachment. The numerical solution has been obtained.

scholarly journals Maximal heat transfer between two parallel plates

2018 ◽  
Vol 851 ◽  
Author(s):  
Shingo Motoki ◽  
Genta Kawahara ◽  
Masaki Shimizu
Keyword(s):  
Heat Transfer ◽  
Velocity Field ◽  
Large Scale ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Solution Branch ◽  
Search Range ◽  
Dimensional Solution

The divergence-free time-independent velocity field has been determined so as to maximise heat transfer between two parallel plates with a constant temperature difference under the constraint of fixed total enstrophy. The present variational problem is the same as that first formulated by Hassanzadeh et al. (J. Fluid Mech., vol. 751, 2014, pp. 627–662); however, the search range for optimal states has been extended to a three-dimensional velocity field. A scaling of the Nusselt number $Nu$ with the Péclet number $Pe$ (i.e., the square root of the non-dimensionalised enstrophy with thermal diffusion time scale), $Nu\sim Pe^{2/3}$, has been found in the three-dimensional optimal states, corresponding to the asymptotic scaling with the Rayleigh number $Ra$, $Nu\sim Ra^{1/2}$, expected to appear in an ultimate state, and thus to the Taylor energy dissipation law in high-Reynolds-number turbulence. At $Pe\sim 10^{0}$, a two-dimensional array of large-scale convection rolls provides maximal heat transfer. A three-dimensional optimal solution emerges from bifurcation on the two-dimensional solution branch at $Pe\sim 10^{1}$, and the three-dimensional solution branch has been tracked up to $Pe\sim 10^{4}$ (corresponding to $Ra\approx 2.7\times 10^{6}$). At $Pe\gtrsim 10^{3}$, the optimised velocity fields consist of convection cells with hierarchical self-similar vortical structures, and the temperature fields exhibit a logarithmic-like mean profile near the walls.

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