Closure to “Two-Dimensional Solution for Straight and Meandering Overbank Flows” by D. Alan Ervine, K. Babaeyan- Koopaei, and Robert H. J. Sellin

2002 ◽  
Vol 128 (5) ◽  
pp. 551-552 ◽  
Author(s):  
D. Alan Ervine ◽  
K. Babaeyan-Koopaei ◽  
Robert H. J. Sellin
Keyword(s):  
Two Dimensional ◽  
Dimensional Solution ◽  
Overbank Flows

Two-Dimensional Solution for Straight and Meandering Overbank Flows

2000 ◽  
Vol 126 (9) ◽  
pp. 653-669 ◽  
Author(s):  
D. Alan Ervine ◽  
K. Babaeyan-Koopaei ◽  
Robert H. J. Sellin
Keyword(s):  
Two Dimensional ◽  
Dimensional Solution ◽  
Overbank Flows

Diffraction by a half plane perpendicular to the distinguished axis of a gyrotropic medium (oblique incidence)

1981 ◽  
Vol 59 (3) ◽  
pp. 403-424 ◽  
Author(s):  
S. Przeździecki ◽  
R. A. Hurd
Keyword(s):  
Half Plane ◽  
Fourier Transforms ◽  
Boundary Value ◽  
Diffraction Problem ◽  
Closed Form Solution ◽  
Second Order ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Electromagnetic Plane Wave

An exact, closed form solution is found for the following half plane diffraction problem. (I) The medium surrounding the half plane is gyrotropic. (II) The scattering half plane is perfectly conducting and oriented perpendicular to the distinguished axis of the medium. (III) The direction of propagation of the incident electromagnetic plane wave is arbitrary (skew) with respect to the edge of the half plane. The result presented is a generalization of a solution for the same problem with incidence normal to the edge of the half plane (two-dimensional case).The fundamental, distinctive feature of the problem is that it constitutes a boundary value problem for a system of two coupled second order partial differential equations. All previously solved electromagnetic diffraction problems reduced to boundary value problems for either one or two uncoupled second order equations. (Exception: the two-dimensional case of the present problem.) The problem is formulated in terms of the (generalized) scalar Hertz potentials and leads to a set of two coupled Wiener–Hopf equations. This set, previously thought insoluble by quadratures, yields to the Wiener–Hopf–Hilbert method.The three-dimensional solution is synthesized from appropriate solutions to two-dimensional problems. Peculiar waves of ghost potentials, which correspond to zero electromagnetic fields play an essential role in this synthesis. The problem is two-moded: that is, superpositions of both ordinary and extraordinary waves are necessary for the spectral representation of the solution. An important simplifying feature of the problem is that the coupling of the modes is purely due to edge diffraction, there being no reflection coupling. The solution is simple in that the Fourier transforms of the potentials are just algebraic functions. Basic properties of the solution are briefly discussed.

The adsorption of lower trialkylphosphates at the dodecane – water interface

1980 ◽  
Vol 58 (24) ◽  
pp. 2789-2795 ◽  
Author(s):  
Norman H. Sagert ◽  
Woon Lee
Keyword(s):  
Equation Of State ◽  
Chain Length ◽  
Water Interface ◽  
Two Dimensional ◽  
Free Energies ◽  
Dimensional Solution ◽  
Interfacial Tensions ◽  
Enthalpy Of Adsorption ◽  
Solution Models ◽  
Methylene Group

The adsorption of tripropylphosphate, triethylphosphate, and trimethylphosphate at the dodecane–water interface has been studied at temperatures from 293 to 313 K. Standard free energies of adsorption were obtained from the lowering of interfacial tensions in the low (< 10−4) solute mole fraction region. Standard enthalpies and entropies of adsorption were then obtained from the temperature variation of the standard free energies of adsorption.Standard free energies of adsorption from dodecane showed little variation with solute chain length, with the exception of trimethylphosphate. On the other hand, free energies of adsorption from water decreased by 3.45 kJ/mol for each methylene group added, again with the exception of trimethylphosphate. Enthalpies of adsorption increased linearly with increasing solute chain length for adsorption from either phase. For each methylene group added, the enthalpy of adsorption from dodecane increased by 2.9 kJ/mol, while that from water increased by 2.4 kJ/mol.Results for tripropylphosphate adsorption and for triethylphosphate adsorption at higher temperatures could be adequately described by the Schofield–Rideal equation of state, but not by simple two-dimensional solution models. Results for trimethylphosphate adsorption and for triethylphosphate adsorption at lower temperatures could not be fitted adequately by either type of equation of state.

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.

Analysis of Conduction-Controlled Rewetting of a Vertical Surface

1975 ◽  
Vol 97 (2) ◽  
pp. 161-165 ◽  
Author(s):  
C. L. Tien ◽  
L. S. Yao
Keyword(s):  
Initial Temperature ◽  
Empirical Relation ◽  
Vertical Surface ◽  
Dimensionless Temperature ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Functional Relationships ◽  
Semi Empirical ◽  
Biot Numbers

The present paper presents a two-dimensional analysis of conduction-controlled rewetting of a vertical surface, whose initial temperature is greater than the rewetting temperature. The physical model consists of an infinitely extended vertical slab with the surface of the dry region adiabatic and the surface of the wet region associated with a constant heat transfer coefficient. The physical problem is characterized by three parameters: the Peclet number or the dimensionless wetting velocity, the Biot number, and a dimensionless temperature. Limiting solutions for large and small Peclet numbers obtained by utilizing the Wiener-Hopf technique and the kernel-substitution method exhibit simple functional relationships among the three dimensionless parameters. A semi- empirical relation has been established for the whole range of Peclet numbers. The solution for large Peclet numbers possesses a functional form different from existing approximate two-dimensional solutions, while the solution for small Peclet numbers reduces to existing one-dimensional solution for small Biot numbers. Discussion of the present findings has been made with respect to previous analyses and experimental observations.

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