Two-dimensional polyelectrolyte hollow sphere arrays at a liquid–air interface

Soft Matter ◽  
2011 ◽  
Vol 7 (2) ◽  
pp. 359-362 ◽  
Author(s):  
Weixing Song ◽  
Yang Yang ◽  
Helmuth Moehwald ◽  
Junbai Li
Keyword(s):  
Hollow Sphere ◽  
Two Dimensional ◽  
Air Interface

scholarly journals Calculations of the Effective Thermal Conductivity in a Model of Syntactic Metallic Hollow Sphere Structures Using a Lattice Monte Carlo Method

2008 ◽  
Vol 273-276 ◽  
pp. 216-221 ◽  
Author(s):  
Thomas Fiedler ◽  
Andreas Öchsner ◽  
Irina V. Belova ◽  
Graeme E. Murch
Keyword(s):  
Thermal Conductivity ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Effective Thermal Conductivity ◽  
Hollow Sphere ◽  
Cutting Planes ◽  
Two Dimensional ◽  
Adhesively Bonded ◽  
Lattice Monte Carlo ◽  
The Matrix

In this paper, a Lattice Monte Carlo method is used to determine the effective thermal conductivity in two dimensional models of adhesively bonded metallic hollow sphere structures (MHSS). In contrast to earlier approaches, more realistic distributions of spheres without the simplification of cubic symmetric arrangements are considered in this study. For the Monte Carlo analyses, two-dimensional periodic lattices representing different cutting planes through MHSS are generated. Therefore, an algorithm is used which sequentially fills the lattice by adding cut spherical shells and inclusions in the matrix. Another focus of this work is the analysis of the influence of different geometric circle distributions on the effective thermal conductivity. The findings of the random arrangements are also compared to a regular primitive cubic arrangement and with a Maxwell-type approach.

Boundary conditions at a liquid/air interface in lubrication flows

1982 ◽  
Vol 119 ◽  
pp. 107-120 ◽  
Author(s):  
K. J. Ruschak
Keyword(s):  
Finite Element Method ◽  
Boundary Conditions ◽  
Problem Solution ◽  
Lubrication Approximation ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Air Interface ◽  
Outer Expansion ◽  
Two Dimensional Flow ◽  
Representative Problem

A difficulty in applying the lubrication approximation to flows where a liquid/air interface forms lies in supplying boundary conditions at the point of formation of the interface that are consistent with the lubrication approximation. The method of matched asymptotic expansions is applied to the flow between partially submerged, counter-rotating rollers, a representative problem from this class, and the lubrication approximation is found to generate the first term of an outer expansion of the problem solution. The first term of an inner expansion describes the two-dimensional flow in the vicinity of the interface, and approximate results are found by the finite-element method. Matching between the inner and outer solutions determines boundary conditions on the pressure and the pressure gradient at the point of formation of the interface which allow the solution to the outer, lubrication flow to be completed.

Two-dimensional piezothermoelastic analysis of a smart FGM hollow sphere

2015 ◽  
Vol 226 (7) ◽  
pp. 2195-2224 ◽  
Author(s):  
A. R. Barati ◽  
M. Jabbari
Keyword(s):  
Hollow Sphere ◽  
Two Dimensional

Diffusion of electromagnetic fields into a two‐dimensional earth: A finite‐difference approach

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 870-894 ◽  
Author(s):  
M. L. Oristaglio ◽  
G. W. Hohmann
Keyword(s):  
Finite Difference ◽  
Half Space ◽  
Small Time ◽  
Two Dimensional ◽  
Time Step ◽  
Small Peak ◽  
Transient Electromagnetic ◽  
The Earth ◽  
Air Interface ◽  
Equation Boundary

We describe a numerical method for time‐stepping Maxwell’s equations in the two‐dimensional (2-D) TE‐mode, which in a conductive earth reduces to the diffusion equation. The method is based on the classical DuFort‐Frankel finite‐difference scheme, which is both explicit and stable for any size of the time step. With this method, small time steps can be used at early times to track the rapid variations of the field, and large steps can be used at late times, when the field becomes smooth and its rates of diffusion and decay slow down. The boundary condition at the earth‐air interface is handled explicitly by calculating the field in the air from its values at the earth’s surface with an upward continuation based on Laplace’s equation. Boundary conditions in the earth are imposed by using a large, graded grid and setting the values at the sides and bottom to those for a haft‐space. We use the 2-D model to simulate transient electromagnetic (TE) surveys over a thin vertical conductor embedded in a half‐space and in a half‐space with overburden. At early times (microseconds), the patterns of diffusion in the earth are controlled mainly by geometric features of the models and show a great deal of complexity. But at late times, the current concentrates at the center of the thin conductor and, with a large contrast (1000:1) between conductor and half‐space, produces the characteristic crossover and peaked anomalies in the surface profiles of the vertical and horizontal emfs. With a smaller contrast (100:1), however, the crossover in the vertical emf is obscured by the halfspace response, although the horizontal emf still shows a small peak directly above the target.

Stabilization of a Fragile Two-Dimensional Protein Crystal at the Water−Air Interface:  The Square Lattice of Apoferritin

Langmuir ◽  
1996 ◽  
Vol 12 (2) ◽  
pp. 431-435 ◽  
Author(s):  
Tschangiz Scheybani ◽  
Hideyuki Yoshimura ◽  
Wolfgang Baumeister ◽  
Kuniaki Nagayama
Keyword(s):  
Protein Crystal ◽  
Square Lattice ◽  
Two Dimensional ◽  
Air Interface
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