Uniform Asymptotics of Green's Kernels for Mixed and Neumann Problems in Domains with Small Holes and Inclusions

2008 ◽  
pp. 277-316 ◽  
Author(s):  
Vladimir Maz'ya ◽  
Alexander Movchan
Keyword(s):  
Uniform Asymptotics ◽  
Neumann Problems ◽  
Small Holes

Stereo Electron Microscopy Applied to High Resolution Freeze-Etch Replicas

1970 ◽  
Vol 28 ◽  
pp. 306-307
Author(s):  
L. Andrew Staehelin
Keyword(s):  
Electron Microscopy ◽  
Plastic Deformation ◽  
High Resolution ◽  
Smooth Surfaces ◽  
Small Particles ◽  
Membrane Surfaces ◽  
Wide Acceptance ◽  
New Information ◽  
Number Of Particles ◽  
Small Holes

Freeze-etched membranes usually appear as relatively smooth surfaces covered with numerous small particles and a few small holes (Fig. 1). In 1966 Branton (1“) suggested that these surfaces represent split inner mem¬brane faces and not true external membrane surfaces. His theory has now gained wide acceptance partly due to new information obtained from double replicas of freeze-cleaved specimens (2,3) and from freeze-etch experi¬ments with surface labeled membranes (4). While theses studies have fur¬ther substantiated the basic idea of membrane splitting and have shown clearly which membrane faces are complementary to each other, they have left the question open, why the replicated membrane faces usually exhibit con¬siderably fewer holes than particles. According to Branton's theory the number of holes should on the average equal the number of particles. The absence of these holes can be explained in either of two ways: a) it is possible that no holes are formed during the cleaving process e.g. due to plastic deformation (5); b) holes may arise during the cleaving process but remain undetected because of inadequate replication and microscope techniques.

Numerical Analysis of the Age-Sex-Structured Population Dynamics Taking into Account Spatial Diffusion

2005 ◽  
Vol 10 (4) ◽  
pp. 365-381 ◽  
Author(s):  
Š. Repšys ◽  
V. Skakauskas
Keyword(s):  
Population Dynamics ◽  
Numerical Analysis ◽  
Population Model ◽  
Local Stability ◽  
Deterministic Model ◽  
Random Mating ◽  
Spatial Diffusion ◽  
Neumann Problems ◽  
Structured Population ◽  
Structured Population Dynamics

We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability.

scholarly journals Analysis of Multi-Physics Coupling of Small Holes in GH4169 Alloy by Electrolytic Processing of Tube Electrodes

Micromachines ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 828
Author(s):  
Zhaolong Li ◽  
Ye Dai
Keyword(s):  
Oxide Layer ◽  
Small Hole ◽  
Machining Accuracy ◽  
Tool Electrode ◽  
Metallic Oxide ◽  
Power Sources ◽  
Processing Stability ◽  
Hole Structure ◽  
Gh4169 Alloy ◽  
Small Holes

This paper presents a simulation and experimental study of the structure of small holes in GH4169 alloy electrolytic ally processed by tube electrodes with different characteristic power sources. It analyzes the multi-physical field coupling relationship of flow, temperature, and electric fields within the interstitial space. The results indicate that the tube electrode electrolytic processing of the GH4169 alloy small hole structure with a pulsed power supply has more uniform temperature and current density distribution within the gap, which is beneficial to the processing accuracy and smoothness of the small hole structure. Meanwhile, SEM was used to analyze the microscopic morphology of the electrode end surface during short-circuiting, and it was concluded that as the processing continued, the electrode end surface gradually produced a non-metallic oxide layer, which destroyed the electric field of the gap and affected the processing stability. The use of high-frequency positive and negative pulse power can effectively avoid the generation of a non-metallic oxide layer. Through the combination of simulation analysis and experimental verification, it is concluded that increasing electrolyte pressure in stages can effectively improve machining accuracy and stability. The interstitial current increases as the feed rate of the tool electrode increases, and the diameter of the machined small hole decreases as it increases.

scholarly journals Existence and uniqueness in the theory of bending of elastic plates

1986 ◽  
Vol 29 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Integral Equation Method ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Dimensional Theory ◽  
Neumann Problems ◽  
Image Position

Kirchhoff's kinematic hypothesis that leads to an approximate two-dimensional theory of bending of elastic plates consists in assuming that the displacements have the form [1]In general, the Dirichlet and Neumann problems for the equilibrium equations obtained on the basis of (1.1) cannot be solved by the boundary integral equation method both inside and outside a bounded domain because the corresponding matrix of fundamental solutions does not vanish at infinity [2]. However, as we show in this paper, the method is still applicable if the asymptotic behaviour of the solution is suitably restricted.

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