A simple formula for obtaining OIFs on Neumann boundary in 2D potential problems and its applications

2022 ◽  
Vol 134 ◽  
pp. 581-590
Author(s):  
Bin Chen ◽  
Wenzhen Qu ◽  
Kaiou Shu ◽  
Lei Zhang
Keyword(s):  
Simple Formula ◽  
Neumann Boundary ◽  
Potential Problems

A simple method of summing Bessel series

1968 ◽  
Vol 64 (3) ◽  
pp. 705-710 ◽  
Author(s):  
J. A. Greenwood
Keyword(s):  
Simple Formula ◽  
Bessel Functions ◽  
Convergent Series ◽  
Axially Symmetric ◽  
Simple Method ◽  
Symmetric Potential ◽  
Potential Problems ◽  
Direct Substitution

AbstractA simple formula is derived for transforming the slowly convergent series involving Bessel functions which arise in axially symmetric potential problems into more rapidly convergent series. Using it, sums of series previously found by elaborate special methods may be obtained by direct substitution. The necessary numerical coefficients are given.

Microbulldozing and Microchiseling

1969 ◽  
Vol 27 ◽  
pp. 134-135
Author(s):  
J.N. Ramsey ◽  
D.P. Cameron ◽  
F.W. Schneider
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Material Handling ◽  
Microprobe Analysis ◽  
Foreign Matter ◽  
Specific Location ◽  
Potential Problems ◽  
Knoop Indenter ◽  
Scanning Electron ◽  
Microhardness Tester

As computer components become smaller the analytical methods used to examine them and the material handling techniques must become more sensitive, and more sophisticated. We have used microbulldozing and microchiseling in conjunction with scanning electron microscopy, replica electron microscopy, and microprobe analysis for studying actual and potential problems with developmental and pilot line devices. Foreign matter, corrosion, etc, in specific locations are mechanically loosened from their substrates and removed by “extraction replication,” and examined in the appropriate instrument. The mechanical loosening is done in a controlled manner by using a microhardness tester—we use the attachment designed for our Reichert metallograph. The working tool is a pyramid shaped diamond (a Knoop indenter) which can be pushed into the specimen with a controlled pressure and in a specific location.

The “Mixing” of Implant Systems

1991 ◽  
Vol 4 (02) ◽  
pp. 38-45 ◽  
Author(s):  
F. Baumgart
Keyword(s):  
Stainless Steel ◽  
Additional Risk ◽  
Bone Screw ◽  
Application Technique ◽  
Quality Controls ◽  
Implant Materials ◽  
Osteosynthesis Plate ◽  
Potential Problems ◽  
Manufacturing Procedure

SummaryThe so-called “mixing” of implants and instruments from different producers entertain certain risks.The use of standardized implant materials (e.g. stainless steel ISO 5832/1) from different producers is necessary but is not sufficient to justify the use of an osteosynthesis plate from one source and a bone screw from another.The design, dimensions, tolerances, manufacturing procedure, quality controls, and application technique of the instruments and implants also vary according to make. This can lead to damage, failure or fracture of the biomechanical system called “osteosynthesis” and hence the failure of the treatment undertaken. In the end, it is the patient who pays for these problems.Some examples also illustrate the potential problems for the staff and institutions involved.The use of a unique, consistent, well-tested, and approved set of implants and instruments is to be strongly recommended to avoid any additional risk.

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