A refined mathematical model for prediction of bubble evolution in transformers

1989 ◽  
Vol 4 (1) ◽  
pp. 391-404 ◽  
Author(s):  
W.A. Fessler ◽  
T.O. Rouse ◽  
W.J. McNutt ◽  
O.R. Compton
Keyword(s):  
Mathematical Model ◽  
Bubble Evolution

scholarly journals A model of extravascular bubble evolution: effect of changes in breathing gas composition

1999 ◽  
Vol 87 (4) ◽  
pp. 1521-1531 ◽  
Author(s):  
J. F. Himm ◽  
L. D. Homer
Keyword(s):  
Mathematical Model ◽  
Bubble Growth ◽  
Inert Gas ◽  
Gas Composition ◽  
Adipose Tissues ◽  
Exponential Time ◽  
Transient Period ◽  
Bubble Evolution ◽  
Evolution Effect ◽  
Single Exponential

Observations of bubble evolution in rats after decompression from air dives (O. Hyldegaard and J. Madsen. Undersea Biomed. Res. 16: 185–193, 1989; O. Hyldegaard and J. Madsen. Undersea Hyperbaric Med. 21: 413–424, 1994; O. Hyldegaard, M. Moller, and J. Madsen. Undersea Biomed. Res. 18: 361–371, 1991) suggest that bubbles may resolve more safely when the breathing gas is a heliox mixture than when it is pure O2. This is due to a transient period of bubble growth seen during switches to O2 breathing. In an attempt to understand these experimental results, we have developed a multigas-multipressure mathematical model of bubble evolution, which consists of a bubble in a well-stirred liquid. The liquid exchanges gas with the bubble via diffusion, and the exchange between liquid and blood is described by a single-exponential time constant for each inert gas. The model indicates that bubbles resolve most rapidly in spinal tissue, in adipose tissue, and in aqueous tissues when the breathing gas is switched to O2 after surfacing. In addition, the model suggests that switching to heliox breathing may prolong the existence of the bubble relative to breathing air for bubbles in spinal and adipose tissues. Some possible explanations for the discrepancy between model and experiment are discussed.

Mathematical model of hit phenomena and its application to movie advertisement

2008 ◽  
Author(s):  
Ishii Akira ◽  
Yoshida Narihiko ◽  
Hayashi Takafumi ◽  
Umemura Sanae ◽  
Nakagawa Takeshi
Keyword(s):  
Mathematical Model

Imprecision of Laboratory Determinations and Diagnostic Accuracy: Theoretical Considerations

1974 ◽  
Vol 13 (03) ◽  
pp. 151-158 ◽  
Author(s):  
D. A. B. Lindbebo ◽  
Fr. R. Watson
Keyword(s):  
Mathematical Model ◽  
Diagnostic Accuracy ◽  
Diagnostic Process ◽  
Clinical Laboratories ◽  
Non Linear ◽  
Theoretical Considerations ◽  
Made In

Recent studies suggest the determinations of clinical laboratories must be made more precise than at present. This paper presents a means of examining benefits of improvement in precision. To do this we use a mathematical model of the effect upon the diagnostic process of imprecision in measurements and the influence upon these two of Importance of Diagnosis and Prevalence of Disease. The interaction of these effects is grossly non-linear. There is therefore no proper intuitive answer to questions involving these matters. The effects can always, however, be calculated.Including a great many assumptions the modeling suggests that improvements in precision of any determination ought probably to be made in hospital rather than screening laboratories, unless Importance of Diagnosis is extremely high.

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