Application of the Mandelbrot–Zipf Law for the Quantitative Evaluation of the Average Size of Steel Grains

2021 ◽  
Author(s):  
І. М. Zhuravel ◽  
L. Z. Michuda
Keyword(s):  
Quantitative Evaluation ◽  
Average Size ◽  
Zipf Law

scholarly journals STUDIES ON THE BACTERIOPHAGE OF D'HERELLE

1925 ◽  
Vol 42 (4) ◽  
pp. 483-497 ◽  
Author(s):  
Jacques J. Bronfenbrenner ◽  
Charles Korb
Keyword(s):  
Quantitative Evaluation ◽  
Bacterial Species ◽  
Relative Concentration ◽  
Serial Dilution ◽  
The Other ◽  
Resistant Bacteria ◽  
Dilution Method ◽  
High Concentration ◽  
Average Size ◽  
Broth Dilution

The experiments reported above confirm the fact that lytic principle is distributed in active solution in a state of indivisible units. This permits its quantitative evaluation by serial dilution, as well as by plating on agar. The latter method, however, often gives readings considerably lower than those obtained by the broth dilution method of titration. By varying the concentration of agar it has been possible to show that the discrepancy is due to adsorption of the lytic agent on agar. When the concentration of the latter is increased from 0.3 per cent to 2.5 per cent the number of plaques of lysis is reduced more than 100 times. At the same time the average size of the plaques also decreases approximately to one-tenth of the original. The size, as well as the number of plaques, has been found to depend also on the condition of the culture employed in titration. Thus, when the culture exposed to the action of lytic agent is composed of young susceptible bacteria, the greater the concentration of bacteria, the smaller the plaques. When the culture is composed partly of young and partly of old susceptible bacteria, both the size and the number of the plaques are diminished with the increase in the relative concentration of old bacteria. On the other hand, presence in the culture of resistant bacteria does not affect either the size or the number of the plaques so long as the relative concentration of susceptible bacteria in the culture is sufficient to allow formation of them. The plaques appearing in the presence of a high concentration of resistant variants in the culture are relatively indistinct owing to overgrowth. Under carefully controlled conditions the size of plaques is found to be determined by the character of the lytic filtrate. Thus in the case of lytic agents which act upon more than one bacterial species the size of the plaques remains constant, irrespective of the bacterial substratum used for the production of the active filtrate.

Grain Refinement in Titanium-Erbium Alloys

1974 ◽  
Vol 32 ◽  
pp. 522-523
Author(s):  
B. B. Rath ◽  
J. E. O'Neal ◽  
R. J. Lederich
Keyword(s):  
Electron Microscopy ◽  
Size Distribution ◽  
Grain Refinement ◽  
Grain Growth ◽  
Volume Fraction ◽  
Pure Titanium ◽  
Systematic Investigation ◽  
Second Phase ◽  
Titanium Matrix ◽  
Average Size

Addition of small amounts of erbium has a profound effect on recrystallization and grain growth in titanium. Erbium, because of its negligible solubility in titanium, precipitates in the titanium matrix as a finely dispersed second phase. The presence of this phase, depending on its average size, distribution, and volume fraction in titanium, strongly inhibits the migration of grain boundaries during recrystallization and grain growth, and thus produces ultimate grains of sub-micrometer dimensions. A systematic investigation has been conducted to study the isothermal grain growth in electrolytically pure titanium and titanium-erbium alloys (Er concentration ranging from 0-0.3 at.%) over the temperature range of 450 to 850°C by electron microscopy.

Identification by Electron Microdiffraction of Intermetallic Phases in a Duplex Stainless Steel

1990 ◽  
Vol 48 (2) ◽  
pp. 494-495
Author(s):  
A. Redjaïmia ◽  
J.P. Morniroli ◽  
G. Metauer ◽  
M. Gantois
Keyword(s):  
Stainless Steel ◽  
Duplex Stainless Steel ◽  
Convergent Beam Electron Diffraction ◽  
Intermetallic Phases ◽  
Small Particles ◽  
Parallel Beam ◽  
Diffraction Patterns ◽  
Average Size ◽  
Convergent Beam ◽  
Electron Microdiffraction

2D and especially 3D symmetry information required to determine the crystal structure of four intermetallic phases present as small particles (average size in the range 100-500nm) in a Fe.22Cr.5Ni.3Mo.0.03C duplex stainless steel is not present in most Convergent Beam Electron Diffraction (CBED) patterns. Nevertheless it is possible to deduce many crystal features and to identify unambiguously these four phases by means of microdiffraction patterns obtained with a nearly parallel beam focused on a very small area (50-100nm).From examinations of the whole pattern reduced (RS) and full (FS) symmetries the 7 crystal systems and the 11 Laue classes are distinguished without ambiguity (1). By considering the shifts and the periodicity differences between the ZOLZ and FOLZ reflection nets on specific Zone Axis Patterns (ZAP) which depend on the crystal system, the centering type of the cell and the glide planes are simultaneously identified (2). This identification is easily done by comparisons with the corresponding simulated diffraction patterns.

Quantitative evaluation of -ray spectra from scintillation measurements

Physica ◽  
1952 ◽  
Vol 18 (2) ◽  
pp. 1147-1150
Author(s):  
D MAEDER ◽  
V WINTERSTEIGER
Keyword(s):  
Quantitative Evaluation

Qualitative-Quantitative Evaluation of Depressive Symptomatology

2017 ◽  
Author(s):  
Francesca Serra ◽  
Andrea Spoto ◽  
Marta Ghisi ◽  
Giulio Vidotto
Keyword(s):  
Quantitative Evaluation ◽  
Depressive Symptomatology

Quantitative evaluation of post-bone marrow transplant engraftment status using fluorescent-labeled variable number of tandem repeats

2000 ◽  
Vol 05 (2) ◽  
pp. 129-138
Author(s):  
Robert A. Luhm ◽  
Daniel B. Bellissimo ◽  
Arejas J. Uzgiris ◽  
William R. Drobyski ◽  
Martin J. Hessner
Keyword(s):  
Bone Marrow ◽  
Bone Marrow Transplant ◽  
Quantitative Evaluation ◽  
Tandem Repeats ◽  
Marrow Transplant ◽  
Variable Number

Quantitative Evaluation of Myocardial Stress/Rest 201TISPECT: Results of a ROI-Based Method in 108 Patients with CHD

1987 ◽  
Vol 26 (06) ◽  
pp. 234-240 ◽  
Author(s):  
H. Stirner ◽  
J. Dahl ◽  
R. Uebis ◽  
E. Kleinhans ◽  
M. Biedermann ◽  
...  
Keyword(s):  
Coronary Heart Disease ◽  
Heart Disease ◽  
Quantitative Evaluation ◽  
Myocardial Infarctions ◽  
Myocardial Spect ◽  
Luminal Diameter ◽  
Myocardial Stress ◽  
Threshold Criterion ◽  
Combined Evaluation ◽  
Severity Of The Disease

ROI-based polar maps (33 ROIs) were employed to evaluate quantitatively stress/rest myocardial 201TI SPECT in 108 patients with angiographically proven coronary heart disease (CHD) in comparison with 30 controls. Sensitivity in detecting a CHD with stenoses of > 50% of luminal diameter was determined versus normal regional values (± 2.5 SD) employing vitality (VI) and wash-out corrected redistribution (RD). The method was evaluated referring to the severity of the disease, to the number of ROIs displaying changes [(a) 1 ROI, (b) >2 ROIs], to validity of VI, RD or a combination thereof, and for specificity. Wash-out values were found to depend on degree of stress individually achieved and thus were not used as a threshold criterion. Sensitivity in supply areas with old myocardial infarctions was 95% (a) and 86% (b), resp. With no infarction, it was 96% (a) and 79% (b), resp. VI in stenosis > 75% was more sensitive than RD. However, combined evaluation of VI and RD yielded sensitivities from 91-100% (a) and 77-94% (b), resp. for different main supply areas. In stenosis < 50% with normal VI, RD was positive in 18-31 %. Specificity turned out to be 91 % (a) and 97% (b), resp. We conclude that the method presented is reliable to quantify numerically 201TI kinetics in myocardial SPECT, aimed at detecting and describing CHD.

Sign in / Sign up

Export Citation Format

Share Document