Cauchy–Born Rule and the Stability of Crystalline Solids: Static Problems

When crystalline solids exhibit cleavage fracture, the associated deformation processes produce wedge shaped microcracks and the criteria for their stability are of paramount importance when discussing the conditions for complete fracture of a solid. Previously, consideration has been given to the behaviour of an isolated wedge shaped crack, but little attention has been given to problems involving distributions of such cracks. The present paper examines the stability of two coplanar wedge shaped cracks, and demonstrates under what conditions interaction effects are important.

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Open discussion

Symposium - International Astronomical Union ◽

10.1017/s0074180900029533 ◽

1982 ◽

Vol 99 ◽

pp. 605-613

Author(s):

P. S. Conti

Keyword(s):

Buenos Aires ◽

Large Mass ◽

List Type ◽

Common Phenomenon ◽

Open Discussion ◽

The Stability ◽

Ring Nebulae

Conti: One of the main conclusions of the Wolf-Rayet symposium in Buenos Aires was that Wolf-Rayet stars are evolutionary products of massive objects. Some questions:–Do hot helium-rich stars, that are not Wolf-Rayet stars, exist?–What about the stability of helium rich stars of large mass? We know a helium rich star of ∼40 MO. Has the stability something to do with the wind?–Ring nebulae and bubbles : this seems to be a much more common phenomenon than we thought of some years age.–What is the origin of the subtypes? This is important to find a possible matching of scenarios to subtypes.

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Symmetric Multistep Methods Revisited: II. Numerical Experiments

International Astronomical Union Colloquium ◽

10.1017/s0252921100031602 ◽

1999 ◽

Vol 173 ◽

pp. 309-314 ◽

Cited By ~ 3

Author(s):

T. Fukushima

Keyword(s):

Multistep Methods ◽

Computational Time ◽

Integration Time ◽

Implicit Methods ◽

Symmetric Methods ◽

Celestial Bodies ◽

The Stability ◽

Predictor Corrector ◽

Symmetric Multistep Methods ◽

Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

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Uniformity of Magnification from Different Electron Microscopes

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100060179 ◽

1967 ◽

Vol 25 ◽

pp. 32-33

Author(s):

Godfrey C. Hoskins ◽

V. Williams ◽

V. Allison

Keyword(s):

Diffraction Grating ◽

The Other ◽

Carbon Replica ◽

Electron Microscopes ◽

The Stability

The method demonstrated is an adaptation of a proven procedure for accurately determining the magnification of light photomicrographs. Because of the stability of modern electrical lenses, the method is shown to be directly applicable for providing precise reproducibility of magnification in various models of electron microscopes.A readily recognizable area of a carbon replica of a crossed-line diffraction grating is used as a standard. The same area of the standard was photographed in Phillips EM 200, Hitachi HU-11B2, and RCA EMU 3F electron microscopes at taps representative of the range of magnification of each. Negatives from one microscope were selected as guides and printed at convenient magnifications; then negatives from each of the other microscopes were projected to register with these prints. By deferring measurement to the print rather than comparing negatives, correspondence of magnification of the specimen in the three microscopes could be brought to within 2%.

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Effect of Improved ThO2 Particle Dispersion in Nickel on High-Temperature Strength

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100069211 ◽

1970 ◽

Vol 28 ◽

pp. 444-445

Author(s):

E. R. Kimmel ◽

H. L. Anthony ◽

W. Scheithauer

Keyword(s):

High Temperature ◽

Metal Matrix ◽

Oxide Particle ◽

Oxide Phase ◽

Dislocation Motion ◽

Particle Dispersion ◽

High Temperature Strength ◽

Strengthening Effect ◽

Oxide Particles ◽

The Stability

The strengthening effect at high temperature produced by a dispersed oxide phase in a metal matrix is seemingly dependent on at least two major contributors: oxide particle size and spatial distribution, and stability of the worked microstructure. These two are strongly interrelated. The stability of the microstructure is produced by polygonization of the worked structure forming low angle cell boundaries which become anchored by the dispersed oxide particles. The effect of the particles on strength is therefore twofold, in that they stabilize the worked microstructure and also hinder dislocation motion during loading.

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An Analysis of Dissociation of Molecules in a High Resolution Electron Microscope

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100072873 ◽

1973 ◽

Vol 31 ◽

pp. 486-487

Author(s):

Mihir Parikh

Keyword(s):

Electron Microscope ◽

High Resolution ◽

Cross Sections ◽

Resolving Power ◽

Peak Intensity ◽

Molecular Film ◽

Resolution Electron ◽

Dissociation Cross Section ◽

High Resolution Electron Microscope ◽

The Stability

It is well known that the resolution of bio-molecules in a high resolution electron microscope depends not just on the physical resolving power of the instrument, but also on the stability of these molecules under the electron beam. Experimentally, the damage to the bio-molecules is commo ly monitored by the decrease in the intensity of the diffraction pattern, or more quantitatively by the decrease in the peaks of an energy loss spectrum. In the latter case the exposure, EC, to decrease the peak intensity from IO to I’O can be related to the molecular dissociation cross-section, σD, by EC = ℓn(IO /I’O) /ℓD. Qu ntitative data on damage cross-sections are just being reported, However, the microscopist needs to know the explicit dependence of damage on: (1) the molecular properties, (2) the density and characteristics of the molecular film and that of the support film, if any, (3) the temperature of the molecular film and (4) certain characteristics of the electron microscope used

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