The High Temperature Crossover for General 2D Coulomb Gases

We study systems of $n$ points in the Euclidean space of dimension $d\geqslant 1$ interacting via a Riesz kernel $|x|^{-s}$ and confined by an external potential, in the regime where $d-2\leqslant s<d$. We also treat the case of logarithmic interactions in dimensions 1 and 2. Our study includes and retrieves all cases previously studied in Sandier and Serfaty [2D Coulomb gases and the renormalized energy, Ann. Probab. (to appear); 1D log gases and the renormalized energy: crystallization at vanishing temperature (2013)] and Rougerie and Serfaty [Higher dimensional Coulomb gases and renormalized energy functionals, Comm. Pure Appl. Math. (to appear)]. Our approach is based on the Caffarelli–Silvestre extension formula, which allows one to view the Riesz kernel as the kernel of an (inhomogeneous) local operator in the extended space $\mathbb{R}^{d+1}$.As $n\rightarrow \infty$, we exhibit a next to leading order term in $n^{1+s/d}$ in the asymptotic expansion of the total energy of the system, where the constant term in factor of $n^{1+s/d}$ depends on the microscopic arrangement of the points and is expressed in terms of a ‘renormalized energy’. This new object is expected to penalize the disorder of an infinite set of points in whole space, and to be minimized by Bravais lattice (or crystalline) configurations. We give applications to the statistical mechanics in the case where temperature is added to the system, and identify an expected ‘crystallization regime’. We also obtain a result of separation of the points for minimizers of the energy.

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Influence of Thermo-Mechanical Processing on the Microstructure of Beryllia Dispersed Nickel Alloys

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100071363 ◽

1973 ◽

Vol 31 ◽

pp. 184-185

Author(s):

M.S. Grewal ◽

S.A. Sastri ◽

N.J. Grant

Keyword(s):

High Temperature ◽

Nickel Alloys ◽

Thermomechanical Processing ◽

Cold Work ◽

High Temperature Strength ◽

Strengthening Effect ◽

Mechanical Processing ◽

Uniform Dispersion ◽

Oxide Particles ◽

Nickel Base

Currently there is a great interest in developing nickel base alloys with fine and uniform dispersion of stable oxide particles, for high temperature applications. It is well known that the high temperature strength and stability of an oxide dispersed alloy can be greatly improved by appropriate thermomechanical processing, but the mechanism of this strengthening effect is not well understood. This investigation was undertaken to study the dislocation substructures formed in beryllia dispersed nickel alloys as a function of cold work both with and without intermediate anneals. Two alloys, one Ni-lv/oBeo and other Ni-4.5Mo-30Co-2v/oBeo were investigated. The influence of the substructures produced by Thermo-Mechanical Processing (TMP) on the high temperature creep properties of these alloys was also evaluated.

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Application of TEM to Deformation, Wear, and Fracture of Ceramics

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100052377 ◽

1974 ◽

Vol 32 ◽

pp. 472-473

Author(s):

B. J. Hockey

Keyword(s):

Wear Resistance ◽

High Temperature ◽

Mechanical Behavior ◽

Brittle Materials ◽

High Temperature Strength ◽

Wide Range ◽

Corrosive Environments ◽

Further Development

Ceramics, such as Al2O3 and SiC have numerous current and potential uses in applications where high temperature strength, hardness, and wear resistance are required often in corrosive environments. These materials are, however, highly anisotropic and brittle, so that their mechanical behavior is often unpredictable. The further development of these materials will require a better understanding of the basic mechanisms controlling deformation, wear, and fracture.The purpose of this talk is to describe applications of TEM to the study of the deformation, wear, and fracture of Al2O3. Similar studies are currently being conducted on SiC and the techniques involved should be applicable to a wide range of hard, brittle materials.

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Lattice Imaging of Grain Boundaries in Ceramics

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100078171 ◽

1977 ◽

Vol 35 ◽

pp. 114-115

Author(s):

D. R. Clarke ◽

G. Thomas

Keyword(s):

Mechanical Properties ◽

High Temperature ◽

Silicon Nitride ◽

Grain Boundaries ◽

High Temperature Strength ◽

Current Interest ◽

Lattice Imaging ◽

Special Significance ◽

Structural Applications ◽

Refractory Ceramics

Grain boundaries have long held a special significance to ceramicists. In part, this has been because it has been impossible until now to actually observe the boundaries themselves. Just as important, however, is the fact that the grain boundaries and their environs have a determing influence on both the mechanisms by which powder compaction occurs during fabrication, and on the overall mechanical properties of the material. One area where the grain boundary plays a particularly important role is in the high temperature strength of hot-pressed ceramics. This is a subject of current interest as extensive efforts are being made to develop ceramics, such as silicon nitride alloys, for high temperature structural applications. In this presentation we describe how the techniques of lattice fringe imaging have made it possible to study the grain boundaries in a number of refractory ceramics, and illustrate some of the findings.

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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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The Ordered Phase Formation in Ti-Al-Ga Alloys

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100069193 ◽

1970 ◽

Vol 28 ◽

pp. 440-441

Author(s):

Shiro Fujishiro ◽

Harold L. Gegel

Keyword(s):

Thermal Stability ◽

High Temperature ◽

Titanium Alloys ◽

Growth Kinetics ◽

Stoichiometric Composition ◽

Good Potential ◽

Alpha Titanium ◽

Cold Rolled ◽

Kinetics Of ◽

Thermal Stability Of

Ordered-alpha titanium alloys having a DO19 type structure have good potential for high temperature (600°C) applications, due to the thermal stability of the ordered phase and the inherent resistance to recrystallization of these alloys. Five different Ti-Al-Ga alloys consisting of equal atomic percents of aluminum and gallium solute additions up to the stoichiometric composition, Ti3(Al, Ga), were used to study the growth kinetics of the ordered phase and the nature of its interface.The alloys were homogenized in the beta region in a vacuum of about 5×10-7 torr, furnace cooled; reheated in air to 50°C below the alpha transus for hot working. The alloys were subsequently acid cleaned, annealed in vacuo, and cold rolled to about. 050 inch prior to additional homogenization

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Albumins as Embedding Media for Electron Microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100064025 ◽

1969 ◽

Vol 27 ◽

pp. 422-423 ◽

Cited By ~ 1

Author(s):

J. L. Farrant ◽

J. D. McLean

Keyword(s):

Electron Microscopy ◽

Electron Microscope ◽

High Temperature ◽

Biological Material ◽

Globular Proteins ◽

The Past ◽

Antibody Staining ◽

Thin Sectioning ◽

Embedding Medium

For electron microscope techniques such as ferritin-labeled antibody staining it would be advantageous to have available a simple means of thin sectioning biological material without subjecting it to lipid solvents, impregnation with plastic monomers and their subsequent polymerization. With this aim in view we have re-examined the use of protein as an embedding medium. Gelatin which has been used in the past is not very satisfactory both because of its fibrous nature and the high temperature necessary to keep its solutions fluid. We have found that globular proteins such as the serum and egg albumins can be cross-linked so as to yield blocks which are suitable for ultrathin sectioning.

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