On distribution functions of the derivatives of weakly differentiable mappings
Anisotropic functions : a genericity result with crystallographic implications
In the 1950’s and 1960’s surface physicists/metallurgists such as Herring and Mullins applied ingenious thermodynamic arguments to explain a number of experimentally observed surface phenomena in crystals. These insights permitted the successful engineering of a large number of alloys, where the major mathematical novelty was that the surface response to external stress was anisotropic. By examining step/terrace (vicinal) surface defects it was discovered through lengthy and tedious experiments...
Anisotropic functions: a genericity result with crystallographic implications
In the 1950's and 1960's surface physicists/metallurgists such as Herring and Mullins applied ingenious thermodynamic arguments to explain a number of experimentally observed surface phenomena in crystals. These insights permitted the successful engineering of a large number of alloys, where the major mathematical novelty was that the surface response to external stress was . By examining step/terrace () surface defects it was discovered through lengthy and tedious experiments that the stored...
A variational problem modelling behavior of unorthodox silicon crystals
Controlling growth at crystalline surfaces requires a detailed and quantitative understanding of the thermodynamic and kinetic parameters governing mass transport. Many of these parameters can be determined by analyzing the isothermal wandering of steps at a vicinal [“step-terrace”] type surface [for a recent review see [4]]. In the case of crystals one finds that these meanderings develop larger amplitudes as the equilibrium temperature is raised (as is consistent with the statistical mechanical...
A Variational Problem Modelling Behavior of Unorthodox Silicon Crystals
Controlling growth at crystalline surfaces requires a detailed and quantitative understanding of the thermodynamic and kinetic parameters governing mass transport. Many of these parameters can be determined by analyzing the isothermal wandering of steps at a vicinal [“step-terrace”] type surface [for a recent review see [4]]. In the case of crystals one finds that these meanderings develop larger amplitudes as the equilibrium temperature is raised (as is consistent with the statistical mechanical...
On a gap phenomenon for isoperimetrically constrained variational problems.
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