Atomistic Theory of Elasticity
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We have developed a formulation of elasticity which is suitable for strain calculations in epitaxial growth and other mesoscopic systems. Our primary goal is the development of an efficient numerical method. Our method is really a hybrid atomistic/continuum theory. The core of our method is the formulation of an elastic energy which is a leading order approximation to both an atomistic and continuum energy. The energy can be minimized by a variety of different methods, and their is great potential to exploit the continuum strucure of the method to employ fast solution techniques. The method is especially powerful for computing strain effects in epitaxial growth of thin films and other systems of comparable size. With several collaborators we have applied our technique to the study of step bunching in heteriepitaxy. We are currently working on various applications such as facets and quantum dots. We are also working to extend various fast solution techniques, such as fast fourier methods, boundary integral and fast multipole methods in our strain calculations.