Atomistic Models of Materials: Mathematical Challenges
نویسندگان
چکیده
منابع مشابه
Mathematical models in materials science
Modelling has now become a routine part of materials science. It is appropriate therefore to assess some of the successes and failures of the method and to understand how and if modelling differs from ordinary quantitative science. The subject is now sufficiently mature to bear some constructive self-criticism and to temper exaggerated claims. The discussion here of modelling methods and outcom...
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Four challenges to mathematics research posed by the field of materials science are given, plus an additional challenge purely from the field of geometric measure theory. The problems all concern the effects of surface and grain boundary free energy: motion by weighted mean curvature and/or surface diffusion and/or other kinetics, proofs of minimality of soap bubble clusters and their anisotrop...
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We examine the role of atomistic simulations in multiscale modeling of mechanical behavior of stressed solids. Theoretical strength is defined through modes of structural instability which, in the long wavelength limit, are specified by criteria involving elastic stiffness coefficients and the applied stress; more generally, strength can be characterized by the onset of soft vibrational modes i...
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In contrast to diffraction methods, which deal with the coherence lengths ofabout 150 –200 nm, only very few unit cells of a definite structure are required forRaman scattering identification. This allows the micro-structural analysis ofamorphous materials. However, until the vibrational properties of glasses are betterunderstood in terms of their structure and bonding, vibratio...
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Activated processes in materials are important for many of the properties that make them function. Batteries and catalysts are examples for which understanding how the component materials function on a timescale of milliseconds to seconds is critical to making improvements in a rational way. Modeling materials over these long timescales, relative to the timescale of atomic vibrations, is one of...
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ژورنال
عنوان ژورنال: Oberwolfach Reports
سال: 2008
ISSN: 1660-8933
DOI: 10.4171/owr/2008/21