Abstract
The complexity and variety of applications on the nanoscale are as great, or arguably greater, than on the macroscale. While a detailed account of nanoscale problems in a single book is impossible, one can make a general observation on the importance of the nanoscale: the properties of materials are strongly affected by their nanoscale structure.
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Notes
- 1.
There is a notable exception in variational methods: rigorous pointwise error bounds can, for some classes of problems, be established using dual formulations (see Sect. 3.13.3.3 for more information). However, this requires numerical solution of a separate auxiliary problem for Green’s function at each point where the error bound is sought.
- 2.
In the first edition of the book, I provided web links to these packages. But some of the resources, especially ones in the public domain, tend to migrate to different sites over the years. The interested reader can easily find the relevant information via Google (or whatever the equivalent of Google is a hundred years from now, if the book is perused then).
- 3.
Not exactly the same as “engineering mathematics,” a more utilitarian, user-oriented approach.
- 4.
J.M. Haile, Molecular Dynamics Simulation: Elementary Methods, Wiley-Interscience, 1997; D. Frenkel & B. Smit, Understanding Molecular Simulation, Academic Press, 2001; D.C. Rapaport, The Art of Molecular Dynamics Simulation, Cambridge University Press, 2004; T. Schlik [Sch02], and others.
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Tsukerman, I. (2020). Introduction. In: Computational Methods for Nanoscale Applications. Nanostructure Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-43893-7_1
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DOI: https://doi.org/10.1007/978-3-030-43893-7_1
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