mikroskopický tenzor napětí
| Název práce v češtině: | mikroskopický tenzor napětí |
|---|---|
| Název v anglickém jazyce: | Microscopic Stress Tensor |
| Klíčová slova: | tenzor napětí, molekulární dynamika, mechanika kontinua |
| Klíčová slova anglicky: | stress tensor, molecular dynamics, molecular simulation, continuum theory, programming |
| Akademický rok vypsání: | 2023/2024 |
| Typ práce: | diplomová práce |
| Jazyk práce: | |
| Ústav: | Matematický ústav UK (32-MUUK) |
| Vedoucí / školitel: | Christoph Allolio, Ph.D. |
| Řešitel: |
| Zásady pro vypracování |
| The stress tensor is fundamental quantity in continuum mechanics. However, its computation from atomistic dynamics poses various problems, that have puzzled the community for 70 years.[1,2]
This is due to ambiguities that arise from the balance equations used in its derivation.[3] Unfortunately, the moments of the stress tensor, that define, e.g. the surface of tension or the Gaussian bending modulus of lipid membranes depend on the choices made when computing it. Furthermore, technical problems arise when many-body potentials are used in the molecular interactions underlying the stress[4,5], the same goes for constraints and long-range interactions. Some of these problems have been solved by using pairwise force-decompositions[6], but the problem remains fundamentally unsolved. The master thesis consists of verifying the conserved quantities such as angular moment of the different proposed decompositions, and to write a numerically stable implementation of the microscopic stress for the best method into the molecular simulation code gromacs. Special attention will be given to constraint algorithms and many-body potentials. The optimal result will be able to incorporate Ewald summation techniques for electrostatic interactions. |
| Seznam odborné literatury |
| [1] J. H. Irving and J. G. Kirkwood, J. Chem. Phys. 18, 817 (1950).
[2] H.-J. Kreuzer, Nonequilibrium thermodynamics and its statistical foundations. (Clarendon Press, Oxford, 1981). [3] P. Schofield, J. R. Henderson, and J. S. Rowlinson, Proc. R. Soc. A 379, 231 (1982). [4] R. Goetz and R. Lipowsky, J. Chem. Phys. 108, 7397 (1998). [5] M. Sega, B. Fábián, and P. Jedlovszky, J. Chem. Theory Comput. 12, 4509 (2016). [6] J. M. Vanegas, A. Torres-Sánchez, and M. Arroyo, J. Chem. Theory Comput. 10, 691 (2014). |