curvedspacesim
molecular-dynamics-like simulations on curved surfaces
Science Score: 44.0%
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Low similarity (8.8%) to scientific vocabulary
Repository
molecular-dynamics-like simulations on curved surfaces
Basic Info
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- Stars: 1
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- Forks: 1
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Metadata Files
README.md
curvedSpaceSimulation
curvedSpaceSimulation implements molecular-dynamics-like evolution of degrees of freedom on meshed (triangulated) surfaces embedded in 3D space. All motion of particles follows discrete geodesics on a given surface, and all distances are compute as geodesic distances along the surface (i.e., particles interact via "curved lines of force" rather than interacting according to the Euclidean distance). Parallel transport (e.g., of velocity vectors during the update of equations of motion) is implemented as part of what it means to displace a particle along a geodesic.
The standard all-to-all geodesic-finding algorithm implemented has O(v^2) computational complexity, where v is the number of vertices of the surface mesh (although, in practice, the scaling does not seem to be that bad on representative surfaces). In the case of simulations of particles with short-range interactions, submeshing routines have been implemented so that the computational cost scales like N log N (where N is the particle number) and like (w^2), where w is the typical number of vertices in a patch of surface spanning the maximum interaction range.
Information on installing the project can be found here. A very rough outline of some of the main classes andthe basic operating flow of the primary branches can be found here. A very brief description of the main executables distributed can be found here.
Project documentation
Additional files in the doc director provide some basic documentation
Owner
- Name: Sussman Lab
- Login: sussmanLab
- Kind: organization
- Website: https://www.dmsussman.org/
- Repositories: 2
- Profile: https://github.com/sussmanLab
Soft matter physics @ Emory
Citation (Citations.md)
# Citations for curvedSpaceSimulation If you use this software packagefor a publication or project, please cite the main curvedSpaceSimulation methods paper: (1) [The current arXiv version of the paper](https://arxiv.org/abs/2404.19751): Toler H. Webb and Daniel M. Sussman. "curvedSpaceSim: A framework for simulating particles interacting along geodesics." arXiv preprint arXiv:2404.19751 (2024). The core algorithm used to compute geodesic distances and paths comes from (2) [Shi-Qing Xin and Guo-Jin Wang](https://dl.acm.org/doi/10.1145/1559755.1559761). Improving chen and han's algorithm on the discrete geodesic problem. ACM Trans. Graph., 28(4):104:1–104:8, September 2009 This paper is itself an improvement on the work of (3) Chen and Han (Shortest paths on a polyhedron. Internat. J. Comput. Geom. Appl., 6:127–144, 1996), which itself improves on the original MMP algorithm for finding discrete geodesics: (4) Joseph S. B. Mitchell, D. M. Mount, and C. H. Papadimitriou. The discrete geodesic problem. SIAM J. Comput., 16:647–668, 1987 The Xin and Wang algorithm is as-implemented by CGAL: (5a) CGAL,Computational Geometry Algorithms Library, http://www.cgal.org (5b) Stephen Kiazyk and Sébastien Loriot and Éric Colin de Verdière. Triangulated Surface Mesh Shortest Paths. In CGAL User and Reference Manual. CGAL Editorial Board, 5.6 edition, 2023
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