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The Mordell-Lang conjecture for semiabelian varieties defined over fields of positive characteristic
No full texthttp://dx.doi.org/10.1017/S000497271200033
Locally finite simple groups whose non-nilpotent subgroups are pronormal
No full texthttp://dx.doi.org/10.1017/S000497271200033
A note on normalised ground states for the two-dimensional cubic-quintic nonlinear Schrödinger equation
No full textIhttp://dx.doi.org/10.1017/S000497271200033
Nowhere-zero -flows in Cayley graphs of order 8
No full texthttp://dx.doi.org/10.1017/S000497271200033
Strict regularity for -cocycles of finite groups
No full texthttp://dx.doi.org/10.1017/S000497271200033
Accurate and efficient multiscale simulation of a heterogeneous elastic beam via computation on small sparse patches
Get PDFModern `smart' materials have complex microscale structure, often with unknown macroscale closure. The Equation-Free Patch Scheme empowers us to non-intrusively, efficiently, and accurately simulate over large scales through computations on only small well-separated patches of the microscale system. Here the microscale system is a solid beam of random heterogeneous elasticity. The continuing challenge is to compute the given physics on just the microscale patches, and couple the patches across un-simulated macroscale space, in order to establish efficiency, accuracy, consistency, and stability on the macroscale. Dynamical systems theory supports the scheme. This research program is to develop a systematic non-intrusive approach, both computationally and analytically proven, to model and compute accurately macroscale system levels of general complex physical and engineering systems.
References
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J. E. Bunder, I. G. Kevrekidis, and A. J. Roberts. Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling. Numer. Math. 149.2 (2021), pp. 229–272. doi: 10.1007/s00211-021-01232-5
J. E. Bunder, A. J. Roberts, and I. G. Kevrekidis. Good coupling for the multiscale patch scheme on systems with microscale heterogeneity. J. Comput. Phys. 337 (2017), pp. 154–174. doi: 10.1016/j.jcp.2017.02.004 References C175
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J. Divahar, A. J. Roberts, T. W. Mattner, J. E. Bunder, and I. G. Kevrekidis. Two novel families of multiscale staggered patch schemes efficiently simulate large-scale, weakly damped, linear waves. Comput. Meth. Appl. Mech. Eng. 413 (2023), p. 116133. doi: 10.1016/j.cma.2023.116133. (Cit. on pp. C163, C165, C172).
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A. J. Roberts. Macroscale, slowly varying, models emerge from the microscale dynamics in long thin domains. IMA J. Appl. Math. 80.5 (2015), pp. 1492–1518. doi: 10.1093/imamat/hxv004
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A. J. Roberts, T. MacKenzie, and J. Bunder. A dynamical systems approach to simulating macroscale spatial dynamics in multiple dimensions. J. Eng. Math. 86.1 (2014), pp. 175–207. doi: 10.1007/s10665-013-9653-6
A. J. Roberts, J. Maclean, and J. E. Bunder. Equation-Free function toolbox for Matlab/Octave. Tech. rep. https://github.com/uoa1184615/EquationFreeGit, 2019–2024
G. Samaey, A. J. Roberts, and I. G. Kevrekidis. Equation-free computation: An overview of patch dynamics. Multiscale methods: bridging the scales in science and engineering. Ed. by J. Fish. Oxford University Press, 2010. Chap. 8, pp. 216–246. doi: 10.1093/acprof:oso/9780199233854.003.0008
J. Somnic and B. W. Jo. Status and challenges in homogenization methods for lattice materials. Materials 15.2 (2022), p. 605. doi: 10.3390/ma15020605
H. Whitney. Differentiable manifolds. Annal. Math. 37.3 (1936), pp. 645–680. doi: 10.2307/196848
Left and right eigenvectors of a variant of the Sylvester-Kac Matrix
No full texthttp://dx.doi.org/10.1017/S000497271200033
The restricted connected hull: filling the hole
No full texthttp://dx.doi.org/10.1017/S000497271200033