Next Article in Journal
A Proof of the Standard Completeness for the Involutive Uninorm Logic
Next Article in Special Issue
Finite Element Modelling of a Composite Shell with Shear Connectors
Previous Article in Journal
Anti-Periodic Boundary Value Problems for Nonlinear Langevin Fractional Differential Equations
Previous Article in Special Issue
New Numerical Method for the Rotation form of the Oseen Problem with Corner Singularity
Article Menu
Issue 4 (April) cover image

Export Article

Open AccessArticle

Towards Infinite Tilings with Symmetric Boundaries

1
Institute of Scientific Computing, TU Dresden, 01062 Dresden, Germany
2
Dresden Center for Computational Materials Science (DCMS), TU Dresden, 01062 Dresden, Germany
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(4), 444; https://doi.org/10.3390/sym11040444
Received: 11 February 2019 / Revised: 21 March 2019 / Accepted: 22 March 2019 / Published: 27 March 2019
(This article belongs to the Special Issue Finite Elements and Symmetry)
  |  
PDF [7445 KB, uploaded 27 March 2019]
  |  

Abstract

Large-time coarsening and the associated scaling and statistically self-similar properties are used to construct infinite tilings. This is realized using a Cahn–Hilliard equation and special boundaries on each tile. Within a compromise between computational effort and the goal to reduce recurrences, an infinite tiling has been created and software which zooms in and out evolve forward and backward in time as well as traverse the infinite tiling horizontally and vertically. We also analyze the scaling behavior and the statistically self-similar properties and describe the numerical approach, which is based on finite elements and an energy-stable time discretization. View Full-Text
Keywords: symmetric boundary condition; pattern formation; computational design; finite-element method symmetric boundary condition; pattern formation; computational design; finite-element method
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Supplementary material

SciFeed

Share & Cite This Article

MDPI and ACS Style

Stenger, F.; Voigt, A. Towards Infinite Tilings with Symmetric Boundaries. Symmetry 2019, 11, 444.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top