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Effect of shape on the self-assembly of faceted patchy nanoplates with irregular shape into tiling patterns

Jaime A. Millan, Daniel Ortiz, Sharon C. Glotzer
2015 Soft Matter  
Recent reports of the synthesis and assembly of faceted nanoplates with a wide range of shapes and composition motivates the possibility of a new class of two-dimensional materials with specific patterns  ...  targeted for a host of exciting properties.  ...  that of the regular polygon at x ¼ 0.5.  ... 
doi:10.1039/c4sm01612b pmid:25579173 fatcat:bqck3rqh3reenmvwpfbluwqdwi

A Short History of an Elusive Yet Ubiquitous Structure in Chemistry, Materials, and Mathematics

Stephen T. Hyde, Michael O'Keeffe, Davide M. Proserpio
2008 Angewandte Chemie International Edition  
Nets and Tilings Some years ago in an effort to develop a taxonomy of three-periodic nets (which are special kinds of a periodic graph), it was decided to focus on the nets, rather than the tilings that  ...  We note that in the case of the regular nets, the natural tiling is the unique tiling that has the full symmetry of the net.  ... 
doi:10.1002/anie.200801519 pmid:18767088 fatcat:7ehvvo24djhijncfqeoher3vhu

Taxonomy of periodic nets and the design of materials

Olaf Delgado-Friedrichs, Michael O'Keeffe, Omar M. Yaghi
2007 Physical Chemistry, Chemical Physics - PCCP  
The concept of a natural tiling for a periodic net is introduced and used to derive a transitivity associated with the structure.  ...  Edge-transitive polyhedra, layers and 3-periodic nets are then described. Some other nets of special importance in crystal chemistry are also identified.  ...  Our own work has been generously supported by grants from the US National Science Foundation (grant number DMR 0451443) and by the donors of the American Chemical Society Petroleum Research Fund.  ... 
doi:10.1039/b615006c pmid:17311144 fatcat:3a7twyxmnjcjvil3zglg2ilsc4

An integer representation for periodic tilings of the plane by regular polygons

José Ezequiel Soto Sánchez, Tim Weyrich, Asla Medeiros e Sá, Luiz Henrique de Figueiredo
2021 Computers & graphics  
We describe a representation for periodic tilings of the plane by regular polygons.  ...  Our approach is to represent explicitly a small subset of seed vertices from which we systematically generate all elements of the tiling by translations.  ...  This research was done in the Visgraf Computer Graphics laboratory at IMPA, at FGV EMAp, and at the Department of Computer Science, University College London.  ... 
doi:10.1016/j.cag.2021.01.007 fatcat:oxicyhputnbgnlabbocv3sd3vm

Nets, tiles, and metal-organic frameworks

Michael O'Keeffe
2014 APL Materials  
three-periodic nets that admit tilings.  ...  Instead, we defined regular nets which have embeddings in which the coordination figures (patterns of nearest neighbors) are regular polygons or polyhedra required by the symmetry. 16 The only regular  ... 
doi:10.1063/1.4901292 fatcat:vtwumnjv5zbwni6df5ncikfzkm

Artisan procedures to generate uniform tilings

Miguel Carlos Fernandez-Cabo
2014 International Mathematical Forum  
This empiric way to develop tilings led not only to discover all uniform tilings but later discovering of aperiodic tilings.  ...  Artisans used same tools to carry out their ornamental patterns but at some point they began to work manually using physical representations of figures or tiles previously drawing by means of ruler and  ...  University of Madrid.  ... 
doi:10.12988/imf.2014.45103 fatcat:wxauqp53y5b3xglikholdqjzti

Meditation on an Engraving of Fricke and Klein (The Modular Group and Geometrical Chemistry)

Stephen T. Hyde, Ann-Kristin Larsson, Tiziana Di Matteo, Stuart Ramsden, Vanessa Robins
2003 Australian journal of chemistry (Print)  
Limited discussion of the projection process from 2D hyperbolic to 3D euclidean space via mapping onto triply periodic minimal surfaces is presented.  ...  The prime examples in the former space are derived from Felix Klein's engraving of the modular group structure within the hyperbolic plane; these include various tilings, networks and trees.  ...  The figures of knots and links were generated with the KnotPlot package, freely available [35] thanks to the efforts of its creator, Dr Rob Scharein.  ... 
doi:10.1071/ch03191 fatcat:uqjmg3auw5exjn4rplz7lhs33m

Precise Molecular Design of Complex Polymers and Morphology Control of Their Hierarchical Multiphase Structures

Yushu Matsushita
2008 Polymer journal  
The second one is represented by star-shaped terpolymers of the ABC type, which easily form three-phase cylinder-like structure whose cross sections exhibit periodic tiling structures.  ...  They show several Archimedean tilings and one of them forms quasicrystalline tiling with dodecagonal symmetry.  ...  The research achievements on the molecular design of complex polymer systems and their hierarchical structures have been attained under the collaboration of the present author(YM) with many co-workers.  ... 
doi:10.1295/polymj.pj2007132 fatcat:rpbnqgnzqjfcjnmcgvh3nqjlye

Intrinsic universality and the computational power of self-assembly

Damien Woods
2013 Electronic Proceedings in Theoretical Computer Science  
Towards the end of our trip, we find one tile to rule them all: a single rotatable flipable polygonal tile that can simulate any tile assembly system.  ...  This short survey of recent work in tile self-assembly discusses the use of simulation to classify and separate the computational and expressive power of self-assembly models.  ...  I thank all my co-authors on the topic of intrinsic universality in tile assembly, I have enjoyed working with you all immensely. It has been a fun ride so far, yet it seems there is much to learn.  ... 
doi:10.4204/eptcs.128.5 fatcat:6vd74phg4nanzgmukhh4yig27i

Intrinsic universality and the computational power of self-assembly

Damien Woods
2015 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
Towards the end of our trip, we find one tile to rule them all: a single rotatable flipable polygonal tile that simulates any tile assembly system.  ...  Our journey begins with the result that there is a single intrinsically universal tile set that, with appropriate initialization and spatial scaling, simulates any instance of Winfree's abstract Tile Assembly  ...  I thank all my co-authors on the topic of intrinsic universality in tile assembly, I have enjoyed working with you all immensely. It has been a fun ride so far, yet it seems there is much to learn.  ... 
doi:10.1098/rsta.2014.0214 pmid:26078347 fatcat:caya6imjvvgyvfy527kzv4sftm

Unified Graph Theory-Based Modeling and Control Methodology of Lattice Converters

Jingyang Fang
2021 Electronics  
In addition, this article proposes a plurality of novel lattice converter topologies, which complement state-of-the-art options.  ...  By use of graph theory, this article proposes a unified modeling and control methodology for various lattice converters, resulting in the satisfaction of their key control objectives, including selected  ...  ., 360°) and the angles of polygons, there are only three lattice converters on the basis of regular tiling.  ... 
doi:10.3390/electronics10172146 doaj:320283fb9255410c8da258471d232bfe fatcat:k6tz5zuje5dxfpwjfh4wuc6jwa

Review on Recent Patents in Texture Synthesis

Weiming Dong, Jean-Claude Paul
2009 Recent Patents on Computer Science  
The goal of texture synthesis can be stated as follows: given a texture example, synthesize a new texture that, when perceived by a human observer, appears to be generated by the same underlying process  ...  Then we discuss the applications of texture synthesis in texture magnification and image repairing. This paper also points out future works on this issue.  ...  An alternative approach is to use texture synthesis to pre-compute a set of small tiles (textures) and use these tiles to generate arbitrary size of non-periodic images at run time.  ... 
doi:10.2174/2213275910902020111 fatcat:3gabemdirrahdaxb23umvgpwzy

Review on Recent Patents in Texture Synthesis

Weiming Dong, Jean-Claude Paul
2010 Recent Patents on Computer Science  
The goal of texture synthesis can be stated as follows: given a texture example, synthesize a new texture that, when perceived by a human observer, appears to be generated by the same underlying process  ...  Then we discuss the applications of texture synthesis in texture magnification and image repairing. This paper also points out future works on this issue.  ...  An alternative approach is to use texture synthesis to pre-compute a set of small tiles (textures) and use these tiles to generate arbitrary size of non-periodic images at run time.  ... 
doi:10.2174/1874479610902020111 fatcat:jbx772hxxfaf5imkehktegif2y

Just-in-Time Texture Synthesis

Lili Wang, Yulong Shi, Yi Chen, Voicu Popescu
2012 Computer graphics forum (Print)  
The lack of an appropriate level-of-detail (LoD) scheme results in severe minification artifacts. We present a just-intime texturing method that addresses these two problems.  ...  Texture bombing is a texture synthesis approach that saves memory by stopping short of assembling the output texture from the arrangement of input texture patches; instead, the arrangement is used directly  ...  This work is the part of Project 61272349 supported by National Natural Science Foundation of China and  ... 
doi:10.1111/cgf.12003 fatcat:4gdkzokyfvfglgnplp2lvwtjvu

Star-shaped metrics for mechanical metamaterial design

Jonàs Martínez, Mélina Skouras, Christian Schumacher, Samuel Hornus, Sylvain Lefebvre, Bernhard Thomaszewski
2019 ACM Transactions on Graphics  
Our method generates a smoothly-graded pattern (a) when interpolating between three star-shaped distance functions (b) on a regular honeycomb lattice.  ...  This capability opens up a rich space of structures with interesting aesthetics and a wide range of mechanical properties, including isotropic, tetragonal, orthotropic, as well as smoothly graded materials  ...  Periodicity. The lattices that we consider are periodic and can be obtained by translating a primitive cell, in our case a regular polygon, along two or three directions.  ... 
doi:10.1145/3306346.3322989 fatcat:tuyzpoupz5bjdllj7vzkfmt4ym
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