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Effect of shape on the self-assembly of faceted patchy nanoplates with irregular shape into tiling patterns
2015
Soft Matter
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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
2008
Angewandte Chemie International Edition
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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
2007
Physical Chemistry, Chemical Physics - PCCP
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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
2021
Computers & graphics
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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
2014
APL Materials
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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
2014
International Mathematical Forum
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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)
2003
Australian journal of chemistry (Print)
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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
2008
Polymer journal
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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
2013
Electronic Proceedings in Theoretical Computer Science
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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
2015
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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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
2021
Electronics
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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
2009
Recent Patents on Computer Science
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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
2010
Recent Patents on Computer Science
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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
2012
Computer graphics forum (Print)
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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
2019
ACM Transactions on Graphics
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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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