scholarly journals The sensual Apollonian circle packing

2016 ◽  
Vol 34 (4) ◽  
pp. 364-395 ◽  
Author(s):  
Katherine E. Stange
Keyword(s):  
Circle Packing ◽  
Apollonian Circle Packing

The action at infinity of conservative groups of hyperbolic motions need not have atoms

1991 ◽  
Vol 11 (3) ◽  
pp. 577-582 ◽  
Author(s):  
John A. Velling ◽  
Katsuhiko Matsuzaki
Keyword(s):  
Positive Measure ◽  
Circle Packing ◽  
Discrete Groups ◽  
Apollonian Circle Packing

AbstractHerein the authors show that discrete groups of motions on Hn+1 may be conservative on Sn but have no positive measure ergodic components for this boundary action. An explicit example of such a group is given for H3 using the Apollonian circle packing of R2.

A Bottom-Up Approach to Solution-Processed, Atomically Precise Graphitic Cylinders on Surfaces

2018 ◽  
Author(s):  
Erik Leonhardt ◽  
Jeff M. Van Raden ◽  
David Miller ◽  
Lev N. Zakharov ◽  
Benjamin Aleman ◽  
...  
Keyword(s):  
Self Assembly ◽  
Carbon Nanostructures ◽  
Carbon Nanomaterials ◽  
Circle Packing ◽  
Pyrolytic Graphite ◽  
Building Blocks ◽  
Bottom Up ◽  
Casting Technique ◽  
New Class ◽  
Solution Casting Technique

Extended carbon nanostructures, such as carbon nanotubes (CNTs), exhibit remarkable properties but are difficult to synthesize uniformly. Herein, we present a new class of carbon nanomaterials constructed via the bottom-up self-assembly of cylindrical, atomically-precise small molecules. Guided by supramolecular design principles and circle packing theory, we have designed and synthesized a fluorinated nanohoop that, in the solid-state, self-assembles into nanotube-like arrays with channel diameters of precisely 1.63 nm. A mild solution-casting technique is then used to construct vertical “forests” of these arrays on a highly-ordered pyrolytic graphite (HOPG) surface through epitaxial growth. Furthermore, we show that a basic property of nanohoops, fluorescence, is readily transferred to the bulk phase, implying that the properties of these materials can be directly altered via precise functionalization of their nanohoop building blocks. The strategy presented is expected to have broader applications in the development of new graphitic nanomaterials with π-rich cavities reminiscent of CNTs.

Improved Domain Partitions for Variational Circle Packing

2018 ◽  
Vol 30 (7) ◽  
pp. 1251
Author(s):  
Lijuan Yu ◽  
Juan Cao ◽  
Zhonggui Chen
Keyword(s):  
Circle Packing

scholarly journals Advancing front circle packing to approximate conformal strips

2013 ◽  
Vol 46 (1) ◽  
pp. 105-118 ◽  
Author(s):  
R. Dorado ◽  
B. Pivec ◽  
E. Torres-Jimenez
Keyword(s):  
Circle Packing ◽  
Advancing Front

scholarly journals Price-and-verify: a new algorithm for recursive circle packing using Dantzig–Wolfe decomposition

2018 ◽  
Vol 284 (2) ◽  
pp. 527-555 ◽  
Author(s):  
Ambros Gleixner ◽  
Stephen J. Maher ◽  
Benjamin Müller ◽  
João Pedro Pedroso
Keyword(s):  
Circle Packing

Polynomial-Time Approximation Schemes for Circle Packing Problems

2014 ◽  
pp. 713-724 ◽  
Author(s):  
Flávio K. Miyazawa ◽  
Lehilton L. C. Pedrosa ◽  
Rafael C. S. Schouery ◽  
Maxim Sviridenko ◽  
Yoshiko Wakabayashi
Keyword(s):  
Polynomial Time ◽  
Circle Packing ◽  
Approximation Schemes ◽  
Packing Problems ◽  
Time Approximation ◽  
Polynomial Time Approximation
Sign in / Sign up

Export Citation Format

Share Document