scholarly journals Planar Maps, Random Walks and Circle Packing

2020 ◽  
Author(s):  
Asaf Nachmias
Keyword(s):  
Random Walks ◽  
Circle Packing ◽  
Planar Maps

Non-homogeneous Random Walks

2016 ◽  
Author(s):  
Mikhail Menshikov ◽  
Serguei Popov ◽  
Andrew Wade
Keyword(s):  
Random Walks

Random walks with sign reversals and the intrinsic angular momentum behaviour on lattices

1981 ◽  
Vol 42 (3) ◽  
pp. 427-435
Author(s):  
C. Tresser ◽  
C. Brot ◽  
J. Coste
Keyword(s):  
Angular Momentum ◽  
Random Walks ◽  
Intrinsic Angular Momentum

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

Recurrence of Symmetric Random Walks.

1983 ◽  
Author(s):  
S. W. Dharmadhikari ◽  
Kumar Joag-dev
Keyword(s):  
Random Walks
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