scholarly journals Some criteria for circle packing types and combinatorial Gauss-Bonnet theorem

2021 ◽  
pp. 1
Author(s):  
Byung-Geun Oh
Keyword(s):  
Circle Packing ◽  
Bonnet Theorem

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 Path Planning and Replanning for Mobile Robot Navigation on 3D Terrain: An Approach Based on Geodesic

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Kun-Lin Wu ◽  
Ting-Jui Ho ◽  
Sean A. Huang ◽  
Kuo-Hui Lin ◽  
Yueh-Chen Lin ◽  
...  
Keyword(s):  
Mobile Robot ◽  
Robot Navigation ◽  
Tangent Plane ◽  
Intersection Point ◽  
Mobile Robot Navigation ◽  
Complete Manifold ◽  
Geodesic Triangle ◽  
Planning Stage ◽  
3D Terrain ◽  
Bonnet Theorem

In this paper, mobile robot navigation on a 3D terrain with a single obstacle is addressed. The terrain is modelled as a smooth, complete manifold with well-defined tangent planes and the hazardous region is modelled as an enclosing circle with a hazard grade tuned radius representing the obstacle projected onto the terrain to allow efficient path-obstacle intersection checking. To resolve the intersections along the initial geodesic, by resorting to the geodesic ideas from differential geometry on surfaces and manifolds, we present a geodesic-based planning and replanning algorithm as a new method for obstacle avoidance on a 3D terrain without using boundary following on the obstacle surface. The replanning algorithm generates two new paths, each a composition of two geodesics, connected via critical points whose locations are found to be heavily relying on the exploration of the terrain via directional scanning on the tangent plane at the first intersection point of the initial geodesic with the circle. An advantage of this geodesic path replanning procedure is that traversability of terrain on which the detour path traverses could be explored based on the local Gauss-Bonnet Theorem of the geodesic triangle at the planning stage. A simulation demonstrates the practicality of the analytical geodesic replanning procedure for navigating a constant speed point robot on a 3D hill-like terrain.

105.14 Cubes, cones and the Gauss-Bonnet theorem

2021 ◽  
Vol 105 (562) ◽  
pp. 148-153
Author(s):  
J. N. Ridley
Keyword(s):  
Bonnet Theorem

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 The Gauss-Bonnet theorem for vector bundles

2006 ◽  
Vol 85 (1-2) ◽  
pp. 15-21 ◽  
Author(s):  
Denis Bell
Keyword(s):  
Vector Bundles ◽  
Bonnet Theorem

scholarly journals Applications of the Gauss–Bonnet theorem to gravitational lensing

2008 ◽  
Vol 25 (23) ◽  
pp. 235009 ◽  
Author(s):  
G W Gibbons ◽  
M C Werner
Keyword(s):  
Gravitational Lensing ◽  
Bonnet Theorem

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

scholarly journals Weak Deflection Angle of some Classes of non-linear Electrodynamics Black Holes via Gauss-Bonnet Theorem

2020 ◽  
Author(s):  
Hasan El Moumni ◽  
Karima Masmar ◽  
Ali Övgün
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Weak Field ◽  
Leading Order ◽  
Plasma Medium ◽  
Non Linear ◽  
The Deflection Angle ◽  
Bonnet Theorem

In this paper, we study the gravitational lensing by some black hole classes within the non-linear electrodynamics in weak field limits. First, we calculate an optical geometry of the non-linear electrodynamics black hole then we use the Gauss-Bonnet theorem for finding deflection angle in weak field limits. The effect of non-linear electrodynamics on the deflection angle in leading order terms is studied. Furthermore, we discuss the effects of the plasma medium on the weak deflection angle.

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