Combinatorial Ricci Flow for Degenerate Circle Packing Metrics

2019 ◽  
Vol 24 (3) ◽  
pp. 298-311
Author(s):  
Ruslan Yu. Pepa ◽  
Theodore Yu. Popelensky
Keyword(s):  
Ricci Flow ◽  
Circle Packing ◽  
Combinatorial Ricci Flow

Equilibrium for a combinatorial Ricci flow with generalized weights on a tetrahedron

2017 ◽  
Vol 22 (5) ◽  
pp. 566-578 ◽  
Author(s):  
Ruslan Yu. Pepa ◽  
Theodore Yu. Popelensky
Keyword(s):  
Ricci Flow ◽  
Combinatorial Ricci Flow

scholarly journals Combinatorial Ricci Flows with Applications to the Hyperbolization of Cusped 3-Manifolds

2021 ◽  
Author(s):  
Ke Feng ◽  
Huabin Ge ◽  
Bobo Hua ◽  
Xu Xu
Keyword(s):  
Ricci Flow ◽  
Hyperbolic Metric ◽  
Effective Algorithm ◽  
Hyperbolic Structure ◽  
Ricci Flows ◽  
Long Time Existence ◽  
The Hyperbolic Metric ◽  
Long Time ◽  
Combinatorial Ricci Flow ◽  
Time Existence

Abstract In this paper, we adopt combinatorial Ricci flow to study the existence of hyperbolic structure on cusped 3-manifolds. The long-time existence and the uniqueness for the extended combinatorial Ricci flow are proven for general pseudo 3-manifolds. We prove that the extended combinatorial Ricci flow converges to a decorated hyperbolic polyhedral metric if and only if there exists a decorated hyperbolic polyhedral metric of zero Ricci curvature, and the flow converges exponentially fast in this case. For an ideally triangulated cusped 3-manifold admitting a complete hyperbolic metric, the flow provides an effective algorithm for finding the hyperbolic metric.

Ricci Flow on Quasi Einstein Manifold

2010 ◽  
Vol 0 (-1) ◽  
pp. 447-454
Author(s):  
A. Bhattacharyya ◽  
T. De
Keyword(s):  
Ricci Flow ◽  
Einstein Manifold

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 Deformation classes in generalized Kähler geometry

2020 ◽  
Vol 7 (1) ◽  
pp. 241-256
Author(s):  
Matthew Gibson ◽  
Jeffrey Streets
Keyword(s):  
Symmetry Group ◽  
Ricci Flow ◽  
Kahler Geometry ◽  
Poisson Tensor ◽  
Natural Extensions ◽  
Generalized Kähler Geometry ◽  
Kähler Structures

AbstractWe describe natural deformation classes of generalized Kähler structures using the Courant symmetry group, which determine natural extensions of the notions of Kähler class and Kähler cone to generalized Kähler geometry. We show that the generalized Kähler-Ricci flow preserves this generalized Kähler cone, and the underlying real Poisson tensor.

scholarly journals Sliding Mode Control and Geometrization Conjecture in Seismic Response

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 353
Author(s):  
Ligia Munteanu ◽  
Dan Dumitriu ◽  
Cornel Brisan ◽  
Mircea Bara ◽  
Veturia Chiroiu ◽  
...  
Keyword(s):  
Sliding Mode Control ◽  
Ricci Flow ◽  
Lyapunov Functions ◽  
Seismic Waves ◽  
Sliding Mode ◽  
Flow Process ◽  
Mode Control ◽  
Finite Period ◽  
The Stability ◽  
Story Building

The purpose of this paper is to study the sliding mode control as a Ricci flow process in the context of a three-story building structure subjected to seismic waves. The stability conditions result from two Lyapunov functions, the first associated with slipping in a finite period of time and the second with convergence of trajectories to the desired state. Simulation results show that the Ricci flow control leads to minimization of the displacements of the floors.

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