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The character of Thurston’s circle packings
We introduce the character of Thurston’s circle packings in the hyperbolic background geometry Consequently, some quite simple criteria are obtained...
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Circle packings from tilings of the plane
We introduce a new class of fractal circle packings in the plane, generalizing the polyhedral packings defined by Kontorovich and Nakamura. The...
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On the Deformation of Thurston’s Circle Packings with Obtuse Intersection Angles
We study Thurston’s circle packings with obtuse intersection angles on closed surfaces. By using combinatorial Ricci/Calabi flows and variational...
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A Geometric Study of Circle Packings and Ideal Class Groups
A family of fractal arrangements of circles is introduced for each imaginary quadratic field K . Collectively, these arrangements contain (up to an...
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Rigidity and deformation of generalized sphere packings on 3-dimensional manifolds with boundary
Motivated by Guo–Luo’s generalized circle packings on surfaces with boundary (Guo–Luo in Geom Topol 13(3):1265–1312, 2009), we introduce the...
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Ball Packings in Hyperbolic Space
It is natural to extend the study of packing and covering problems to the hyperbolic plane, as well as hyperbolic spaces of higher dimension....
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Growth Kinetics of Random Sequential Adsorption Packings Built of Two-Dimensional Shapes with Discrete Orientations
We studied random sequential adsorption packings constructed from rectangles, ellipses, and discorectangles, where the orientations of constituent...
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Sparse Hard-Disk Packings and Local Markov Chains
We propose locally stable sparse hard-disk packings, as introduced by Böröczky, as a model for the analysis and benchmarking of Markov-chain Monte...
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Thurston’s sphere packings on 3-dimensional manifolds, I
Thurston’s sphere packing on a 3-dimensional manifold is an analogue of Thurston’s circle packing on a surface, the rigidity of which has been open...
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Density of Binary Disc Packings: The Nine Compact Packings
A disc packing in the plane is compact if its contact graph is a triangulation. There are nine values of r such that a compact packing by discs of...
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A Process-Based Pore Network Model Construction for Granular Packings Under Large Plastic Deformations
We propose a process-based method for constructing a pore network model of granular packings under large deformations. The method uses the radical...
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Voronoi tiling and circle packing on spiral lattices with rotational symmetry
It is shown that the bifurcation diagram of circle packings on logarithmic spiral lattices with rotational symmetry is graph-theoretically dual to...
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Self-assembly of homogeneous systems
The circle packings including non-periodic packings can be analysed for physical and thermodynamic stability for a triangular net with T 4=3–6...
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Apollonian packings in seven and eight dimensions
In an earlier work, we proposed a generalization for the Apollonian packing in arbitrary dimensions and showed that the resulting object in four,...
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Recurrence of a weighted random walk on a circle packing with parabolic carrier
In this paper we show that given a circle packing of an infinite planar triangulation such that its carrier is parabolic, placing weights on the...
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Deformation of discrete conformal structures on surfaces
In Glickenstein (J Differ Geom 87: 201–237, 2011), Glickenstein introduced the discrete conformal structures on polyhedral surfaces in an axiomatic...