Dense packings of congruent circles in a circle
TLDR
The problem of finding packings of congruent circles in a circle, or, equivalently, of spreading points in acircle, is considered.About:
This article is published in Discrete Mathematics.The article was published on 1998-02-15 and is currently open access. It has received 214 citations till now. The article focuses on the topics: Six circles theorem & Five circles theorem.read more
Citations
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Journal ArticleDOI
Solving circle packing problems by global optimization: Numerical results and industrial applications
TL;DR: This work highlights the relevance of global optimization in solving circle packing problems, and points towards the necessary advancements in both theory and numerical practice.
Journal ArticleDOI
Multiple-mouse MRI.
TL;DR: In parallel imaging with a four‐coil array, the time required for three‐dimensional (3D) high‐resolution imaging of four mice is reduced to one‐fourth the time that it would take to image the mice sequentially.
Proceedings ArticleDOI
Shepherding Behaviors with Multiple Shepherds
TL;DR: This work extends the previous work of shepherding behaviors with a single shepherd to multiple shepherds to study how a group ofShepherds can work cooperatively without communication to efficiently control the flock.
Journal ArticleDOI
Optimizing the packing of cylinders into a rectangular container: A nonlinear approach
TL;DR: In this work, a procedure based on a nonlinear decision problem to solve the cylinder packing problem with identical diameters is presented and better results are achieved.
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Direct imaging of magnetic field-driven transitions of skyrmion cluster states in FeGe nanodisks
Xuebing Zhao,Chiming Jin,Chao Wang,Haifeng Du,Haifeng Du,Jiadong Zang,Mingliang Tian,Mingliang Tian,Renchao Che,Yuheng Zhang,Yuheng Zhang +10 more
TL;DR: The magnetic field-driven dynamics of individual skyrmions in FeGe nanodisks with diameters on the order of severalskyrmion sizes are reported by using Lorentz transmission electron microscopy, and a dynamics is found at elevated temperatures, at which the thermal energy competes with the energy barrier between the skyrnion cluster states.
References
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Book
Sphere packings, lattices, and groups
TL;DR: The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space?
Posted Content
Sphere packings I
TL;DR: A program to prove the Kepler conjecture on sphere packings is described and it is shown that every Delaunay star that satisfies a certain regularity condition satisfies the conjecture.
Book
Unsolved problems in geometry
TL;DR: A monograph on geometry, each section in the book describes a problem or a group of related problems, capable of generalization of variation in many directions.
Journal ArticleDOI
How to simulate billiards and similar systems
TL;DR: A new efficient serial event-driven algorithm is described for simulating an N -component continuous-time dynamic system whose components evolve independently all the time except for discrete asynchronous instances of pairwise interactions.