Symmetric Satellite Swarms and Choreographic Crystals.

@article{Boyle2016SymmetricSS,
  title={Symmetric Satellite Swarms and Choreographic Crystals.},
  author={Latham A. Boyle and Jun Yong Khoo and Kendrick Smith},
  journal={Physical review letters},
  year={2016},
  volume={116 1},
  pages={
          015503
        }
}
In this Letter, we introduce a natural dynamical analogue of crystalline order, which we call choreographic order. In an ordinary (static) crystal, a high degree of symmetry may be achieved through a careful arrangement of the fundamental repeated elements. In the dynamical analogue, a high degree of symmetry may be achieved by having the fundamental elements perform a carefully choreographed dance. For starters, we show how to construct and classify all symmetric satellite constellations. Then… 

Figures and Topics from this paper

Time Quasilattices in Dissipative Dynamical Systems
  • F. Flicker
  • Physics, Mathematics
    SciPost Physics
  • 2018
We establish the existence of ‘time quasilattices’ as stable trajectories in dissipative dynamical systems. These tilings of the time axis, with two unit cells of different durations, can be
Spatio-Temporal Symmetry - Point Groups with Time Translations
TLDR
The derivation of these ’spatio-temporal’ groups from conventional point groups and their irreducible representations is outlined, followed by a complete listing of groups.
Antisymmetry: Fundamentals and Applications
Symmetry is fundamental to understanding our physical world. An antisymmetry operation switches between two different states of a trait, such as two time-states, position-states, charge-states,
Transient hexagonal structures in sheared emulsions of isotropic inclusions on smectic bubbles in microgravity conditions
TLDR
It is found that droplets can form two-dimensional hexagonal structures changing with time, and the possibility of spatial and temporal periodicity of such structures of droplets is indicated.
Anharmonic Phonons in Graphene from First Principles
Anharmonic Phonons in Graphene from First Principles
Rotating periodic patterns in reaction diffusion systems
  • He Zhang, Fei Xu, Yong Li
  • Communications in Nonlinear Science and Numerical Simulation
  • 2021
Colloidal Dynamics on a Choreographic Time Crystal.
TLDR
Using simulations, colloids interacting with a choreographic crystal consisting of traps that could be created optically are examined and it is shown that transitions between these states can be understood in terms of vertex frustration effects that occur during a certain portion of the choreographic cycle.

References

SHOWING 1-10 OF 35 REFERENCES
Sphere packings, I
  • T. Hales
  • Mathematics, Computer Science
    Discret. Comput. Geom.
  • 1997
TLDR
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.
The Symmetries of Things
I Symmetries of Finite Objects and Plane Repeating Patterns 1. Symmetries Kaleidoscopes Gyrations Rosette Patterns Frieze Patterns Repeating Patterns on the Plane and Sphere Where Are We? 2. Planar
Space groups for solid state scientists
This comprehensively revised - essentially rewritten - new edition of the 1990 edition (described as "extremely useful" by MATHEMATICAL REVIEWS and as "understandable and comprehensive" by Scitech)
Infinite-dimensional Lie algebras
1. Basic concepts.- 1. Preliminaries.- 2. Nilpotency and solubility.- 3. Subideals.- 4. Derivations.- 5. Classes and closure operations.- 6. Representations and modules.- 7. Chain conditions.- 8.
Solid-State Physics
These are a set of notes I have made, based on lectures given by M.Moore at the University of Manchester Jan-June ’08. Please e-mail me with any comments/corrections: jap@watering.co.uk.
111
  • The Devil's Fork
  • 2018
Phys
  • Rev. Lett. 110, 118901
  • 2013
Phys. Rev. Lett
  • Phys. Rev. Lett
  • 2013
Physical Review Letters , 110 , 118901 [ 8 ] F . Wilczek
  • Phys . Rev . Lett .
  • 2013
Phys
  • Rev. Lett. 109, 160401
  • 2012
...
1
2
3
4
...