Vectorial crystallization problems and collective behavior.

@article{DeLuca2021VectorialCP,
  title={Vectorial crystallization problems and collective behavior.},
  author={Lucia De Luca and A. R. Del Ninno and Marcello Ponsiglione},
  journal={Journal of mathematical biology},
  year={2021},
  volume={84 1-2},
  pages={
          6
        }
}
We propose and analyze a class of vectorial crystallization problems, with applications to crystallization of anisotropic molecules and collective behavior such as birds flocking and fish schooling. We focus on two-dimensional systems of "oriented" particles: Admissible configurations are represented by vectorial empirical measures with density in [Formula: see text]. We endow such configurations with a graph structure, where the bonds represent the "convenient" interactions between particles… 
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References

SHOWING 1-10 OF 30 REFERENCES
Emergence of Rigid Polycrystals from Atomistic Systems with Heitmann–Radin Sticky Disk Energy
We investigate the emergence of rigid polycrystalline structures from atomistic particle systems. The atomic interaction is governed by a suitably normalized pair interaction energy, where the…
A Proof of Crystallization in Two Dimensions
TLDR
This work shows rigorously that under suitable assumptions on the potential V which are compatible with the growth behavior of the Lennard-Jones potential the ground state energy per particle converges to an explicit constant E*: where E* ∈ ℝ is the minimum of a simple function on [0,∞).
Minimizing atomic configurations of short range pair potentials in two dimensions: crystallization in the Wulff shape
We investigate ground state configurations of atomic systems in two dimensions interacting via short range pair potentials. As the number of particles tends to infinity, we show that low-energy…
Crystallization to the Square Lattice for a Two-Body Potential
We consider two-dimensional zero-temperature systems of $N$ particles to which we associate an energy of the form $$ \mathcal{E}[V](X):=\sum_{1\le i<j\le N}V(|X(i)-X(j)|), $$ where $X(j)\in\mathbb…
$$\varGamma $$Γ-Convergence of the Heitmann–Radin Sticky Disc Energy to the Crystalline Perimeter
TLDR
A compactness result is proved which shows the emergence of polycrystalline structures when the limit configuration is a single crystal, and it is shown that the anisotropic perimeter is the Finsler metric determined by the orientation of the single crystal.
The stability of a crystal with diamond structure for patchy particles with tetrahedral symmetry.
TLDR
Even though the diamond phase is never thermodynamically stable for the longer-ranged model, direct coexistence simulations of the interface between the fluid and the body-centered-cubic crystal and between the fluids and the diamond crystal show that at sufficiently low pressures, it is quite probable that in both cases the solid grows into a diamond crystal, albeit involving some defects.
Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study
TLDR
It is argued that a topological interaction is indispensable to maintain a flock's cohesion against the large density changes caused by external perturbations, typically predation, and supported by numerical simulations.
A review of fish swimming mechanics and behaviour in altered flows
  • J. Liao
  • Environmental Science, Biology
    Philosophical Transactions of the Royal Society B: Biological Sciences
  • 2007
TLDR
New data are presented here which show that behaviour changes in altered flows when either the lateral line or vision is blocked, showing that fish rely on multi-modal sensory inputs to negotiate complex flow environments.
Energetics of Swimming and Flying in Formation
  • Physics
  • 2005
Formation movement during swimming and flying has been hypothesized to reduce an individual animal’s energy expenditure. Individuals in a formation distort the flow pattern, creating vorticity in…
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