# Nonhexagonal Lattices From a Two Species Interacting System

@article{Luo2020NonhexagonalLF, title={Nonhexagonal Lattices From a Two Species Interacting System}, author={Senping Luo and Xiaofeng Ren and Juncheng Wei}, journal={SIAM J. Math. Anal.}, year={2020}, volume={52}, pages={1903-1942} }

A two species interacting system motivated by the density functional theory for triblock copolymers contains long range interaction that affects the two species differently. In a two species periodic assembly of discs, the two species appear alternately on a lattice. A minimal two species periodic assembly is one with the least energy per lattice cell area. There is a parameter $b$ in $[0,1]$ and the type of the lattice associated with a minimal assembly varies depending on $b$. There are…

## 13 Citations

Crystallization to the Square Lattice for a Two-Body Potential

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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…

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. We consider the minimizing problem for energy functionals with two types of competing particles and completely monotone potential on a lattice. We prove that the minima of sum of two completely…

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We study minimizers of a Gross-Pitaevskii energy describing a two-component Bose-Einstein condensate set into rotation. We consider the case of segregation of the components in the Thomas-Fermi…

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- 2019

We consider a deformation $E_{L,\Lambda}^{(m)}(it)$ of the Dedekind eta function depending on two $d$-dimensional simple lattices $(L,\Lambda)$ and two parameters $(m,t)\in (0,\infty)$, initially…

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- MathematicsBulletin of the Australian Mathematical Society
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In the case of inverse power laws and Lennard-Jones-type potentials, necessary and sufficient conditions are given on non-shifted periodic vacancies or substitutional defects for the conservation of minimality results at fixed density.

On the optimality of the rock-salt structure among lattices with charge distributions

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The goal of this work is to investigate the optimality of the $d$-dimensional rock-salt structure, i.e., the cubic lattice $V^{1/d}\mathbb{Z}^d$ of volume $V$ with an alternation of charges $\pm 1$…

On minima of difference of theta functions and application to hexagonal crystallization

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- 2022

. Let z = x + iy ∈ H := { z = x + iy ∈ C : y > 0 } and θ ( α ; z ) = (cid:80) ( m,n ) ∈ Z 2 e − α πy | mz + n | 2 be the theta function associated with the lattice L = Z ⊕ z Z . In this paper we…

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