Disc–Disc Structure in a Two-Species Interacting System on a Flat Torus

Autor: Guanning Zhang, Xiaofeng Ren
Rok vydání: 2021
Předmět:
Zdroj: Journal of Nonlinear Science. 32
ISSN: 1432-1467
0938-8974
DOI: 10.1007/s00332-021-09760-y
Popis: A two-species interacting system, motivated by the triblock copolymers theory, is studied on a flat torus, the quotient space of the complex plane by a lattice. The free energy of the system, which contains both short-range and long-range interactions, admits disc–disc-like stationary points. The relative displacement of the disc centres in a stationary point is related to Green’s function of the Laplace operator on the flat torus. When restricted to disc–disc configurations with relative displacements equal to half periods, the free energy is minimized with respect to the lattice and its half periods. The resulting optimal lattice depends on a single parameter. As this parameter varies, the optimal lattice may be rectangular, square, rhombic, or hexagonal. This is in sharp contrast to single-species systems where optimal lattices are always hexagonal.
Databáze: OpenAIRE
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