Structural transitions for 2D systems with competing interactions in logarithmic traps.

We propose a confinement model and study numerically the structural properties of particles with competing interactions in logarithmic traps (i.e., the confinement potential is a logarithmic function). A rich variety of cluster structures are observed as a function of trap steepness, trap size, and particle density. In addition to the consistent results with previous studies for a harmonic confinement, we observe some new stable structures, including a hybrid cluster structure consisting of clumps surrounded by a circular stripe, parallel stripes, or homogeneous voids surrounded by a ringlike arrangement of clumps, and a gear-like cluster with fringed outer rims evenly arranged along the circumference. Our work reveals that such self-organized structures arise due to the radial density reconfiguration in a finite confined system corresponding to the unconstrained systems, which is controlled by the interplay between the long-range repulsions and the attractions to the minimum of the confinement potential. Such results are likely relevant in understanding the structural properties of confined mermaid systems.