(Color online) Structural change for various values of for . Top view (left) and side view (right) are shown to help visualize the three-dimensional structures.
(Color online) 1D Coulomb chain. (A) Simulation (, ). (B) Experimental observation in laboratory [courtesy of Dr. N. Sato and Dr. S. Iizuka (Ref. 31)].
(Color online) 2D regular polygon structures (simulation).
Equipotential lines for numerical 2D dust structures .
Large dust cluster .
Fundamental crystal configurations in a spherical harmonic potential. (a) , (b) , (c) . The structures are characterized by two sets of particles in two parallel planes. The projections of the particles on an plane are regular polygons, or a square, a regular hexagon, and a regular octagon.
(Color online) The configurations of minimum energy (CME) for four particles for various values of . Broken lines show the axis or the direction of . For , the particles are at the corners of a square in an plane. When becomes larger than 0.68, the structure becomes three-dimensional. For , the structure becomes uniquely characterized by two interparticle lines, one -directional and the other in an plane. For , a rhombic structure is formed followed by a deformed diamond shape for . A chain structure is formed for .
(Color online) Total potential energy , radial potential energy , and -component potential energy vs elongation parameter . The potential energy is dominantly in a radial component for , while more of the potential energy shifts to the component for . Simulation results are marked by solid markers (, , ), while analytical results are shown by lines with labels (1), (2), and (3). Detailed behavior around is shown as an inset.
(Color online) Coordinates and analytical expressions for the configurations for various ranges of for .
(Color online) The edge lengths (neighboring interparticle distances) as a function of for . Variation of edge lengths corresponds to the variation of configurations of minimum energy (CME) for four particles. The regular tetrahedron is characterized by four equal lengths of 1.260.
(Color online) Spindle-like configurations with (A) top view and (B) side view for (1) , , (2) , , (3) , , (4) , .
Spindle-shape crystal observed in the Tohoku laboratory experiment [courtesy of Dr. N. Sato and Dr. S. Iizuka (Ref. 31)].
Spindle-shape configurations. (A) , ; (B) , ; (C) , . Top: side view; bottom: cross-sectional view. The inner structures are characterized by (A) square, (B) octagonal, and (C) hexagonal cross sections.
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