Effect of Boundaries on Pattern Formation in a Monolayer of Interacting Dipoles

Self-organization can be defined as a process of arrangement of entities that start out in an irregular arrangement and evolve into a stable, regular pattern without the aid of an external agent. A system of magnetic particles that are constrained to move only in a plane is reported. The individual components in the system have dipole moments in an orientation perpendicular to the plane of motion and the interaction between components is purely repulsive. For such a system, it is attempted to understand the influence of the boundary of the monolayer on the patterns that emerge. A system with a small number of magnets is found where the range of the magnetic interactions is of the size of the boundary; the symmetry of the boundary imposed on the monolayer plays a crucial role in determining the pattern types, the number of different pattern types, and the frequency of appearance of a particular pattern type. The effect of scaling up the size of the system while maintaining the characteristics of individual components as well as the component areal density is also discussed.     

X-ray Structure Analysis of 4–[(3,3–Dimethyloxiranyl)–methoxy]-7H-furo[3,2-g][1]benzopyran-7-one

The title compound, C₁₆H₁₄O₅, a furanocoumarin crystallizes in the triclinic space group P1 . The unit cell parameters are a = 7.852(2), b = 8.485(1), c = 11.095(1) Å; α = 105.90(1), β = 103.18(2), γ = 95.07(1)°. The structure has been solved by direct methods. Final R = 0.048 for 1943 observed reflections. The furanocoumarin system is almost planar. The epoxide ring makes a dihedral angle with the fused ring system of 98.21(11)°. Molecules are held together by C—H… O hydrogen bonds.     

Refined Crystal and Molecular Structure of Andrographolide — Diterpene

A refined crystal structure of andrographolide has been obtained by X-ray anaysis using CuKα radiation. It crystallizes in the monoclinic crystal system with unique b-axis in space group P2₁. The unit cell parameters are a = 6.552(2) Å, b = 8.009(1) Å, c = 17.989(1) Å and interaxial angle β = 97.32(1)°. The structure has been solved by direct methods and was refined up to R = 0.041, ωR = 0.0464. Both the cyclohexane rings are in chair conformation with the furan ring in twist conformation. The crystal structure is stabilized by hydrogen bonding.     

Crystal Structure of N-methyl Crotananinium Iodide — A Pyrrolizidine Alkaloid

The crystal structure of N-methyl crotananinium iodide has been determined by X-ray structure analysis. The compound crystallizes in the orthorhombic space group P2₁2₁2₁ with cell parameters a = 19.37(2), b = 7.70(2), c = 13.38(2) Å. The structure has been solved by Patterson and successive Fourier methods and refined by full matrix least-squares methods to an R-index of 0.075. The structural features of the title compound are noted and are compared with those of similar others of such pyrrolizidine alkaloids.     

Crystal Structure of 5,7-Dimethoxy-8-(2-oxo-3-methylbutyl)-2 H-1-benzopyran-2-one (Isosibiricin)

The title compound, C₁₆H₁₈O₅, a simple coumarin crystallizes in the monoclinic space group P2₁/c with unit cell parameters a = 7.321(3), b = 21.111(9), c = 11.649(3) Å; β = 123.14(2)°. The structure has been solved by direct methods. The coumarin ring system is planar. The methoxy groups at C5 and C7 are almost coplanar with the coumarin mean plane. The crystal structure is stabilized by C–H… O hydrogen bonds.