The Generation of Maximal Triangle-Free Graphs

In this paper we present an efficient algorithm for generating maximal triangle-free graphs. A program based on this algorithm has been used to check a conjecture of Erdo´´s about the local density of triangle-free graphs and turned out to be very powerful for the computation of triangle Ramsey numbers.     

Dipolar Order in Molecular Fluids: I. Toward an Understanding

The origin behind the dipolar order in molecular fluids is investigated by using a simple dipolar fluid and Monte Carlo simulation technique. A penalty function is employed to separately manipulate the positional and orientational structure of the fluid. By considering the distance-dependent Kirkwood function G _k, which in turn is related to the dielectric permittivity of the fluid, it is observed that both positional and orientational ordering are involved to establish dipolar order.     

Dipolar Order in Molecular Fluids: II. Molecular Influence

The influence on the short-range packing in dipolar fluids by molecular shape and by additional higher order electrostatic moments has been investigated by molecular dynamic simulations. The dipole polarization was found to decrease as the particles were elongated parallel to the dipole and to increase for elongation perpendicular to the dipole, eventually forming a nematic order. The addition of a quadrupole lead to a reduction of the polarization, and the influence of an axial octupole was weaker and more complex. Both a decrease and an increase of the polarization is possible depending on the relative dipole–dipole and octupole–octupole interaction strengths and the relative direction of the symmetry axes of the moments. These observations were attributed to the different parity of a dipole and a quadrupole and the same parity of a dipole and an axial octupole under reflection. In addition, further insights into the formation of dipole polarization were obtained. Short polar and long equatorial radii and strong dipole–dipole interaction are particle properties that promote a fluid with a high dipole polarization.