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Reference [<] [>] [x] : Figure [<] [>] [x]

23.

Freezing transition of hard hyperspheres R. Finken, M. Schmidt, and H. Löwen, Phys. Rev. E 65, 016108 (2002). Locate in [bare] [illustrated] list. Get [full paper] as pdf. Abstract. We investigate the system of D-dimensional hard spheres in D-dimensional space, where D>3. For the fluid phase of these hyperspheres, we generalize scaled-particle theory to arbitrary D and furthermore use the virial expansion and the Percus-Yevick integral equation. For the crystalline phase, we adopt cell theory based on elementary geometrical assumptions about close-packed lattices. Regardless of the approximation applied, and for dimensions as high as D=50, we find a first-order freezing transition, which preempts the Kirkwood second-order instability of the fluid. The relative density jump increases with D, and a generalized Lindemann rule of melting holds. We have also used ideas from fundamental-measure theory to obtain a free energy density functional for hard hyperspheres. Finally, we have calculated the surface tension of a hypersphere fluid near a hard smooth hyper-wall within scaled-particle theory. [figures] Read the [full paper] as pdf.

Hard spheres

The hard sphere system freezes between [2] and [3], and in ~[23] dimensions (tags as contents!), as well as on stripe-patterned substrates [26]. Deep relations to dimensional crossover exist [5] [6]. Hard spheres were immersed in emulsions [9], confined to a flexible container [18], exposed to surfaces of other quenched spheres [37] and of random fiber networks [39], and subject to gravity [51]. Recently, the Rosenfeld functional [5] [6] was generalized to non-additive mixtures [53].

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