Surface tension of isotropic-nematic interfaces: Fundamental Measure Theory for hard spherocylinders

A fluid constituted of hard spherocylinders is studied using a density functional theory for non-spherical hard particles, which can be written as a function of weighted densities. This is based on an extended deconvolution of the Mayer $f$-function for arbitrarily shaped convex hard bodies in tensorial weight functions, which depend each only on the shape and orientation of a single particle. In the course of an examination of the isotropic- nematic interface at coexistence the functional is applied to anisotropic and inhomogeneous problems for the first time. We find good qualitative agreement with other theoretical predictions and also with Monte-Carlo simulations

Unimodular lattice triangulations as small-world and scale-free random graphs

Real-world networks, e.g. the social relations or world-wide-web graphs, exhibit both small-world and scale-free behaviour. We interpret lattice triangulations as planar graphs by identifying triangulation vertices with graph nodes and one-dimensional simplices with edges. Since these triangulations are ergodic with respect to a certain Pachner flip, applying different Monte-Carlo simulations enables us to calculate average properties of random triangulations, as well as canonical ensemble averages using an energy functional that is approximately the variance of the degree distribution. All considered triangulations have clustering coefficients comparable with real world graphs, for the canonical ensemble there are inverse temperatures with small shortest path length independent of system size. Tuning the inverse temperature to a quasi-critical value leads to an indication of scale-free behaviour for degrees $k \geq 5$. Using triangulations as a random graph model can improve the understanding of real-world networks, especially if the actual distance of the embedded nodes becomes important.Comment: 17 pages, 6 figures, will appear in New J. Phy

Entropy of unimodular Lattice Triangulations

Triangulations are important objects of study in combinatorics, finite element simulations and quantum gravity, where its entropy is crucial for many physical properties. Due to their inherent complex topological structure even the number of possible triangulations is unknown for large systems. We present a novel algorithm for an approximate enumeration which is based on calculations of the density of states using the Wang-Landau flat histogram sampling. For triangulations on two-dimensional integer lattices we achive excellent agreement with known exact numbers of small triangulations as well as an improvement of analytical calculated asymptotics. The entropy density is $C=2.196(3)$ consistent with rigorous upper and lower bounds. The presented numerical scheme can easily be applied to other counting and optimization problems.Comment: 6 pages, 7 figure

Motion by Stopping: Rectifying Brownian Motion of Non-spherical Particles

We show that Brownian motion is spatially not symmetric for mesoscopic particles embedded in a fluid if the particle is not in thermal equilibrium and its shape is not spherical. In view of applications on molecular motors in biological cells, we sustain non-equilibrium by stopping a non-spherical particle at periodic sites along a filament. Molecular dynamics simulations in a Lennard-Jones fluid demonstrate that directed motion is possible without a ratchet potential or temperature gradients if the asymmetric non-equilibrium relaxation process is hindered by external stopping. Analytic calculations in the ideal gas limit show that motion even against a fluid drift is possible and that the direction of motion can be controlled by the shape of the particle, which is completely characterized by tensorial Minkowski functionals.Comment: 11 pages, 5 figure