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

Density functional theory for hard-sphere mixtures: the White-Bear version Mark II

In the spirit of the White-Bear version of fundamental measure theory we derive a new density functional for hard-sphere mixtures which is based on a recent mixture extension of the Carnahan-Starling equation of state. In addition to the capability to predict inhomogeneous density distributions very accurately, like the original White-Bear version, the new functional improves upon consistency with an exact scaled-particle theory relation in the case of the pure fluid. We examine consistency in detail within the context of morphological thermodynamics. Interestingly, for the pure fluid the degree of consistency of the new version is not only higher than for the original White-Bear version but also higher than for Rosenfeld's original fundamental measure theory.Comment: 16 pages, 3 figures; minor changes; J. Phys.: Condens. Matter, accepte

Using the filaments in the LCRS to test the LambdaCDM model

It has recently been established that the filaments seen in the Las Campanas Redshift Survey (LCRS) are statistically significant at scales as large as 70 to 80 Mpc/h in the $-3^{\circ}$ slice, and 50 to 70 Mpc/h in the five other LCRS slices. The ability to produce such filamentary features is an important test of any model for structure formation. We have tested the LCDM model with a featureless, scale invariant primordial power spectrum by quantitatively comparing the filamentarity in simulated LCRS slices with the actual data. The filamentarity in an unbiased LCDM model, we find, is less than the LCRS. Introducing a bias b=1.15, the model is in rough consistency with the data, though in two of the slices the filamentarity falls below the data at a low level of statistical significance. The filamentarity is very sensitive to the bias parameter and a high value b=1.5, which enhances filamentarity at small scales and suppresses it at large scales, is ruled out. A bump in the power spectrum at k~0.05 Mpc/h is found to have no noticeable effect on the filamentarity.Comment: 16 pages, 3 figures; Minor Changes, Accepted to Ap

Goodness-of-fit tests for complete spatial randomness based on Minkowski functionals of binary images

We propose a class of goodness-of-fit tests for complete spatial randomness (CSR). In contrast to standard tests, our procedure utilizes a transformation of the data to a binary image, which is then characterized by geometric functionals. Under a suitable limiting regime, we derive the asymptotic distribution of the test statistics under the null hypothesis and almost sure limits under certain alternatives. The new tests are computationally efficient, and simulations show that they are strong competitors to other tests of CSR. The tests are applied to a real data set in gamma-ray astronomy, and immediate extensions are presented to encourage further work