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

Thermal noise influences fluid flow in thin films during spinodal dewetting

Experiments on dewetting thin polymer films confirm the theoretical prediction that thermal noise can strongly influence characteristic time-scales of fluid flow and cause coarsening of typical length scales. Comparing the experiments with deterministic simulations, we show that the Navier-Stokes equation has to be extended by a conserved bulk noise term to accomplish the observed spectrum of capillary waves. Due to thermal fluctuations the spectrum changes from an exponential to a power law decay for large wavevectors. Also the time evolution of the typical wavevector of unstable perturbations exhibits noise induced coarsening that is absent in deterministic hydrodynamic flow.Comment: 4 pages, 3 figure

Morphological Thermodynamics of Fluids: Shape Dependence of Free Energies

We examine the dependence of a thermodynamic potential of a fluid on the geometry of its container. If motion invariance, continuity, and additivity of the potential are fulfilled, only four morphometric measures are needed to describe fully the influence of an arbitrarily shaped container on the fluid. These three constraints can be understood as a more precise definition for the conventional term "extensive" and have as a consequence that the surface tension and other thermodynamic quantities contain, beside a constant term, only contributions linear in the mean and Gaussian curvature of the container and not an infinite number of curvatures as generally assumed before. We verify this numerically in the entropic system of hard spheres bounded by a curved wall.Comment: 4 pages, 3 figures, accepted for publication in PR

Primordial Non-Gaussianity and Analytical Formula for Minkowski Functionals of the Cosmic Microwave Background and Large-scale Structure

We derive analytical formulae for the Minkowski Functions of the cosmic microwave background (CMB) and large-scale structure (LSS) from primordial non-Gaussianity. These formulae enable us to estimate a non-linear coupling parameter, f_NL, directly from the CMB and LSS data without relying on numerical simulations of non-Gaussian primordial fluctuations. One can use these formulae to estimate statistical errors on f_NL from Gaussian realizations, which are much faster to generate than non-Gaussian ones, fully taking into account the cosmic/sampling variance, beam smearing, survey mask, etc. We show that the CMB data from the Wilkinson Microwave Anisotropy Probe should be sensitive to |f_NL|\simeq 40 at the 68% confidence level. The Planck data should be sensitive to |f_NL|\simeq 20. As for the LSS data, the late-time non-Gaussianity arising from gravitational instability and galaxy biasing makes it more challenging to detect primordial non-Gaussianity at low redshifts. The late-time effects obscure the primordial signals at small spatial scales. High-redshift galaxy surveys at z>2 covering \sim 10Gpc^3 volume would be required for the LSS data to detect |f_NL|\simeq 100. Minkowski Functionals are nicely complementary to the bispectrum because the Minkowski Functionals are defined in real space and the bispectrum is defined in Fourier space. This property makes the Minksowski Functionals a useful tool in the presence of real-world issues such as anisotropic noise, foreground and survey masks. Our formalism can be extended to scale-dependent f_NL easily.Comment: 16 pages, 5 figures, accepted for publication in ApJ (Vol. 653, 2006

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

Second order analysis of geometric functionals of Boolean models

This paper presents asymptotic covariance formulae and central limit theorems for geometric functionals, including volume, surface area, and all Minkowski functionals and translation invariant Minkowski tensors as prominent examples, of stationary Boolean models. Special focus is put on the anisotropic case. In the (anisotropic) example of aligned rectangles, we provide explicit analytic formulae and compare them with simulation results. We discuss which information about the grain distribution second moments add to the mean values.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jensen. (The second version mainly resolves minor LaTeX problems.

Appearance of the Single Gyroid Network Phase in Nuclear Pasta Matter

Nuclear matter under the conditions of a supernova explosion unfolds into a rich variety of spatially structured phases, called nuclear pasta. We investigate the role of periodic network-like structures with negatively curved interfaces in nuclear pasta structures, by static and dynamic Hartree-Fock simulations in periodic lattices. As the most prominent result, we identify for the first time the {\it single gyroid} network structure of cubic chiral $I4_123$ symmetry, a well known configuration in nanostructured soft-matter systems, both as a dynamical state and as a cooled static solution. Single gyroid structures form spontaneously in the course of the dynamical simulations. Most of them are isomeric states. The very small energy differences to the ground state indicate its relevance for structures in nuclear pasta.Comment: 7 pages, 4 figure

Radial Distribution Function for Semiflexible Polymers Confined in Microchannels

An analytic expression is derived for the distribution $G(\vec{R})$ of the end-to-end distance $\vec{R}$ of semiflexible polymers in external potentials to elucidate the effect of confinement on the mechanical and statistical properties of biomolecules. For parabolic confinement the result is exact whereas for realistic potentials a self-consistent ansatz is developed, so that $G(\vec{R})$ is given explicitly even for hard wall confinement. The theoretical result is in excellent quantitative agreement with fluorescence microscopy data for actin filaments confined in rectangularly shaped microchannels. This allows an unambiguous determination of persistence length $L_P$ and the dependence of statistical properties such as Odijk's deflection length $\lambda$ on the channel width $D$. It is shown that neglecting the effect of confinement leads to a significant overestimation of bending rigidities for filaments