Gravity-Induced Shape Transformations of Vesicles

We theoretically study the behavior of vesicles filled with a liquid of higher density than the surrounding medium, a technique frequently used in experiments. In the presence of gravity, these vesicles sink to the bottom of the container, and eventually adhere even on non - attractive substrates. The strong size-dependence of the gravitational energy makes large parts of the phase diagram accessible to experiments even for small density differences. For relatively large volume, non-axisymmetric bound shapes are explicitly calculated and shown to be stable. Osmotic deflation of such a vesicle leads back to axisymmetric shapes, and, finally, to a collapsed state of the vesicle.Comment: 11 pages, RevTeX, 3 Postscript figures uuencode

Complex Line Bundles over Simplicial Complexes and their Applications

Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete classification of discrete vector bundles over finite simplicial complexes. In particular, we obtain a discrete analogue of a theorem of Andr\'e Weil on the classification of hermitian line bundles. Moreover, we associate to each discrete hermitian line bundle with curvature a unique piecewise-smooth hermitian line bundle of piecewise constant curvature. This is then used to define a discrete Dirichlet energy which generalizes the well-known cotangent Laplace operator to discrete hermitian line bundles over Euclidean simplicial manifolds of arbitrary dimension

Thermodynamics of a Colloidal Particle in a Time-Dependent Non-Harmonic Potential

We study the motion of an overdamped colloidal particle in a time-dependent non-harmonic potential. We demonstrate the first law-like balance between applied work, exchanged heat, and internal energy on the level of a single trajectory. The observed distribution of applied work is distinctly non-Gaussian in good agreement with numerical calculations. Both the Jarzynski relation and a detailed fluctuation theorem are verified with good accuracy

Plant Disease Resistance Inducing Activity of 7-Oxo- and 7-Hydroxysterols

The 7-oxosterols 1–2 and the 7-hydroxysterols 3–6 induce resistance toward the fungal pathogens Puccinia striiformis West, and Puccinia hordei Otth in barley and wheat. Primary leaves of the plants were sprayed with solutions of the compounds (10-4 mol/l in 1% aqu. ethanol) followed, 2 days later, by challenge inoculation with the fungal pathogens. The results indicate that 7a- and 7β-hydroxylated epimers of β-sitosterol and cholesterol show the highest value of induced resistance (39-49% reduction of infection sites). No enhanced resistance toward the fungi Erysiphe graminis DC f. sp. tritici and hordei and Cochliobolus sativus Ito & Kuribayashi was observed. © 1995 Verlag der Zeitschrift für Naturforschung. All rights reserved

Quantum Invariants, Modular Forms, and Lattice Points II

We study the SU(2) Witten--Reshetikhin--Turaev invariant for the Seifert fibered homology spheres with M-exceptional fibers. We show that the WRT invariant can be written in terms of (differential of) the Eichler integrals of modular forms with weight 1/2 and 3/2. By use of nearly modular property of the Eichler integrals we shall obtain asymptotic expansions of the WRT invariant in the large-N limit. We further reveal that the number of the gauge equivalent classes of flat connections, which dominate the asymptotics of the WRT invariant in N ->\infinity, is related to the number of integral lattice points inside the M-dimensional tetrahedron

Elastic deformation of a fluid membrane upon colloid binding

When a colloidal particle adheres to a fluid membrane, it induces elastic deformations in the membrane which oppose its own binding. The structural and energetic aspects of this balance are theoretically studied within the framework of a Helfrich Hamiltonian. Based on the full nonlinear shape equations for the membrane profile, a line of continuous binding transitions and a second line of discontinuous envelopment transitions are found, which meet at an unusual triple point. The regime of low tension is studied analytically using a small gradient expansion, while in the limit of large tension scaling arguments are derived which quantify the asymptotic behavior of phase boundary, degree of wrapping, and energy barrier. The maturation of animal viruses by budding is discussed as a biological example of such colloid-membrane interaction events.Comment: 14 pages, 9 figures, REVTeX style, follow-up on cond-mat/021242

Vesicles in solutions of hard rods

The surface free energy of ideal hard rods near curved hard surfaces is determined to second order in curvature for surfaces of general shape. In accordance with previous results for spherical and cylindrical surfaces it is found that this quantity is non-analytical when one of the principal curvatures changes signs. This prohibits writing it in the common Helfrich form. It is shown that the non-analytical terms are the same for any aspect ratio of the rods. These results are used to find the equilibrium shape of vesicles immersed in solutions of rod-like (colloidal) particles. The presence of the particles induces a change in the equilibrium shape and to a shift of the prolate-oblate transition in the vesicle phase diagram, which are calculated within the framework of the spontaneous curvature model. As a consequence of the special form of the energy contribution due to the rods these changes cannot be accounted for by a simple rescaling of the elastic constants of the vesicle as for solutions of spherical colloids or polymers.Comment: 11 pages, 7 figures, submitted to Phys. Rev.

Development of a chromium-thoria alloy

Low temperature ductility and high temperature strength of pure chromium and chromium-thoria alloy prepared from vapor deposited powder

Is flow velocity a significant parameter in flood damage modelling?

Flow velocity is generally presumed to influence flood damage. However, this influence is hardly quantified and virtually no damage models take it into account. Therefore, the influences of flow velocity, water depth and combinations of these two impact parameters on various types of flood damage were investigated in five communities affected by the Elbe catchment flood in Germany in 2002. 2-D hydraulic models with high to medium spatial resolutions were used to calculate the impact parameters at the sites in which damage occurred. A significant influence of flow velocity on structural damage, particularly on roads, could be shown in contrast to a minor influence on monetary losses and business interruption. Forecasts of structural damage to road infrastructure should be based on flow velocity alone. The energy head is suggested as a suitable flood impact parameter for reliable forecasting of structural damage to residential buildings above a critical impact level of 2 m of energy head or water depth. However, general consideration of flow velocity in flood damage modelling, particularly for estimating monetary loss, cannot be recommended