External watchman routes

We consider the problem of finding a shortest watchman route from which the exterior of a polygon is visible (external watchman route). We present an O (n ⁴ log logn) algorithm to find shortest external watchman routes for simple polygons by transforming the external watchman route problem to a set of internal watchman route problems. Also, we present faster external watchman route algorithms for special cases. These include optimal O (n) algorithms for convex, monotone, star and spiral polygons and an O (n log logn) algorithm for rectilinear polygons.This work was supported in part by a grant from Texas Instruments, Inc. to S. Ntafos     

A Semi-Lagrangian Method for 3-D Fokker Planck Equations for Stochastic Dynamical Systems on the Sphere

In this paper, we consider stochastic dynamical systems on the sphere and the associated Fokker–Planck equations. A semi-Lagrangian method combined with a Finite Volume discretization of the sphere is presented to solve the Fokker–Planck equation. The method is applied to a typical problem in fiber dynamics and textile production. The numerical results are compared to explicit solutions and Monte-Carlo solutions.     

A method for the calculation of interfacial energies in Al2O3 and ZrO2/liquid-metal and liquid-alloy systems

A method is proposed by which the interfacial energy, γ_SL, of polycrystalline solid oxides (Al₂O₃, ZrO₂) in contact with liquid metals and certain binary liquid alloys can be calculated from the values of the surface energy of the oxides, γ_SV, and the liquid metals or liquid alloys, γ_LV, respectively. According to this method, the interfacial energy depends on the geometric mean of surface interactions, (γ_SV γ_LV)^1/2, the molar volumes, V, of the solid and liquid phases, and a parameter, K, which depends on the geometric details of the oxide surface defined by the ion sites in the oxide as well as the stoichiometry of the elements in the oxide and is given by the equation, $$\gamma _{SL} = \left( {K\frac{{V_{metal} }}{{V_{oxide} }} + 1} \right)^{2/3} (\gamma _{SV} \gamma _{LV} )^{1/2}$$ The method was verified using interfacial energy data obtained by measurements of the contact angle, θ, formed between the oxides and the liquid metals and liquid alloys with the sessile drop technique. A good agreement was observed between the calculated and the experimentally estimated values of γ_SL at the melting point of the metals and alloys.     

Adaptive isogeometric analysis by local h-refinement with T-splines

Isogeometric analysis based on non-uniform rational B-splines (NURBS) as basis functions preserves the exact geometry but suffers from the drawback of a rectangular grid of control points in the parameter space, which renders a purely local refinement impossible. This paper demonstrates how this difficulty can be overcome by using T-splines instead. T-splines allow the introduction of so-called T-junctions, which are related to hanging nodes in the standard FEM. Obeying a few straightforward rules, rectangular patches in the parameter space of the T-splines can be subdivided and thus a local refinement becomes feasible while still preserving the exact geometry. Furthermore, it is shown how state-of-the-art a posteriori error estimation techniques can be combined with refinement by T-splines. Numerical examples underline the potential of isogeometric analysis with T-splines and give hints for further developments.     

Fabrication and characterization of robust hydrophobic lotus leaf-like surface on Si3N4 porous membrane via polymer-derived SiNCO inorganic nanoparticle modification

Robust hydrophobic surface was produced by modifying the surface of porous Si₃N₄ membrane, via aminolysis and pyrolysis process, with organosilane-derived inorganic SiNCO nanoparticles, which are tightly adhered to the Si₃N₄ grains. The resultant material had a high water contact angle of 142°, attributed to -Si-CH₃ surface terminal groups and a lotus leaf-like hierarchical structure of the nanoparticles, which had a frame structure with Si-N and Si-O covalent bonds in their bulk. The hydrophobic behavior remained practically unchanged after exposure of the produced membranes to aqueous solutions of humic acid, HCl and NaOH, to benzene, as well as to stirring abrasive slurry with SiC particles, and after exposure at high temperatures, up to 500?°C, to air. The inorganic membrane can be considered for use in a broad range of applications which require robust hydrophobic surfaces.     

Automatic h-Scaling for the Efficient Time Integration of Stiff Mechanical Systems

When solving stiff mechanical systems, implicit time integrators overestimate the error and tend to use small stepsizes due to the order reduction phenomenon. This article introduces an algorithm for the detection of stiff components that allows automatic scaling of the stepsize h in the error estimation. It is based on an investigation of the local error and applies existing embedded formulas of implicit Runge–Kutta methods. Thus, implementation and calculation effort are low. Three examples are integrated with the code RADAU5, a linear DAE in two different formulations and a slider crank mechanism.     

Comparison of the fatty acids of the tunicateBotryllus schlosseri from the Black Sea with two associated bacterial strains

The fatty acid composition of the tunicateBotryllus schlosseri and of two bacterial strains found within the tunicate, namelyVibrio parahaemolyticus and of an associated but previously unreported gram positive cocci were studied. The polyunsaturated fatty acids 6,9,12-octadecatrienoic acid, 5,8,11,14,17-eicosapentaenoic acid, and 4,7,10,13,16,19-docosahexaenoic acid were particularly abundant inB. schlosseri and were not detected in the two bacterial strains found in the tunicate. Theiso/anteiso pair, 13-methyltetradecanoic acid and 12-methyltetradecanoic acid, were the principal fatty acids in the gram positive cocci, and the 9- and 11-hexadecenoic acids were particulary abundant inV. parahaemolyticus. The diunsaturated fatty acid 9,12-octadecadienoic acid was also shown to be present inV. parahaemolyticus. The fatty acid composition of a third bacterial strain, characterized as either aPseudomonas or anAlteromonas species, and shown to be present only in the sea water from the Black Sea and not inB. schlosseri, is also reported. This is the first investigation on fatty acids from Black Sea bacteria.