Exact Scaling Functions for One-Dimensional Stationary KPZ Growth

We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a Riemann–Hilbert problem related to the Painlevé II equation. We solve these equations numerically with very high precision and compare our, up to numerical rounding exact, result with the prediction of Colaiori and Moore⁽¹⁾ obtained from the mode coupling approximation.     

An eulerian trail traversing specified edges in given order

The following results are proved in this paper. Let G be a 2k-edge-connected eulerian graph. (i) For every set {e₁, e₂, ?, e_2k+1} ? E(G) there is an eulerian trail T of the form e₁, e₂, ?, e_2k+1, ?. (ii) For every set E* = {e₁, e₂, ?, e_k} ? E(G) there is an eulerian trail T = e₁, ?, e₂, ?, e_k, ? in which the elements of E* are traversed in accordance with a prescribed orientation. © 1995 John Wiley & Sons, Inc.     

Preparation and mechanical properties of layers made of recombinant spider silk proteins and silk from silk worm

Layers of recombinant spider silks and native silks from silk worms were prepared by spin-coating and casting of various solutions. FT-IR spectra were recorded to investigate the influence of the different mechanical stress occurring during the preparation of the silk layers. The solubility of the recombinant spider silk proteins SO1-ELP, C16, AQ24NR3, and of the silk fibroin from Bombyx mori were investigated in hexafluorisopropanol, ionic liquids and concentrated salt solutions. The morphology and thickness of the layers were determined by Atomic Force Microscopy (AFM) or with a profilometer. The mechanical behaviour was investigated by acoustic impedance analysis by using a quartz crystal microbalance (QCMB) as well as by microindentation. The density of silk layers (d<300 nm) was determined based on AFM and QCMB measurements. At silk layers thicker than 300 nm significant changes of the half-band-half width can be correlated with increasing energy dissipation. Microhardness measurements demonstrate that recombinant spider silk and sericine-free Bombyx mori silk layers achieve higher elastic penetration modules E_EP and Martens hardness values H_M than those of polyethylenterephthalate (PET) and polyetherimide (PEI) foils.