Free Path Lengths in Quasicrystals

Previous studies of kinetic transport in the Lorentz gas have been limited to cases where the scatterers are distributed at random (e.g., at the points of a spatial Poisson process) or at the vertices of a Euclidean lattice. In the present paper we investigate quasicrystalline scatterer configurations, which are non-periodic, yet strongly correlated. A famous example is the vertex set of a Penrose tiling. Our main result proves the existence of a limit distribution for the free path length, which answers a question of Wennberg. The limit distribution is characterised by a certain random variable on the space of higher dimensional lattices, and is distinctly different from the exponential distribution observed for random scatterer configurations. The key ingredients in the proofs are equidistribution theorems on homogeneous spaces, which follow from Ratner’s measure classification.     

On differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays

In this paper, we consider a class of nonlinear neutral differential equations with state-dependent delays in both the neutral and the retarded terms. We study well-posedness and continuous dependence issues and differentiability of the parameter map with respect to the initial function and other possibly infinite dimensional parameters in a pointwise sense and also in the C-norm.     

Assignment of h.f.s. constants of 1,4-benzosemiquinones by additivity rules. The free rotation of t-butyl groups

A set of equations for assigning hyperfine coupling constants of substituted 1,4-benzosemiquinones are presented. The equations, based on additivity rules, yield assignments for a range of substituents with a correlation between predicted and experimental constants to better than five per cent. The investigation shows that t-butyl groups in semiquinones rotate freely against prior assertions.     

Electroactive Polymers: Developments of and Perspectives for Dielectric Elastomers

We present the development and applications of dielectric elastomers. For the last 10 years the significance of this class of polymers has risen as more applications seem possible and first products have been commercialized.