Invariants and chaotic maps

A one-dimensional mapf(x) is called an invariant of a two-dimensional mapg(x, y) ifg(x, f(x))=f(f(x)). The logistic map is an invariant of a class of two-dimensional maps. We construct a class of two-dimensional maps which admit the logistic maps as their invariant. Moreover, we calculate their Lyapunov exponents. We show that the two-dimensional map can show hyperchaotic behavior.     

Symmetries of non-linear reaction-diffusion equations and their solutions

This paper is concerned with the symmetries of a certain class of non-linear reaction-diffusion equations. The symmetries are used for deriving solutions of these equations. Subsequently, we compare the solutions with those given by other authors.     

Painleve property of anharmonic systems with an external periodic field

The Painlevé property of anharmonic systems with an external periodic field is investigated. This property tell us that the only movable singularities exhibited by the solutions are poles. The Painlevé property can serve to distinguish between integrable and nonintegrable systems.     

Numerical homogenization of foam-like structures based on the FE2-approach

The computation of foam–like structures is still a topic of research. There are two basic approaches: the microscopic model where the foam–like structure is entirely resolved by a discretization (e.g. with Timoshenko beams) on a micro level, and the macroscopic approach which is based on a higher order continuum theory. A combination of both of them is the FE²-approach where the mechanical parameters of the macroscopic scale are obtained by solving a Dirichlet boundary value problem for a representative microstructure at each integration point. In this contribution, we present a two–dimensional geometrically nonlinear FE²-framework of first order (classical continuum theories on both scales) where the microstructures are discretized by continuum finite elements based on the p-version. The p-version elements have turned out to be highly efficient for many problems in structural mechanics. Further, a continuum–based approach affords two additional advantages: the formulation of geometrical and material nonlinearities is easier, and there is no problem when dealing with thicker beam–like structures. In our numerical example we will investigate a simple macroscopic shear test. Both the macroscopic load displacement behavior and the evolving anisotropy of the microstructures will be discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vector Product and an Integrable Dynamical System

We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals. The connection with Nambu mechanics is established. The extension to higher dimensions is also discussed.     

Dynamic analysis of porous materials: Numerical simulation with an adaptive space-time FEM

We investigated a space-time Galerkin method applied to the dynamic analysis of fully-saturated porous material. The governing set of equations are derived from the well-studied Theory of Porous Media (TPM). The numerical scheme consists of a coupled finite element discretization in the space-time domain. Discontinuous approximations of the primary variables in time are employed. A natural flux treatment is applied in time to impose the consistency between the adjacent time intervals. A simple space-time decoupled adaptive strategy based on the “jumps” in time and the ZZ error indicator in space is investigated. Numerical experiments demonstrate the efficiency and reliability of the proposed approach. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient electronic communication between two identical ferrocene centers in a hydrogen-bonded dimer

A novel ferrocene derivative that contains a donor-donor-acceptor-acceptor (DDAA) hydrogen bonding motif forms highly stable, noncovalent dimers in chloroform and dichloromethane solutions. Its voltammetric behavior and the observation of an intervalence charge-transfer band reveal that the two equivalent ferrocene centers in the hydrogen-bonded dimer exhibit a surprisingly efficient level of electronic communication.     

Modelling of thin polymer films

If we bond substrates like metal sheets by a thin polymer film we know about the existence of a boundary layer between the polymer and the substrate. The properties of this boundary layer differ from the bulk properties and influence the overall behavior of the bond. Here we present a mechanical theory based on a scalar-valued order parameter that allows us to describe these effects. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)