We use FLUENT to calculate the wind profile over barchans and transverse dunes. The form of the streamlines of flow separation at the lee side of the dunes is determined for a symmetric barchan dune in three dimensions, and for the height profile of a measured transverse dune field in the...

The motion of dunes and their morphology is a fascinating, largely unexplored subject. Already the barchan, the simplest moving dune, poses many questions. We will present some results of field measurements on desert and costal dunes. Then we will present a model which consists of three coupled...

We present a model to describe the collective motion of barchan dunes in a field. Our model is able to reproduce the observation that a typical dune stays confined within a stripe. We also obtain some of the pattern structures which resemble those observed from aerial photos which we do analyse...

We present models to describe the dynamics of the surface of a dry granular bed, like a desert. These models, based on coupled differential equations can describe the formation and evolution of dunes. Field measurements have been performed to compare the numerical results. The concept of the...

The constitutive quantities in Mori's theory, the residual forces, are expanded in terms of time-dependent correlation functions and products of operators at t = 0, where it is assumed that the time derivatives of the observables are given by products of them. As a first consequence the...

A response theory in quantum systems, which can discuss the stability of the total system and the appearance of subharmonics, is proposed. The propagator of the system in the Liouville space is decomposed into the periodic factor with the same frequency as the external field and the remaining...

A previously given formalism for the steady state statistical operator ϱη (t) is illustrated for the case of a periodically driven oscillator coupled to a bath of oscillators. The application to several types of observables is investigated. Explicit evaluation shows that ϱη (t) gives the...

Combined first and second order dynamic susceptibilities for a set of observables are expressed by a matrix resolvent operator in Liouville-space. A well-defined triangular projector is introduced to rewrite second order susceptibilities in terms of frequencies and memory functions. For these a...

The variational principle for expectation values is discussed for the case of driven systems. Examples are considered to find possibilities for an appropriate trial ansatz. Approximate equations of motion for expectation values are evaluated and compared with results of other treatments.

It is pointed out that the Schwinger variational principle of scattering theory directly applies to the case of dynamic susceptibilities in statistical mechanics. The relation to other dynamic approximation schemes is discussed.