Loewner evolution driven by a stochastic boundary point

We consider evolution in the unit disk in which the sample paths are represented by the trajectories of points evolving randomly under the generalized Loewner equation. The driving mechanism differs from the SLE evolution, but nevertheless solutions possess similar invariance properties.Comment: 23 pages, 6 figure

Integrable (2+1)-dimensional systems of hydrodynamic type

We describe the results that have so far been obtained in the classification problem for integrable (2+1)-dimensional systems of hydrodynamic type. The systems of Gibbons--Tsarev type are the most fundamental here. A whole class of integrable (2+1)-dimensional models is related to each such system. We present the known GT systems related to algebraic curves of genus g=0 and g=1 and also a new GT system corresponding to algebraic curves of genus g=2. We construct a wide class of integrable models generated by the simplest GT system, which was not considered previously because it is in a sense trivial.Comment: 47 pages, no figure

Conformal invariance in two-dimensional turbulence

Simplicity of fundamental physical laws manifests itself in fundamental symmetries. While systems with an infinity of strongly interacting degrees of freedom (in particle physics and critical phenomena) are hard to describe, they often demonstrate symmetries, in particular scale invariance. In two dimensions (2d) locality often promotes scale invariance to a wider class of conformal transformations which allow for nonuniform re-scaling. Conformal invariance allows a thorough classification of universality classes of critical phenomena in 2d. Is there conformal invariance in 2d turbulence, a paradigmatic example of strongly-interacting non-equilibrium system? Here, using numerical experiment, we show that some features of 2d inverse turbulent cascade display conformal invariance. We observe that the statistics of vorticity clusters is remarkably close to that of critical percolation, one of the simplest universality classes of critical phenomena. These results represent a new step in the unification of 2d physics within the framework of conformal symmetry.Comment: 10 pages, 5 figures, 1 tabl

Proposal for a new LOD and multi-representation concept for CityGML

The Open Geospatial Consortium (OGC) CityGML standard offers a Level of Detail (LoD) concept that enables the representation of CityGML features from a very detailed to a less detailed description. Due to a rising application variety, the current LoD concept seems to be too inflexible. Here, we present a multi representation concept (MRC) that enables a user-defined definition of LoDs. Because CityGML is an international standard, official profiles of the MRC are proposed. However, encoding of the defined profiles reveals many problems including mapping the conceptual model to the normative encoding, missing technologies and so on. Therefore, we propose to use the MRC as a meta model for the further definition of an LoD concept for CityGML 3.0