Stochastic Process Associated with Traveling Wave Solutions of the Sine-Gordon Equation

Stochastic processes associated with traveling wave solutions of the sine-Gordon equation are presented. The structure of the forward Kolmogorov equation as a conservation law is essential in the construction and so is the traveling wave structure. The derived stochastic processes are analyzed numerically. An interpretation of the behaviors of the stochastic processes is given in terms of the equation of motion.Comment: 12 pages, 9 figures; corrected typo

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

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

PROPOSAL for A NEW LOD and MULTI-REPRESENTATION CONCEPT for CITYGML

10.5194/isprs-annals-IV-2-W1-3-2016ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences42W13-1