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

Operator monotones, the reduction criterion and the relative entropy

We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we prove a new lower bound on the relative entropy of entanglement and other properties of entanglement measures.Comment: Final version accepted for publication, added references in reference [1] and [13

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

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

The Energy Application Domain Extension for CityGML: enhancing interoperability for urban energy simulations

The road towards achievement of the climate protection goals requires, among the rest, a thorough rethinking of the energy planning tools (and policies) at all levels, from local to global. Nevertheless, it is in the cities where the largest part of energy is produced and consumed, and therefore it makes sense to focus the attention particularly on the cities as they yield great potentials in terms of energy consumption reduction and efficiency increase. As a direct consequence, a comprehensive knowledge of the demand and supply of energy resources, including their spatial distribution within urban areas, is therefore of utmost importance. Precise, integrated knowledge about 3D urban space, i.e. all urban (above and underground) features, infrastructures, their functional and semantic characteristics, and their mutual dependencies and interrelations play a relevant role for advanced simulation and analyses. As a matter of fact, what in the last years has proven to be an emerging and effective approach is the adoption of standard-based, integrated semantic 3D virtual city models, which represent an information hub for most of the abovementioned needs. In particular, being based on open standards (e.g. on the CityGML standard by the Open Geospatial Consortium), virtual city models firstly reduce the effort in terms of data preparation and provision. Secondly, they offer clear data structures, ontologies and semantics to facilitate data exchange between different domains and applications. However, a standardised and omni-comprehensive urban data model covering also the energy domain is still missing at the time of writing (January 2018). Even CityGML falls partially short when it comes to the definition of specific entities and attributes for energy-related applications. Nevertheless, and starting from the current version of CityGML (i.e. 2.0), this article describes the conception and the definition of an Energy Application Domain Extension (ADE) for CityGML. The Energy ADE is meant to offer a unique and standard-based data model to fill, on one hand, the above-mentioned gap, and, on the other hand, to allow for both detailed single-building energy simulation (based on sophisticated models for building physics and occupant behaviour) and city-wide, bottom-up energy assessments, with particular focus on the buildings sector. The overall goal is to tackle the existing data interoperability issues when dealing with energy-related applications at urban scale. The article presents the rationale behind the Energy ADE, it describes its main characteristics, the relation to other standards, and provides some examples of current applications and case studies already adopting it

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