On the critical exponent in an isoperimetric inequality for chords

The problem of maximizing the $L^p$ norms of chords connecting points on a closed curve separated by arclength $u$ arises in electrostatic and quantum--mechanical problems. It is known that among all closed curves of fixed length, the unique maximizing shape is the circle for $1 \le p \le 2$, but this is not the case for sufficiently large values of $p$. Here we determine the critical value $p_c(u)$ of $p$ above which the circle is not a local maximizer finding, in particular, that $p_c(\frac12 L)=\frac52$. This corrects a claim made in \cite{EHL}.Comment: LaTeX, 12 pages, with 1 eps figur

A remark on helical waveguides

Motivated by a proposal to create an optical helix-shaped waveguides for cold atoms and molecules, we discuss local perturbations which can create bound states in such a setting. This is known about a local slowdown of the twist; we show that a similar effect can result from a local tube protrusion or a change of the helix radius in correlation with its pitch angle.Comment: LaTeX, 12 page

Resonance asymptotics in the generalized Winter model

We consider a modification of the Winter model describing a quantum particle in presence of a spherical barrier given by a fixed generalized point interaction. It is shown that the three classes of such interactions correspond to three different types of asymptotic behaviour of resonances of the model at high energies.Comment: LaTeX, 10 pages with one figur

The decay law can have an irregular character

Within a well-known decay model describing a particle confined initially within a spherical $\delta$ potential shell, we consider the situation when the undecayed state has an unusual energy distribution decaying slowly as $k\to\infty$; the simplest example corresponds to a wave function constant within the shell. We show that the non-decay probability as a function of time behaves then in a highly irregular, most likely fractal way.Comment: 4 pages, 3 eps figure

Consensus report: E. coli O104:H4 (HUSEC041) and the potential threat to European water supplies.

Among the 3rd Seminar for PhD students working on Water and Health which was held in Cannes on 27–29 June 2011, experts from a number of universities and research institutes took the opportunity to discuss the emergence of Escherichia coli O104:H4 in Europe. Especially, possible threats for European water suppliers were considered. The consensus is summarized in this report. The main conclusion was that E. coli O104:H4 would not pose a substantial risk to well managed water supplies, especially where regular monitoring of indicator E. coli is negative. However, this may not apply for small and very small water systems which are quite common in Europe. New strategies like the Water Safety Plan approach are needed to protect also small scale drinking water systems and private wells in Europe. Water used in the processing of foods likely to be eaten raw, especially sprouts, should be of drinking water quality

Urban Emotions – Tools of Integrating People’s Perception into Urban Planning

This paper introduces the research field “Urban Emotions” – an interdisciplinary approach combining not only spatial planning and (geo-) informatics, but also computer linguistics and sensor technology methods. A new set of methods will be formed for the area of urban and spatial planning, resulting in a fundamental change of the understanding of planning. One of the main objectives is the involvement of citizens into planning processes. Therefore, new techniques are developed to collect and analyse data on the emotional perception of space and provide it to the people and also planners. Not only the human perception in the context of the city, and the combination with human sensory processes are contents of this paper, but also the critical discussion of these effects to privacy issues. Based on the topics “mental maps” and psychogeography in combination with the field of digital emotional urban tagging, the potential of integrating objectively quantified emotions in the context of citizen participation will be explained. In the following, partly established and partly experimental methods for collecting and analysing “Urban Emotions” will be introduced. Based on two studies, the possibilities of transfering these methodsinto the planning praxis will be shown on the one hand and on the other hand the potential for further development for other disciplines will be more evident

Small-Energy Analysis for the Selfadjoint Matrix Schroedinger Operator on the Half Line

The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the most general selfadjoint boundary condition at the origin. When the matrix potential is integrable and has a first moment, it is shown that the corresponding scattering matrix is continuous at zero energy. An explicit formula is provided for the scattering matrix at zero energy. The small-energy asymptotics are established also for the corresponding Jost matrix, its inverse, and various other quantities relevant to the corresponding direct and inverse scattering problems.Comment: This published version has been edited to improve the presentation of the result

Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles

As is well-known, there exists a four parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum dependent terms, and we determine all cases leading to many-body systems of distinguishable particles which are exactly solvable by the coordinate Bethe Ansatz. We find two such families of systems, one with two independent coupling constants deforming the well-known delta interaction model to non-identical particles, and the other with a particular one-parameter combination of the delta- and (so-called) delta-prime interaction. We also find that the model of non-identical particles gives rise to a somewhat unusual solution of the Yang-Baxter relations. For the other model we write down explicit formulas for all eigenfunctions.Comment: 23 pages v2: references adde

Experiences and Future of Using VR in the Construction Sector

Living in the era of digitalization shapes more or less all the aspects of one's life. The multitude of available technologies extends the range of tools, established processes, and available affordances in many spheres. Cities of the future will not only impact the living patterns of their inhabitants but also require special conditions and requirements for their planning and design. Virtual reality as an interactive tool for visualization and urban planning is no more tomorrow’s technology, as it can be seen from the appearance of cheaper and portable virtual reality devices. However, we still lack established routine and multidisciplinary best practices for designing VR educational applications. There are also not enough “visionary approaches” attempting to cross-sectoral exploitation of technologies. In this paper we will try to extrapolate and extend learning use cases of construction and mechatronics to the broader areas of construction and planning sector. We will discuss our experiences and use-cases of integrating innovative visualizations tools in the learning context of construction and planning related fields. Based on this, we will discuss potential applications and links to other disciplines and their integration into the construction and planning sector