Characterization of laser hardened steels by laser induced ultrasonic surface waves

Ultrasonic surface waves are suitable for the characterization of surface hardened materials. This is shown on laser hardened turbine blades. The martensitic microstructure within the surface layer of surface hardened steels has a lower surface wave propagation velocity than the annealed or normalized substrate material. Because the propagation velocity depends on the ratio of layer thickness to wavelengthd/, its measurement allows the determination of the hardening depth. If the surface wave frequency is high enough, the surface wave propagates mainly within the hardened layer. A correlation of the surface wave velocity to the surface hardness has been found. Because the variation of the surface velocity in hardened steels is small, a high measurement accuracy is necessary to obtain the interesting hardening parameters with sufficient certainty. Therefore, a measuring arrangement has been developed where laser pulses, guided by optical fibers to the surface hardened structure, generate simultaneously surface wave pulses at two different positions. The two ultrasonic pulses are received by a piezoelectric transducer. The surface wave velocity is obtained from the time delay between these pulses which is determined by the cross-correlation method. To evaluate simultaneously surface waves with different penetration depths from the same signal acquisition, digital filtering has been used in connection with the cross-correlation.     

A non-autonomous optimal control model of renewable energy production under the aspect of fluctuating supply and learning by doing

Given the constantly raising world-wide energy demand and the accompanying increase in greenhouse gas emissions that pushes the progression of climate change, the possibly most important task in future is to find a carbon-low energy supply that finds the right balance between sustainability and energy security. For renewable energy generation, however, especially the second aspect turns out to be difficult as the supply of renewable sources underlies strong volatility. Further on, investment costs for new technologies are so high that competitiveness with conventional energy forms is hard to achieve. To address this issue, we analyze in this paper a non-autonomous optimal control model considering the optimal composition of a portfolio that consists of fossil and renewable energy and which is used to cover the energy demand of a small country. While fossil energy is assumed to be constantly available, the supply of the renewable resource fluctuates seasonally. We further on include learning effects for the renewable energy technology, which will underline the importance of considering the whole life span of such a technology for long-term energy planning decisions.     

Marking student programs using graph similarity

We present a novel approach to the automated marking of student programming assignments. Our technique quantifies the structural similarity between unmarked student submissions and marked solutions, and is the basis by which we assign marks. This is accomplished through an efficient novel graph similarity measure (AssignSim). Our experiments show good correlation of assigned marks with that of a human marker.     

A visual digital library approach for time-oriented scientific primary data

Digital Library support for textual and certain types of non-textual documents has significantly advanced over the last years. While Digital Library support implies many aspects along the whole library workflow model, interactive and visual retrieval allowing effective query formulation and result presentation are important functions. Recently, new kinds of non-textual documents which merit Digital Library support, but yet cannot be fully accommodated by existing Digital Library technology, have come into focus. Scientific data, as produced for example, by scientific experimentation, simulation or observation, is such a document type. In this article we report on a concept and first implementation of Digital Library functionality for supporting visual retrieval and exploration in a specific important class of scientific primary data, namely, time-oriented research data. The approach is developed in an interdisciplinary effort by experts from the library, natural sciences, and visual analytics communities. In addition to presenting the concept and to discussing relevant challenges, we present results from a first implementation of our approach as applied on a real-world scientific primary data set. We also report from initial user feedback obtained during discussions with domain experts from the earth observation sciences, indicating the usefulness of our approach.     

On the number of higher order Delaunay triangulations

Higher order Delaunay triangulations are a generalization of the Delaunay triangulation that provides a class of well-shaped triangulations, over which extra criteria can be optimized. A triangulation is order-k Delaunay if the circumcircle of each triangle of the triangulation contains at most k points. In this paper we study lower and upper bounds on the number of higher order Delaunay triangulations, as well as their expected number for randomly distributed points. We show that arbitrarily large point sets can have a single higher order Delaunay triangulation, even for large orders, whereas for first order Delaunay triangulations, the maximum number is 2ⁿ⁻³. Next we show that uniformly distributed points have an expected number of at least 2^{ρ₁n(1+o(1))} first order Delaunay triangulations, where ρ₁ is an analytically defined constant (ρ₁≈0.525785), and for k>1, the expected number of order-k Delaunay triangulations (which are not order-i for any i<k) is at least 2^{ρ_kn(1+o(1))}, where ρ_k can be calculated numerically.     

In vivo interactive visualization of four-dimensional blood flow patterns

In this paper we give an overview over a series of experiments to visualize and measure flow fields in the human vascular system with respect to their diagnostic capabilities. The experiments utilize a selection of GPU-based sparse and dense flow visualization algorithms to show the diagnostic opportunities for volumetric cardiovascular phase contrast magnetic resonance imaging data sets. Besides classical hardware accelerated particle and line-based approaches, an extensible tublet-based visualization, a four-dimensional volumetric line integral convolution and a new two-dimensional cutting plane tool for three-dimensional velocity data sets have been implemented. To evaluate the results, several hearts of human subjects have been investigated and a flow phantom was built to artificially simulate distinctive flow features. Our results demonstrate that we are able to provide an interactive tool for cardiovascular diagnostics with complementary hardware accelerated visualizations. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.

On packing shortest cycles in graphs

We study the problems to find a maximum packing of shortest edge-disjoint cycles in a graph of given girth g (g-ESCP) and its vertex-disjoint analogue g-VSCP. In the case g=3, Caprara and Rizzi (2001) have shown that g-ESCP can be solved in polynomial time for graphs with maximum degree 4, but is APX-hard for graphs with maximum degree 5, while g-VSCP can be solved in polynomial time for graphs with maximum degree 3, but is APX-hard for graphs with maximum degree 4. For g∈{4,5}, we show that both problems allow polynomial time algorithms for instances with maximum degree 3, but are APX-hard for instances with maximum degree 4. For each g?6, both problems are APX-hard already for graphs with maximum degree 3.     

Exact Algorithms for <Emphasis Type="Italic">L</Emphasis>(2,1)-Labeling of Graphs

The notion of distance constrained graph labelings, motivated by the Frequency Assignment Problem, reads as follows: A mapping from the vertex set of a graph G=(V,E) into an interval of integers {0,…,k} is an L(2,1)-labeling of G of span k if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common neighbor are mapped onto distinct integers. It is known that for any fixed k≥4, deciding the existence of such a labeling is an NP-complete problem. We present exact exponential time algorithms that are faster than the naive O ^*((k+1) ⁿ ) algorithm that would try all possible mappings. The improvement is best seen in the first NP-complete case of k=4, where the running time of our algorithm is O(1.3006 ⁿ ). Furthermore we show that dynamic programming can be used to establish an O(3.8730 ⁿ ) algorithm to compute an optimal L(2,1)-labeling.     

Bandwidth on AT-free graphs

We study the classical Bandwidth problem from the viewpoint of parametrised algorithms. Given a graph G=(V,E) and a positive integer k, the Bandwidth problem asks whether there exists a bijective function β:{1,…,∣V∣}→V such that for every edge uv∈E, ∣β⁻¹(u)−β⁻¹(v)∣≤k. It is known that under standard complexity assumptions, no algorithm for Bandwidth with running time of the form f(k)n^O(1) exists, even when the input is restricted to trees. We initiate the search for classes of graphs where such algorithms do exist. We present an algorithm with running time n⋅2^O(klogk) for Bandwidth on AT-free graphs, a well-studied graph class that contains interval, permutation, and cocomparability graphs. Our result is the first non-trivial algorithm that shows fixed-parameter tractability of Bandwidth on a graph class on which the problem remains NP-complete.