Analysis of Flatness Measurement and Form Stability of a Granite Surface Plate

It is rather difficult to compare quantitatively flatness measuring results of one and the same object (e.g. in case of a long-term stability investigation) or the results of a series of products (e.g. from the same machinetool in order to indicate machinetool-influences). An extension of a computerprogram applied to the evaluation of flatness measurement (as described in the CIRP-Annals, vol. 26 (1977), no.1), separates the form deviations of a surface into a geometrical part and a random part.\ud The geometric part consists of a best-fitting non-flat, reference plane, composed of the single curvature of a sphere and the double curvature of a real twisted plane. Three parameters (the dimensionless curvature parameters of sphericity and torsion, together with the direction of the torsionvector) are able to characterize the geometrical part of the surface; a fourth one is a measure for the random part.\ud Advantages of the method are demonstrated with the aid of a long-term investigation into the form stability of a granite surface plate.\ud Another extension of the program makes it now possible to measure surfaces with non-rectangular contours in the same way as it is being done in case of a rectangular surface plate.\u

The Quadratic Cycle Cover Problem: special cases and efficient bounds

The quadratic cycle cover problem is the problem of finding a set of node-disjoint cycles visiting all the nodes such that the total sum of interaction costs between consecutive arcs is minimized. In this paper we study the linearization problem for the quadratic cycle cover problem and related lower bounds. In particular, we derive various sufficient conditions for the quadratic cost matrix to be linearizable, and use these conditions to compute bounds. We also show how to use a sufficient condition for linearizability within an iterative bounding procedure. In each step, our algorithm computes the best equivalent representation of the quadratic cost matrix and its optimal linearizable matrix with respect to the given sufficient condition for linearizability. Further, we show that the classical Gilmore-Lawler type bound belongs to the family of linearization based bounds, and therefore apply the above mentioned iterative reformulation technique. We also prove that the linearization vectors resulting from this iterative approach satisfy the constant value property. The best among here introduced bounds outperform existing lower bounds when taking both quality and efficiency into account

Influence of intensity distribution on the meltpool and clad shape for laser cladding

The influence of the optical system on the laser cladding process is studied, in particular with respect to the burn-in shape: the penetration of the meltpool into the substrate. The beam caustic and intensity profiles for the commonly used out-of-focus laser clad operation are presented and discussed. To avoid the disadvantages of the out-of-focus operation, a novel telezoom optical system is developed, which allows in-focus operation with a sufficiently large focus with a uniform intensity distribution and a spot diameter ranging from 3 up to over 6 mm. Different typical burn-in shapes are indicated, as they can be found in cross sections of experimental clads. The influence of the intensity distribution on the occurring burn-in shapes is discussed, as well as other phenomena that can play a role, such as flow recirculation cells in the meltpool

Robot-sensor synchronization for real-time seamtracking in robotic laser welding

The accuracy requirements of laser welding put high demands on the manipulator that is used. To use industrial six-axis robots for manipulating the laser welding optics, sensors measuring the seam trajectory close to the focal spot are required to meet the accuracy demands. When the measurements are taken while the robot is moving, it is essential that they are synchronized with the robot motion. This paper presents a synchronization mechanism between a seam-tracking sensor and an industrial 6-axis robot, which uses Ethernet-based UDP communication. Experimental validation is carried out to determine the accuracy of the proposed synchronization mechanism. Furthermore, a new control architecture, called trajectory-based control is presented, which embeds the synchronization method and allows various sensor-based applications like teaching of a seam trajectory with a moving robot and real-time seam-tracking during laser welding

Optical characteristics of Nd:YAG optics and distortions at high power

The intensity profile and beam caustics of a fiber coupled high power Nd:YAG laser beam through a lens system are studied. The thermal lensing effect and its influence on the beam profile and focal position are discussed. Asymmetry of the intensity profile in planes above and below the focal plane is demonstrated. Also the influence of small pollutions on the protective window is explained. Three different methods are used to measure the occurrence\ud of thermal lensing and quantify these effects

Forming the Moon from terrestrial silicate-rich material

Recent high-precision measurements of the isotopic composition of lunar rocks demonstrate that the bulk silicate Earth and the Moon show an unexpectedly high degree of similarity. This is inconsistent with one of the primary results of classic dynamical simulations of the widely accepted giant impact model for the formation of the Moon, namely that most of the mass of the Moon originates from the impactor, not Earth. Resolution of this discrepancy without changing the main premises of the giant impact model requires total isotopic homogenisation of Earth and impactor material after the impact for a wide range of elements including O, Si, K, Ti, Nd and W. Even if this process could explain the O isotope similarity, it is unlikely to work for the much heavier, refractory elements. Given the increasing uncertainty surrounding the giant impact model in light of these geochemical data, alternative hypotheses for lunar formation should be explored. In this paper, we revisit the hypothesis that the Moon was formed directly from terrestrial mantle material. We show that the dynamics of this scenario requires a large amount of energy, almost instantaneously generated additional energy. The only known source for this additional energy is nuclear fission. We show that it is feasible to form the Moon through the ejection of terrestrial silicate material triggered by a nuclear explosion at Earths core-mantle boundary (CMB), causing a shock wave propagating through the Earth. Hydrodynamic modelling of this scenario shows that a shock wave created by rapidly expanding plasma resulting from the explosion disrupts and expels overlying mantle and crust material.Comment: 26 pages, 5 figures, 1 tabl

Coexistence of bulk and surface states probed by Shubnikov-de Haas oscillations in Bi2_2Se3_3 with high charge-carrier density

Topological insulators are ideally represented as having an insulating bulk with topologically protected, spin-textured surface states. However, it is increasingly becoming clear that these surface transport channels can be accompanied by a finite conducting bulk, as well as additional topologically trivial surface states. To investigate these parallel conduction transport channels, we studied Shubnikov-de Haas oscillations in Bi$_2$Se$_3$ thin films, in high magnetic fields up to 30 T so as to access channels with a lower mobility. We identify a clear Zeeman-split bulk contribution to the oscillations from a comparison between the charge-carrier densities extracted from the magnetoresistance and the oscillations. Furthermore, our analyses indicate the presence of a two-dimensional state and signatures of additional states the origin of which cannot be conclusively determined. Our findings underpin the necessity of theoretical studies on the origin of and the interplay between these parallel conduction channels for a careful analysis of the material's performance.Comment: Manuscript including supplemental materia

Exploiting the full power of temporal gene expression profiling through a new statistical test: Application to the analysis of muscular dystrophy data

Background: The identification of biologically interesting genes in a temporal expression profiling dataset is challenging and complicated by high levels of experimental noise. Most statistical methods used in the literature do not fully exploit the temporal ordering in the dataset and are not suited to the case where temporal profiles are measured for a number of different biological conditions. We present a statistical test that makes explicit use of the temporal order in the data by fitting polynomial functions to the temporal profile of each gene and for each biological condition. A Hotelling T2-statistic is derived to detect the genes for which the parameters of these polynomials are significantly different from each other. Results: We validate the temporal Hotelling T2-test on muscular gene expression data from four mouse strains which were profiled at different ages: dystrophin-, beta-sarcoglycan and gammasarcoglycan deficient mice, and wild-type mice. The first three are animal models for different muscular dystrophies. Extensive biological validation shows that the method is capable of finding genes with temporal profiles significantly different across the four strains, as well as identifying potential biomarkers for each form of the disease. The added value of the temporal test compared to an identical test which does not make use of temporal ordering is demonstrated via a simulation study, and through confirmation of the expression profiles from selected genes by quantitative PCR experiments. The proposed method maximises the detection of the biologically interesting genes, whilst minimising false detections. Conclusion: The temporal Hotelling T2-test is capable of finding relatively small and robust sets of genes that display different temporal profiles between the conditions of interest. The test is simple, it can be used on gene expression data generated from any experimental design and for any number of conditions, and it allows fast interpretation of the temporal behaviour of genes. The R code is available from V.V. The microarray data have been submitted to GEO under series GSE1574 and GSE3523

Integrality and cutting planes in semidefinite programming approaches for combinatorial optimization

Many real-life decision problems are discrete in nature. To solve such problems as mathematical optimization problems, integrality constraints are commonly incorporated in the model to reflect the choice of finitely many alternatives. At the same time, it is known that semidefinite programming is very suitable for obtaining strong relaxations of combinatorial optimization problems. In this dissertation, we study the interplay between semidefinite programming and integrality, where a special focus is put on the use of cutting-plane methods. Although the notions of integrality and cutting planes are well-studied in linear programming, integer semidefinite programs (ISDPs) are considered only recently. We show that manycombinatorial optimization problems can be modeled as ISDPs. Several theoretical concepts, such as the Chvátal-Gomory closure, total dual integrality and integer Lagrangian duality, are studied for the case of integer semidefinite programming. On the practical side, we introduce an improved branch-and-cut approach for ISDPs and a cutting-plane augmented Lagrangian method for solving semidefinite programs with a large number of cutting planes. Throughout the thesis, we apply our results to a wide range of combinatorial optimization problems, among which the quadratic cycle cover problem, the quadratic traveling salesman problem and the graph partition problem. Our approaches lead to novel, strong and efficient solution strategies for these problems, with the potential to be extended to other problem classes