Thomas Fincke und die <Emphasis Type="Italic">Geometria rotundi</Emphasis>

Thomas Fincke (January 6^th, 1561–April 24^th, 1656), born in Flensburg (Germany), was one of the very most important and significant scientists in Denmark during the seventeenth century, a mathematician and astrologer and physician in the beginning of modern science, a representative of humanism and an influentual academic organizer. He studied in Strasbourg (since 1577) and Padua (since 1583) and received his M.D. in Basel (1587), he practised as a physician throughout his life (since 1587 or 1590) and became a professor at Copenhagen (1591). But he was best known because of his Geometriae rotundi libri XIIII (1583), a famous book on plane and spherical trigonometry, based not on Euclid but on Petrus Ramus. In this influentual work, in which Fincke introduced the terms tangent and secant and probable first noticed the Law of Tangents and the so-called Newton-Oppel-Mauduit-Simpson-Mollweide-Gauss-formula, he showed himself to be „abreast of the mathematics of his time“.      

Fault-aware Communication Mapping for NoCs with Guaranteed Latency

As feature sizes shrink, transient failures of on-chip network links become a critical problem. At the same time, many applications require guarantees on both message arrival probability and response time. We address the problem of transient link failures by means of temporally and spatially redundant transmission of messages, such that designer-imposed message arrival probabilities are guaranteed. Response time minimisation is achieved by a heuristic that statically assigns multiple copies of each message to network links, intelligently combining temporal and spatial redundancy. Concerns regarding energy consumption are addressed in two ways. First, we reduce the total amount of transmitted messages, and, second, we minimise the application response time such that the resulted time slack can be exploited for energy savings through voltage reduction. The advantages of the proposed approach are guaranteed message arrival probability and guaranteed worst case application response time.     

Effect of deformation route on microstructural development in aluminum processed by equal channel angular extrusion

Aluminum has been deformed by equal channel angular extrusion (ECAE) to obtain submicron-grained structures under different deformation routes. The deformation routes were varied by rotating billets through 0, 90, and 180 deg between each extrusion pass, and were designated as route A, B_C, and C, respectively. Based on quantitative microstructural analysis, the effectiveness of the deformation route is shown to depend upon the different definition used. The order of effectiveness is (a) A > B_C > C for both 90 and 120 deg dies, in terms of the generation of high-angle grain boundaries (HAGBs); (b) B_C > C > A for both 90 and 120 deg dies, in terms of the formation of equiaxed shape of grains; and (c) B_C > A > C for 90 deg die and B_C ∼ A > C for 120 die, in terms of reducing grain size. It is suggested that the generation of HAGBs can be related to the accumulation of nonredundant strain, while the shape and orientation of grains may be linked to the shearing patterns of the deformation route.     

Copper-zirconium tungstate composites exhibiting low and negative thermal expansion influenced by reinforcement phase transformations

A fully-dense Cu-75 vol pct ZrW₂O₈ metal matrix composite was fabricated by hot isostatic pressing of Cu-coated ZrW₂O₈ particles. A small amount of the high-pressure γ-ZrW₂O₈ phase was created during the cooldown and depressurization following densification; near complete transformation to γ-ZrW₂O₈ was achieved by subsequent cold isostatic pressing. The thermal expansion behavior of the composite between 25°C and 325°C was altered by the cold isostatic pressing treatment, and also depended on the length of time that had passed between thermal cycles. The measured thermal expansion coefficients within specific temperature ranges varied from −6·10⁻⁶ K⁻¹ to far above the thermal expansion coefficient of the copper matrix. The complex temperature-dependent expansion/contraction behavior could be justified by considering the evolution of phase transformations taking place in the ZrW₂O₈ phase, which were observed by in-situ synchrotron X-ray diffraction measurements.     

Midplane-symmetry breaking in the flow between two counter-rotating disks

This paper considers the axisymmetric steady flow driven by exact counter rotation of two co-axial disks of finite radius. At the edges of the rotating disks one of three conditions is (typically) imposed: (i) zero velocity, corresponding to a stationary, impermeable, cylindrical shroud (ii) zero normal velocity and zero tangential fluid traction, corresponding to a (confined) free surface and (iii) an edge constraint that is consistent with a similarity solution of von Kármán form. The similarity solution is valid in an infinite geometry and possesses a pitchfork bifurcation that breaks the midplane symmetry at a critical Reynolds number. In this paper, similar bifurcations of the global (finite-domain) flow are sought and comparisons are made between the resulting bifurcation structure and that found for the similarity solution. The aim is to assess the validity of the nonlinear similarity solutions in finite domains and to explore the sensitivity of the solution structure to edge conditions that are implicitly neglected when assuming a self-similar flow. It is found that, whilst the symmetric similarity solution can be quantitatively useful for a range of boundary conditions, the bifurcated structure of the finite-domain flow is rather different for each boundary condition and bears little resemblance to the self-similar flow.     

The effect of solidification time and heat treatment on the fatigue properties of a cast 319 aluminum alloy

Solidification time and heat treatment are known to have a large effect on the microstructure of cast aluminum alloys. This study was conducted to quantify how the fatigue properties of a 319-type aluminum alloy are affected by solidification time and heat treatment. Both porosity-containing (non-hot isostatically pressed (HIP)) and porosity-free (HIP) samples in the T6 (“peak aged”) or T7 (“overaged”) heattreated conditions were tested. As the solidification time increased, the average initiating pore diameter increased and stress-controlled fatigue life decreased. Heat treatment was observed to have a large effect on fatigue properties of the HIP samples. However, in the non-HIP fatigue samples, heat treatment did not significantly change the fatigue life or fatigue strength of the cast 319-type alloy. The absence of an influence of heat treatment on fatigue response is attributed to the predominance of the microporosity in fatigue crack initiation in cast aluminum.     

Analytical results for the plectonemic response of supercoiled DNA

The DNA molecule is modeled as an elastic rod with bending and twisting rigidities, subjected to external tension and twist applied at one end, the other end being clamped. We study the plectonemic equilibrium of such a rod, taking into account the impenetrability constraint. Numerical solutions of this boundary value problem have previously shown that purely elastic models can reproduce the supercoiling response of the DNA molecule. Using a variational approach, we derive analytical formulae for the elastic response of the filament, and extend former numerical results.     

In Situ Performance Testing of Deteriorating Water Tanks for Durability Assessment

Reports of failure of existing concrete structures due to a lack of durability, rather than a deficiency in structural strength, has made concrete technologists, engineers, and researchers focus research on the parameters influencing durability performance with respect to time. Systematic performance monitoring, with respect to chosen durability parameters of existing concrete structures, will decide the direction of future research in this area. Inferences based on laboratory simulations and testing need to be confirmed by in situ field measurements and studies. In situ condition rating and performance monitoring surveys have been conducted by many researchers, scientists, and professional associations, and reported in literature. Inferences of few such studies are summarized and discussed. Deterioration of concrete structures constructed in recent times is observed at relatively faster rates, and has been mainly attributed to cracking. Cracking is associated with the use of faster-hydrating portland cements with increased fineness and the tricalcium silicate (C3S) content to support the high speed of modern construction. In the present research, a case study of deteriorated water tank structures situated in the semitropical region of India is presented. Some selected parameters—such as concrete cover, carbonation depth, chloride concentration, compressive strength, etc. which influence long term durability of structures—have been measured.