The Nonconvergence of h-Refinement in Prolate Elements

Prolate elements are a “plug-compatible” modification of spectral elements in which Legendre polynomials are replaced by prolate spheroidal wave functions of order zero. Prolate functions contain a“bandwidth parameter” $c \ge 0 $ c ≥ 0 whose value is crucial to numerical performance; the prolate functions reduce to Legendre polynomials for $c\,=\,0$ c = 0 . We show that the optimal bandwidth parameter $c$ c not only depends on the number of prolate modes per element $N$ N , but also on the element widths $h$ h . We prove that prolate elements lack $h$ h -convergence for fixed $c$ c in the sense that the error does not go to zero as the element size $h$ h is made smaller and smaller. Furthermore, the theoretical predictions that Chebyshev and Legendre polynomials require $\pi $ π degrees of freedom per wavelength to resolve sinusoidal functions while prolate series need only 2 degrees of freedom per wavelength are asymptotic limits as $N \rightarrow \infty $ N → ∞ ; we investigate the rather different behavior when $N \sim O(4-10)$ N ～ O ( 4 ? 10 ) as appropriate for spectral elements and prolate elements. On the other hand, our investigations show that there are certain combinations of $N,\,h$ N , h and $c>0$ c > 0 where a prolate basis clearly outperforms the Legendre polynomial approximation.     

Gaussian process internal model control

Nonlinear modelling approaches such as neural networks, fuzzy models and multiple model networks have been proposed for model based control, to improve the poor transient response of adaptive control techniques. The quality of control is known to be strongly related to the accuracy of the model which represents the process. A Bayesian Gaussian process (GP) approach provides an analytic prediction of the model uncertainty, which makes the GP model an ideal candidate for model based control strategies. This article extends the use of the GP model for nonlinear internal model control. The invertibility of the GP model is discussed and the use of predicted variance is illustrated on a simulated example.     

Der Schau- und Lehrstollen Arzberg/Steiermark: Beispiel für eine intelligente Nachnutzung eines Altbergbaus

Touristic mines are by far not only of public interest. During guided tours the importance of mining and mineral resources for society can be explained in a proper way. Mineral deposits, for long time not accessible and only known from old literature can now be studied in detail by scientists. Old underground mines can be used for different purposes. With respect to Arzberg the different possibilities of utilization of old underground workings are described in detail: A touristic mine serves not only as an attraction, but also as a training centre for underground geological mapping, geochemistry and geophysics research laboratory of universities. For many years the ZAMG (Central Institute for Meteorology and Geodynamics) has been operating a seismic station, and parts of the old mine workings have been used for cheese refinery since 2006. Furthermore, the mine water is utilized for extracting geothermal energy and serves the cooling chambers. The combined use of the old mine workings by different parties permits sharing the substantial maintenance costs.     

An optimized FAIRE procedure for low cell numbers in yeast

We report an optimized low‐input FAIRE‐seq (Formaldehyde‐Assisted Isolation of Regulatory Elements‐sequencing) procedure to assay chromatin accessibility from limited amounts of yeast cells. We demonstrate that the method performs well on as little as 4 mg of cells scraped directly from a few colonies. Sensitivity, specificity and reproducibility of the scaled‐down method are comparable with those of regular, higher input amounts, and allow the use of 100‐fold fewer cells than existing procedures. The method enables epigenetic analysis of chromatin structure without the need for cell multiplication of exponentially growing cells in liquid culture, thus opening the possibility of studying colony cell subpopulations, or those that can be isolated directly from environmental samples.     

A Meshless Approach Towards Solution of Macrosegregation Phenomena

The simulation of macrosegregation as a consequence of solidification of a binary Al-4.5%Cu alloy in a 2-dimensional rectangular enclosure is tackled in the present paper. Coupled volume-averaged governing equations for mass, energy, momentum and species transfer are considered. The phase properties are resolved from the Lever solidification rule, the mushy zone is modeled by the Darcy law and the liquid phase is assumed to behave like an incompressible Newtonian fluid. Double diffusive effects in the melt are modeled by the thermal and solutal Boussinesq hypothesis. The physical model is solved by the novel Local Radial Basis Function Collocation Method (LRBFCM). The involved physical relevant fields are represented on overlapping 5-noded sub-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBFs. The fields are solved through explicit time stepping. The pressure-velocity coupling is calculated through a local pressure correction scheme. The evolution of the solidification process is presented through temperature, velocity, liquid fraction and species concentration histories in four sampling points. The fully solidified state is analyzed through final macrosegregation map in three vertical and three horizontal cross-sections. The results are compared with the classical Finite Volume Method (FVM). A surprisingly good agreement of the numerical solution of both methods is shown and therefore the results can be used as a reference for future verification studies. The advantages of the represented meshless approach are its simplicity, accuracy, similar coding in 2D and 3D, and straightforward applicability in non-uniform node arrangements. The paper probably for the first time shows an application of a meshless method in such a highly non-linear and multi-physics problem.     

Management of complex data flows in the ASDEX Upgrade plasma control system

Establishing adequate technical and physical boundary conditions for a sustained nuclear fusion reaction is a challenging task. Phased feedback control and monitoring for heating, fuelling and magnetic shaping is mandatory, especially for fusion devices aiming at high performance plasmas. Technical and physical interrelations require close collaboration of many components in sequential as well as in parallel processing flows. Moreover, handling of asynchronous, off-normal events has become a key element of modern plasma performance optimisation and machine protection recipes.The manifoldness of plasma states and events, the variety of plant system operation states and the diversity in diagnostic data sampling rates can hardly be mastered with a rigid control scheme. Rather, an adaptive system topology in combination with sophisticated synchronisation and process scheduling mechanisms is suited for such an environment. Moreover, the system is subject to real-time control constraints: response times must be deterministic and adequately short.Therefore, the experimental tokamak device ASDEX Upgrade employs a discharge control system DCS, whose core has been designed to meet these requirements. In the paper we will compare the scheduling schemes for the parallelised realisation of a control workflow and show the advantage of a data-driven workflow over a managed workflow. The data-driven workflow as used in DCS is based on signals connecting process outputs and inputs. These are implemented as real-time streams of data samples. Consequently, real-time signal management forms the foundation of DCS. The paper explains the principal features such as tagged samples, signal groups, algorithmic blocks and processes as well as scheduling schemes which allow DCS control applications to be defined as self-contained modular building blocks glued together by a software framework.By virtue of this sound foundation, DCS is a mature but still evolving system for reliable, distributed control of an entire tokamak device coordinating and monitoring 20 diagnostic systems, 14 magnetic power supplies, 5 heating systems with a total power of more than 25 MW, 8 gas fuelling channels, a pellet injector and a killer gas gun.     

Feedforward-feedback control of a solid oxide fuel cell power system

One of the main challenges for wide-spread utilization of the solid oxide fuel cell (SOFC) power systems is how to achieve high electrical efficiency without increasing the degradation rate of the fuel cells. To run the SOFC power system at high efficiency over a long period of time, properly designed controllers are indispensable.Although a number of various approaches to control SOFC have been proposed so far, it seems that the design of control system, along with simple tuning procedure, has not been treated in a consistent manner. This issue is addressed in the present paper resulting in a feedforward-feedback control structure. The feedforward part is based on the stoichiometry of electro-oxidation, reforming and combustion reactions, which allow immediate response to variable current demand. The feedback part performs additional fine adjustment of fuel and air supply in order to minimize the undesired system temperatures variations. The selection of pairings of manipulated and controlled variables for control is based on physical knowledge of the system. Input/output pairing for single-loop feedback control is assessed by the relative gain analysis. An efficient procedure for tuning the parameters of the feedback controllers is suggested, relying on simple open-loop step responses of the system.The proposed low-level control is assessed on a detailed physical model of a 2.5 kW SOFC power system by simulating two nonstationary load regimes. Simulations show that the control provides a robust operation under large load variations while meeting the operating constraints. Due to its simplicity, the control is feasible for implementation on a real SOFC system.     

Continuous phase stabilization and active interferometer control using two modes

We present a computer-based active interferometer stabilization method that can be set to an arbitrary phase difference and does not rely on modulation of the interfering beams. The scheme utilizes two orthogonal modes propagating through the interferometer with a constant phase difference between them to extract a common relative phase and generate a linear feedback signal. Switching times of 50?ms over a range of 0–6π radians at 632.8?nm are experimentally demonstrated. The relative interferometer phase can be stabilized up to several days to within ± 3°.