An adaptive moving mesh approach for hyperbolic conservation laws on time-dependent domains

The general idea of moving mesh approaches is to improve the approximation quality and the numerical performance by redistributing a fixed number of discretization points. This is called rrefinement. The classical approaches are applied to partial differential equations on fixed domains. An extension to time-dependent (expanding) domains is presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On discrete Fourier transform,ambiguity, and Hamming-autocorrelation of pseudorandom sequences

We estimate discrete Fourier transform, ambiguity, and Hamming-auto-correlation of \(m\) -ary sequences in terms of their (periodic) correlation measure of order 4. Roughly speaking, we show that every pseudorandom sequence, that is, any sequence with small correlation measure up to a sufficiently large order, cannot have a large discrete Fourier transform, ambiguity, or Hamming-autocorrelation. Conversely, there are sequences, for example the two-prime generator, with large correlation measure of order 4 but small discrete Fourier transform, ambiguity, autocorrelation, and Hamming-autocorrelation.     

K-Theory of Surfaces at the Prime 2

We prove that for smooth surfaces over real closed fields, and a class of smooth projective surfaces over a real number field, the map between mod 2 algebraic and étale K-theory is an isomorphism in sufficiently large degrees. For a class of smooth projective surfaces over a real closed field, including rational surfaces, complete intersections and K3-surfaces over the real numbers, we explicate the abutment of the mod 2 motivic cohomology to algebraic K-theory spectral sequence.     

On a new class of inversive pseudorandom numbers for parallelized simulation methods

Inversive methods are attractive alternatives to the linear method for pseudorandom number generation. A particularly attractive method is the digital explicit inversive method recently introduced by the authors. We establish some new results on the statistical properties of parallel streams of pseudorandom numbers generated by this method. In particular, we extend the results of the first author on the statistical properties of pseudorandom numbers generated by the explicit inversive congruential method introduced by Eichenauer-Herrmann. These results demonstrate that the new method is eminently suitable for the generation of parallel streams of pseudorandom numbers with desirable properties.     

Predictability in deterministic theories

A mathematical model for the general notion of a deterministic physical theory is introduced, and incompleteness results analogous to the halting theorem for Turing machines are demonstrated for this model. The discussion is not limited to algorithmic systems.     

The influence of contact surface microstructure on vacuum arcstability and voltage

The authors present the results of DC vacuum arc lifetime and voltage measurements for contacts with different surface microstructures. This was realized by treating the contact surface with emery paper of varying roughness. The contact surface microstructure was found to have a large effect on the DC arc lifetime (several tens of times difference at the most) and arc voltage (30% difference at the most). The mechanism of the surface microstructure effect on DC arc stability was analyzed and is explained preliminarily. The rougher the contact surface is, the longer the arc lifetime and the more stable. The arc itself has a tendency to condition the surface in a way that is unfavorable for a sustained arc lifetime. The crater size for a rough surface is smaller than for a smooth one. The rougher the contact is, the lower the arc voltage (both DC and HF components). The arc erosion has a tendency to increase the arc voltage. It is probable that type I cathode spots (fast motion, small crater size) correspond not only to the surface contamination, but also to the surface roughness