Peer methods for the one-dimensional shallow-water equations with CWENO space discretization

For many practical problems an efficient solution of the one-dimensional shallow-water equations (Saint–Venant equations) is important, especially when large networks of rivers, channels or pipes are considered. In order to test and develop numerical methods four test problems are formulated. These tests include the well-known dam break and hydraulic jump problems and two steady state problems with varying channel bottom, channel width and friction.The space discretization of the partial differential equations is based on a finite volume approach with central WENO interpolation and local Lax–Friedrich fluxes (Kurganov and Levy, 2000) [7]. For time-integration new linearly-implicit two-step peer methods of orders three and four are developed. These methods are especially adapted to the usage within the method of lines framework. They show a good performance compared to the well-established methods like ode15s, radau5 or rodasp.     

Synthese und Strukturuntersuchungen von Ba2H[α-FeO4W12O36] · 26 H2O

Synthesis and Structure Studies of Ba₂H[α-FeO₄W₁₂O₃₆] · 26 H₂O The heteropolyanion compound Ba₂H[α-FeO₄W₁₂O₃₆] · 26 H₂O (I) crystallizes in the tetragonal space group P4 n2 with the lattice parameters a = 12.398(6), c = 18.721(6) Å; Z = 2; D_x = 4.128 g · cm^?3. The structure was solved on a twinned crystal from 1029 observed reflections and refined to an index R of 7.6%. The calculations were done by means of a modified ORFLS-programme by Eitel and Bärnighausen. The heteropolyanion [α-FeO₄W₁₂O₃₆]^5? has the well known α-Keggin structure. The average distance of the four central oxygen atoms to the Fe^III position (0, 0, 0) is 1.84 Å. The angles ? O? Fe? O are 112.3° (4X) and 103.9 (2X), respectively, which leads to an disphenoidal distortion of the FeO₄ tetrahedron. The powder and single crystal ESR spectra of I show the anisotropy of the Fe^III fine structure transition 1/2 ? ?1/2. The Mößbauer spectra confirm the tetragonal distortion of the central FeO₄ tetrahedron (quadrupole splitting Δ ≈ 0.50 mm · s^?1).     

InP D-HBT ICs for 40-Gb/s and higher bitrate lightwave transceivers

The combination of device speed (f/sub T/, f/sub max/ > 150 GHz) and breakdown voltage (V/sub bceo/ > 8 V) makes the double heterojunction bipolar InP-based transistor (D-HBT) an attractive technology to implement the most demanding analog functions of 40-Gb/s transceivers. This is illustrated by the performance of a number of analog circuits realized in an InP D-HBT technology with an 1.2- or 1.6-/spl mu/m-wide emitter finger: a low phase noise push-push voltage-controlled oscillator with -7-dBm output power at 146 GHz, a 40-GHz bandwidth and low-jitter 40-Gb/s limiting amplifier, a lumped 40-Gb/s limiting driver amplifier with 4.5-V/sub pp/ differential output swing, a distributed 40-Gb/s driver amplifier with 6-V/sub pp/ differential output swing, and a number of distributed preamplifiers with up to 1.3-THz gain-bandwidth product.     

Equilibrium attractivity of Krylov-W-methods for nonlinear stiff ODEs

Since implicit integration schemes for differential equations which use Krylov methods for the approximate solution of linear systems depend nonlinearly on the actual solution a classical stability analysis is difficult to perform. A different, weaker property of autonomous dissipative systemsy′=f(y) is that the norm ‖f(y(t))‖ decreases for any solutiony(t). This property can also be analysed for W-methods using a Krylov-Arnoldi approximation. We discuss different additional assumptions onf and conditions on the Arnoldi process that imply this kind of attractivity to equilibrium points for the numerical solution. One assumption is general enough to cover quasilinear parabolic problems. This work was supported by Deutsche Forschungsgemeinschaft.     

Conformal Covariance and Positivity of Energy in Charged Sectors

It has been recently noted that diffeomorphism covariance of a Chiral Conformal QFT in the vacuum sector automatically ensures Möbius covariance in all charged sectors. In this article it is shown that diffeomorphism covariance and positivity of the energy in the vacuum sector even ensure the positivity of energy in the charged sectors.The main observation of this paper is that the positivity of energy — at least in case of a Chiral Conformal QFT — is a local concept: it is related to the fact that the energy density, when smeared with some local nonnegative test functions, remains bounded from below (with the bound depending on the test function).The presented proof relies in an essential way on recently developed methods concerning the smearing of the stress-energy tensor with nonsmooth functions.     

Time-Domain Measurement of the Frequency-Dependent Delay of Broadband Antennas

We present a new time-domain technique for direct measurement of the frequency-dependent delay of broadband antenna structures. By utilizing a series of fixed-bandwidth, variable center frequency waveforms synthesized in a photonics-based electromagnetic pulse shaper, we perform high time resolution (~54 ps over ~10 ns) measurements of several broadband antenna structures. Our results show excellent agreement with the delay extracted via time-domain impulse response measurements, however, compared to conventional impulse response measurements, our method ensures a higher signal-to-noise ratio because it relies on several relatively narrowband measurements as opposed to a single broadband measurement. In addition, the delay uncertainty in our technique (~54 ps) is significantly below that of impulse response measurements (~300 ps) where numerical differentiation of noisy data leads to substantial errors. Our technique is well suited as a diagnostic tool for future variable-frequency fixed-bandwidth systems.     

High performance pseudomorphic InGaP/InGaAs power HEMTs

Power transistors with a low d.c. supply voltage were demonstrated with pseudomorphic InGaP/In_0.2Ga_0.8As/GaAs heterostructure field effect transistors on GaAs substrates and 1 μm gate length technology. A current density of 200 mA mm⁻¹ and an extrinsic transconductance of 300 mS mm⁻¹ were exhibited on a 400 μm gate width process control monitor device. For a 1 cm gate width device measured at 850 MHz and V_ds = 1.3 V, state-of-the-art results, 57.4% for the PAE, 12.7 dB for the linear gain and 21.5 dBm for the output power, were obtained.     

Partitioned adaptive Runge-Kutta methods for the solution of nonstiff and stiff systems

Summary For the numerical solution of initial value problems of ordinary differential equations partitioned adaptive Runge-Kutta methods are studied. These methods consist of an adaptive Runge-Kutta methods for the treatment of a stiff system and a corresponding explicit Runge-Kutta method for a nonstiff system. First we modify the theory of Butcher series for partitioned adaptive Runge-Kutta methods. We show that for any explicit Runge-Kutta method there exists a translation invariant partitoned adaptive Runge-Kutta method of the same order. Secondly we derive a special translaton invariant partitioned adaptive Runge-Kutta method of order 3. An automatic stiffness detection and a stepsize control basing on Richardson-extrapolation are performed. Extensive tests and comparisons with the partitioned RKF4RW-algorithm from Rentrop [16] and the partitioned algorithm LSODA from Hindmarsh [9] and Petzold [15] show that the partitoned adaptive Runge-Kutta algorithm works reliable and gives good numericals results. Furthermore these tests show that the automatic stiffness detection in this algorithm is effective.     

Efficiency of short-pulse type-I second-harmonic generation with simultaneous spatial walk-off, temporal walk-off, and pump depletion

We have developed a theory which for the first time predicts the efficiency of type-I second-harmonic generation (SHG) with simultaneous spatial and temporal walk-offs and with pump depletion. In order to validate our theory, we have compared its predictions with a numerical solver. We also have measured the conversion efficiency for type-I SHG in experiments with /spl sim/120--fs laser pulses in BBO and LBO crystals long enough that both temporal and spatial walk-off are important. Comparison supports our theoretical analysis. Our theory provides a useful tool for estimating SHG efficiency with pulsed sources in both nondepletion and depletion regions.