Multiadaptive Galerkin Methods for ODEs III: A Priori Error Estimates

The multiadaptive continuous/discontinuous Galerkin methods mcG(q) and mdG(q) for the numerical solution of initial value problems for ordinary differential equations are based on piecewise polynomial approximation of degree q on partitions in time with time steps which may vary for different components of the computed solution. In this paper, we prove general order a priori error estimates for the mcG(q) and mdG(q) methods. To prove the error estimates, we represent the error in terms of a discrete dual solution and the residual of an interpolant of the exact solution. The estimates then follow from interpolation estimates, together with stability estimates for the discrete dual solution

Sludge management paradigms: impact of priority substances and priority hazardous substances

As a by-product of treatment processes, municipal wastewater treatment plants (WWTP) generate large quantities of sludge, with sludge treatment focused on sterilisation, volume reduction and biogas production. Whilst the EU Sewage Sludge Directive sets limits on the concentrations of selected metals in sludge applied to agricultural land, the potential impact of many EU Water Framework Directive priority and priority hazardous substances (PS/PHS) on human or environmental health has yet to be fully addressed. Research presented here shows that treated sludge from five urban WWTPs experiencing differing local conditions contain a range of PS/PHS including substances whose use has been banned or heavily restricted. Concentrations reported in this study do not exceed the limit values set for the four PS/PHS currently included in the EU Sewage Sludge Directive. However, more stringent national limits are exceeded. The basis for developing and applying Predicted No Effect Concentration (PNEC) values for the application of sludge to agricultural land is still unclear. However, comparison between PS/PHS sludge concentrations and available PNEC soil values clearly indicate the need for further research. Implications and research priorities arising from these findings in terms of achieving compliance with EU Sewage Sludge and Water Framework Directives are discussed

A dual weighted residual method applied to complex periodic gratings

An extension of the dual weighted residual (DWR) method to the analysis of electromagnetic waves in a periodic diffraction grating is presented. Using the α,0-quasi-periodic transformation, an upper bound for the a posteriori error estimate is derived. This is then used to solve adaptively the associated Helmholtz problem. The goal is to achieve an acceptable accuracy in the computed diffraction efficiency while keeping the computational mesh relatively coarse. Numerical results are presented to illustrate the advantage of using DWR over the global a posteriori error estimate approach. The application of the method in biomimetic, to address the complex diffraction geometry of the Morpho butterfly wing is also discussed

Second Harmonic Coherent Driving of a Spin Qubit in a Si/SiGe Quantum Dot

We demonstrate coherent driving of a single electron spin using second harmonic excitation in a Si/SiGe quantum dot. Our estimates suggest that the anharmonic dot confining potential combined with a gradient in the transverse magnetic field dominates the second harmonic response. As expected, the Rabi frequency depends quadratically on the driving amplitude and the periodicity with respect to the phase of the drive is twice that of the fundamental harmonic. The maximum Rabi frequency observed for the second harmonic is just a factor of two lower than that achieved for the first harmonic when driving at the same power. Combined with the lower demands on microwave circuitry when operating at half the qubit frequency, these observations indicate that second harmonic driving can be a useful technique for future quantum computation architectures.Comment: 9 pages, 9 figure

Fundamental parameters of 16 late-type stars derived from their angular diameter measured with VLTI/AMBER

Thanks to their large angular dimension and brightness, red giants and supergiants are privileged targets for optical long-baseline interferometers. Sixteen red giants and supergiants have been observed with the VLTI/AMBER facility over a two-years period, at medium spectral resolution (R=1500) in the K band. The limb-darkened angular diameters are derived from fits of stellar atmospheric models on the visibility and the triple product data. The angular diameters do not show any significant temporal variation, except for one target: TX Psc, which shows a variation of 4% using visibility data. For the eight targets previously measured by Long-Baseline Interferometry (LBI) in the same spectral range, the difference between our diameters and the literature values is less than 5%, except for TX Psc, which shows a difference of 11%. For the 8 other targets, the present angular diameters are the first measured from LBI. Angular diameters are then used to determine several fundamental stellar parameters, and to locate these targets in the Hertzsprung-Russell Diagram (HRD). Except for the enigmatic Tc-poor low-mass carbon star W Ori, the location of Tc-rich stars in the HRD matches remarkably well the thermally-pulsating AGB, as it is predicted by the stellar-evolution models. For pulsating stars with periods available, we compute the pulsation constant and locate the stars along the various sequences in the Period -- Luminosity diagram. We confirm the increase in mass along the pulsation sequences, as predicted by the theory, except for W Ori which, despite being less massive, appears to have a longer period than T Cet along the first-overtone sequence.Comment: 15 pages, 9 figures, 6 table