Composing Scalable Nonlinear Algebraic Solvers

Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for nonlinear algebraic systems, where nonlinear composition of different nonlinear solvers may significantly improve the time to solution. We describe the basic concepts of nonlinear composition and preconditioning and present a number of solvers applicable to nonlinear partial differential equations. We have developed a software framework in order to easily explore the possible combinations of solvers. We show that the performance gains from using composed solvers can be substantial compared with gains from standard Newton-Krylov methods.Comment: 29 pages, 14 figures, 13 table

Climbing the Jaynes-Cummings Ladder and Observing its Sqrt(n) Nonlinearity in a Cavity QED System

The already very active field of cavity quantum electrodynamics (QED), traditionally studied in atomic systems, has recently gained additional momentum by the advent of experiments with semiconducting and superconducting systems. In these solid state implementations, novel quantum optics experiments are enabled by the possibility to engineer many of the characteristic parameters at will. In cavity QED, the observation of the vacuum Rabi mode splitting is a hallmark experiment aimed at probing the nature of matter-light interaction on the level of a single quantum. However, this effect can, at least in principle, be explained classically as the normal mode splitting of two coupled linear oscillators. It has been suggested that an observation of the scaling of the resonant atom-photon coupling strength in the Jaynes-Cummings energy ladder with the square root of photon number n is sufficient to prove that the system is quantum mechanical in nature. Here we report a direct spectroscopic observation of this characteristic quantum nonlinearity. Measuring the photonic degree of freedom of the coupled system, our measurements provide unambiguous, long sought for spectroscopic evidence for the quantum nature of the resonant atom-field interaction in cavity QED. We explore atom-photon superposition states involving up to two photons, using a spectroscopic pump and probe technique. The experiments have been performed in a circuit QED setup, in which ultra strong coupling is realized by the large dipole coupling strength and the long coherence time of a superconducting qubit embedded in a high quality on-chip microwave cavity.Comment: ArXiv version of manuscript published in Nature in July 2008, 5 pages, 5 figures, hi-res version at http://www.finkjohannes.com/SqrtNArxivPreprint.pd

Effect of strain on surface diffusion in semiconductor heteroepitaxy

We present a first-principles analysis of the strain renormalization of the cation diffusivity on the GaAs(001) surface. For the example of In/GaAs(001)-c(4x4) it is shown that the binding of In is increased when the substrate lattice is expanded. The diffusion barrier \Delta E(e) has a non-monotonic strain dependence with a maximum at compressive strain values (e 0) studied. We discuss the consequences of spatial variations of both the binding energy and the diffusion barrier of an adatom caused by the strain field around a heteroepitaxial island. For a simplified geometry, we evaluate the speed of growth of two coherently strained islands on the GaAs(001) surface and identify a growth regime where island sizes tend to equalize during growth due to the strain dependence of surface diffusion.Comment: 10 pages, 8 figures, LaTeX2e, to appear in Phys. Rev. B (2001). Other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm

Pancreatic adenocarcinoma in type 2 progressive familial intrahepatic cholestasis

<p>Abstract</p> <p>Background</p> <p>BSEP disease results from mutations in ABCB11, which encodes the bile salt export pump (BSEP). BSEP disease is associated with an increased risk of hepatobiliary cancer.</p> <p>Case Presentation</p> <p>A 36 year old woman with BSEP disease developed pancreatic adenocarcinoma at age 36. She had been treated with a biliary diversion at age 18. A 1.7 × 1.3 cm mass was detected in the pancreas on abdominal CT scan. A 2 cm mass lesion was found at the neck and proximal body of the pancreas. Pathology demonstrated a grade 2-3 adenocarcinoma with invasion into the peripancreatic fat.</p> <p>Conclusions</p> <p>Clinicians should be aware of the possibility of pancreatic adenocarcinoma in patients with BSEP disease.</p

An extended association screen in multiple sclerosis using 202 microsatellite markers targeting apoptosis-related genes does not reveal new predisposing factors

Apoptosis, the programmed death of cells, plays a distinct role in the etiopathogenesis of Multiple sclerosis (MS), a common disease of the central nervous system with complex genetic background. Yet, it is not clear whether the impact of apoptosis is due to altered apoptotic behaviour caused by variations of apoptosis-related genes. Instead, apoptosis in MS may also represent a secondary response to cellular stress during acute inflammation in the central nervous system. Here, we screened 202 apoptosis-related genes for association by genotyping 202 microsatellite markers in initially 160 MS patients and 160 controls, both divided in 4 sets of pooled DNA samples, respectively. When applying Bonferroni correction, no significant differences in allele frequencies were detected between MS patients and controls. Nevertheless, we chose 7 markers for retyping in individual DNA samples, thereby eliminating 6 markers from the list of candidates. The remaining candidate, the ERBB3 gene microsatellite, was genotyped in additional 245 MS patients and controls. No association of the ERBB3 marker with the disease was detected in these additional cohorts. In consequence, we did not find further evidence for apoptosis-related genes as predisposition factors in MS