Pseudo-High-Order Symplectic Integrators

Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly with order in timestep, rendering higher-order methods impractical. However, symplectic integrators are often applied to systems in which perturbations between bodies are a small factor of the force due to a dominant central mass. In this case, it is possible to create optimized symplectic algorithms that require fewer substeps per timestep. This is achieved by only considering error terms of order epsilon, and neglecting those of order epsilon^2, epsilon^3 etc. Here we devise symplectic algorithms with 4 and 6 substeps per step which effectively behave as 4th and 6th-order integrators when epsilon is small. These algorithms are more efficient than the usual 2nd and 4th-order methods when applied to planetary systems.Comment: 14 pages, 5 figures. Accepted for publication in the Astronomical Journa

Stellar laboratories: new Ge V and Ge VI oscillator strengths and their validation in the hot white dwarf RE 0503-289

State-of-the-art spectral analysis of hot stars by means of non-LTE model-atmosphere techniques has arrived at a high level of sophistication. The analysis of high-resolution and high-S/N spectra, however, is strongly restricted by the lack of reliable atomic data for highly ionized species from intermediate-mass metals to trans-iron elements. Especially data for the latter has only been sparsely calculated. Many of their lines are identified in spectra of extremely hot, hydrogen-deficient post-AGB stars. A reliable determination of their abundances establishes crucial constraints for AGB nucleosynthesis simulations and, thus, for stellar evolutionary theory. In a previous analysis of the UV spectrum of RE 0503-289, spectral lines of highly ionized Ga, Ge, As, Se, Kr, Mo, Sn, Te, I, and Xe were identified. Individual abundance determinations are hampered by the lack of reliable oscillator strengths. Most of these identified lines stem from Ge V. In addition, we identified Ge VI lines for the first time. We calculated Ge V and Ge VI oscillator strengths to consider their radiative and collisional bound-bound transitions in detail in our non-LTE stellar-atmosphere models for the analysis of the Ge IV - VI spectrum exhibited in high-resolution and high-S/N UV spectra of RE 0503-289. We identify four Ge IV, 37 Ge V, and seven Ge VI lines. Most of these are identified for the first time in any star. We reproduce almost all Ge IV, Ge VI, and Ge VI lines in the observed spectrum of RE 0503-289 (Teff = 70 kK, log g = 7.5) at log Ge = -3.8 +/- 0.3 (mass fraction, about 650 times solar). Reliable measurements and calculations of atomic data are a prerequisite for stellar-atmosphere modeling. Our oscillator-strength calculations have allowed, for the first time, Ge V and Ge VI lines to be successfully reproduced in a white dwarf's spectrum and to determine its photospheric Ge abundance.Comment: 54 pages, 8 figure

Fractal geometry of critical Potts clusters

Numerical simulations on the total mass, the numbers of bonds on the hull, external perimeter, singly connected bonds and gates into large fjords of the Fortuin-Kasteleyn clusters for two-dimensional q-state Potts models at criticality are presented. The data are found consistent with the recently derived corrections-to-scaling theory. However, the approach to the asymptotic region is slow, and the present range of the data does not allow a unique identification of the exact correction exponentsComment: 7 pages, 8 figures, Late

Theory of minimum effort control

Optimum control theory formulations for solving problems in optimum guidance for interplanetary manned space flight mission

Superlattice with hot electron injection: an approach to a Bloch oscillator

A semiconductor superlattice with hot electron injection into the miniband is considered. The injection changes the stationary distribution function and results in a qualitative change of the frequency behaviour of the differential conductivity. In the regime with Bloch oscillating electrons and injection into the upper part of the miniband the region of negative differential conductivity is shifted from low frequencies to higher frequencies. We find that the dc differential conductivity can be made positive and thus the domain instability can be suppressed. At the same time the high-frequency differential conductivity is negative above the Bloch frequency. This opens a new way to make a Bloch oscillator operating at THz frequencies.Comment: RevTeX, 8 pages, 2 figures, to be published in Phys. Rev. B, 15 Januar 200

On the density-potential mapping in time-dependent density functional theory

The key questions of uniqueness and existence in time-dependent density functional theory are usually formulated only for potentials and densities that are analytic in time. Simple examples, standard in quantum mechanics, lead however to non-analyticities. We reformulate these questions in terms of a non-linear Schr\"odinger equation with a potential that depends non-locally on the wavefunction.Comment: 8 pages, 2 figure

NAIP proteins are required for cytosolic detection of specific bacterial ligands in vivo.

NLRs (nucleotide-binding domain [NBD] leucine-rich repeat [LRR]-containing proteins) exhibit diverse functions in innate and adaptive immunity. NAIPs (NLR family, apoptosis inhibitory proteins) are NLRs that appear to function as cytosolic immunoreceptors for specific bacterial proteins, including flagellin and the inner rod and needle proteins of bacterial type III secretion systems (T3SSs). Despite strong biochemical evidence implicating NAIPs in specific detection of bacterial ligands, genetic evidence has been lacking. Here we report the use of CRISPR/Cas9 to generate Naip1(-/-) and Naip2(-/-) mice, as well as Naip1-6(Δ/Δ) mice lacking all functional Naip genes. By challenging Naip1(-/-) or Naip2(-/-) mice with specific bacterial ligands in vivo, we demonstrate that Naip1 is uniquely required to detect T3SS needle protein and Naip2 is uniquely required to detect T3SS inner rod protein, but neither Naip1 nor Naip2 is required for detection of flagellin. Previously generated Naip5(-/-) mice retain some residual responsiveness to flagellin in vivo, whereas Naip1-6(Δ/Δ) mice fail to respond to cytosolic flagellin, consistent with previous biochemical data implicating NAIP6 in flagellin detection. Our results provide genetic evidence that specific NAIP proteins function to detect specific bacterial proteins in vivo