Limitations of atom interferometry for gravitational wave observations in space

A paper published recently (Hogan et al. in Gen. Relativ. Gravit. 43:1953–2009, 2011) suggests the use of atom interferometry between satellites in Earth orbit to observe gravitational waves. The proposed altitude and satellite separation are about 1,000 and 30 km respectively. The difference in acceleration between clouds of ultracold atoms in atom interferometers near the two satellites would be detected by using laser beams between the interferometers. Because of the measurement path being very short compared with the million km or longer measurement path for a proposed laser interferometer gravitational wave antenna in space, the sensitivity to differential fluctuations in the laser phase as seen by the atoms in the two atom interferometers is very high. Problems introduced by this high sensitivity to spurious laser beam phase changes will be described in the first part of this paper. Then other limitations on the performance and on the suggested types of sources that could be observed will be discussed.     

Spatio-temporal dynamics of security investments in an interdependent risk environment

In a globalised world where risks spread through contagion, the decision of an entity to invest in securing its premises from stochastic risks no longer depends solely on its own actions but also on the actions of other interacting entities in the system. This phenomenon is commonly seen in many domains including airline, logistics and computer security and is referred to as Interdependent Security (IDS). An IDS game models this decision problem from a game-theoretic perspective and deals with the behavioural dynamics of risk-reduction investments in such settings. This paper enhances this model and investigates the spatio-temporal aspects of the IDS games. The spatio-temporal dynamics are studied using simple replicator dynamics on a variety of network structures and for various security cost tradeoffs that lead to different Nash equilibria in an IDS game. The simulation results show that the neighbourhood configuration has a greater effect on the IDS game dynamics than network structure. An in-depth empirical analysis of game dynamics is carried out on regular graphs, which leads to the articulation of necessary and sufficient conditions for dominance in IDS games under spatial constraints.     

Interface of GaN grown on Ge(1 1 1) by plasma assisted molecular beam epitaxy

Early efforts to grow GaN layers on germanium substrates by plasma assisted molecular beam epitaxy led to GaN domains, rotated by 8° relative to each other. Increased insight in the growth of GaN on germanium resulted in the suppression of these domain and consequently high quality layers. In this study the interface of these improved layers is investigated with transmission electron microscopy. The GaN layers show high crystal quality and an atomically abrupt interface with the Ge substrate. A thin, single crystalline Ge₃N₄ layer is observed in between the GaN layer and Ge substrate. This Ge₃N₄ layer remains present even at growth temperatures (850 °C) far above the decomposition temperature of Ge₃N₄ in vacuum (600 °C). Triangular voids in the Ge substrate are observed after growth. Reducing the Ga flux at the onset of GaN growth helps to reduce the triangular defect size. This indicates that the formation of voids in the Ge substrate strongly depends on the presence of Ga atoms at the onset of growth. However complete elimination was not achieved. The formation of voids in the germanium substrate leads to diffusion of Ge into the GaN layer. Therefore we examined the diffusion of Ge atoms into the GaN layer and Ga atoms into the Ge substrate. It was found that the diffusion of Ge into the GaN layer and Ga into the Ge substrate can be influenced by the growth temperature but cannot be completely suppressed. Our results suggest that Ga atoms diffuse through small imperfections in the Ge₃N₄ interlayer and locally etch the Ge substrate, leading to the diffusion of Ga and Ge atoms.     

Characterization of SIPOS films by spectroscopic ellipsometry and transmission electron microscopy

The structural and compositional properties of undoped SIPOS thin films have been studied by spectroscopic ellipsometry and transmission electron microscopy. It is shown that in most cases the former method provides fast and reliable results. The growth rate and crystallinity of SIPOS layers are studied as a function of N₂O concentration in the gas phase and annealing temperature.     

The asymptotic number of non-negative integer matrices with given row and column sums

Asymptotics are obtained for the number of m×n non-negative integer matrices subject to the following constraints: (i) each row and each column sum is specified and bounded, (ii) the entries are bounded, and (iii) a specified “sparse” set of entries must be zero. The result can be interpreted in terms of incidence matrices for labeled digraphs.     

Isotope shifts in transitions between low-lying levels of Sr I by laser-atomic-beam spectroscopy

High-resolution laser-atomic-beam spectroscopy has been used to determine isotope shifts in five transitions between low-lying states of Sr I. With these results and existing data a parametric analysis of level isotope shifts has been performed. The transition isotope shifts have been separated into field shift and mass shift contributions with a King-plot procedure using model-independent nuclear charge equivalent radiiR _k from muonic x-ray measurements. Values for the mean-square nuclear charge radiiδ〈r ₂ 〉 have been calculated from the field shifts in the optical transitions 5s ^{2 1} S ₀-5s5p ³ P ₁ and 5s5p ³ P ₀-5s6s ³ S ₁ and compared with correspondingδ〈r ² 〉 values evaluated from muonic x-ray data.     

Ligandenaustauschreaktionen von Fluoratomen mit Chloratomen bei Phosphorverbindungen der Koordinationszahl 3 und 4

Ligand-exchange reactions of fluorine versus chlorine atoms in phosphorus compounds with coordination number 3 or 4 Fluorine versus chlorine ligand-exchange reactions were carried out on the following phosphorus-based central moieties: CH₃P <, CH₃P(O)<, CH₃P(S)< and CH₃P(Se)<. The measured equilibrium distributions were shown to favour the species which result from an accumulation of like substituents on the central moieties, whereas the equilibrium distribution of chlorine vs bromine on CH₃P(O) < was found to be almost random. These fluorine exchanging systems thus represent the unusual case of large positive deviation from random distribution. It is also noteworthy that the equilibrium distributions depend only very little on the nature of the atom which is bonded to phosphorus in the “isolated” position. System CH₃PF₂/CH₃PCl₂ could not be studied quantitatively owing to the competitive dismutation of CH₃PF₂; however, evidence is given for fast initial redistribution of the halogens on the methylphosphorus moiety and for the transient formation of CH₃PFCl.     

Data analysis procedures for pulse ELDOR measurements of broad distance distributions

The reliability of procedures for extracting the distance distribution between spins from the dipolar evolution function is studied with particular emphasis on broad distributions. A new numerically stable procedure for fitting distance distributions with polynomial interpolation between sampling points is introduced and compared to Tikhonov regularization in the dipolar frequency and distance domains and to approximate Pake transformation. Distance distribution with only narrow peaks are most reliably extracted by distance-domain Tikhonov regularization, while frequency-domain Tikhonov regularization is favorable for distributions with only broad peaks. For the quantification of distributions by their mean distance and variance, Hermite polynomial interpolation provides the best results. Distributions that contain both broad and narrow peaks are most difficult to analyze. In this case a high signal-to-noise ratio is strictly required and approximate Pake transformation should be applied. A procedure is given for renormalizing primary experimental data from protein preparations with slightly different degrees of spin labelling, so that they can be compared directly. Performance of all the data analysis procedures is demonstrated on experimental data for a shape-persistent biradical with a label-to-label distance of 5 nm, for a [2]catenane with a broad distance distribution, and for a doubly spin-labelled double mutant of plant light harvesting complex II     

Fe-Hydroxysulphates from Bacterial Fe2+ Oxidation

The perturbed angular correlation method (PAC) was applied to investigate the lattice location of implanted ¹¹¹In probe ions in Hf₂Ni and Zr₂Ni intermetallic compounds. It is concluded that the ¹¹¹In/¹¹¹Cd probe nuclei experiencing the highly asymmetric electric field gradient (EFG) occupy the unique hafnium or zirconium 8(h) sites in the investigated phases. Above room temperature, the EFGs decrease linearly with temperature. The results are compared with that of previous PAC measurements with ¹⁸¹Ta probes.     

Thermal analysis of apatite structure

Two types of thermal effects, caused by substitutions (Ca²⁺↔ Na⁺, ↔ CO₃ ^2-, SO₄ ^2-, OH^-↔ F^-) in synthetic precipitated apatites as well as by sorption of Cd²⁺, Zn²⁺, and Cr³⁺ ions from the solutions were studied by TG/DTA, XRD and FTIR analysis. The temperatures of exothermic effect at 330-340°C and of decomposition of carbonate and sulfate apatites at 650-950°C were shown to depend on the substitutions in the apatite structure. This revised version was published online in July 2006 with corrections to the Cover Date.