Critical Hardy–Lieb–Thirring Inequalities for Fourth-Order Operators in Low Dimensions

This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order operators on the half-line is developed, and the trace inequality

Mesoscopic Fluctuations for the Thinned Circular Unitary Ensemble

In this paper we study the asymptotic behavior of mesoscopic fluctuations for the thinned Circular Unitary Ensemble. The effect of thinning is that the eigenvalues start to decorrelate. The decorrelation is stronger on the larger scales than on the smaller scales. We investigate this behavior by studying mesoscopic linear statistics. There are two regimes depending on the scale parameter and the thinning parameter. In one regime we obtain a CLT of a classical type and in the other regime we retrieve the CLT for CUE. The two regimes are separated by a critical line. On the critical line the limiting fluctuations are no longer Gaussian, but described by infinitely divisible laws. We argue that this transition phenomenon is universal by showing that the same transition and their laws appear for fluctuations of the thinned sine process in a growing box. The proofs are based on a Riemann-Hilbert problem for integrable operators.     

Recent Progress with the SMILETRAP Penning Mass Spectrometer

The Penning trap mass spectrometer SMILETRAP has been considerably improved during the last two years. The helium pressure has been carefully stabilized and is now independent of irregular air pressure. The temperature of the hyperboloidal precision trap is stabilized to ±0.03°C. Remaining temperature instabilities are compensated by changes in the current of a warm coil surrounding the precision trap. The frequency synthesizer is now locked to GPS. This means that it is much easier to accurately measure resonances during several days. The improvements have demonstrated that in mass doublet measurements with an excitation time of 1 s it is possible to determine the mass of ions with q/A=1/2 at an uncertainty to a few times of 0.1 ppb, using selected rather than cooled ions. In routine measurements lasting for one day it is possible to reach a mass uncertainty of 1 ppb. The masses of the following particles and atoms have been measured with uncertainties in the region 0.3–2 ppb: p, ³H, ³He, ⁴He, ²²Ne, ²⁸Si, ³⁶Ar, ⁷⁶Ge, ⁷⁶Se, ⁸⁶Kr and ¹³³Cs. It has also been shown that though we are using a warm bore the trap pressure is sufficiently low to prevent electron capture from the rest gas for excitation times of 3 s and for ion charges as high as 50+. This revised version was published online in July 2006 with corrections to the Cover Date.     

A First-Passage Kinetic Monte Carlo algorithm for complex diffusion–reaction systems

We develop an asynchronous event-driven First-Passage Kinetic Monte Carlo (FPKMC) algorithm for continuous time and space systems involving multiple diffusing and reacting species of spherical particles in two and three dimensions. The FPKMC algorithm presented here is based on the method introduced in Oppelstrup et al. [10] and is implemented in a robust and flexible framework. Unlike standard KMC algorithms such as the n-fold algorithm, FPKMC is most efficient at low densities where it replaces the many small hops needed for reactants to find each other with large first-passage hops sampled from exact time-dependent Green’s functions, without sacrificing accuracy. We describe in detail the key components of the algorithm, including the event-loop and the sampling of first-passage probability distributions, and demonstrate the accuracy of the new method. We apply the FPKMC algorithm to the challenging problem of simulation of long-term irradiation of metals, relevant to the performance and aging of nuclear materials in current and future nuclear power plants. The problem of radiation damage spans many decades of time-scales, from picosecond spikes caused by primary cascades, to years of slow damage annealing and microstructure evolution. Our implementation of the FPKMC algorithm has been able to simulate the irradiation of a metal sample for durations that are orders of magnitude longer than any previous simulations using the standard Object KMC or more recent asynchronous algorithms.     

Submillimeter ESR spectra of Fe<Superscript>2+</Superscript> ions in synthetic and natural beryl crystals

Electron spin resonance spectra of non-Kramers bivalent iron (Fe²⁺) ions have been detected in synthetic and natural beryl crystals with an iron impurity. The observed ESR spectra have been attributed to resonance transitions of Fe²⁺ ions from the ground (singlet) state to excited (doublet) levels with the splitting Δ = 12.7 cm^–1 between the levels. The experimental angular and frequency dependences of the resonance field of the ESR signal have been described by the spin Hamiltonian with the effective spin S = 1. The analysis of the ESR data and optical absorption spectra indicates that the Fe²⁺ ions are situated in tetrahedral positions and substitute Be²⁺ cations in the beryl structure.     

High sensitivity gas spectroscopy of porous, highly scattering solids

We present minimalistic and cost-efficient instrumentation employing tunable diode laser gas spectroscopy for the characterization of porous and highly scattering solids. The sensitivity reaches 3 x 10(-6) (absorption fraction), and the improvement with respect to previous work in this field is a factor of 10. We also provide the first characterization of the interference phenomenon encountered in high-resolution spectroscopy of turbid samples. Revealing that severe optical interference originates from the samples, we discuss important implications for system design. In addition, we introduce tracking coils and sample rotation as new and efficient tools for interference suppression. The great value of the approach is illustrated in an application addressing structural properties of pharmaceutical materials.     

Janus Face All-cis 1,2,4,5-tetrakis(trifluoromethyl)- and All-cis 1,2,3,4,5,6-hexakis(trifluoromethyl)- Cyclohexanes

We report the synthesis of all-cis 1,2,4,5-tetrakis (trifluoromethyl)- and all-cis 1,2,3,4,5,6-hexakis (trifluoromethyl)- cyclohexanes by direct hydrogenation of precursor tetrakis- or hexakis- (trifluoromethyl)benzenes. The resultant cyclohexanes have a stereochemistry such that all the CF₃ groups are on the same face of the cyclohexyl ring. All-cis 1,2,3,4,5,6-hexakis(trifluoromethyl)cyclohexane is the most sterically demanding of the all-cis hexakis substituted cyclohexanes prepared to date, with a barrier (ΔG) to ring inversion calculated at 27 kcal mol⁻¹. The X-ray structure of all-cis 1,2,3,4,5,6-hexakis(trifluoromethyl)cyclohexane displays a flattened chair conformation and the electrostatic profile of this compound reveals a large diffuse negative density on the fluorine face and a focused positive density on the hydrogen face. The electropositive hydrogen face can co-ordinate chloride (K≈10³) and to a lesser extent fluoride and iodide ions. Dehydrofluorination promoted decomposition occurs with fluoride ion acting as a base.     

Implementation of comprehensive two-dimensional gas chromatography–time-of-flight mass spectrometry for the simultaneous determination of halogenated contaminants and polycyclic aromatic hydrocarbons in fish

In the presented study, comprehensive two-dimensional gas chromatography coupled to time-of-flight mass spectrometry (GC?×?GC-TOFMS) was shown to be a powerful tool for the simultaneous determination of various groups of contaminants including 18 polychlorinated biphenyls (PCBs), seven polybrominated diphenyl ethers (PBDEs), and 16 polycyclic aromatic hydrocarbons (PAHs). Since different groups of analytes (traditionally analyzed separately) were included into one instrumental method, significant time savings were achieved. Following the development of an integrated sample preparation procedure for an effective and rapid isolation of several groups of contaminants from fish tissue, the GC?×?GC-TOFMS instrumental method was optimized to obtain the best chromatographic resolution and low quantification limits (LOQs) of all target analytes in a complex mixture. Using large-volume programmable temperature vaporization, the following LOQs were achieved-PCBs, 0.01-0.25 μg/kg; PBDEs, 0.025-5 μg/kg; PAHs 0.025-0.5 μg/kg. Furthermore, several capillary column combinations (BPX5, BPX50, and Rxi-17Sil-ms in the first dimension and BPX5, BPX50, Rt-LC35, and HT8 in the second dimension) were tested during the experiments, and the optimal separation of all target analytes even of critical groups of PAHs (group (a): benz[a]anthracene, cyclopenta[cd]pyrene and chrysene; group (b): benzo[b]fluoranthene, benzo[j]fluoranthene and benzo[k]fluoranthene; group (c): dibenz[ah]anthracene, indeno[1,2,3-cd]pyrene and benzo[ghi]perylene) was observed on BPX5?×?BPX50 column setup. Moreover, since the determination of target analytes was performed using TOFMS detector, further identification of other non-target compounds in real life samples was also feasible.     

Adsorption and viscoelastic properties of fractionated mucin (BSM) and bovine serum albumin (BSA) studied with quartz crystal microbalance (QCM-D)

The adsorption profile and viscoelastic properties of bovine submaxillary gland mucin (BSM) and bovine serum albumin (BSA), extracted from a commercial mucin preparation, adsorbing to polystyrene surfaces has been studied using quartz crystal microbalance with dissipation monitoring (QCM-D). A significant difference in the adsorption properties of the different proteins was detected; with the BSA adsorbing in a flat rigid layer whilst the mucin adsorbed in a diffuse, highly viscoelastic layer. Subsequent addition of BSA to the preadsorbed mucin layer resulted in stiffening of the protein layer which was attributed to complexation of the mucin by BSA. In contrast, a preadsorbed layer of BSA prevented mucin adsorption altogether. Combined mixtures of mucin and BSA in well defined ratios revealed intermediate properties between the two separate protein species which varied systematically with the protein ratios. The results shed light on the synergistic effects of complexation of lower molecular weight biomolecular species with mucin. The possibility to selectively control protein uptake and tailor the physical properties of the adsorbed layer makes mucin an attractive option for application in biomaterial coatings.