Structure and reactivity of the polarised liquid–liquid interface: what we know and what we do not

Charge transfer phenomena at the interface between two immiscible electrolyte solutions (ITIES) are electrochemical reactions taking place in soft media. Owing to their liquid nature, the ITIES shows a large panel of electrochemical reactions including electron transfer reactions, ion transfer reactions, coupled electron–ion transfer reactions or biomimetic redox reactions. Nevertheless, the mechanisms by which these reactions proceed are yet to be fully understood. The goal of this short review is to summarise the work accomplished over the past decades towards the elucidation of the structure and reactivity at the ITIES, highlighting the main questions still to be answered.     

Basis-set limit of the aurophilic attraction using the MP2 method: the examples of [ClAuPH3]2 dimer and [P(AuPH3)4]+ ion

The basis-set limit of the aurophilic attraction is studied at the MP2 level for the free model dimer [ClAuPH(3)](2) and for a [P(AuPH(3))(4)](+) ion. The latter system is found to prefer a C(4v) symmetry, instead of T(d), in agreement with Li and Pyykko [Inorg. Chem. 32, 2630 (1993)] but in contradiction to recent results of Fang and Wang [J. Phys. Chem. A. 111, 1562 (2006)]. The Karlsruhe split valence and the Dunning correlation-consistent basis sets converge to the same limit.     

Adatom dynamics in a periodic potential under time-periodic bias

We study the dynamics of a Brownian particle in a 1D external potential under the influence of a time-periodic bias with an amplitude small with respect to the potential barriers. We consider both a periodic potential corresponding to a smooth crystal surface and a regular array of steps with an extra Ehrlich–Schwoebel barrier for step crossing. For the smooth surface, we extend our previous work in the high friction limit to the low friction case and find that the oscillating bias enhances the diffusion coefficient D_T due to the broadening of the jump length distribution. In the case of a stepped surface with terraces of length L, the bias induces a non-zero average current J_ave in the direction of descending steps as long as the driving frequency is smaller than a threshold frequency Ω_T≈L⁻¹. The current shows a maximum as a function of temperature for fixed L. However, no evidence of stochastic resonance type of enhancement can be found either in D_T or J_ave.     

Hubble Law: Measure and Interpretation

We have had the chance to live through a fascinating revolution in measuring the fundamental empirical cosmological Hubble law. The key progress is analysed: (1) improvement of observational means (ground-based radio and optical observations, space missions); (2) understanding of the biases that affect both distant and local determinations of the Hubble constant; (3) new theoretical and observational results. These circumstances encourage us to take a critical look at some facts and ideas related to the cosmological red-shift. This is important because we are probably on the eve of a new understanding of our Universe, heralded by the need to interpret some cosmological key observations in terms of unknown processes and substances.     

Magnetic resonance imaging of the uterus in vivo and in vitro at an ultra low magnetic field (0.02 T): Assessment of its normal structure and of leiomyomas

The purpose of this investigation was to analyze the normal anatomy and leiomyomas of the uterus with an ultra low field (0.02 T) magnetic resonance imaging (MRI) device. MR imaging was performed on 18 uteri, 11 of which were imaged both preoperatively (in vivo) and as an operative specimen (in vitro), 6 only as an operative specimen, and 1 only preoperatively. All uteri were examined histologically after imaging. The junctional zone was much better delineated in vivo than in vitro, indicating that its appearance on MR is partly due to blood flow. No structures contributing to its visibility in vitro could be demonstrated histologically. Twenty leiomyomas (size range 7–79 mm) in 12 uteri were found with MRI. They were slightly better discerned in vivo than in vitro. The leiomyomas, having no degenerative changes, had a signal intensity which was the same or lower than that of the myometrium. On images obtained in vitro the signal intensity of these leiomyomas relative to that of myometrium correlated directly with their muscular content (R = 0.74, p = .002). The authors conclude that the junctional zone is a sum of physiological and structural factors, the latter being responsible for its in vitro delineation. MR imaging of the uterus in vitro did not give more information than MR imaging in vivo. All leiomyomas larger than 10 mm could be detected, indicating that MR imaging at 0.02 T is an accurate method for the imaging of the uterine leiomyomas.     

The determination of the past and the future of a physical system in quantum mechanics

The determination of the past and the future of a physical system are complementary aims of measurements. An optimal determination of the past of a system can be achieved by an informationally complete set of physical quantities. Such a set is always strongly noncommutative. An optimal determination of the future of a physical system can be obtained by a Boolean complete set of quantities. The two aims can be reconciled to a reasonable degree with using unsharp measurements.This work was partly supported by the Bundesministerium für Forschung und Technologie, Bonn, the Research Institute for Theoretical Physics, Helsinki, and the University of Turku Foundation, Turku.     

High‐power‐load DCLM monochromator for a computed tomography program at BMIT at energies of 25–150 keV

The research program at the biomedical imaging facility requires a high‐flux hard‐X‐ray monochromator that can also provide a wide beam. A wide energy range is needed for standard radiography, phase‐contrast imaging, K‐edge subtraction imaging and monochromatic beam therapy modalities. The double‐crystal Laue monochromator, developed for the BioMedical Imaging and Therapy facility, is optimized for the imaging of medium‐ and large‐scale samples at high energies with the resolution reaching 4 µm. A pair of 2 mm‐thick Si(111) bent Laue‐type crystals were used in fixed‐exit beam mode with a 16 mm vertical beam offset and the first crystal water‐cooled. The monochromator operates at energies from 25 to 150 keV, and the measured size of the beam is 189 mm (H) × 8.6 mm (V) at 55 m from the source. This paper presents our approach in developing a complete focusing model of the monochromator. The model uses mechanical properties of crystals and benders to obtain a finite‐element analysis of the complete assembly. The modeling results are compared and calibrated with experimental measurements. Using the developed analysis, a rough estimate of the bending radius and virtual focus (image) position of the first crystal can be made, which is also the real source for the second crystal. On the other hand, by measuring the beam height in several points in the SOE‐1 hutch, the virtual focus of the second crystal can be estimated. The focusing model was then calibrated with measured mechanical properties, the values for the force and torque applied to the crystals were corrected, and the actual operating parameters of the monochromator for fine‐tuning were provided.     

Coherent States and Number-Phase Uncertainty Relations

The number-phase uncertainty relations arerevisited in view of the recent discovery of a propercovariant phase observable. The high-amplitude limits ofthe coherent-state expectations of the moment operators of the phase observable are determined and thebehavior of the number-phase uncertainty product in thatlimit is investigated.     

On the notion of coexistence in quantum mechanics

The notion of coexistence of quantum observables was introduced to describe the possibility of measuring two or more observables together. Here we survey the various different formalisations of this notion and their connections. We review examples illustrating the necessary degrees of unsharpness for two noncommuting observables to be jointly measurable (in one sense of the phrase). We demonstrate the possibility of measuring together (in another sense of the phrase) noncoexistent observables. This leads us to a reconsideration of the connection between joint measurability and noncommutativity of observables and of the statistical and individual aspects of quantum measurements.     

Regularity of the Inverse of a Planar Sobolev Homeomorphism

Let be a domain. Suppose that f ∈ W^1,1_loc(Ω,R²) is a homeomorphism such that Df(x) vanishes almost everywhere in the zero set of J_f. We show that f^-1 ∈ W^1,1_loc(f(Ω),R²) and that Df⁻¹(y) vanishes almost everywhere in the zero set of Sharp conditions to quarantee that f⁻¹ ∈ W^1,q(f(Ω),R²) for some 1<q≤2 are also given.