A Maximum Entropy Resolution to the Wine/Water Paradox.

The Principle of Indifference ('PI': the simplest non-informative prior in Bayesian probability) has been shown to lead to paradoxes since Bertrand (1889). Von Mises (1928) introduced the 'Wine/Water Paradox' as a resonant example of a 'Bertrand paradox', which has been presented as demonstrating that the PI must be rejected. We now resolve these paradoxes using a Maximum Entropy (MaxEnt) treatment of the PI that also includes information provided by Benford's 'Law of Anomalous Numbers' (1938). We show that the PI should be understood to represent a family of informationally identical MaxEnt solutions, each solution being identified with its own explicitly justified boundary condition. In particular, our solution to the Wine/Water Paradox exploits Benford's Law to construct a non-uniform distribution representing the universal constraint of scale invariance, which is a physical consequence of the Second Law of Thermodynamics.

Relating a System's Hamiltonian to Its Entropy Production Using a Complex Time Approach.

We exploit the properties of complex time to obtain an analytical relationship based on considerations of causality between the two Noether-conserved quantities of a system: its Hamiltonian and its entropy production. In natural units, when complexified, the one is simply the Wick-rotated complex conjugate of the other. A Hilbert transform relation is constructed in the formalism of quantitative geometrical thermodynamics, which enables system irreversibility to be handled analytically within a framework that unifies both the microscopic and macroscopic scales, and which also unifies the treatment of both reversibility and irreversibility as complementary parts of a single physical description. In particular, the thermodynamics of two unitary entities are considered: the alpha particle, which is absolutely stable (that is, trivially reversible with zero entropy production), and a black hole whose unconditional irreversibility is characterized by a non-zero entropy production, for which we show an alternate derivation, confirming our previous one. The thermodynamics of a canonical decaying harmonic oscillator are also considered. In this treatment, the complexification of time also enables a meaningful physical interpretation of both "imaginary time" and "imaginary energy".

How "Berry Phase" Analysis of Non-Adiabatic Non-Hermitian Systems Reflects Their Geometry.

There is currently great interest in systems represented by non-Hermitian Hamiltonians, including a wide variety of real systems that may be dissipative and whose behaviour can be represented by a "phase" parameter that characterises the way "exceptional points" (singularities of various sorts) determine the system. These systems are briefly reviewed here with an emphasis on their geometrical thermodynamics properties.

Thin film depth profiling by ion beam analysis.

The analysis of thin films is of central importance for functional materials, including the very large and active field of nanomaterials. Quantitative elemental depth profiling is basic to analysis, and many techniques exist, but all have limitations and quantitation is always an issue. We here review recent significant advances in ion beam analysis (IBA) which now merit it a standard place in the analyst's toolbox. Rutherford backscattering spectrometry (RBS) has been in use for half a century to obtain elemental depth profiles non-destructively from the first fraction of a micron from the surface of materials: more generally, "IBA" refers to the cluster of methods including elastic scattering (RBS; elastic recoil detection, ERD; and non-Rutherford elastic backscattering, EBS), nuclear reaction analysis (NRA: including particle-induced gamma-ray emission, PIGE), and also particle-induced X-ray emission (PIXE). We have at last demonstrated what was long promised, that RBS can be used as a primary reference technique for the best traceable accuracy available for non-destructive model-free methods in thin films. Also, it has become clear over the last decade that we can effectively combine synergistically the quite different information available from the atomic (PIXE) and nuclear (RBS, EBS, ERD, NRA) methods. Although it is well known that RBS has severe limitations that curtail its usefulness for elemental depth profiling, these limitations are largely overcome when we make proper synergistic use of IBA methods. In this Tutorial Review we aim to briefly explain to analysts what IBA is and why it is now a general quantitative method of great power. Analysts have got used to the availability of the large synchrotron facilities for certain sorts of difficult problems, but there are many much more easily accessible mid-range IBA facilities also able to address (and often more quantitatively) a wide range of otherwise almost intractable thin film questions.

Certified ion implantation fluence by high accuracy RBS.

From measurements over the last two years we have demonstrated that the charge collection system based on Faraday cups can robustly give near-1% absolute implantation fluence accuracy for our electrostatically scanned 200 kV Danfysik ion implanter, using four-point-probe mapping with a demonstrated accuracy of 2%, and accurate Rutherford backscattering spectrometry (RBS) of test implants from our quality assurance programme. The RBS is traceable to the certified reference material IRMM-ERM-EG001/BAM-L001, and involves convenient calibrations both of the electronic gain of the spectrometry system (at about 0.1% accuracy) and of the RBS beam energy (at 0.06% accuracy). We demonstrate that accurate RBS is a definitive method to determine quantity of material. It is therefore useful for certifying high quality reference standards, and is also extensible to other kinds of samples such as thin self-supporting films of pure elements. The more powerful technique of Total-IBA may inherit the accuracy of RBS.

Patterned ion beam implantation of Co ions into a SiO2 thin film via ordered nanoporous alumina masks.

Spatially patterned ion beam implantation of 190 keV Co(+) ions into a SiO(2) thin film on a Si substrate has been achieved by using nanoporous anodic aluminum oxide with a pore diameter of 125 nm as a mask. The successful synthesis of periodic embedded Co regions using pattern transfer is demonstrated for the first time using cross-sectional (scanning) transmission electron microscopy (TEM) in combination with analytical TEM. Implanted Co regions are found at the correct relative lateral periodicity given by the mask and at a depth of about 120 nm.

Effect of irradiation-induced disorder on the conductivity and critical temperature of the organic superconductor kappa-(BEDT-TTF)2Cu(SCN)2.

We have introduced defects into clean samples of the organic superconductor kappa-(BEDT-TTF)(2)Cu(SCN)(2) in order to determine their effect on the temperature dependence of the interlayer conductivity and the critical temperature T(c). We find a violation of Matthiessen's rule that can be explained by a model of involving a defect-assisted interlayer channel which acts in parallel with the bandlike conductivity. We observe an unusual dependence of T(c) on residual resistivity, inconsistent with the generalized Abrikosov-Gor'kov theory for an order parameter with a single component, providing an important constraint on models of the superconductivity in this material.

Distribution of surfactants in latex films: a Rutherford Backscattering study.

Uneven distribution of surfactant in dried latex films can affect the final film properties such as its water-resistance, gloss, and adhesiveness. Therefore, it is important to understand the driving force for surfactant transport during drying. In this paper, the accumulation of surfactant on the surface of poly(styrene-co-butyl acrylate) latex is studied using Rutherford Backscattering (RBS) and compared with results from a model that is based on the diffusive transport of particles and surfactant. Experimentally, a 30-50 nm thick surface layer, rich in surfactant, is seen and the concentration in the bulk of the film, obtained from RBS, agrees, at least qualitatively, with the model predictions for two of the surfactants tested.