Abstract: There is a type of filament that forms dosed contours encircling regions of one polarity of magnetic field, while the surrounding region has the opposite polarity One distribution of ring-filaments has sizes 2R = 40,000 to 160,000 km with the maximum around 100,000 km; the other distribution (with filaments and filament channels) has bigger sizes, with a maximum around 300,000 km. At low and mid latitudes the radial component B-rs (radial for the Sun) in the region outlined by filaments varies from 50 to 100 gauss, while the longitudinal component B-phi varies from 10 to 30 gauss. The total current inside the filament is 10(10) – 10(11) A, the ratio R/a approximate to 5 to 10, the magnetic flux crossing the surface is approximate to 10(21) – 10(22) MX; th, magnetic energy is approximate to 10(29) – 10(31) erg. Polar ring-filaments at latitudes 60 degrees-80 degrees are related to the polar magnetic field reversal and the quasi-flare processes at the poles during the field reversal. Correlation between B-rs and B-phi for the polar filament bands cannot be satisfactorily explained. A theoretical model using the conservation laws is used to study the relations between the various fields, currents, etc, of shrinking polar ring-filaments and their evolution. According to this theory ring-filaments should rise higher above the photosphere when shrinking. However, observations show that the height lowers. Presumably the discrepancy is due to the lack of dissipation in the model.

Abstract: We show that a superconducting quantum nanowire undergoes a new type of BCS-BEC crossover each time when an electron subband approaches the Fermi surface. In this case the longitudinal Cooper-pair size drops by two-three orders of magnitude down to a few nanometers. This unconventional BCS-BEC crossover is driven by quantum-size effects rather than by tuning the fermion-fermion interaction.

Abstract: Recent technological advances resulted in high-quality superconducting metallic nanofilms and nanowires. The physical properties of such nanostructures are governed by the size-quantization of the transverse electron spectrum. This has a substantial impact on the basic superconducting characteristics, e.g., the order parameter, the critical temperature and the critical magnetic field. In the present paper we give an overview of our theoretical results on this subject. Based on a numerical self-consistent solution of the Bogoliubov-de Gennes equations, we investigate how the superconducting properties are modified in the quantum-size regime.

Abstract: Our scientific and technological worldviews are largely dominated by the concepts of entropy and complexity. Originating in 19th-century thermodynamics, the concept of entropy merged with information in the last century, leading to definitions of entropy and complexity by Kolmogorov, Shannon and others. In its simplest form, this worldview is an application of the normal rules of arithmetic. In this worldview, when tossing a coin, a million heads or tails in a row is theoretically possible, but impossible in practice and in real life. On this basis, the impossible (in the binary case, the outermost entries of Pascal's triangle xn and yn for large values of n) can be safely neglected, and one can concentrate fully on what is common and what conforms to the law of large numbers, in fields ranging from physics to sociology and everything in between. However, in recent decades it has been shown that what is most improbable tends to be the rule in nature. Indeed, if one combines the outermost entries xn and yn with the normal rules of arithmetic, either addition or multiplication, one obtains Lamé curves and power laws respectively. In this article, some of these correspondences are highlighted, leading to a double conclusion. First, Gabriel Lamé's geometric footprint in mathematics and the sciences is enormous. Second, conic sections are at the core once more. Whereas mathematics so far has been exclusively the language of patterns in the sciences, the door is opened for mathematics to also become the language of the individual. The probabilistic worldview and Lamé's footprint can be seen as dual methods. In this context, it is to be expected that the notions of information, complexity, simplicity and redundancy benefit from this different viewpoint.

Abstract: Strain fields introduced by coherent Ni4Ti3 precipitates in austenitic Ni-Ti are believed to be a possible origin of why the R-phase transformation is introduced as an extra step before transforming to the B19'. The presence of this strain field was already confirmed in the past by conventional transmission electron microscopy (TEM) techniques and measured quantitatively by high resolution TEM (HRTEM). This time the geometrical phase method is applied on HRTEM micrographs to measure the full 3D strain tensor of the strain fields. Since each atomic resolution micrograph only results in a 2D measurement of the strain, observations in two different zone orientations are combined to retrieve the 3 x 3 strain tensor. In this work observations in a [1-1 1](B2) and [1 0-1](B2) zone orientation are used and this in case of precipitates with a diameter of around 50nm. In a next step the measured strain tensor is compared to the calculated eigenstrain of the R-phase in reference to the B2 matrix. This comparison shows that the introduced strain is very similar to the eigenstrain of one R-phase variant. Since for both structures, Ni4Ti3 and R-phase, four orientation variants are possible, each variant of the R-phase is thus able to accommodate the strain field of one of the Ni4Ti3 variants.

Abstract: Infrared absorption spectra of oxygen precipitates in boron doped silicon with a boron concentration between 10(17) and 10(19) cm(-3) are analyzed, applying the spectral function theory of the composite precipitates. The aspect ratio of the platelet precipitates has been determined by transmission electron microscopy measurements. Our analysis shows that in samples with moderate doping levels (<10(18) B cm(-3)) SiOgamma precipitates are formed with stoichiometry as in the lightly doped case. In the heavily (>10(18) cm(-3)) boron doped samples, however, the measured spectra of the precipitates are consistent with a mixture of SiO2 and B2O3. with a volume fraction of B2O3 as high as 0.41 in the most heavily doped case.