Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard

This article presents experimental results on properties of waves propagating in an unbounded and a bounded photonic crystal consisting of metallic cylinders which are arranged in a triangular lattice. First, we present transmission measurements of plane waves traversing a photonic crystal. The experiments are performed in the vicinity of a Dirac point, i.e., an isolated conical singularity of the photonic band structure. There, the transmission shows a pseudodiffusive 1/L dependence, with $L$ being the thickness of the crystal, a phenomenon also observed in graphene. Second, eigenmode intensity distributions measured in a microwave analog of a relativistic Dirac billiard, a rectangular microwave billiard that contains a photonic crystal, are discussed. Close to the Dirac point states have been detected which are localized at the straight edge of the photonic crystal corresponding to a zigzag edge in graphene

Soccer: is scoring goals a predictable Poissonian process?

The non-scientific event of a soccer match is analysed on a strictly scientific level. The analysis is based on the recently introduced concept of a team fitness (Eur. Phys. J. B 67, 445, 2009) and requires the use of finite-size scaling. A uniquely defined function is derived which quantitatively predicts the expected average outcome of a soccer match in terms of the fitness of both teams. It is checked whether temporary fitness fluctuations of a team hamper the predictability of a soccer match. To a very good approximation scoring goals during a match can be characterized as independent Poissonian processes with pre-determined expectation values. Minor correlations give rise to an increase of the number of draws. The non-Poissonian overall goal distribution is just a consequence of the fitness distribution among different teams. The limits of predictability of soccer matches are quantified. Our model-free classification of the underlying ingredients determining the outcome of soccer matches can be generalized to different types of sports events

Application of a trace formula to the spectra of flat three-dimensional dielectric resonators

The length spectra of flat three-dimensional dielectric resonators of circular shape were determined from a microwave experiment. They were compared to a semiclassical trace formula obtained within a two-dimensional model based on the effective index of refraction approximation and a good agreement was found. It was necessary to take into account the dispersion of the effective index of refraction for the two-dimensional approximation. Furthermore, small deviations between the experimental length spectrum and the trace formula prediction were attributed to the systematic error of the effective index of refraction approximation. In summary, the methods developed in this article enable the application of the trace formula for two-dimensional dielectric resonators also to realistic, flat three-dimensional dielectric microcavities and -lasers, allowing for the interpretation of their spectra in terms of classical periodic orbits.Comment: 13 pages, 12 figures, 1 tabl

Experimental Observation of Localized Modes in a Dielectric Square Resonator

We investigated the frequency spectra and field distributions of a dielectric square resonator in a microwave experiment. Since such systems cannot be treated analytically, the experimental studies of their properties are indispensable. The momentum representation of the measured field distributions shows that all resonant modes are localized on specific classical tori of the square billiard. Based on these observations a semiclassical model was developed. It shows excellent agreement with all but a single class of measured field distributions that will be treated separately.Comment: 6 pages, 5 figures, 1 tabl

Scattering Experiments with Microwave Billiards at an Exceptional Point under Broken Time Reversal Invariance

Scattering experiments with microwave cavities were performed and the effects of broken time-reversal invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate resonances were investigated. All elements of the effective Hamiltonian of this two-level system were extracted. As a function of two experimental parameters, the doublet and also the associated eigenvectors could be tuned to coalesce at a so-called exceptional point (EP). The behavior of the eigenvalues and eigenvectors when encircling the EP in parameter space was studied, including the geometric amplitude that builds up in the case of broken TRI. A one-dimensional subspace of parameters was found where the differences of the eigenvalues are either real or purely imaginary. There, the Hamiltonians were found PT-invariant under the combined operation of parity (P) and time reversal (T) in a generalized sense. The EP is the point of transition between both regions. There a spontaneous breaking of PT occurs

Boundary field induced first-order transition in the 2D Ising model: numerical study

In a recent paper, Clusel and Fortin [J. Phys. A.: Math. Gen. 39 (2006) 995] presented an analytical study of a first-order transition induced by an inhomogeneous boundary magnetic field in the two-dimensional Ising model. They identified the transition that separates the regime where the interface is localized near the boundary from the one where it is propagating inside the bulk. Inspired by these results, we measured the interface tension by using multimagnetic simulations combined with parallel tempering to determine the phase transition and the location of the interface. Our results are in very good agreement with the theoretical predictions. Furthermore, we studied the spin-spin correlation function for which no analytical results are available.Comment: 12 pages, 7 figures, 2 table

Protein aggregates nucleate ice: the example of apoferritin

Biological material has gained increasing attention recently as a source of ice-nucleating particles that may account for cloud glaciation at moderate supercooling. While the ice-nucleation (IN) ability of some bacteria can be related to membrane-bound proteins with epitaxial fit to ice, little is known about the IN-active entities present in biological material in general. To elucidate the potential of proteins and viruses to contribute to the IN activity of biological material, we performed bulk freezing experiments with the newly developed drop freezing assay DRoplet Ice Nuclei Counter Zurich (DRINCZ), which allows the simultaneous cooling of 96 sample aliquots in a chilled ethanol bath. We performed a screening of common proteins, namely the iron storage protein ferritin and its iron-free counterpart apoferritin, the milk protein casein, the egg protein ovalbumin, two hydrophobins, and a yeast ice-binding protein, all of which revealed IN activity with active site densities > 0.1 mg−1 at −10 ∘C. The tobacco mosaic virus, a plant virus based on helically assembled proteins, also proved to be IN active with active site densities increasing from 100 mg−1 at −14 ∘C to 10 000 mg−1 at −20 ∘C. Among the screened proteins, the IN activity of horse spleen ferritin and apoferritin, which form cages of 24 co-assembled protein subunits, proved to be outstanding with active site densities > 10 mg−1 at −5 ∘C. Investigation of the pH dependence and heat resistance of the apoferritin sample confirmed the proteinaceous nature of its IN-active entities but excluded the correctly folded cage monomer as the IN-active species. A dilution series of apoferritin in water revealed two distinct freezing ranges, an upper one from −4 to −11 ∘C and a lower one from −11 to −21 ∘C. Dynamic light scattering measurements related the upper freezing range to ice-nucleating sites residing on aggregates and the lower freezing range to sites located on misfolded cage monomers or oligomers. The sites proved to persist during several freeze–thaw cycles performed with the same sample aliquots. Based on these results, IN activity seems to be a common feature of diverse proteins, irrespective of their function, but arising only rarely, most probably through defective folding or aggregation to structures that are IN active.This research has been supported by the Swiss National Foundation (grant nos. IZSEZ0_179149/1 and 200021_156581), the Basque government (Elkartek programmes ng 15 and ng 17), and the Spanish MINECO (grant no. MAT2013- 46006-R, programme MDM-2016-0618)