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

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

Estrogenic chemicals often leach from BPA-free plastic products that are replacements for BPA-containing polycarbonate products

Background: Xenobiotic chemicals with estrogenic activity (EA), such as bisphenol A (BPA), have been reported to have potential adverse health effects in mammals, including humans, especially in fetal and infant stages. Concerns about safety have caused many manufacturers to use alternatives to polycarbonate (PC) resins to make hard and clear, reusable, plastic products that do not leach BPA. However, no study has focused on whether such BPA-free PC-replacement products, chosen for their perceived higher safety, especially for babies, also release other chemicals that have EA. Methods: We used two, well-established, mammalian cell-based, assays (MCF-7 and BG1Luc) to assess the EA of chemicals that leached into over 1000 saline or ethanol extracts of 50 unstressed or stressed (autoclaving, microwaving, and UV radiation) BPA-free PC-replacement products. An EA antagonist, ICI 182,780, was used to confirm that agonist activity in leachates was due to chemicals that activated the mammalian estrogen receptor. Results: Many unstressed and stressed, PC-replacement-products made from acrylic, polystyrene, polyethersulfone, and Tritan™ resins leached chemicals with EA, including products made for use by babies. Exposure to various forms of UV radiation often increased the leaching of chemicals with EA. In contrast, some BPA-free PC-replacement products made from glycol-modified polyethylene terephthalate or cyclic olefin polymer or co-polymer resins did not release chemicals with detectable EA under any conditions tested. Conclusions: This hazard assessment survey showed that many BPA-free PC- replacement products still leached chemicals having significant levels of EA, as did BPA-containing PC counterparts they were meant to replace. That is, BPA-free did not mean EA-free. However, this study also showed that some PC-replacement products did not leach chemicals having significant levels of EA. That is, EA-free PC-replacement products could be made in commercial quantities at prices that compete with PC-replacement products that were not BPA-free. Since plastic products often have advantages (price, weight, shatter-resistance, etc.) compared to other materials such as steel or glass, it is not necessary to forgo those advantages to avoid release into foodstuffs or the environment of chemicals having EA that may have potential adverse effects on our health or the health of future generations.This work was supported by the following NIH/NIEHS grants: R44 ES011469, 01–03 (CZY); 1R43/44 ES014806, 01–03 (CZY); subcontract (CZY, PI) on an NIH Grant 01–03 43/44ES018083-01 to PlastiPure (DK, SY PIs).Neuroscienc

Quantum transport in chains with noisy off-diagonal couplings

We present a model for conductivity and energy diffusion in a linear chain described by a quadratic Hamiltonian with Gaussian noise. We show that when the correlation matrix is diagonal, the noise-averaged Liouville-von Neumann equation governing the time-evolution of the system reduces to the Lindblad equation with Hermitian Lindblad operators. We show that the noise-averaged density matrix for the system expectation values of the energy density and the number density satisfy discrete versions of the heat and diffusion equations. Transport coefficients are given in terms of model Hamiltonian parameters. We discuss conditions on the Hamiltonian under which the noise-averaged expectation value of the total energy remains constant. For chains placed between two heat reservoirs, the gradient of the energy density along the chain is linear.Comment: 6 pages, to appear in J. Chem. Phy

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

Lattice Models of Quantum Gravity

Standard Regge Calculus provides an interesting method to explore quantum gravity in a non-perturbative fashion but turns out to be a CPU-time demanding enterprise. One therefore seeks for suitable approximations which retain most of its universal features. The $Z_2$-Regge model could be such a desired simplification. Here the quadratic edge lengths $q$ of the simplicial complexes are restricted to only two possible values $q=1+\epsilon\sigma$, with $\sigma=\pm 1$, in close analogy to the ancestor of all lattice theories, the Ising model. To test whether this simpler model still contains the essential qualities of the standard Regge Calculus, we study both models in two dimensions and determine several observables on the same lattice size. In order to compare expectation values, e.g. of the average curvature or the Liouville field susceptibility, we employ in both models the same functional integration measure. The phase structure is under current investigation using mean field theory and numerical simulation.Comment: 4 pages, 1 figure