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Gravitational waves, electromagnetic radiation, and the emission of high energy particles probe the phase structure of the equation of state of dense matter produced at the crossroad of the closely related relativistic collisions of heavy ions and of binary neutron stars mergers. 3 + 1 dimensional special- and general relativistic hydrodynamic simulation studies reveal a unique window of opportunity to observe phase transitions in compressed baryon matter by laboratory based experiments and by astrophysical multimessenger observations. The astrophysical consequences of a hadron-quark phase transition in the interior of a compact star will be focused within this article. Especially with a future detection of the post-merger gravitational wave emission emanated from a binary neutron star merger event, it would be possible to explore the phase structure of quantum chromodynamics. The astrophysical observables of a hadron-quark phase transition in a single compact star system and binary hybrid star merger scenario will be summarized within this article. The FAIR facility at GSI Helmholtzzentrum allows one to study the universe in the laboratory, and several astrophysical signatures of the quark-gluon plasma have been found in relativistic collisions of heavy ions and will be explored in future experiments.
The long-awaited detection of a gravitational wave from the merger of a binary neutron star in August 2017 (GW170817) marks the beginning of the new field of multi-messenger gravitational wave astronomy. By exploiting the extracted tidal deformations of the two neutron stars from the late inspiral phase of GW170817, it is now possible to constrain several global properties of the equation of state of neutron star matter. However, the most interesting part of the high density and temperature regime of the equation of state is solely imprinted in the post-merger gravitational wave emission from the remnant hypermassive/supramassive neutron star. This regime was not observed in GW170817, but will possibly be detected in forthcoming events within the current observing run of the LIGO/VIRGO collaboration. Numerous numerical-relativity simulations of merging neutron star binaries have been performed during the last decades, and the emitted gravitational wave profiles and the interior structure of the generated remnants have been analysed in detail. The consequences of a potential appearance of a hadron-quark phase transition in the interior region of the produced hypermassive neutron star and the evolution of its underlying matter in the phase diagram of quantum cromo dynamics will be in the focus of this article. It will be shown that the different density/temperature regions of the equation of state can be severely constrained by a measurement of the spectral properties of the emitted post-merger gravitational wave signal from a future binary compact star merger event.
In this work, we discuss the dense matter equation of state (EOS) for the extreme range of conditions encountered in neutron stars and their mergers. The calculation of the properties of such an EOS involves modeling different degrees of freedom (such as nuclei, nucleons, hyperons, and quarks), taking into account different symmetries, and including finite density and temperature effects in a thermodynamically consistent manner. We begin by addressing subnuclear matter consisting of nucleons and a small admixture of light nuclei in the context of the excluded volume approach. We then turn our attention to supranuclear homogeneous matter as described by the Chiral Mean Field (CMF) formalism. Finally, we present results from realistic neutron-star-merger simulations performed using the CMF model that predict signatures for deconfinement to quark matter in gravitational wave signals.
The catalytic mechanism, electron transfer coupled to proton pumping, of heme-copper oxidases is not yet fully understood. Microsecond freeze-hyperquenching single turnover experiments were carried out with fully reduced cytochrome aa(3) reacting with O(2) between 83 micros and 6 ms. Trapped intermediates were analyzed by low temperature UV-visible, X-band, and Q-band EPR spectroscopy, enabling determination of the oxidation-reduction kinetics of Cu(A), heme a, heme a(3), and of a recently detected tryptophan radical (Wiertz, F. G. M., Richter, O. M. H., Cherepanov, A. V., MacMillan, F., Ludwig, B., and de Vries, S. (2004) FEBS Lett. 575, 127-130). Cu(B) and heme a(3) were EPR silent during all stages of the reaction. Cu(A) and heme a are in electronic equilibrium acting as a redox pair. The reduction potential of Cu(A) is 4.5 mV lower than that of heme a. Both redox groups are oxidized in two phases with apparent half-lives of 57 micros and 1.2 ms together donating a single electron to the binuclear center in each phase. The formation of the heme a(3) oxoferryl species P(R) (maxima at 430 nm and 606 nm) was completed in approximately 130 micros, similar to the first oxidation phase of Cu(A) and heme a. The intermediate F (absorbance maximum at 571 nm) is formed from P(R) and decays to a hitherto undetected intermediate named F(W)(*). F(W)(*) harbors a tryptophan radical, identified by Q-band EPR spectroscopy as the tryptophan neutral radical of the strictly conserved Trp-272 (Trp-272(*)). The Trp-272(*) populates to 4-5% due to its relatively low rate of formation (t((1/2)) = 1.2 ms) and rapid rate of breakdown (t((1/2)) = 60 micros), which represents electron transfer from Cu(A)/heme a to Trp-272(*). The formation of the Trp-272(*) constitutes the major rate-determining step of the catalytic cycle. Our findings show that Trp-272 is a redox-active residue and is in this respect on an equal par to the metallocenters of the cytochrome c oxidase. Trp-272 is the direct reductant either to the heme a(3) oxoferryl species or to Cu (2+)(B). The potential role of Trp-272 in proton pumping is discussed.
In 2020, Germany and Spain experienced lockdowns of their school systems. This resulted in a new challenge for learners and teachers: lessons moved from the classroom to the children’s homes. Therefore, teachers had to set rules, implement procedures and make didactical–methodical decisions regarding how to handle this new situation. In this paper, we focus on the roles of mathematics teachers in Germany and Spain. The article first describes how mathematics lessons were conducted using distance learning. Second, problems encountered throughout this process were examined. Third, teachers drew conclusions from their mathematics teaching experiences during distance learning. To address these research interests, a questionnaire was answered by N = 248 teachers (N1 = 171 German teachers; N2 = 77 Spanish teachers). Resulting from a mixed methods approach, differences between the countries can be observed, e.g., German teachers conducted more lessons asynchronously. In contrast, Spanish teachers used synchronous teaching more frequently, but still regard the lack of personal contact as a main challenge. Finally, for both countries, the digitization of mathematics lessons seems to have been normalized by the pandemic.
Linking mathematics with reality is not new. It is also not new to use outdoor activities to learn mathematics. It seems to be new, to combine such mathematical outdoor activities with mobile technology, like the geocache community which makes use of GPS technology to guide their members to special places and points of interest. The use of mobile technologies to learn at any time and any location is known as “mobile learning”. This type of learning can be seen as an extension of eLearning. Considering the definition of O’Malley one notices that this definition does not exactly match with the idea of the MathCityMap-Project (MCM), because the learning environment in the MCM-Project is predetermined. Combined with the math trail method the project enables mobile learning within math trails with latest technology.In the MCM-Project students experience mathematics at real places and within real situations in out-of-school activities,with help of GPS-enabled smartphones and special math problems. In contrast to the paper versions of math trails we are able to give direct feedback on the solutions by using “mobile devices” such as smartphones or tablets. If the user has difficulties in solving the modeling task, stepped hints can be provided. The teacher is able to use the MCM-Portal to upload tasks developed by himself or by his students and he is also able to build a personal math trail for his students.
Tasks are a key resource in the process of teaching and learning mathematics, which is why task design continues to be one of the main research issues in mathematics education. Different settings can influence the principles underlying the formulation of tasks, and so does the outdoor context. Specifically, a math trail can be a privileged context, known to promote positive attitudes and additional engagement for the learning of mathematics, confronting students with a sequence of real-life tasks, related to a particular mathematical theme. Recently, mobile devices and apps, i.e., MathCityMap, have been recognized as an important resource to facilitate the extension of the classroom to the outdoors. The study reported in this paper intends to identify the principles of design for mobile theme-based math trails (TBT) that result in rich learning experiences in early algebraic thinking. A designed-based research is used, through a qualitative approach, to develop and refine design principles for TBT about Sequences and Patterns. The iterative approach is described by cycles with the intervention of the researchers, pre-service and in-service teachers and students of the targeted school levels. The results are discussed taking into account previous research and data collected along the cycles, conducing to the development of general design principles for TBT tasks.
Eine Billion ist mathematisch leicht darstellbar. Es ist eine Eins mit 12 Nullen: 1 000 000 000 000, mathematisch kurz und prägnant als 10^12 geschrieben. Aber darstellbar heißt nicht unbedingt vorstellbar. Versuchen wir, diese Anzahlen zu veranschaulichen, entstehen teilweise surreale, aber einprägsame Bilder.
As a surrogate of live cells, proteo-lipobeads are presented, encapsulating functional membrane proteins in a strict orientation into a lipid bilayer. Assays can be performed just as on live cells, for example using fluorescence measurements. As a proof of concept, we have demonstrated proton transport through cytochrome c oxidase.
This paper investigates extensions of the method of endogenous gridpoints (ENDGM) introduced by Carroll (2006) to higher dimensions with more than one continuous endogenous state variable. We compare three different categories of algorithms: (i) the conventional method with exogenous grids (EXOGM), (ii) the pure method of endogenous gridpoints (ENDGM) and (iii) a hybrid method (HYBGM). ENDGM comes along with Delaunay interpolation on irregular grids. Comparison of methods is done by evaluating speed and accuracy. We find that HYBGM and ENDGM both dominate EXOGM. In an infinite horizon model, ENDGM also always dominates HYBGM. In a finite horizon model, the choice between HYBGM and ENDGM depends on the number of gridpoints in each dimension. With less than 150 gridpoints in each dimension ENDGM is faster than HYBGM, and vice versa. For a standard choice of 25 to 50 gridpoints in each dimension, ENDGM is 1.4 to 1.7 times faster than HYBGM in the finite horizon version and 2.4 to 2.5 times faster in the infinite horizon version of the model.