Fractionalized conductivity and emergent self-duality near topological phase transitions

The experimental discovery of the fractional Hall conductivity in two-dimensional electron gases revealed new types of quantum particles, called anyons, which are beyond bosons and fermions as they possess fractionalized exchange statistics. These anyons are usually studied deep inside an insulating topological phase. It is natural to ask whether such fractionalization can be detected more broadly, say near a phase transition from a conventional to a topological phase. To answer this question, we study a strongly correlated quantum phase transition between a topological state, called a $${{\mathbb{Z}}}_{2}$$ Z 2 quantum spin liquid, and a conventional superfluid using large-scale quantum Monte Carlo simulations. Our results show that the universal conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulator-to-superfluid transition. Moreover, a dynamically self-dual optical conductivity emerges at low temperatures above the transition point, indicating the presence of the elusive vison particles. Our study opens the door for the experimental detection of anyons in a broader regime, and has ramifications in the study of quantum materials, programmable quantum simulators, and ultra-cold atomic gases. In the latter case, we discuss the feasibility of measurements in optical lattices using current techniques.

Using different solutions for radiative transfer of solar-induced fluorescence in a land surface model

<p>Chlorophyll fluorescence (ChlF) takes place in green leaves of the plants during photosynthesis. It has therefore been proposed that ChlF can be used to track the photosynthetic activity of plants and the current possibility to observe sun-induced chlorophyll fluorescence (SIF) via remote sensing provides an unprecedented tool to monitor terrestrial photosynthesis at global scale. However, the relationship between photosynthesis and ChlF is not linear at all scales and is partly controlled by the non-photochemical quenching - which dissipates excess energy as heat. The relationship between the photochemical and fluorescence yields changes when the photochemical quenching is dominating at low irradiance conditions or at high stress conditions. Interpretation of observed SIF is complicated by its dependence on incoming absorbed radiation, observation geometry and radiative transfer of SIF photons within the canopy. To fully exploit remotely sensed SIF to estimate photosynthesis at ecosystem and global scales, it is important to account for these aspects through modelling that include ecosystem processes.</p><p>In this work we have implemented a ChlF model into a state-of-the-art land surface model QUantifying Interactions between terrestrial Nutrient CYcles and the climate system (QUINCY) simulating the terrestrial energy, water and biogeochemical cycles of carbon, nitrogen and phosphorus. The simulation of radiative transfer is highly influential for the simulated SIF signal, but the complex solutions of radiative transfer are computationally too heavy, making them impractical approaches at global scale. Therefore, we have investigated different radiative transfer techniques for the SIF signal of varying complexity at site scale in Niwot Ridge, U.S. <!-- we have now one clean growing season of data in a beech forests if you want to compare a deciduous and a evergreen, and of course a coule of years of grasslands (even if you don't want to put it in the abstract) -->The most complex solution is based on the mSCOPE and Fluspects model, that explicitly calculates signal transfer. The intermediate solution is based on a two-stream flux approach and the most simple is using a simple fraction for the escape ratio of SIF. Our aim is to assess which solution is most suitable for simulating the SIF signal at different scales and also test different formulations for modelling of non-photochemical quenching.</p>

Upaya Meningkatkan Hasil Belajar Matematika pada Pembelajaran Pecahan Sederhana melalui Media Kartu Pecahan pada Siswa Kelas VI SDN Temon Kecamatan Trowulan Kabupaten Mojokerto Tahun Pelajaran 2018/2019

In general, students think that Mathematics is the most difficult subject than other subjects, most students are less interested in mathematics because mathematics is a science related to something abstract, so they are less motivated to learn mathematics. For this reason, it is necessary to have an activity that is concrete, interesting and fun in improving student learning outcomes in learning simple fractions through fraction card media for Grade VI students of SDN Temon, Trowulan District, Mojokerto Regency, 2018/2019 Academic Year. Fraction card media is a learning media that researchers created based on the concept of fractions using fraction cards made of bright colored paper and there are fraction numbers in the form of decimals on the left side and fraction forms that are equivalent to decimal fractions on the right side. The number of fraction cards that the researcher made were 36 cards. This research was conducted in the first semester of the 2018/2019 academic year with classroom action research techniques which were carried out in 2 cycles. Based on the data analysis carried out, it was concluded that in cycle I the percentage of student learning outcomes reached 69% and based on the conversion of the minimum completeness criteria set by SDN Temon, Trowulan District, Mojokerto Regency, the percentage of student learning completeness was in the sufficient category, so it is necessary for researchers to continue research in cycle II. In cycle II the percentage of student learning outcomes showed a significant increase, reaching 91%, so it can be concluded that fraction card media can improve student learning outcomes on simple fraction material.

Pengetahuan Didaktika Calon Guru Sekolah Dasar tentang Pecahan Ditinjau dari Teori Antropologi Didaktik

Prospective elementary teachers (PET) are required to have sufficient mathematical and didactic knowledge about fractions, but many of them have difficulties explaining various concepts of fractions to students. Given the importance of prospective teachers’ knowledge of fractions, this study aims to investigate further the didactic knowledge of PETs’ didactic knowledge of fractions. Their knowledge is seen from their ability to construct contextual tasks about fractions based on number sense, problem-solving, mathematical literacy, and problem posing. PETs’ didactical knowledge is analyzed based on the anthropological theory of the didactic. This research method is qualitative with an internet-based research approach. The subjects of this study consist of 38 PsETs from a teacher education institution in Pekanbaru, Riau, Indonesia. The results of this study indicate that PsETs’ didactic knowledge of fractions is inappropriate, especially in the aspect of constructing contextual tasks about the division of fractions by fractions. PsETs tend to present the type of task associated with simple fraction operations and techniques in the form of standard algorithms. This study also indicates that PsETs’ theoretical knowledge is still limited to informal knowledge to support standard algorithms.

Pengembangan Media Ular Tangga Terhadap Pembelajaran Matematika Materi Pecahan Sederhana Pada Siswa Sekolah Dasar

One of the problems in the teaching and learning process is the lack of use of instructional media. This resulted in learning mathematics becoming boring and not in demand by students. So here we need a media that can be used in learning mathematics, one of which is the snake ladder media that is developed for learning mathematics for simple fraction material in elementary school students. Development research uses the ADDIE model which has 5 stages: (1) Analysis, (2) Design, (3) Development, (4) Implementation, (5) Evalution. But at the stage of the implementation of this study could not be applied because of the outbreak of COVID-19, so this study stopped at the stage of media expert validation and material validation as a measure of the feasibility of ladder snake media. The results of media validation were 90%, while the results of material validation 1 were 90% and material validation 2 were 92%. Then it can be concluded that the snake ladder media can be used for learning mathematics in simple fraction material in elementary school students.

Fractions in Transrational Arithmetic

In transrational arithmetic each closed fraction may be written as a simple fraction. It is shown that unlike in involutive meadows, in transrational arithmetic open fractions cannot be written as a sum of simple fractions (i.e. fractions the numerator and denominator of which are polynomials). It is also not the case that each open fraction with a single variable can be written as a mixed fraction.

Genotype x Harvest Cycles Interaction in Sugarcane on the South Coast of Pernambuco

Aims: To quantify the magnitude of the genotype x harvest cycle interaction (GxC) of sugarcane during three harvest cycles and to select superior clones for cultivation on the Coast of the Southern Forest of Pernambuco. Study Design: The experiment was conducted in a randomized complete block design. Place and Duration of Study: Evaluated during the 2011/2012, 2012/2013 and 2013/2014 harvest years in the agricultural area of the Cucaú Plant, located in the Municipality of Rio Formoso (8°39' 49" S and 35º09'31" W, altitude of 5 m), Microregion of the Southern Forest of Pernambuco. Methodology: 11 genotypes Republic of Brazil of the RB 2004 series and three RB cultivars were evaluated. Each plot was represented by five grooves of 8.0 m in length, spaced in 1.0 m, totaling 40 m². The crops were harvested 15 months after planting (MAP) for the first crop cycle and 12 MAP during the two subsequent cycles were evaluated tons of sugarcane per hectare (TCH), tons of pol per hectare (TPH) and total recoverable sugar (ATR). The variance analyses, the Scott and Knott clustering test, the estimative of the simple and complex parts of the G x C interaction and the Pearson correlation coefficient were processed in the Genes program. Results: The genotypes showed a significant reduction of TCH from the first to the second cycle and that only the genotype UFRPE11 showed a significant decrease for the third. The genotypes UFRPE10, UFRPE6, UFRPE11, UFRPE7, UFRPE2, UFRPE9 and UFRPE1 exceeded all commercial varieties in TPH. It was observed for the variable ATR that there were no significant differences between the genotypes in the third cycle. The simple fraction of the interaction G x C were predominant between cycles C1 and C2 for TCH (67.91%) and TPH (69.35%), while for ATR (56.42%) the complex fraction was predominant. For the pair C2 x C3, the simple fraction of the interaction G x C predominated only in the TCH (62.85%) and TPH (62.41%) variables, but was not significant for the variable ATR. It is worth mentioning that the C1 x C3 cycle pair presented predominantly complex type interactions for all variables TCH (50.42%), TPH (52.20%) and ATR (59.66%). Conclusion: The simple fraction of the genotype x harvest cycles (G x C) interaction provides genetic gain for yield of sugarcane and sugar in selection in subsequent pairs of harvest cycles, year by year. The complex fraction of G x C interaction reduces the predictability of genetic gain, making it difficult to select new cultivars. Local selection favors expressive genetic gain in a few selection cycles. However, it does not favor the selection of genotypes with high adaptability and phenotypic stability, requiring tests in several environments. The UFRPE06 and UFRPE10 clones can be selected to continue the selection cycles for the southern coastal conditions of the Mata de Pernambuco.

The unified rule of phyllotaxis explaining both spiral and non-spiral arrangements

Leaf-like appendages of different plant groups are arranged in common phyllotaxis patterns categorized into two types: spiral and non-spiral arrangements. The adaptive reason for this morphological convergence is unknown. In the non-spiral arrangement, the divergence angle between successive leaves is a simple fraction of 360°, e.g. distichy, decussate and whorled phyllotaxis. In the spiral arrangement, the divergence angle of nascent leaves at the shoot apex is fixed at the golden angle 137.5°, whereas those of the developed leaves varies within a sequence of Fibonacci fractions, such as 1/3, 2/5, 3/8, 5/13, etc. The optimality of the golden angle has been shown recently by assuming that the pattern of developed leaves varies during growth in a manner depending on the divergence angle of nascent leaves. Here we propose a unified rule of phyllotaxis to explain both types of arrangement: the developed leaves form vertical rows along the stem. In the non-spiral arrangement, nascent to developed leaves always follow this rule, so that the number of leaf rows is kept constant irrespective of stem growth. In the spiral arrangement, developed leaves attain this rule by adjusting the divergence angle from the golden angle. The spiral arrangement is adaptive in that the number of leaf rows varies during growth depending on shoot thickness.

UPAYA MENINGKATKAN HASIL BELAJAR MATEMATIKA PADA MATERI PECAHAN SEDERHANA MELALUI MEDIA KARTU PECAHAN DI KELAS VI SD NEGERI 011 DESA BARU KECAMATAN SIAK HULU

The background of this study is the low mathematics learning outcomes of class VI students at SD Negeri 011 Desa Baru, to overcome this problem a classroom action research was conducted by applying fraction card media. This research was conducted in SD Negeri 011 Desa Baru, the subject of this study was class VI students with a total of 24 students. The results of this study show that mathematics learning outcomes have increased in pre-cycle average value obtained is 59.8, in the first cycle obtained an average value of 68.3. And in the second cycle obtained an average value of 82.9. Based on the results of this study, it can be concluded that the mathematics learning outcomes in simple fraction material increase after the fraction card media are applied.

Paper-folding and cutting activities to demonstrate five-fold symmetry

We can obtain a two-fold symmetric figure by folding a square sheet of paper in the middle and then cutting along some curves drawn on the paper. By making two perpendicular folds through the centre of the paper and then cutting, we can obtain a four-fold symmetric figure. We can also get an eight-fold symmetric figure by making a fold bisecting an angle made by the two perpendicular folds before cutting. But it is not possible to obtain a three-fold, five-fold or six-fold symmetric figure in this way; we need to make more folds before cutting. Making a three-fold (respectively five-fold and six-fold) figure involves the division of the angle at the centre (360°) of a square sheet of a paper into six (respectively ten and twelve) equal parts. In other words, we need to construct the angles 60°, 36° and 30°. But these angles cannot be obtained by repeated bisections of 180° by simple folding as in the making of two-fold, four-fold and eight-fold figures. In [1], we see that each of the constructions of 60° and 30° applies the fact that sin 30° = ½ and takes only a few simple folding steps. The construction of 36° is more tedious (see, for example, [2] and [3]) as sin 36° is not a simple fraction but an irrational number. In this Article, we show how to make, by paper-folding and cutting a regular pentagon, a five-pointed star and create any five-fold figure as we want. The construction obtained by dividing the angle at the centre of a square paper into ten equal parts is called apentagon base. We gained much insight from [2] and [3] when developing the method for making the pentagon base to be presented below.