Position space formulation for Dirac fermions on honeycomb lattice

We study how to construct Dirac fermion defined on the honeycomb lattice in position space. Starting from the nearest neighbor interaction in tight binding model, we show that the Hamiltonian is constructed by kinetic term and second derivative term of three flavor Dirac fermions in which one flavor has a mass of cutoff order and the other flavors are massless. In this formulation the structure of the Dirac point is simplified so that its uniqueness can be easily shown even if we consider the next-nearest neighbor interaction. We also show the chiral symmetry at finite lattice spacing, which protects the masslessness of the Dirac fermion, and discuss the analogy with the staggered fermion formulation.Comment: 19 pages, 7 figure

Diophantine equation related to angle bisectors and solutions of Pell's equations

It is important in techniques of drawing to find combinations of the slopes of two straight lines and the bisectors of the angles between them which are all rational numbers. This problem is reduced to solving the Diophantine equation $(a-c)^2(b^2+1) = (b-c)^2(a^2+1).$ We have succeeded to describe all nontrivial integral solutions of the equation with solutions of Pell's equations. The formula is proven by certain properties of solutions of Pell's equations like those of Pell--Lucas and Pell numbers. We also give a formula for its rational solutions produced by Pythagorean triples with identical legs.Comment: 9 page

Rational bisectors and solutions of Pell's equations

On the coordinate plane, the slopes $a,$ $b$ of two straight lines and the slope $c$ of one of the angle bisectors between these lines satisfy the equation $(a-c)^2(b^2+1) = (b-c)^2(a^2+1).$ Recently, a certain formula of non-trivial integral solutions of this equation by using solutions of negative Pell's equation was discovered by the author. In this article, we describe the integeral solutions of $|x^2-dy^2| = k$ ($k$: integer $> 1$) with the fundamental unit of $\mathbb Q(\sqrt d)$ and the fundamental solutions of $|x^2-dy^2| = p^n$ ($p$: prime number, $n$: positive integer), and clarify the structure of the rational solutions of the above equation as its application.Comment: 12 page

Effects of elevated carbon dioxide on photosynthesis and carbon partitioning: a perspective on root sugar sensing and hormonal crosstalk

Plant responses to atmospheric carbon dioxide will be of great concern in the future, as carbon dioxide concentrations ([CO2]) are predicted to continue to rise. Elevated [CO2] causes increased photosynthesis in plants, which leads to greater production of carbohydrates and biomass. Which organ the extra carbohydrates are allocated to varies between species, but also within species. These carbohydrates are a major energy source for plant growth, but they also act as signaling molecules and have a range of uses beyond being a source of carbon and energy. Currently, there is a lack of information on how the sugar sensing and signaling pathways of plants are affected by the higher content of carbohydrates produced under elevated [CO2]. Particularly, the sugar signaling pathways of roots are not well understood, along with how they are affected by elevated [CO2]. At elevated [CO2], some plants allocate greater amounts of sugars to roots where they are likely to act on gene regulation and therefore modify nutrient uptake and transport. Glucose and sucrose also promote root growth, an effect similar to what occurs under elevated [CO2]. Sugars also crosstalk with hormones to regulate root growth, but also affect hormone biosynthesis. This review provides an update on the role of sugars as signaling molecules in plant roots and thus explores the currently known functions that may be affected by elevated [CO2]

Structure and magnetic property changes of epitaxially grown L1₀-FePd isolated nanoparticles on annealing

Isolated 10-nm-sized FePd nanoparticles were fabricated by electron-beam evaporation and postannealing above 773 K. FePd particles were epitaxially grown on a cleaved NaCl(001) substrate and were two-dimensionally dispersed on the substrate. Results showed that coalescence and growth of the particles were not prominent during annealing, indicating that the alloying and atomic ordering reactions proceeded mostly within each nanoparticle.Kazuhisa Sato and Yoshihiko Hirotsu, "Structure and magnetic property changes of epitaxially grown L10-FePd isolated nanoparticles on annealing", Journal of Applied Physics 93, 6291-6298 (2003) https://doi.org/10.1063/1.1568531

Measurement of Antioxidant Effects on the Auto-oxidation Kinetics of Methyl Oleate – Methyl Laurate Blend as a Surrogate Biodiesel System

This research investigates the feasibility of methyl oleate-methyl laurate blend as a surrogate biodiesel system which represents jatropha-coconut oil biodiesel, a potentially suitable formulation for tropical climate, to quantify the efficacy of antioxidant additives in terms of their kinetic parameters. This blend was tested by the Rancimat EN14112 standard method. The Rancimat tests results were used to determine the primary oxidation induction period (OIP) and first-order rate constants and activation energies. Addition of BHT and EcotiveTM antioxidants reduces the rate constants (k, h-1) between 15 to 90% in the 50-200 ppm dose range, with EcotiveTM producing significantly lower k values. Higher dose reduces the rate constant, while oleate/laurate ratio produces no significant impact. Antioxidants increase the oxidation activation energy (Ea, kJ/mol) by 180 to almost 400% relative to the non-antioxidant value of 27.0 kJ/mol. EcotiveTM exhibits lower Ea, implying that its higher efficacy stems from a better steric hindrance as apparent from its higher pre-exponential factors. The ability to quantify oxidation kinetic parameters is indicative of the usefulness of methyl oleate-laurate pure FAME blend as a biodiesel surrogate offering better measurement accuracy due to the absence of pre-existing antioxidants in the test samples.