Period and toroidal knot mosaics

Knot mosaic theory was introduced by Lomonaco and Kauffman in the paper on `Quantum knots and mosaics' to give a precise and workable definition of quantum knots, intended to represent an actual physical quantum system. A knot (m,n)-mosaic is an $m \! \times \! n$ matrix whose entries are eleven mosaic tiles, representing a knot or a link by adjoining properly. In this paper we introduce two variants of knot mosaics: period knot mosaics and toroidal knot mosaics, which are common features in physics and mathematics. We present an algorithm producing the exact enumeration of period knot (m,n)-mosaics for any positive integers m and n, toroidal knot (m,n)-mosaics for co-prime integers m and n, and furthermore toroidal knot (p,p)-mosaics for a prime number p. We also analyze the asymptotics of the growth rates of their cardinality

Enhancement of energy harvesting performance for a piezoelectric cantilever using a spring mass suspension

A spring-mass suspension is proposed in this paper for enhancing vibration energy harvesting performances of piezoelectric cantilevers. The suspension is inserted between the piezoelectric cantilever and the vibration base. Two key criteria are proposed for designing the present structure towards simultaneous broadband and intensive energy harvesting. On the one hand, the natural frequency of the spring-mass suspension is tuned close to that of the piezoelectric beam. On the other hand, the inertial mass of the suspension is chosen much greater than the cantilever mass. The amplification of the dynamic response over a broader frequency band of the proposed configuration is validated via vibration analyses. A prototype device in accordance with the proposed design is subsequently developed for experimental evaluations. The present structure widens the effective bandwidth from 7.6 Hz to 22.2 Hz, while increasing the maximum harvested power from 0.01436 mW/g to 0.4406 mW/g compared to the conventional cantilevered energy harvester

Bond graph-based analysis of energy conversion in vibration-piezoelectricity coupling and its application to a cantilever vibra tion energy harvester

The energy flow in a piezoelectric vibration energy harvester (VEH) involves both the mechanical domain and the electrical domain. To better understand the vibration-piezoelectricity coupling of this device, a unified description approach based on the bond graph is proposed to analyze the influence of the piezoelectric VEH parameters on the electricity harvesting performance in the energy conversion. Both the mechanical structure and the electric circuit are modeled using the bond graph. The present method is applied to analyze the parametric configuration of a piezoelectric VEH, which is further tested on an experimental platform. The results show that the unified model using the bond-graph is well-suited for analyzing the vibration-piezoelectricity coupling. The proposed method can advance the design optimization of piezoelectric VEHs

Development of a thorium coating on an aluminium substrate by using electrodeposition method and alpha spectroscopy

A thin coating of thorium on aluminium substrates with the areal density of 110 to 130 $\mu g/cm^2$ is developed over a circular area of 22 mm diameter by using the electrodeposition method. An electrodeposition system is fabricated to consist of three components; an anode made of a platinum mesh, a cylindrical-shape vessel to contain the thorium solution, and a cathode in the form of a circular aluminium plate. The aluminium plate is mounted horizontally, and the platinum mesh is connected to an axial rod of an electric motor, mounted vertically and normal to the plane of the aluminium. The electrolyte solution is prepared by dissolving a known-weight thorium nitrate powder in 0.8 M HNO3 and isopropanol. The system is operated either in constant voltage (CV) or constant current (CC) mode. Under the electric field between the anode and cathode, thorium ions were deposited on the aluminium substrate mounted on the cathode. In the CV mode at 320, 360, and 400 V and in the CC mode at 15 mA, thorium films were formed over a circular area of the aluminium substrate. The areal density of thorium coating was measured by detecting emitted alpha particles. The areal density of thorium varied from 80 to 130 $\mu g/cm^2$ by changing the deposition time from 10 to 60 min. The results from the CV mode and CC mode are compared, and the radial dependence in the measured areal density is discussed for different modes of the electric field. The developed thorium coatings are to be used in the in-house development of particle detectors, fast neutron converters, targets for thorium fission experiments, and other purposes.Comment: 11 pages, 5 figures, 1 tabl

Understanding the mechanism of glucose-induced relief of Rgt1-mediated repression in yeast

The yeast Rgt1 repressor inhibits transcription of the glucose transporter (HXT) genes in the absence of glucose. It does so by recruiting the general corepressor complex Ssn6-Tup1 and the HXT corepressor Mth1. In the presence of glucose, Rgt1 is phosphorylated by the cAMP-activated protein kinase A (PKA) and dissociates from the HXT promoters, resulting in expression of HXT genes. In this study, using Rgt1 chimeras that bind DNA constitutively, we investigate how glucose regulates Rgt1 function. Our results show that the DNA-bound Rgt1 constructs repress expression of the HXT1 gene in conjunction with Ssn6-Tup1 and Mth1, and that this repression is lifted when they dissociate from Ssn6-Tup1 in high glucose conditions. Mth1 mediates the interaction between the Rgt1 constructs and Ssn6-Tup1, and glucose-induced downregulation of Mth1 enables PKA to phosphorylate the Rgt1 constructs. This phosphorylation induces dissociation of Ssn6-Tup1 from the DNA-bound Rgt1 constructs, resulting in derepression of HXT gene expression. Therefore, Rgt1 removal from DNA occurs in response to glucose but is not necessary for glucose induction of HXT gene expression, suggesting that glucose regulates Rgt1 function by primarily modulating the Rgt1 interaction with Ssn6-Tup1

The Glucose Signaling Network in Yeast

Background Most cells possess a sophisticated mechanism for sensing glucose and responding to it appropriately. Glucose sensing and signaling in the budding yeast Saccharomyces cerevisiae represent an important paradigm for understanding how extracellular signals lead to changes in the gene expression program in eukaryotes. Scope of review This review focuses on the yeast glucose sensing and signaling pathways that operate in a highly regulated and cooperative manner to bring about glucose-induction of HXT gene expression. Major conclusions The yeast cells possess a family of glucose transporters (HXTs), with different kinetic properties. They employ three major glucose signaling pathways—Rgt2/Snf3, AMPK, and cAMP-PKA—to express only those transporters best suited for the amounts of glucose available. We discuss the current understanding of how these pathways are integrated into a regulatory network to ensure efficient uptake and utilization of glucose. General significance Elucidating the role of multiple glucose signals and pathways involved inglucose uptake and metabolism in yeast may reveal the molecular basis of glucose homeostasis in humans, especially under pathological conditions, such as hyperglycemia in diabetics and the elevated rate of glycolysis observed in many solid tumors