Dirac operator on the q-deformed Fuzzy sphere and Its spectrum

The q-deformed fuzzy sphere $S_{qF}^2(N)$ is the algebra of $(N+1)\times(N+1)$ dim. matrices, covariant with respect to the adjoint action of \uq and in the limit $q\to 1$, it reduces to the fuzzy sphere $S_{F}^2(N)$. We construct the Dirac operator on the q-deformed fuzzy sphere-$S_{qF}^{2}(N)$ using the spinor modules of \uq. We explicitly obtain the zero modes and also calculate the spectrum for this Dirac operator. Using this Dirac operator, we construct the \uq invariant action for the spinor fields on $S_{qF}^{2}(N)$ which are regularised and have only finite modes. We analyse the spectrum for both $q$ being root of unity and real, showing interesting features like its novel degeneracy. We also study various limits of the parameter space (q, N) and recover the known spectrum in both fuzzy and commutative sphere.Comment: 19 pages, 6 figures, more references adde

Solid Waste Management Approaches in Trincomalee Urban Council Area

Solid Waste Management is one of the major challenges encountered by the urban areas of Sri Lanka. As a result of inappropriate disposal of solid waste in the open spaces; ecological, health, socio economic problems arise. No research has been undertaken regarding the solid waste management in Trincomalee Urban Council (UC) area of Sri Lanka. This research is carried out with the objectives of identifying the existing solid waste management system of Trincomalee UC area, assessing the problems and challenges in the solid waste management system and proposing recommendations to manage solid wastes properly. Primary data were collected through direct field observation, questionnaire survey with 200 respondents were selected based on purposive sampling, discussion and the secondary data were obtained from resource profiles, statistical handbooks, official websites and published journals. Data was collected from 02.09.2019 to 02.12.2019 and analysed through descriptive statistical method. “SPSS” software is used to analyse the questionnaires. Research revealed that the municipal solid waste generation in Trincomalee UC area has increased temporally due to population increase, expansion of commercial activities, growth of tourism and development activities. 73 tons of municipal solid waste has been generated daily, among them 54% produced from commercial centres and 38% from residential areas. 85% of the waste are degradable organic and 15% are inorganic. Unsorted solid wastes of Trincomalee UC area are disposed at Kanninya open space without any intermediate treatment activities. There is a shortage in appropriate technology, finance and cadres at Trincomalee UC to pursue the recycle activities and the participation of community is low. This situation is the root for the variety of ecological, health and socio-economic problems. Proposed recommendations were included in the conclusion. In this context, this study is the starting point for the policy makers and researchers of solid waste management.DOI: https://doi.org/10.31357/fhss/vjhss.v05i01.03

Practical superconductor development for electrical power applications. Annual report for FY 1995

Development of useful high-critical-temperature (high-{Tc}) superconductors requires synthesis of superconducting compounds; fabrication of wires, tapes, and films from these compounds: production of composite structures that incorporate stabilizers or insulators; and design and testing of efficient components. This report describes the technical progress of research and development efforts aimed at producing superconducting components in the (Bi,Pb)-Sr-Ca-Cu, (Tl,Pb,Bi,V)-(Ba,Sr)-Ca-Cu, and Y-Ba-Cu oxide systems. The topics that are discussed are synthesis and heat treatment of high-{Tc} superconductors, formation of monolithic and composite conductors, characterization of structures and superconducting and mechanical properties, and fabrication and testing of prototype components. Collaboration with industry and academia is documented

Development of ceramic superconductors for electric power applications

The U.S. Department of Energy supports an applied superconductivity program entitled {open_quotes}Superconductivity Program for Electric Power Systems.{close_quotes} Activities under this program are designed to help develop the high-temperature superconductor (HTS) technology that is needed for industry to proceed with the commercial development of electric power applications. Research is conducted in three categories: wire development, systems technology development, and Superconductivity Partnership Initiative (SPI). Wire development activities are devoted to improving the critical current density (J{sub c}) of short-length HTS wire, whereas activities in systems technology development focus on fabrication of long-length wires, coils, and magnets. Finally, SPI activities focus on the development of prototypes that consist of a generator coil, a fault current limiter, a transmission cable, and a motor. A current overview and recent progress in the development of HTSs are outlined in this paper. 48 refs., 6 figs

Noncommutative Chiral Anomaly and the Dirac-Ginsparg-Wilson Operator

It is shown that the local axial anomaly in $2-$dimensions emerges naturally if one postulates an underlying noncommutative fuzzy structure of spacetime . In particular the Dirac-Ginsparg-Wilson relation on ${\bf S}^2_F$ is shown to contain an edge effect which corresponds precisely to the ``fuzzy'' $U(1)_A$ axial anomaly on the fuzzy sphere . We also derive a novel gauge-covariant expansion of the quark propagator in the form $\frac{1}{{\cal D}_{AF}}=\frac{a\hat{\Gamma}^L}{2}+\frac{1}{{\cal D}_{Aa}}$ where $a=\frac{2}{2l+1}$ is the lattice spacing on ${\bf S}^2_F$, $\hat{\Gamma}^L$ is the covariant noncommutative chirality and ${\cal D}_{Aa}$ is an effective Dirac operator which has essentially the same IR spectrum as ${\cal D}_{AF}$ but differes from it on the UV modes. Most remarkably is the fact that both operators share the same limit and thus the above covariant expansion is not available in the continuum theory . The first bit in this expansion $\frac{a\hat{\Gamma}^L}{2}$ although it vanishes as it stands in the continuum limit, its contribution to the anomaly is exactly the canonical theta term. The contribution of the propagator $\frac{1}{{\cal D}_{Aa}}$ is on the other hand equal to the toplogical Chern-Simons action which in two dimensions vanishes identically .Comment: 26 pages, latex fil

Unusual Thermodynamics on the Fuzzy 2-Sphere

Higher spin Dirac operators on both the continuum sphere($S^2$) and its fuzzy analog($S^2_F$) come paired with anticommuting chirality operators. A consequence of this is seen in the fermion-like spectrum of these operators which is especially true even for the case of integer-spin Dirac operators. Motivated by this feature of the spectrum of a spin 1 Dirac operator on $S_F^2$, we assume the spin 1 particles obey Fermi-Dirac statistics. This choice is inspite of the lack of a well defined spin-statistics relation on a compact surface such as $S^2$. The specific heats are computed in the cases of the spin $\frac{1}{2}$ and spin 1 Dirac operators. Remarkably the specific heat for a system of spin $\frac{1}{2}$ particles is more than that of the spin 1 case, though the number of degrees of freedom is more in the case of spin 1 particles. The reason for this is inferred through a study of the spectrums of the Dirac operators in both the cases. The zero modes of the spin 1 Dirac operator is studied as a function of the cut-off angular momentum $L$ and is found to follow a simple power law. This number is such that the number of states with positive energy for the spin 1 and spin $\frac{1}{2}$ system become comparable. Remarks are made about the spectrums of higher spin Dirac operators as well through a study of their zero-modes and the variation of their spectrum with degeneracy. The mean energy as a function of temperature is studied in both the spin $\frac{1}{2}$ and spin 1 cases. They are found to deviate from the standard ideal gas law in 2+1 dimensions.Comment: 19 pages, 7 figures. The paper has been significantly modified. Main results are unchange

STUDY ON THE ANTIMICROBIAL EFFICACY OF HAND SANITIZERS DEVELOPED BY THE PHARMACEUTICAL CORPORATION (I.M) KERALA LTD (OUSHADHI)

Hand sanitizers are used to ensure hygiene in the absence of hand washing facilities or where frequent sanitizing is required especially in the wake of the Covid-19 pandemic. Handsanitizers using different combinations were prepared at Oushadhi using WHO recommendations and also to promote Kerala Government’s initiative of break the chain campaign. The campaign was launched on 15th March 2020 and it aims to cut down the progress of disease transmission. The efficacy of the batches of sanitizers prepared was tested against Escherichia coli and Staphylococcus aureus. They were also tested against common air and water contaminants found in the premises which would be of more significance to the general workforce. The susceptibility test was performed by agar well diffusion method and it revealed that the antimicrobial efficacy of the prepared hand sanitizer Batch III with Cymbopogon citratus oil was the most effective among the three combinations. A hedonic sensory evaluation was carried out for better consumer acceptability

Dynamical generation of a nontrivial index on the fuzzy 2-sphere

In the previous paper hep-th/0312199 we studied the 't Hooft-Polyakov (TP) monopole configuration in the U(2) gauge theory on the fuzzy 2-sphere and showed that it has a nonzero topological charge in the formalism based on the Ginsparg-Wilson relation. In this paper, by showing that the TP monopole configuration is stabler than the U(2) gauge theory without any condensation in the Yang-Mills-Chern-Simons matrix model, we will present a mechanism for dynamical generation of a nontrivial index. We further analyze the instability and decay processes of the U(2) gauge theory and the TP monopole configuration.Comment: Latex2e, 30 pages, 4 figures, the topological charge for a monopole configuration is corrected, reference added, the final version to appear in Physical Review D (the typos mentioned in the erratum are corrected

The Fuzzy Ginsparg-Wilson Algebra: A Solution of the Fermion Doubling Problem

The Ginsparg-Wilson algebra is the algebra underlying the Ginsparg-Wilson solution of the fermion doubling problem in lattice gauge theory. The Dirac operator of the fuzzy sphere is not afflicted with this problem. Previously we have indicated that there is a Ginsparg-Wilson operator underlying it as well in the absence of gauge fields and instantons. Here we develop this observation systematically and establish a Dirac operator theory for the fuzzy sphere with or without gauge fields, and always with the Ginsparg-Wilson algebra. There is no fermion doubling in this theory. The association of the Ginsparg-Wilson algebra with the fuzzy sphere is surprising as the latter is not designed with this algebra in mind. The theory reproduces the integrated U(1)_A anomaly and index theory correctly.Comment: references added, typos corrected, section 4.2 simplified. Report.no: SU-4252-769, DFUP-02-1

Explosive consolidation of (Bi,Pb)-Sr-Ca-Cu-O superconductor powders during powder-in-tube processing

Superconducting (2212) Bi-Sr-Ca-Cu-O (BSCCO) and BSCCO-Ag composites were explosively consolidated in silver tubing and then drawn and rolled into tapes. The silver-sheathed tapes were then subjected to repeated cycles of pressing and heat treatment, which resulted in enhanced texturing and grain growth and a subsequent increase in critical current density (J{sub c}). The effect of silver flake additions to the superconducting powder further increased texturing and J{sub c}, with optimal properties occurring in powders with 10 vol.% silver flake. Density measurements on the superconductor tapes showed that near-theoretical densities had been achieved at the end of the thermomechanical treatment (TMT). Scanning electron microscopy indicated that grain alignment increased after TMT, with an apparent reduction in grain size after the fourth treatment. X-ray diffraction studies showed that grain orientation and conversion of 2212 to Bi{sub 2}Sr{sub 2}Ca{sub 2}Cu{sub 3}O{sub 10{minus}x} are improved when explosive consolidation is introduced before the drawing step in the powder-in-tube process