SiO 2

We reported the SiO2 nanopillars on microscale roughened surface on GaN-based LED to enhance light-extraction efficiency. ZnO nanoparticles were deposited on SiO2 as an etching mask before ICP etching SiO2 by successive ionic layer adsorption and reaction method (SILAR), and the different heights of SiO2 nanopillars on microroughened ITO/GaN were obtained after etching. Compared to a regular (flat surface) GaN-based LED, the light output power for a LED with microroughening was increased by 33%. Furthermore, the proposed LEDs with SiO2 nanopillars on microroughened surface show the enhancement in light output power by 42.7%–49.1% at 20 mA. The increase in light output power is mostly attributed to reduction in Fresnel reflection by rough surface. The height of SiO2 nanopillars was increasing cause resulting in more rough on the microscale surface of GaN-based LEDs

SILAR-Based Application of Various Nanopillars on GaN-Based LED to Enhance Light-Extraction Efficiency

We reported the various nanopillars on GaN-based LED to enhance light-extraction efficiency prepared by successive ionic layer adsorption and reaction method (SILAR). Indium tin oxide (ITO) with thickness of 1 μm as transparent contact layer was grown to improve the electrical characteristics of the LEDs, including series resistance and operating voltage. SILAR-deposition ZnO nanoparticles on SiO2 were used as etching nanomasks. Multiple nanopillars were simultaneously formed on overall surfaces of ITO p- and n-GaN by ICP etching. The proposed GaN-based LEDs with nanopillars increase light output power by 7%–20.3% (at 20 mA) over that of regular GaN-based LEDs. The difference in light output power can be attributed to differences in materials and shapes of nanopillars, resulting in a reduction in Fresnel reflection by the roughened surface of GaN-based LEDs

Large N limit of SO(N) scalar gauge theory

In this paper we study the large $N_c$ limit of SO(N_c) gauge theory coupled to a real scalar field following ideas of Rajeev. We see that the phase space of this resulting classical theory is Sp_1(H)/U(H_+) which is the analog of the Siegel disc in infinite dimensions. The linearized equations of motion give us a version of the well-known 't Hooft equation of two dimensional QCD.Comment: 16 pages, no figure

McDonald Generalized Power Weibull Distribution: Properties, and Applications

This research introduces a novel six-parameter model called the McDonald Generalized Power Weibull distribution. The model contains several sub-models that prove highly valuable in modeling real-life scenarios, including the McDonald Weibull, McDonald exponential, McDonald Nadarajah-Haghighi, beta generalized power Weibull distribution, and Kumaraswamy generalized power distributions, among others. The proposed model demonstrates suitability in modeling survival/reliability data, accommodating various hazard failure rates such as increasing, decreasing, unimodal (upside-down bathtub), modified bathtub, and reversed J-shape. Various properties of the new model are investigated, including moments, quantiles, incomplete moments, moment-generating functions, and order statistics. The maximum likelihood estimation method is employed to estimate the model parameters. The study concludes by illustrating the flexibility of the proposed model through the use of lifetime data to demonstrate its applicability

On two dimensional coupled bosons and fermions

We study complex bosons and fermions coupled through a generalized Yukawa type coupling in the large-N_c limit following ideas of Rajeev [Int. Jour. Mod. Phys. A 9 (1994) 5583]. We study a linear approximation to this model. We show that in this approximation we do not have boson-antiboson and fermion-antifermion bound states occuring together. There is a possibility of having only fermion-antifermion bound states. We support this claim by finding distributional solutions with energies lower than the two mass treshold in the fermion sector. This also has implications from the point of view of scattering theory to this model. We discuss some aspects of the scattering above the two mass treshold of boson pairs and fermion pairs. We also briefly present a gauged version of the same model and write down the linearized equations of motion.Comment: 25 pages, no figure

Large N limit of SO(N) gauge theory of fermions and bosons

In this paper we study the large N_c limit of SO(N_c) gauge theory coupled to a Majorana field and a real scalar field in 1+1 dimensions extending ideas of Rajeev. We show that the phase space of the resulting classical theory of bilinears, which are the mesonic operators of this theory, is OSp_1(H|H )/U(H_+|H_+), where H|H refers to the underlying complex graded space of combined one-particle states of fermions and bosons and H_+|H_+ corresponds to the positive frequency subspace. In the begining to simplify our presentation we discuss in detail the case with Majorana fermions only (the purely bosonic case is treated in our earlier work). In the Majorana fermion case the phase space is given by O_1(H)/U(H_+), where H refers to the complex one-particle states and H_+ to its positive frequency subspace. The meson spectrum in the linear approximation again obeys a variant of the 't Hooft equation. The linear approximation to the boson/fermion coupled case brings an additonal bound state equation for mesons, which consists of one fermion and one boson, again of the same form as the well-known 't Hooft equation.Comment: 27 pages, no figure

Supergrassmannian and large N limit of quantum field theory with bosons and fermions

We study a large N_{c} limit of a two-dimensional Yang-Mills theory coupled to bosons and fermions in the fundamental representation. Extending an approach due to Rajeev we show that the limiting theory can be described as a classical Hamiltonian system whose phase space is an infinite-dimensional supergrassmannian. The linear approximation to the equations of motion and the constraint yields the 't Hooft equations for the mesonic spectrum. Two other approximation schemes to the exact equations are discussed.Comment: 24 pages, Latex; v.3 appendix added, typos corrected, to appear in JM

Induced vacuum condensates in the background of a singular magnetic vortex in 2+1-dimensional space-time

We show that the vacuum of the quantized massless spinor field in 2+1-dimensional space-time is polarized in the presence of a singular magnetic vortex. Depending on the choice of the boundary condition at the location of the vortex, either chiral symmetry or parity is broken; the formation of the appropriate vacuum condensates is comprehensively studied. In addition, we find that current, energy and other quantum numbers are induced in the vacuum.Comment: LaTeX2e, 27 page

Glueballs from 1+1 Dimensional Gauge Theories with Transverse Degrees of Freedom

We study $1+1$-dimensional $SU(N)$ gauge theories with adjoint scalar matter representations, based on a dimensional truncation of $2+1$ and $3+1$-dimensional pure QCD, which approximate the dynamics of transversely polarized gluons. The glueballs are investigated non-perturbatively using light-front quantisation, detailed spectra and wavefunctions being obtained for the large-$N$ limit. In general there is some qualitative agreement of the spectra with lattice Monte Carlo data from the higher dimensional QCD. From the light-front wavefunctions we calculate (polarized) structure functions and interpret the gluon and spin content of glueballs. We discuss the phase structure of the reduced theories in relation to matrix models for relativistic non-critical strings.Comment: To appear in Nucl. Phys. B; some small clarifications and 3 references adde

Dynamical Generation of Extended Objects in a 1+11+1 Dimensional Chiral Field Theory: Non-Perturbative Dirac Operator Resolvent Analysis

We analyze the $1+1$ dimensional Nambu-Jona-Lasinio model non-perturbatively. In addition to its simple ground state saddle points, the effective action of this model has a rich collection of non-trivial saddle points in which the composite fields \sigx=\lag\bar\psi\psi\rag and \pix=\lag\bar\psi i\gam_5\psi\rag form static space dependent configurations because of non-trivial dynamics. These configurations may be viewed as one dimensional chiral bags that trap the original fermions (``quarks") into stable extended entities (``hadrons"). We provide explicit expressions for the profiles of these objects and calculate their masses. Our analysis of these saddle points is based on an explicit representation we find for the diagonal resolvent of the Dirac operator in a \{\sigx, \pix\} background which produces a prescribed number of bound states. We analyse in detail the cases of a single as well as two bound states. We find that bags that trap $N$ fermions are the most stable ones, because they release all the fermion rest mass as binding energy and become massless. Our explicit construction of the diagonal resolvent is based on elementary Sturm-Liouville theory and simple dimensional analysis and does not depend on the large $N$ approximation. These facts make it, in our view, simpler and more direct than the calculations previously done by Shei, using the inverse scattering method following Dashen, Hasslacher, and Neveu. Our method of finding such non-trivial static configurations may be applied to other $1+1$ dimensional field theories