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Starting from the Verma modules of the algebra sl(4, Double-Struck-Capital-C ) we explicitly construct factor representations of the algebra su(2, 2) which are connected with unitary representation of group SU(2, 2). We find a full set of extremal vectors for this kind of representations, so we can solve explicitly the problem of irreducibility of these representations.
We summarize some previous work on SU(4) describing hadron representations and transformations as well as its noncompact “counterpart” SU*(4) being the complex embedding of SL(2,H). So after having related the 16-dim Dirac algebra to SU*(4), on the one hand we have access to real, complex, and quaternionic Lie group chains and their respective algebras, on the other hand it is of course possible to relate physical descriptions to the respective representations. With emphasis on the common maximal compact subgroup USp(4), we are led to projective geometry of the real 3-space and various transfer principles which we use to extend the previous work on the rank 3-algebras above. On real spaces, such considerations are governed by the groups SO(n,m) with n + m = 6. The central thread, however, focuses here on line and Complex geometry which finds its well-known counterparts in descriptions of electromagnetism and special relativity as well as—using transfer principles—in Dirac, gauge, and quantum field theory. We discuss a simple picture where Complexe of second grade play the major and dominant rôle to unify (real) projective geometry, complex representation theory and line/Complex representations in order to proceed to dynamics.
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases.
New York City's Office of Emergency Management (OEM) originally ran hundreds of classroom based courses, where they brought together civil servants to learn how to run a Hurricane Shelter (HS). This approach was found to be costly, time consuming and lacked any sense of an impending disaster and need for emergency response. In partnership with the City of New York University School of Professional studies, Gronstedt Group and Daden Limited, the OEM wanted to create a simulation that overcame these issues, providing users with a more immersive and realistic approach at a lower cost. The HS simulation was built in the virtual world Second Life (SL). Virtual worlds are a genre of online communities that often take the form of a computer-based simulated environments, through which users can interact with one another and use or create objects. Using this technology allowed managers to apply their knowledge in both classroom and remote learning environments. The shelter simulation is operational 24/7, guiding users through a 4 1/2 hour narrative from start to finish. This paper will describe the rationale for the project, the technical approach taken - particularly the use of a web based authoring tool to create and manage the immersive simulation, and the results from operational use.
Highlights: > Mott transition in 2d lattice fermion model. > 3D integrability out of 2D. > Effective field theory for Mott transition in 2d. > Double Chern-Simons. > d-Density waves. - Abstract: We study the Mott transition in a two-dimensional lattice spinless fermion model with nearest neighbors density-density interactions. By means of a two-dimensional Jordan-Wigner transformation, the model is mapped onto the lattice XXZ spin model, which is shown to possess a quantum group symmetry as a consequence of a recently found solution of the Zamolodchikov tetrahedron equation. A projection (from three to two space-time dimensions) property of the solution is used to identify the symmetry of the model at the Mott critical point as U{sub q}(sl(2)-circumflex)xU{sub q}(sl(2)-circumflex), with deformation parameter q = -1. Based on this result, the low-energy effective field theory for the model is obtained and shown to be a lattice double Chern-Simons theory with coupling constant k = 1 (with the standard normalization). By further employing the effective filed theory methods, we show that the Mott transition that arises is of topological nature, with vortices in an antiferromagnetic array and matter currents characterized by a d-density wave order parameter. We also analyze the behavior of the system upon weak coupling, and conclude that it undergoes a quantum gas-liquid transition which belongs to the Ising universality class.
CK chondrites constitute the most oxidized anhydrous carbonaceous chondrite group; most of the Fe occurs in magnetite and in FeO-rich mafic silicates. The two observed CK falls (Karoonda and Kobe), along with thirteen relatively unweathered CK finds, have unfractionated siderophile-element abundance patterns. In contrast, a sizable fraction of CK finds (9 of 24 investigated) shows fractionated siderophile abundance patterns including low abundances of Ni, Co, Se and Au; the most extreme depletions are in Ni (0.24 of normal CK) and Au (0.14 of normal CK). This depletion pattern has not been found in other chondrite groups. Out of the 74 CK chondrites listed in the Meteoritical Bulletin Database (2006; excluded considerably paired specimens; see http://tin.er.usgs.gov/meteor/ metbull.php) we analyzed 24 and subclassified the CK chondrites in terms of their chemical composition and sulfide mineralogy: sL (siderophiles low; six samples) for large depletions in Ni, Co, Se and Au (>50% of sulfides lost); sM (siderophiles medium; two CKs) for moderately low Ni and Co abundances (sulfides are highly altered or partly lost); sH (siderophiles high; one specimen) for enrichments in Ni, Co, Se and Au; 'normal' for unfractionated samples (13 samples). The sole sH sample may have obtained additional sulfide from impact redistribution in the parent asteroid. We infer that these elements became incorporated into sulfides after asteroidal aqueous processes oxidized nebular metal; thermal metamorphism probably also played a role in their mineral siting. The siderophile losses in the SL and sM samples are mainly the result of oxidation of pentlandite, pyrite and violarite by terrestrial alteration followed by leaching of the resulting phases. Some Antarctic CK chondrites have lost most of their sulfides but retained Ni, Co, Se and Au, presumably as insoluble weathering products.
We report the band alignment parameters of the GaN/single-layer (SL) MoS{sub 2} heterostructure where the GaN thin layer is grown by molecular beam epitaxy on CVD deposited SL-MoS{sub 2}/c-sapphire. We confirm that the MoS{sub 2} is an SL by measuring the separation and position of room temperature micro-Raman E{sup 1}{sub 2g} and A{sup 1}{sub g} modes, absorbance, and micro-photoluminescence bandgap studies. This is in good agreement with HRTEM cross-sectional analysis. The determination of band offset parameters at the GaN/SL-MoS{sub 2} heterojunction is carried out by high-resolution X-ray photoelectron spectroscopy accompanying with electronic bandgap values of SL-MoS{sub 2} and GaN. The valence band and conduction band offset values are, respectively, measured to be 1.86 ± 0.08 and 0.56 ± 0.1 eV with type II band alignment. The determination of these unprecedented band offset parameters opens up a way to integrate 3D group III nitride materials with 2D transition metal dichalcogenide layers for designing and modeling of their heterojunction based electronic and photonic devices.
According to the World Health Organization (2014) breast cancer is the main cause of death by cancer in women worldwide. The biggest challenge of radiotherapy in the treatment of cancer is to deposit the entire prescribed dose homogeneously in the breast, sparing the surrounding tissue. In this context, this paper aimed at evaluating and comparing internal dose distribution in the mammary gland based on experimental procedures submitted to two distinct energy spectra produced in breast cancer radiotherapy. The methodology consisted of reproducing opposite parallel fields used in the treatment of breast tumors in a chest phantom. This simulator with synthetic breast, composed of equivalent tissue material (TE), was previously developed by the NRI Research Group (UFMG). The computer tomography (CT) scan of the simulator was obtained antecedently. The radiotherapy planning systems (TPS) in the chest phantom were performed in the ECLIPSE system from Varian Medical Systems and CAT 3D system from MEVIS. The irradiations were reproduced in the Varian linear accelerator, model SL- 20 Precise, 6 MV energy and Varian linear accelerator, 4 MV Clinac 6x SN11 model. Calibrations of the absorbed dose versus optical density from radiochromic films were generated in order to obtain experimental dosimetric distribution at the films positioned within the glandular and skin equivalent tissues of the chest phantom. The spatial dose distribution showed equivalence with the TPS on measurement data performed in the 6 MV spectrum. The average dose found in radiochromic films placed on the skin ranged from 49 to 79%, and from 39 to 49% in the mammary areola, for the prescribed dose. Dosimetric comparisons between the spectra of 4 and 6 MV, keeping the constant geometry of the fields applied in the same phantom, will be presented showing their equivalence in breast radiotherapy, as well as the variations will be discussed. To sum up, the dose distribution has reached the value expected in the breast dose of the 180 cGy in a wide range of the film in the glandular TE in both spectra. (authors)
The thermoelectric properties of n-type InGaN alloys with high In-content and InN/InGaN thin film superlattices (SL) grown by molecular beam epitaxy are investigated. Room-temperature measurements of the thermoelectric properties reveal that an increasing Ga-content in ternary InGaN alloys (0 < x(Ga) < 0.2) yields a more than 10-fold reduction in thermal conductivity (κ) without deteriorating electrical conductivity (σ), while the Seebeck coefficient (S) increases slightly due to a widening band gap compared to binary InN. Employing InN/InGaN SLs (x(Ga) = 0.1) with different periods, we demonstrate that confinement effects strongly enhance electron mobility with values as high as ∼820 cm{sup 2}/V s at an electron density n{sub e} of ∼5×10{sup 19} cm{sup −3}, leading to an exceptionally high σ of ∼5400 (Ωcm){sup −1}. Simultaneously, in very short-period SL structures S becomes decoupled from n{sub e}, κ is further reduced below the alloy limit (κ < 9 W/m-K), and the power factor increases to 2.5×10{sup −4} W/m-K{sup 2} by more than a factor of 5 as compared to In-rich InGaN alloys. These findings demonstrate that quantum confinement in group-III nitride-based superlattices facilitates improvements of thermoelectric properties over bulk-like ternary nitride alloys.
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We study six-point correlation functions in two dimensional conformal field theory, where the six operators are grouped in pairs with equal conformal dimension. Assuming large central charge $c$ and a sparse spectrum, the leading contribution to this correlation function is the six-point Virasoro identity block - corresponding to each distinct pair of operators fusing into the identity and its descendants. We call this the star channel. One particular term in the star channel identity block is the stress tensor $SL(2,\mathbb{R})$ (global) block, for which we derive an explicit expression. In the holographic context, this object corresponds to a direct measure of nonlinear effects in pure gravity. We calculate additional terms in the star channel identity block that contribute at the same order at large $c$ as the global block using the novel theory of reparametrizations, which extends the shadow operator formalism in a natural way. We investigate these blocks' relevance to quantum chaos in the form of six-point scrambling in an out-of time ordered correlator. Interestingly, the global block does not contribute to the scrambling mode of this correlator, implying that, to leading order, six-point scrambling is insensitive to the three-point graviton coupling in the bulk dual. Finally, we compare our findings with a different OPE channel, called the comb channel, and find the same result for the chaos exponent in this decomposition.
2+1d topological phases are well characterized by the fusion rules and braiding/exchange statistics of fractional point excitations. In 4+1d, some topological phases contain only fractional loop excitations. What kind of loop statistics exist? We study the 4+1d gauge theory with 2-form \mathbb{Z}_2 ℤ 2 gauge field (the loop-only toric code) and find that while braiding statistics between two different types of loops can be nontrivial, the self “exchange” statistics are all trivial. In particular, we show that the electric, magnetic, and dyonic loop excitations in the 4+1d toric code are not distinguished by their self-statistics. They tunnel into each other across 3+1d invertible domain walls which in turn give explicit unitary circuits that map the loop excitations into each other. The SL(2, \mathbb{Z}_2 ℤ 2 ) symmetry that permutes the loops, however, cannot be consistently gauged and we discuss the associated obstruction in the process. Moreover, we discuss a gapless boundary condition dubbed the “fractional Maxwell theory” and show how it can be Higgsed into gapped boundary conditions. We also discuss the generalization of these results from the \mathbb{Z}_2 ℤ 2 gauge group to \mathbb{Z}_N ℤ N .
A self-duality group $\cal G$ in quantum field theory can have anomalies. In that case, the space of ordinary coupling constants $\cal M$ can be extended to include the space $\cal F$ of coefficients of counterterms in background fields. The extended space $\cal N$ forms a bundle over $\cal M$ with fiber $\cal F$, and the topology of the bundle is determined by the anomaly. For example, the ${\cal G}=SL(2,\mathbb{Z})$ duality of the 4d Maxwell theory has an anomaly, and the space ${\cal F}=S^1$ for the gravitational theta-angle is nontrivially fibered over ${\cal M}=\mathbb{H}/SL(2,\mathbb{Z})$. We will explain a simple method to determine the anomaly when the 4d theory is obtained by compactifying a 6d theory on a Riemann surface in terms of the anomaly polynomial of the parent 6d theory. Our observations resolve an apparent contradiction associated with the global structure of the Kahler potential on the space of exactly marginal couplings of supersymmetric theories.
We develop a frame and dyad gauge-independent formalism for the calculus of variations of functionals involving spinorial objects. As a part of this formalism, we define a modified variation operator which absorbs frame and spin dyad gauge terms. This formalism is applicable to both the standard spacetime (i.e., SL(2, ℂ)) 2-spinors as well as to space (i.e., SU(2, ℂ)) 2-spinors. We compute expressions for the variations of the connection and the curvature spinors.
Muscles of the hindlimb in the rat have been used to demonstrate the effects of unloading in weightlessness and in animal models used to mimic weightlessness. The vastus medialis (VM) is discussed here. Samples were obtained from rats exposed to weightlessness for 12 days in Cosmos 1887 (Experiment K-6-08, coordinated by Dr. V.S. Oganov). The principal objective of this study was to ascertain if the vastus medialis responded to 12 days of microgravity exposure. The loss in muscle mass is greatest, -43 percent, when comparing F vs B, and least, -13 percent, when comparing F vs. V. Taken at face value these differences may be misleading. Due to the variability of the muscle weight in the basal group, these muscle mass losses may be exaggerated. In terms of percent water, there were no differences between the flight and the control groups. In spite of the limited sample, researchers conclude that muscle mass changes in the VM are not significant. Although some of the morphological parameters suggest a small degree of atrophy in the vastus medialis, the biochemical analyses (protein, RNA and DNA) suggest that these may be minimal and functionally nonsignificant. The relatively similar CS and LDH activities of VM from F and various control groups, as well as the lack of difference in LPL activity between F and S rats, suggests that there is little or no effect on the oxidative or glycolytic function of this muscle. Since the VM is chiefly a mixed fast twitch muscle, these metabolic indices of energy production are relatively unchanged. The results of VM studies are in agreement with previous observations of another type II fast twitch muscle, the EDL, from SL-3 rats which did not respond markedly to weightlessness and whole body suspension.
We show that a Yangian symmetry, namely, Y(su(2)), exists in the Dirac equation with spin symmetry when the potential term takes a Coulomb form. We construct the generators of Y(su(2)) explicitly and get the energy spectrum of this model from the representation theory for Y(su(2)). We also show that this model is integrable, from RTT relations. - Highlights: Black-Right-Pointing-Pointer The Y(sl(2)) symmetry is found in a model, and the generators of Y(sl(2)) are constructed from the so(4) Lie algebra. Black-Right-Pointing-Pointer The energy spectrum is derived on the basis of the representation theory for Y(sl(2)). Black-Right-Pointing-Pointer The integrability of this model is proved from the RTT relation.
The Weather Research and Forecasting (WRF) model can be used to diagnose regional land-atmosphere (L-A) coupling strength in the absence of sufficient observations but subjected to uncertainties associated with model physical parameterizations. In this study, we propose a framework to quantify and reduce model physical parameterization uncertainties associated with surface fluxes and L-A coupling. An ensemble of WRF simulations with different physical schemes is used to simulate surface fluxes and land-atmosphere coupling strength over the Amazon region. The physical parameterizations investigated include cloud microphysics (MP), land surface processes (LSM), planetary boundary layer (PBL), surface layer (SL), and cumulus (CU). We perform 120 ensemble simulations using the WRF model and different combinations of six MPs, three LSMs, six PBLs and SLs and three CUs. The measurements from the GoAMAZON field campaign and satellite data are used to evaluate model performance. A Multi-way analysis of variance (ANOVA) approach is applied to quantify the relative importance of different physics processes on L-A coupling. The Tukey’s test is used to sort schemes that have no significant differences into one group. The suite of physics that result in the best simulations of the corresponding variables are selected based on the Taylor skill score. Results show that the relative importance of processes and their interaction vary with the variables of interest. For example, CU was the most important process in modulating soil moisture, 2 m-humidity, latent heat, and net radiation. LSM showed dominant effects on 2 m-temperature and also has the largest impact on sensible heat and the lifting condensation level. The best physical parameterization ensembles show much narrower ranges of the variables of interest than the priori ensemble. Results of this study show the roles of different physical processes in modulating L-A interactions, quantify model uncertainties from physical processes, and provide insights for improving the model physics parameterizations.
Graphical abstract: Heterogeneous photo Fenton process with dye sensitized mechanism of RhB by Bi{sub 1.56}Sb{sub 1.48}Co{sub 0.96}O{sub 7} compound. - Highlights: • Bi{sub 1.56}Sb{sub 1.48}Co{sub 0.96}O{sub 7} (BSCO) catalyst was synthesized by improved solid state reaction method. • BSCO/H{sub 2}O{sub 2}/UVA and BSCO/H{sub 2}O{sub 2}/SL catalyst systems exhibit excellent photocatalytic activities for rhodamine B. • The photocatalytic degradation was preceded via heterogeneous photo Fenton mechanism process. • ·OH radicals are the main reactive species for the degradation of RhB. - Abstract: Novel nanostructure pyrochlore Bi{sub 1.56}Sb{sub 1.48}Co{sub 0.96}O{sub 7} was successfully synthesized via solid state reaction method in air. The as-synthesized photocatalyst was characterized by X-ray diffraction, Scanning electron microscopy and UV–vis diffuse reflectance spectroscopy techniques. The results showed that the BSCO was crystallized with the pyrochlore-type structure, cubic crystal system and space group Fd3m. The average particle size and band gap for BSCO were D = 76.29 nm and E{sub g} = 1.50 eV respectively. Under the optimum conditions for discoloration of the dye: initial concentration of 20 mg L{sup −1} RhB, pH 7, 25 °C, 0.5 mL H{sub 2}O{sub 2} and BSCO/dye mass ration of 1 g L{sup −1}, 97.77 and 90.16% of RhB were removed with BSCO/H{sub 2}O{sub 2} photocatalytic system within 60 min of irradiation time under UVA- and SL irradiations respectively. Pseudo-second-order kinetic model gave the best fit, with highest correlation coefficients (R{sup 2} ≥ 0.99). On the base of these results, the mechanism of the enhancement of the discoloration efficiency was discussed. .