Regular maps of high density

A regular map is a surface together with an embedded graph, having properties similar to those of the surface and graph of a platonic solid. We analyze regular maps with reflection symmetry and a graph of density strictly exceeding 1/2, and we conclude that all regular maps of this type belong to a family of maps naturally defined on the Fermat curves x^n+y^n+z^n=0, excepting the one corresponding to the tetrahedron.Comment: 13 pages, 4 figure

Properties of 3-manifolds for relativists

In canonical quantum gravity certain topological properties of 3-manifolds are of interest. This article gives an account of those properties which have so far received sufficient attention, especially those concerning the diffeomorphism groups of 3-manifolds. We give a summary of these properties and list some old and new results concerning them. The appendix contains a discussion of the group of large diffeomorphisms of the $l$-handle 3-manifold.Comment: 20 pages. Plain-TeX, no figures, 1 Table (A4 format

An Analysis of the Representations of the Mapping Class Group of a Multi-Geon Three-Manifold

It is well known that the inequivalent unitary irreducible representations (UIR's) of the mapping class group $G$ of a 3-manifold give rise to ``theta sectors'' in theories of quantum gravity with fixed spatial topology. In this paper, we study several families of UIR's of $G$ and attempt to understand the physical implications of the resulting quantum sectors. The mapping class group of a three-manifold which is the connected sum of $\R^3$ with a finite number of identical irreducible primes is a semi-direct product group. Following Mackey's theory of induced representations, we provide an analysis of the structure of the general finite dimensional UIR of such a group. In the picture of quantized primes as particles (topological geons), this general group-theoretic analysis enables one to draw several interesting qualitative conclusions about the geons' behavior in different quantum sectors, without requiring an explicit knowledge of the UIR's corresponding to the individual primes.Comment: 52 pages, harvmac, 2 postscript figures, epsf required. Added an appendix proving the semi-direct product structure of the MCG, corrected an error in the characterization of the slide subgroup, reworded extensively. All our analysis and conclusions remain as befor

Model-based Aeroservoelastic Design and Load Alleviation of Large Wind Turbine Blades

This paper presents an aeroservoelastic modeling approach for dynamic load alleviation in large wind turbines with trailing-edge aerodynamic surfaces. The tower, potentially on a moving base, and the rotating blades are modeled using geometrically non-linear composite beams, which are linearized around reference conditions with arbitrarily-large structural displacements. Time-domain aerodynamics are given by a linearized 3-D unsteady vortexlattice method and the resulting dynamic aeroelastic model is written in a state-space formulation suitable for model reductions and control synthesis. A linear model of a single blade is used to design a Linear-Quadratic-Gaussian regulator on its root-bending moments, which is finally shown to provide load reductions of about 20% in closed-loop on the full wind turbine non-linear aeroelastic model

Symmetry and Control of Spin-Scattering Processes in Two-Dimensional Transition Metal Dichalcogenides

Transition metal dichalcogenides (TMDs) combine interesting optical and spintronic properties in an atomically-thin material, where the light polarization can be used to control the spin and valley degrees-of-freedom for the development of novel opto-spintronic devices. These promising properties emerge due to their large spin-orbit coupling in combination with their crystal symmetries. Here, we provide simple symmetry arguments in a group-theory approach to unveil the symmetry-allowed spin scattering mechanisms, and indicate how one can use these concepts towards an external control of the spin lifetime. We perform this analysis for both monolayer (inversion asymmetric) and bilayer (inversion symmetric) crystals, indicating the different mechanisms that play a role in these systems. We show that, in monolayer TMDs, electrons and holes transform fundamentally differently -- leading to distinct spin-scattering processes. We find that one of the electronic states in the conduction band is partially protected by time-reversal symmetry, indicating a longer spin lifetime for that state. In bilayer and bulk TMDs, a hidden spin-polarization can exist within each layer despite the presence of global inversion symmetry. We show that this feature enables control of the interlayer spin-flipping scattering processes via an out-of-plane electric field, providing a mechanism for electrical control of the spin lifetime.Comment: 9 pages, 3 figure

Mechanistic insight in the selective delignification of wheat straw by three white-rot fungal species through quantitative 13C-IS py-GC–MS and whole cell wall HSQC NMR

Background The white-rot fungi Ceriporiopsis subvermispora (Cs), Pleurotus eryngii (Pe), and Lentinula edodes (Le) have been shown to be high-potential species for selective delignification of plant biomass. This delignification improves polysaccharide degradability, which currently limits the efficient lignocellulose conversion into biochemicals, biofuels, and animal feed. Since selectivity and time efficiency of fungal delignification still need optimization, detailed understanding of the underlying mechanisms at molecular level is required. The recently developed methodologies for lignin quantification and characterization now allow for the in-depth mapping of fungal modification and degradation of lignin and, thereby, enable resolving underlying mechanisms. Results Wheat straw treated by two strains of Cs (Cs1 and Cs12), Pe (Pe3 and Pe6) and Le (Le8 and Le10) was characterized using semi-quantitative py-GC–MS during fungal growth (1, 3, and 7 weeks). The remaining lignin after 7 weeks was quantified and characterized using ¹³C lignin internal standard based py-GC–MS and whole cell wall HSQC NMR. Strains of the same species showed similar patterns of lignin removal and degradation. Cs and Le outperformed Pe in terms of extent and selectivity of delignification (Cs ≥ Le >> Pe). The highest lignin removal [66% (w/w); Cs1] was obtained after 7 weeks, without extensive carbohydrate degradation (factor 3 increased carbohydrate-to-lignin ratio). Furthermore, though after treatment with Cs and Le comparable amounts of lignin remained, the structure of the residual lignin vastly differed. For example, Cα-oxidized substructures accumulated in Cs treated lignin up to 24% of the total aromatic lignin, a factor two higher than in Le-treated lignin. Contrarily, ferulic acid substructures were preferentially targeted by Le (and Pe). Interestingly, Pe-spent lignin was specifically depleted of tricin (40% reduction). The overall subunit composition (H:G:S) was not affected by fungal treatment. Conclusions Cs and Le are both able to effectively and selectively delignify wheat straw, though the underlying mechanisms are fundamentally different. We are the first to identify that Cs degrades the major β-O-4 ether linkage in grass lignin mainly via Cβ–O–aryl cleavage, while Cα–Cβ cleavage of inter-unit linkages predominated for Le. Our research provides a new insight on how fungi degrade lignin, which contributes to further optimizing the biological upgrading of lignocellulose. Electronic supplementary material The online version of this article (10.1186/s13068-018-1259-9) contains supplementary material, which is available to authorized users

Quadruple junction polymer solar cells with four complementary absorber layers

A monolithic two‐terminal solution‐processed quadruple junction polymer solar cell in an n–i–p (inverted) configuration with four complementary polymer:fullerene active bulk‐heterojunction layers is presented. The subcells possess different optical bandgaps ranging from 1.90 to 1.13 eV. Optical modeling using the transfer matrix formalism enables prediction of the fraction of absorbed photons from sunlight in each subcell and determine the optimal combination of layer thicknesses. The quadruple junction cell features an open‐circuit voltage of 2.45 V and has a power conversion efficiency of 7.6%, only slightly less than the modeled value of 8.2%. The external quantum efficiency spectrum, determined with appropriate light and voltage bias conditions, exhibits in general an excellent agreement with modeled spectrum. The device performance is presently limited by bimolecular recombination, which prevents using thick photoactive layers that could absorb light more efficiently