Subvarieties of generic hypersurfaces in any variety

Let W be a projective variety of dimension n+1, L a free line bundle on W, X in $H^0(L^d)$ a hypersurface of degree d which is generic among those given by sums of monomials from $L$, and let $f : Y \to X$ be a generically finite map from a smooth m-fold Y. We suppose that f is r-filling, i.e. upon deforming X in $H^0(L^d)$, f deforms in a family such that the corresponding deformations of $Y^r$ dominate $W^r$. Under these hypotheses we give a lower bound for the dimension of a certain linear system on the Cartesian product $Y^r$ having certain vanishing order on a diagonal locus as well as on a double point locus. This yields as one application a lower bound on the dimension of the linear system |K_{Y} - (d - n + m)f^*L - f^*K_{W}| which generalizes results of Ein and Xu (and in weaker form, Voisin). As another perhaps more surprising application, we conclude a lower bound on the number of quadrics containing certain projective images of Y.Comment: We made some improvements in the introduction and definitions. In an effort to clarify the arguments we separated the 1-filling case from the r-filling case and we gave a more detailed proof of the key lemma. The article will appear in the Math. Proc. Cambridge Philos. So

Quantum Kagome antiferromagnet ZnCu3(OH)6Cl2

The frustration of antiferromagnetic interactions on the loosely connected kagome lattice associated to the enhancement of quantum fluctuations for S=1/2 spins was acknowledged long ago as a keypoint to stabilize novel ground states of magnetic matter. Only very recently, the model compound Herbersmithite, ZnCu3(OH)6Cl2, a structurally perfect kagome antiferromagnet, could be synthesized and enables a close comparison to theories. We review and classify various experimental results obtained over the past years and underline some of the pending issues.Comment: 23 pages, 16 figures, invited paper in J. Phys. Soc. Jpn, special topics issue on "Novel States of Matter Induced by Frustration", to be published in Jan. 201

Investigation of multi-phase tubular permanent magnet linear generator for wave energy converters

In this article, an investigation into different magnetization topologies for a long stator tubular permanent magnet linear generator is performed through a comparison based on the cogging force disturbance, the power output, and the cost of the raw materials of the machines. The results obtained from finite element analysis simulation are compared with an existing linear generator described in [1]. To ensure accurate results, the generator developed in [1] is built with 3D CAD and simulated using the finite-element method, and the obtained results are verified with the source.The PRIMaRE project

Ti(3)C(2) MXene co-catalyst on metal sulfide photo-absorbers for enhanced visible-light photocatalytic hydrogen production

Scalable and sustainable solar hydrogen production through photocatalytic water splitting requires highly active and stable earth-abundant co-catalysts to replace expensive and rare platinum. Here we employ density functional theory calculations to direct atomic-level exploration, design and fabrication of a MXene material, Ti3C2 nanoparticles, as a highly efficient co-catalyst. Ti3C2 nanoparticles are rationally integrated with cadmium sulfide via a hydrothermal strategy to induce a super high visible-light photocatalytic hydrogen production activity of 14,342 μmol h-1 g-1 and an apparent quantum efficiency of 40.1% at 420 nm. This high performance arises from the favourable Fermi level position, electrical conductivity and hydrogen evolution capacity of Ti3C2 nanoparticles. Furthermore, Ti3C2 nanoparticles also serve as an efficient co-catalyst on ZnS or ZnxCd1-xS. This work demonstrates the potential of earth-abundant MXene family materials to construct numerous high performance and low-cost photocatalysts/photoelectrodes.Jingrun Ran, Guoping Gao, Fa-Tang Li, Tian-Yi Ma, Aijun Du and Shi-Zhang Qia

One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum

We present exact energy eigenvalues and eigenfunctions of the one-dimensional hydrogen atom in the framework of the Generalized (Gravitational) Uncertainty Principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity, black-hole physics, and doubly special relativity and implies a minimal length uncertainty and a maximal momentum. We show that the quantized energy spectrum exactly agrees with the semiclassical results.Comment: 10 pages, 1 figur

One dimensional Coulomb-like problem in deformed space with minimal length

Spectrum and eigenfunctions in the momentum representation for 1D Coulomb potential with deformed Heisenberg algebra leading to minimal length are found exactly. It is shown that correction due to the deformation is proportional to square root of the deformation parameter. We obtain the same spectrum using Bohr-Sommerfeld quantization condition.Comment: 11 pages, typos corrected, references adde

Impact of interfacial molecular orientation on radiative recombination and charge generation efficiency.

A long standing question in organic electronics concerns the effects of molecular orientation at donor/acceptor heterojunctions. Given a well-controlled donor/acceptor bilayer system, we uncover the genuine effects of molecular orientation on charge generation and recombination. These effects are studied through the point of view of photovoltaics-however, the results have important implications on the operation of all optoelectronic devices with donor/acceptor interfaces, such as light emitting diodes and photodetectors. Our findings can be summarized by two points. First, devices with donor molecules face-on to the acceptor interface have a higher charge transfer state energy and less non-radiative recombination, resulting in larger open-circuit voltages and higher radiative efficiencies. Second, devices with donor molecules edge-on to the acceptor interface are more efficient at charge generation, attributed to smaller electronic coupling between the charge transfer states and the ground state, and lower activation energy for charge generation.Molecular orientation profoundly affects the performance of donor-acceptor heterojunctions, whilst it has remained challenging to investigate the detail. Using a controllable interface, Ran et al. show that the edge-on geometries improve charge generation at the cost of non-radiative recombination loss

Pairing in the iron arsenides: a functional RG treatment

We study the phase diagram of a microscopic model for the superconducting iron arsenides by means of a functional renormalization group. Our treatment establishes a connection between a strongly simplified two-patch model by Chubukov et al. and a five-band- analysis by Wang et al.. For a wide parameter range, the dominant pairing instability occurs in the extended s-wave channel. The results clearly show the relevance of pair scattering between electron and hole pockets. We also give arguments that the phase transition between the antiferromagnetic phase for the undoped system and the superconducting phase may be first order

High-strain deformation of conglomerates: Numerical modelling, strain analysis, and an example from the Wutai Mountains, North China Craton

Conglomerates have been widely used to investigate deformation history and rheology, strain, vorticity and viscosity. Previous studies reveal that several factors, such as pebble shapes and concentrations, as well as material properties, affect conglomerate deformation. However, how pebble concentration and interaction between pebbles affect deformation is not understood very well. We use the 2D numerical modelling platform ELLE coupled to the full field crystal visco-plasticity code (VPFFT) to simulate the deformation of conglomerates with various viscosity contrasts between pebbles and matrix and different pebble concentrations, with both linear (stress exponent n = 1) and power-law (n = 3) viscous rheologies, under simple shear conditions up to a shear strain of ten. Pebbles can behave as effectively passive, deformable or effectively rigid. An increase in pebble concentrations/viscosity contrasts enhances pebble deformation, but reduces their rotation. A mean aspect ratio (Rf) - orientation (ϕ) plot is proposed to gain an estimate of pebble deformation behaviour and the amount of bulk strain. Closely spaced rigid or deformable pebbles can form clusters that mechanically act as single inclusions. Rigid clusters rotate and survive for only short strain increments, whereas the more stable deformable ones keep on elongating with minor rotation. We provide a natural example of deformed conglomerates from the Wutai Mountains, North China Craton. These consist of banded-iron-formation (BIF) pebbles embedded in a schistose matrix. Using the mean Rf-ϕ plot, a finite strain of ∼6 under simple shear could be determined. The viscosity of the pebbles is estimated at about 5-8 times that of the matrix for a linear rheology (n = 1), or 2 to 5 times if a power-law rheology with n = 3 is assumed