Selfdual spaces with complex structures, Einstein-Weyl geometry and geodesics

We study the Jones and Tod correspondence between selfdual conformal 4-manifolds with a conformal vector field and abelian monopoles on Einstein-Weyl 3-manifolds, and prove that invariant complex structures correspond to shear-free geodesic congruences. Such congruences exist in abundance and so provide a tool for constructing interesting selfdual geometries with symmetry, unifying the theories of scalar-flat Kahler metrics and hypercomplex structures with symmetry. We also show that in the presence of such a congruence, the Einstein-Weyl equation is equivalent to a pair of coupled monopole equations, and we solve these equations in a special case. The new Einstein-Weyl spaces, which we call Einstein-Weyl ``with a geodesic symmetry'', give rise to hypercomplex structures with two commuting triholomorphic vector fields.Comment: 30 pages, 7 figures, to appear in Ann. Inst. Fourier. 50 (2000

Long-timescale simulations of H2_2O admolecule diffusion on Ice Ih(0001) surfaces

Long-timescale simulations of the diffusion of a H$_2$O admolecule on the (0001) basal plane of ice Ih were carried out over a temperature range of 100 to 200 K using the adaptive kinetic Monte Carlo method and TIP4P/2005f interaction potential function. The arrangement of dangling H atoms was varied from the proton-disordered surface to the perfectly ordered Fletcher surface. A large variety of sites was found leading to a broad distribution in adsorption energy at both types of surfaces. Up to 4 % of the sites on the proton-disordered surface have an adsorption energy exceeding the cohesive energy of ice Ih. The mean squared displacement of a simulated trajectory at 175 K for the proton-disordered surface gave a diffusion constant of 6$\cdot$10$^{-10}$ cm$^2$/s, consistent with an upper bound previously reported from experimental measurements. During the simulation, dangling H atoms were found to rearrange so as to reduce clustering, thereby approaching a linear Fletcher type arrangement. Diffusion on the perfectly ordered Fletcher surface was estimated to be significantly faster, especially in the direction along the rows of dangling hydrogen atoms. From simulations over the range in temperature, an effective activation energy of diffusion was estimated to be 0.16 eV and 0.22 eV for diffusion parallel and perpendicular to the rows, respectively. Even a slight disruption of the rows of the Fletcher surface made the diffusion isotropic.Comment: 24 pages, 8 figures, 1 tabl

Nonlinear photocurrents in two-dimensional systems based on graphene and boron nitride

DC photoelectrical currents can be generated purely as a non-linear effect in uniform media lacking inversion symmetry without the need for a material junction or bias voltages to drive it, in what is termed photogalvanic effect. These currents are strongly dependent on the polarization state of the radiation, as well as on topological properties of the underlying Fermi surface such as its Berry curvature. In order to study the intrinsic photogalvanic response of gapped graphene (GG), biased bilayer graphene (BBG), and hexagonal boron nitride (hBN), we compute the non-linear current using a perturbative expansion of the density matrix. This allows a microscopic description of the quadratic response to an electromagnetic field in these materials, which we analyze as a function of temperature and electron density. We find that the intrinsic response is robust across these systems and allows for currents in the range of pA cm/W to nA cm/W. At the independent-particle level, the response of hBN-based structures is significant only in the ultra-violet due to their sizeable band-gap. However, when Coulomb interactions are accounted for by explicit solution of the Bethe-Salpeter equation, we find that the photoconductivity is strongly modified by transitions involving exciton levels in the gap region, whose spectral weight dominates in the overall frequency range. Biased bilayers and gapped monolayers of graphene have a strong photoconductivity in the visible and infrared window, allowing for photocurrent densities of several nA cm/W. We further show that the richer electronic dispersion of BBG at low energies and the ability to change its band-gap on demand allows a higher tunability of the photocurrent, including not only its magnitude but also, and significantly, its polarity.Comment: Updating with published version and respective references; 14 pages, 11 figure

Electronic and optical properties of graphene antidot lattices: Comparison of Dirac and tight-binding models

The electronic properties of graphene may be changed from semimetallic to semiconducting by introducing perforations (antidots) in a periodic pattern. The properties of such graphene antidot lattices (GALs) have previously been studied using atomistic models, which are very time consuming for large structures. We present a continuum model that uses the Dirac equation (DE) to describe the electronic and optical properties of GALs. The advantages of the Dirac model are that the calculation time does not depend on the size of the structures and that the results are scalable. In addition, an approximation of the band gap using the DE is presented. The Dirac model is compared with nearest-neighbour tight-binding (TB) in order to assess its accuracy. Extended zigzag regions give rise to localized edge states, whereas armchair edges do not. We find that the Dirac model is in quantitative agreement with TB for GALs without edge states, but deviates for antidots with large zigzag regions.Comment: 15 pages, 7 figures. Accepted by Journal of Physics: Condensed matte

Dapagliflozin stimulates glucagon secretion at high glucose: experiments and mathematical simulations of human A-cells.

Glucagon is one of the main regulators of blood glucose levels and dysfunctional stimulus secretion coupling in pancreatic A-cells is believed to be an important factor during development of diabetes. However, regulation of glucagon secretion is poorly understood. Recently it has been shown that Na(+)/glucose co-transporter (SGLT) inhibitors used for the treatment of diabetes increase glucagon levels in man. Here, we show experimentally that the SGLT2 inhibitor dapagliflozin increases glucagon secretion at high glucose levels both in human and mouse islets, but has little effect at low glucose concentrations. Because glucagon secretion is regulated by electrical activity we developed a mathematical model of A-cell electrical activity based on published data from human A-cells. With operating SGLT2, simulated glucose application leads to cell depolarization and inactivation of the voltage-gated ion channels carrying the action potential, and hence to reduce action potential height. According to our model, inhibition of SGLT2 reduces glucose-induced depolarization via electrical mechanisms. We suggest that blocking SGLTs partly relieves glucose suppression of glucagon secretion by allowing full-scale action potentials to develop. Based on our simulations we propose that SGLT2 is a glucose sensor and actively contributes to regulation of glucagon levels in humans which has clinical implications

Error correction in ensemble registers for quantum repeaters and quantum computers

We propose to use a collective excitation blockade mechanism to identify errors that occur due to disturbances of single atoms in ensemble quantum registers where qubits are stored in the collective population of different internal atomic states. A simple error correction procedure and a simple decoherence-free encoding of ensemble qubits in the hyperfine states of alkali atoms are presented.Comment: 4 pages, 2 figure

On the mechanical behaviour of thin perforated plates and their application in silicon condenser microphones

In this paper an alternative approach to the modelling of plates with a large number of holes is presented. By means of plate theory, it is shown that perforated plates can be modelled by conventional orthotropic plates with modified elastic properties. The modification of the elastic constants is derived by equalizing the strain-energy of the perforated and the orthotropic plate. The model obtained is then compared with previous methods and applied in the electrochemical simulation of a silicon micromachined microphone structure. The microphone structures are simulated numerically, using an algorithm based on finite differences

Combined production of broilers and fruits

Combined production of broilers and fruit trees is a subject often discussed in organic fruit production in Denmark. Very little research has been carried out on this type of production system. In organic production in Denmark, nearly no pesticides are allowed, so the need for alternative pest control is large. Apple sawfly (Hoplocampa testudinea) and pear midge (Contarinia pyrivora) cause big crop losses in apples and pears respectively, in unsprayed organic fruit production. Both insects infest fruitlets and cause these to drop prematurely after which the pests pupate in the topsoil. In the present experiment a research orchard with the varieties ‘Discovery’ and ‘Conference’ were used as outdoor area for broilers to minimise the population of sawflies and pear midges, and to reduce the need for weeding and manuring. The trees were kept unsprayed. Fruit yield and fruit quality were assessed at harvest. White sticky traps were placed in the test area in order to measure the occurrence of sawfly over time. The infestation of pear midge was investigated counting the infested fruitlets in clusters on trees at the centre of the plots. The catch of apple sawflies was reduced in the combined apple and broiler production, but no significant effect on the yield or the fruit quality was seen. Experiences from on-farm research show that combining fruit and egg-production is one way to reduce the problem with apple sawfly, but poultry alone is not a sufficient way of controlling sawflies. The welfare and health of the broilers were excellent under fruit trees

Faraday effect revisited: sum rules and convergence issues

This is the third paper of a series revisiting the Faraday effect. The question of the absolute convergence of the sums over the band indices entering the Verdet constant is considered. In general, sum rules and traces per unit volume play an important role in solid state physics, and they give rise to certain convergence problems widely ignored by physicists. We give a complete answer in the case of smooth potentials and formulate an open problem related to less regular perturbations.Comment: Dedicated to the memory of our late friend Pierre Duclos. Accepted for publication in Journal of Physics A: Mathematical and Theoretical