Efficient adaptive integration of functions with sharp gradients and cusps in n-dimensional parallelepipeds

In this paper, we study the efficient numerical integration of functions with sharp gradients and cusps. An adaptive integration algorithm is presented that systematically improves the accuracy of the integration of a set of functions. The algorithm is based on a divide and conquer strategy and is independent of the location of the sharp gradient or cusp. The error analysis reveals that for a $C^0$ function (derivative-discontinuity at a point), a rate of convergence of $n+1$ is obtained in $R^n$. Two applications of the adaptive integration scheme are studied. First, we use the adaptive quadratures for the integration of the regularized Heaviside function---a strongly localized function that is used for modeling sharp gradients. Then, the adaptive quadratures are employed in the enriched finite element solution of the all-electron Coulomb problem in crystalline diamond. The source term and enrichment functions of this problem have sharp gradients and cusps at the nuclei. We show that the optimal rate of convergence is obtained with only a marginal increase in the number of integration points with respect to the pure finite element solution with the same number of elements. The adaptive integration scheme is simple, robust, and directly applicable to any generalized finite element method employing enrichments with sharp local variations or cusps in $n$-dimensional parallelepiped elements.Comment: 22 page

Multi-wavelength, all-solid-state, continuous wave mode locked picosecond Raman laser

We demonstrate the operation of a cascaded continuous wave (CW) mode-locked Raman oscillator. The output pulses were compressed from 28 ps at 532 nm down to 6.5 ps at 559 nm (first Stokes) and 5.5 ps at 589 nm (second Stokes). The maximum output was 2.5 W at 559 nm and 1.4 W at 589 nm with slope efficiencies up to 52%. This technique allows simple and efficient generation of short-pulse radiation to the cascaded Stokes wavelengths, extending the mode-locked operation of Raman lasers to a wider range of visible wavelengths between 500 - 650 nm based on standard inexpensive picosecond Nd:YAG oscillators

FACTORS INFLUENCING THE STRESS-STRAIN BEHAVIOR OF CERAMIC MATERIALS.

The stress-strain behavior of ceramic materials is greatly influenced by microstructural features ranging from the presence of point defects in single crystals to the size and location of pores and nature of grain boundaries in polycrystals. Several factors may affect the behavior at anyone time, and the analysis of experimental data, particularly for polycrystals, is thus extremely difficult. This review examines the interpretation of mechanical behavior in materials having the rock salt structure, with particular emphasis on the role of impurities, the significance of grain boundary and/or intragranular porosity, and the problems associated with the intersection of slip bands. <br/

Angular sensitivity of blowfly photoreceptors: intracellular measurements and wave-optical predictions

The angular sensitivity of blowfly photoreceptors was measured in detail at wavelengths λ = 355, 494 and 588 nm. The measured curves often showed numerous sidebands, indicating the importance of diffraction by the facet lens. The shape of the angular sensitivity profile is dependent on wavelength. The main peak of the angular sensitivities at the shorter wavelengths was flattened. This phenomenon as well as the overall shape of the main peak can be quantitatively described by a wave-optical theory using realistic values for the optical parameters of the lens-photoreceptor system. At a constant response level of 6 mV (almost dark adapted), the visual acuity of the peripheral cells R1-6 is at longer wavelengths mainly diffraction limited, while at shorter wavelengths the visual acuity is limited by the waveguide properties of the rhabdomere. Closure of the pupil narrows the angular sensitivity profile at the shorter wavelengths. This effect can be fully described by assuming that the intracellular pupil progressively absorbs light from the higher order modes. In light-adapted cells R1-6 the visual acuity is mainly diffraction limited at all wavelengths.

Wavelets and graph C∗C^*-algebras

Here we give an overview on the connection between wavelet theory and representation theory for graph $C^{\ast}$-algebras, including the higher-rank graph $C^*$-algebras of A. Kumjian and D. Pask. Many authors have studied different aspects of this connection over the last 20 years, and we begin this paper with a survey of the known results. We then discuss several new ways to generalize these results and obtain wavelets associated to representations of higher-rank graphs. In \cite{FGKP}, we introduced the "cubical wavelets" associated to a higher-rank graph. Here, we generalize this construction to build wavelets of arbitrary shapes. We also present a different but related construction of wavelets associated to a higher-rank graph, which we anticipate will have applications to traffic analysis on networks. Finally, we generalize the spectral graph wavelets of \cite{hammond} to higher-rank graphs, giving a third family of wavelets associated to higher-rank graphs

Model for localised recombination in quantum dots

A new generation of diode lasers is being developed using quantum dots as the gain generating medium. A detailed understanding of the carrier recombination mechanisms and optical gain generation is essential for optimisation of their performance. The aim of this work is to further understand the optical processes occurring in quantum dots. In particular, the effect of the localisation of the energy states in the dots on the recombination mechanisms and the gain/absorption is studied. It is often assumed that the rates of nonradiative recombination via defects, radiative recombination and Auger recombination are proportional to linear, quadratic and cubic functions of the carrier number respectively. The derivation of these functional forms is possible in quantum well and bulk structures because the extended electronic states make it meaningful to talk of a global carrier population. In a quantum dot system the dependence of the recombination processes on the total number of electrons populating the dots is modified by the localisation of all the recombination processes. In this thesis a computer model has been developed in which the dots are occupied by integer numbers of electrons and holes, with electron and hole occupancies controlled by Fermi-Dirac statistics. The recombination processes have similar dependences on the electron number and there is no clear transition from one process to another as the injection level is increased. These dependences cannot be represented by simple power law functions of the carrier number. An alternative model, in which each dot is electrically neutral, has also been studied, and the two models show significant differences for the hole distribution as the injection is increased. It is found that analyses based on power law relations between recombination rates and carrier number, as used for extended state systems, cannot be applied to localised recombination in dots.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Placental expression of pituitary hormones is an ancestral feature of therian mammals

<p>Abstract</p> <p>Background</p> <p>The placenta is essential for supplying nutrients and gases to the developing mammalian young before birth. While all mammals have a functional placenta, only in therian mammals (marsupials and eutherians) does the placenta closely appose or invade the uterine endometrium. The eutherian placenta secretes hormones that are structurally and functionally similar to pituitary growth hormone (GH), prolactin (PRL) and luteinizing hormone (LH). Marsupial and eutherian mammals diverged from a common ancestor approximately 125 to 148 million years ago and developed distinct reproductive strategies. As in eutherians, marsupials rely on a short-lived but functional placenta for embryogenesis.</p> <p>Results</p> <p>We characterized pituitary GH, GH-R, IGF-2, PRL and LHβ in a macropodid marsupial, the tammar wallaby, <it>Macropus eugenii</it>. These genes were expressed in the tammar placenta during the last third of gestation when most fetal growth occurs and active organogenesis is initiated. The mRNA of key growth genes GH, GH-R, IGF-2 and PRL were expressed during late pregnancy. We found significant up-regulation of GH, GH-R and IGF-2 after the start of the rapid growth phase of organogenesis which suggests that the placental growth hormones regulate the rapid phase of fetal growth.</p> <p>Conclusions</p> <p>This is the first demonstration of the existence of pituitary hormones in the marsupial placenta. Placental expression of these pituitary hormones has clearly been conserved in marsupials as in eutherian mammals, suggesting an ancestral origin of the evolution of placental expression and a critical function of these hormones in growth and development of all therian mammals.</p

Half metallic digital ferromagnetic heterostructure composed of a δ\delta-doped layer of Mn in Si

We propose and investigate the properties of a digital ferromagnetic heterostructure (DFH) consisting of a $\delta$-doped layer of Mn in Si, using \textit{ab initio} electronic-structure methods. We find that (i) ferromagnetic order of the Mn layer is energetically favorable relative to antiferromagnetic, and (ii) the heterostructure is a two-dimensional half metallic system. The metallic behavior is contributed by three majority-spin bands originating from hybridized Mn-$d$ and nearest-neighbor Si-$p$ states, and the corresponding carriers are responsible for the ferromagnetic order in the Mn layer. The minority-spin channel has a calculated semiconducting gap of 0.25 eV. Analysis of the total and partial densities of states, band structure, Fermi surfaces and associated charge density reveals the marked two-dimensional nature of the half metallicity. The band lineup is found to be favorable for retaining the half metal character to near the Curie temperature ($T_{C}$). Being Si based and possibly having a high $T_{C}$ as suggested by an experiment on dilutely doped Mn in Si, the heterostructure may be of special interest for integration into mature Si technologies for spintronic applications.Comment: 4 pages, 4 figures, Revised version, to appear in Phys. Rev. Let