LpL^p-approximation of the integrated density of states for Schr\"odinger operators with finite local complexity

We study spectral properties of Schr\"odinger operators on \RR^d. The electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in \ZZ^d, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e.the normalised eigenvalue counting functions. The convergence holds in the space $L^p(I)$ where $I$ is any finite energy interval and $1\leq p< \infty$ is arbitrary.Comment: 15 pages; v2 has minor fixe

An examination of some characteristics of Kepler Short and Long Cadence Data

A close comparison of Kepler short- and long-cadence data released prior to 2011 Nov 1 has shown some subtle differences that make the short-cadence data superior to their long-cadence counterparts. The inevitable results of a faster sampling rate are present: the short-cadence data provide greater time resolution for short-lived events like flares, and have a much higher Nyquist frequency than the long-cadence data; however, they also contain fewer high-amplitude peaks at low frequency and allow a more precise determination of pulsation frequencies, amplitudes and phases. The latter observation indicates that Kepler data are not normally distributed. Moreover, a close inspection of the Pre-search Data Conditioned (PDC) long-cadence data show residuals that have increased noise on time-scales important to asteroseismology, but unimportant to planet searches.Comment: Accepted for publication in MNRAS. 7 pages, 5 figure

Impulsive Hybrid Discrete-Continuous Delay Differential Equations

This thesis deals with impulsive hybrid discrete-continuous delay differential equations (IHDDEs). This new class of differential equations is highly challenging for two reasons. First, because of a dependency of the right-hand-side function on past states, with time delays that depend on the current state. Second, because both the right-hand-side function and the state itself are discontinuous at implicitly defined time points. The theoretical results and numerical methods presented in this thesis are related to the following subject areas: First, solutions of initial value problems (IVPs) in IHDDEs. Second, derivatives of IVP solutions with respect to parameters (“sensitivities”). Third, estimation of parameters in IHDDE models from experimental data. Amongst others, this thesis thereby makes the following contributions: - The theoretical basis of IHDDE-IVPs is established. This includes the definition of a solution concept, the existence of solutions, the uniqueness of solutions, and the differentiability of solutions with respect to parameters. - A new approach for numerically solving IVPs in differential equations with time delays is introduced. A key aspect is the use of extrapolations beyond past discontinuities. Convergence of continuous Runge-Kutta methods realized in the framework of the new approach is shown, and numerical results are presented that demonstrate the benefit of using extrapolations on a practical example. - A “first discretize, then differentiate” approach and a “first differentiate, then discretize” approach for forward sensitivity computation in IHDDEs are investigated. It is revealed that the presence of time delays destroys commutativity of differentiation and discretization in the case of continuous Runge-Kutta methods. - An extension of the concept of Internal Numerical Differentiation is proposed for differential equations with time delays. The use of the extended concept ensures that numerically computed sensitivities converge to the exact sensitivities, and that the convergence order is identical to the convergence order of the method that is used for solving the nominal IVP. - The first practical forward and adjoint schemes are developed that realize Internal Numerical Differentiation for IHDDEs. Numerical investigations show that the developed schemes are drastically more efficient than classical methods for sensitivity computation. - The new numerical methods for solving IVPs and for computing sensitivites are successfully applied to several challenging test cases, and the properties of the methods are analysed. - Numerical methods are presented for solving nonlinear least-squares parameter estimation problems constrained by IHDDEs. - A new epidemiological IHDDE model is developed. Therein, an impulse accounts for the arrival of an infected population. Further, the zeros of state-dependent switching functions characterize the time points at which new medical treatments become available. - A delay differential equation model is presented for the crosstalk of the signaling pathways of two cytokines. In comparison to an ordinary differential equation model, a better fit to experimental data is obtained with a smaller number of differential states. - A novel model is proposed to describe the voting behavior of the viewers of the TV singing competition “Unser Star für Baku” aired in 2012. Numerical results show that the use of a time delay is crucial for a qualitative correct description of the voting behavior. Furthermore, parameter estimation results yield a good quantitative agreeement with data from the TV show. - The practical implementation of all developed methods in the new software packages Colsol-DDE and ParamEDE is described

Multi-trait selection for improved solid wood physical and flexural properties in white spruce

Commercial production of high-quality lumber for Nordic conifers is negatively impacted by long rotation age and adverse negative correlations between growth and wood quality traits. A prospective solution to ensure sufficient fibre quality from future plantations is to identify key wood traits for desired applications and to consider them in tree breeding programs. In this study, we used the widespread and largely reforested white spruce (Picea glauca [Moench] Voss) in Canada to investigate the genetic control of wood flexural properties such as stiffness, i.e. modulus of elasticity (MOE), and strength, i.e. modulus of rupture (MOR). We also looked at their phenotypic and genetic correlations with other wood quality and growth traits to assess the efficiency of indirect methods of selection to improve wood flexural properties in the context of multi-trait selection in tree breeding programs. To achieve this, standardized solid wood samples, growth records and standing tree wood quality traits were collected from 289 trees belonging to 38 white spruce families from a polycross genetic trial established on two different sites in the province of Quebec, Canada. Flexural stiffness and strength, height, diameter at breast height (DBH) and wood density showed moderate to high heritability. Flexural stiffness was also positively correlated at the genetic level with flexural strength, average wood density and acoustic velocity as an indirect measure of dynamic MOE (⁠rG  = 0.99, rG  = 0.78 and rG = 0.78, respectively). When selecting the top 5 per cent of the trees, the expected genetic gains varied from 3.6 per cent for acoustic velocity to 16.5 per cent for MOE. Selection based on wood density and acoustic velocity would result in considerable genetic gains in flexural stiffness. Several multi-trait selection scenarios were tested to investigate the genetic gains obtained from selecting with different combinations of growth and wood quality traits. The results showed that indirect selection for wood flexural properties by means of acoustic velocity and wood density are efficient methods that can be combined in operational white spruce breeding programs to increase simultaneously genetic gains for growth and wood flexural properties

Equality of Lifshitz and van Hove exponents on amenable Cayley graphs

We study the low energy asymptotics of periodic and random Laplace operators on Cayley graphs of amenable, finitely generated groups. For the periodic operator the asymptotics is characterised by the van Hove exponent or zeroth Novikov-Shubin invariant. The random model we consider is given in terms of an adjacency Laplacian on site or edge percolation subgraphs of the Cayley graph. The asymptotic behaviour of the spectral distribution is exponential, characterised by the Lifshitz exponent. We show that for the adjacency Laplacian the two invariants/exponents coincide. The result holds also for more general symmetric transition operators. For combinatorial Laplacians one has a different universal behaviour of the low energy asymptotics of the spectral distribution function, which can be actually established on quasi-transitive graphs without an amenability assumption. The latter result holds also for long range bond percolation models

Relaxation of Loaded ESCRT-III Spiral Springs Drives Membrane Deformation

International audienceESCRT-III is required for lipid membrane remodeling in many cellular processes, from abscission to viral budding and multi-vesicular body biogenesis. However, how ESCRT-III polymerization generates membrane curvature remains debated. Here, we show that Snf7, the main component of ESCRT-III, polymerizes into spirals at the surface of lipid bilayers. When covering the entire membrane surface, these spirals stopped growing when densely packed: they had a polygonal shape, suggesting that lateral compression could deform them. We reasoned that Snf7 spirals could function as spiral springs. By measuring the polymerization energy and the rigidity of Snf7 filaments, we showed that they were deformed while growing in a confined area. Furthermore, we observed that the elastic expansion of compressed Snf7 spirals generated an area difference between the two sides of the membrane and thus curvature. This spring-like activity underlies the driving force by which ESCRT-III could mediate membrane deformation and fission

Aplicação do óxido de cálcio como catalisador heterogêneo para a transesterificação etílica de óleo de soja residual de fritura

Biodiesel can be produced through the transesterification reaction of a short-chain alcohol with a triacylglycerol, that can be obtained from vegetable oils or animal fats, in the presence of a catalyst. The use of ethanol as reactant is justified since its production is consolidated in Brazil. Among the heterogeneous catalysts, CaO shows potential in the transesterification reactions because it has a low cost, can be reused and is not corrosive. The recycling of frying oil for the production of biodiesel represents an alternative for the disposal of a waste and does not compete with the food industry. The residual oil and CaO were subjected to a pre-treatment before the transesterification reactions. A Box-Behnken experimental design was applied with 3 factors: temperature, ethanol:oil molar ratio and reaction time. The reactions were carried out in a batch reactor, in which oil, ethanol and the catalyst were added. The samples were vacuum filtered and conducted to a rotary evaporator, in order to remove excess ethanol. The resulting mixture was centrifuged and, subsequently, a sample was collected from the supernatant phase. The yield was determined by a mass balance based in the concentrations of acylglycerols, that were determined through an HPLC-UV methodology. A second-order linear regression model was built and validated through statistic tests with a 5% significance level. The optimized operational parameters are 15:1 ethanol:oil molar ratio, 81.2 ºC e 6 h of reaction. From the obtained results it can be inferred that it is feasible to use residual frying oil as raw material, ethanol as reactant and CaO as catalyst for the production of biodiesel.O biodiesel pode ser obtido através da reação de transesterificação de um álcool de cadeia curta com um triacilglicerol, que pode ser obtido a partir de óleos vegetais ou gorduras animais na presença de um catalisador. A utilização de etanol como reagente justifica-se porque este tem sua produção consolidada no Brasil. Dentre os catalisadores heterogêneos, o CaO mostra potencial nas reações de transesterificação, pois apresenta baixo custo, pode ser reutilizado e não é corrosivo. A reciclagem do óleo de fritura para a produção de biodiesel representa uma alternativa de destinação de um resíduo e não compete com o mercado alimentício. O óleo residual e o CaO passaram por pré-tratamento antes das reações de transesterificação. Foi aplicado um delineamento experimental Box-Behnken de 3 fatores: temperatura, razão molar etanol:óleo e tempo de reação. As reações foram conduzidas em um reator batelada, em que foram adicionados óleo, etanol e catalisador. As amostras foram filtradas à vácuo e conduzidas a um evaporador rotativo, para remoção do etanol excedente. A mistura resultante foi centrifugada e posteriormente retirada uma amostra da fase sobrenadante. O rendimento foi determinado a partir de um balanço de massa, baseado nas concentrações de acilgliceróis, que foram determiadas através de uma metodologia em HPLC-UV. Um modelo de regressão linear de segunda ordem foi construído e validado através de testes estatísticos com nível de significância de 5%. Os parâmetros operacionais otimizados são razão molar etanol:óleo 15:1, 81,2 ºC e 6 h de reação. A partir dos resultados obtidos infere-se que é viável a utilização do óleo residual de fritura como matéria-prima, etanol como reagente e CaO como catalisador para a produção de biodiesel

Willman 1 - a probable dwarf galaxy with an irregular kinematic distribution

We investigate the kinematic properties and stellar population of the Galactic satellite Willman 1 (Wil 1) by combining Keck/DEIMOS spectroscopy with KPNO mosaic camera imaging. Wil 1 is an ultra-low luminosity Milky Way companion. This object lies in a region of size-luminosity space (M_V ~ -2 mag, d ~ 38 kpc, r_half ~ 20 pc) also occupied by the Galactic satellites Bo\"otes II and Segue 1 and 2, but no other known old stellar system. We use kinematic and color-magnitude criteria to identify 45 stars as possible members of Wil 1. With a systemic velocity of v_helio = -12.8 +/- 1.0 km/s, Wil 1 stars have velocities similar to those of foreground Milky Way stars. Informed by Monte-Carlo simulations, we identify 5 of the 45 candidate member stars as likely foreground contaminants. We confirm a significant spread in the abundances of the likely Wil 1 red giant branch members ([Fe/H] = -1.73 +/- 0.12 and -2.65 +/- 0.12, [Ca/Fe] = -0.4 +/- 0.18 and +0.13 +/- 0.28). This spread supports the scenario that Wil 1 is an ultra-low luminosity dwarf galaxy rather than a star cluster. Wil 1's innermost stars move with radial velocities offset by 8 km/s from its outer stars and have a velocity dispersion consistent with 0 km/s, suggesting that Wil 1 may not be in dynamical equilibrium. The combination of the foreground contamination and unusual kinematic distribution make it difficult to robustly determine the dark matter mass of Wil 1. As a result, X-ray or gamma-ray observations of Wil 1 that attempt to constrain models of particle dark matter using an equilibrium mass model are strongly affected by the systematics in the observations presented here. We conclude that, despite the unusual features in the Wil 1 kinematic distribution, evidence indicates that this object is, or at least once was, a dwarf galaxy.Comment: AJ accepted version. The primary improvements are a detailed investigation of the membership probability (Section 3.4 and new Figures 6, 7 and 8) and the revised spectroscopic [Fe/H] and [Ca/Fe] measurements of the two brightest member stars. Conclusions are unchanged from the submitted versio

Cassini’s CDA observes a variety of dust populations just outside Saturn’s main rings

Before the end of its mission, the Cassini spacecraft orbited Saturn in a series of highly inclined elliptical ‘Ring-Grazing’ orbits (RGO). During the RGO, the spacecraft passed repeatedly through the ring plane outside the F ring, near the orbits of Janus and Epimetheus, at an average relative speed of ∼20 km s–1. For the first time, Cassini’s Cosmic Dust Analyser (CDA) directly sampled dust particles from this region. Here, we analyse the compositions of dust grains sampled within ±15 min relative to nine ring plane crossings of the RGO. The compositions of most analysed RGO grains are similar to those of E ring ice grains, implying that the E ring extends to within at least 2.45 Saturn radii (RS) of Saturn. The compositional distribution of these grains point at a similar average period (decades) since ejection from Enceladus as of particles in the outer E ring (beyond 8 RS). Higher fractions of larger grains are found near the orbits of Janus and Epimetheus, which probably represent ejecta from these moons. Most of these grains have compositions similar to the background E ring grains, indicating that E ring material is coating the surfaces of Janus and Epimetheus. We also report the detection of several types of mineral grains on prograde orbits, one of which, a water ice/silicate mixture, has never been observed by CDA elsewhere. These mineral grains appear to have a different origin from the E ring, and may arise from nearby moons, the F ring, or main rings

Clinical Data-Driven Finite Element Analysis of the Kinetics of Chewing Cycles in Order to Optimize Occlusal Reconstructions

The occlusal design plays a decisive role in the fabrication of dental restorations. Dentists and dental technicians depend on mechanical simulations of mandibular movement that are as accurate as possible, in particular, to produce interference-free yet chewing-efficient dental restorations. For this, kinetic data must be available, i.e., movements and deformations under the influence of forces and stresses. In the present study, so-called functional data were collected from healthy volunteers to provide consistent information for proper kinetics. For the latter purpose, biting and chewing forces, electrical muscle activity and jaw movements were registered synchronously, and individual magnetic resonance tomograms (MRI) were prepared. The acquired data were then added to a large complex finite element model of the complete masticatory system using the functional information obtained and individual anatomical geometries so that the kinetics of the chewing process and teeth grinding could be realistically simulated. This allows developing algorithms that optimize computer-aided manufacturing of dental prostheses close to occlusion. In this way, a failure-free function of the dental prosthesis can be guaranteed and its damage during usage can be reduced or prevented even including endosseous implants