Introduction to geodesics in sub-Riemannian geometry

International audience

Problems in number theory and hyperbolic geometry

In the first part of this thesis we generalize a theorem of Kiming and Olsson concerning the existence of Ramanujan-type congruences for a class of eta quotients. Specifically, we consider a class of generating functions analogous to the generating function of the partition function and establish a bound on the primes ℓ for which their coefficients c(n) obey congruences of the form c(ℓn + a) ≡ 0 (mod ℓ). We use this last result to answer a question of H.C. Chan. In the second part of this thesis [S2] we explore a natural analog of D. Calegari’s result that there are no hyperbolic once-punctured torus bundles over S^1 with trace field having a real place. We prove a contrasting theorem showing the existence of several infinite families of pairs (−χ, p) such that there exist hyperbolic surface bundles over S^1 with trace field of having a real place and with fiber having p punctures and Euler characteristic χ. This supports our conjecture that with finitely many known exceptions there exist such examples for each pair ( −χ, p).

Tectonic expression of an active slab tear from high-resolution seismic and bathymetric data offshore Sicily (Ionian Sea)

Subduction of a narrow slab of oceanic lithosphere beneath a tightly curved orogenic arc requires the presence of at least one lithospheric scale tear fault. While the Calabrian subduction beneath southern Italy is considered to be the type example of this geodynamic setting, the geometry, kinematics and surface expression of the associated lateral, slab tear fault offshore eastern Sicily remain controversial. Results from a new marine geophysical survey conducted in the Ionian Sea, using high-resolution bathymetry and seismic profiling reveal active faulting at the seafloor within a 140 km long, two-branched fault system near Alfeo Seamount. The previously unidentified 60 km long NW trending North Alfeo Fault system shows primarily strike-slip kinematics as indicated by the morphology and steep-dipping transpressional and transtensional faults. Available earthquake focal mechanisms indicate dextral strike-slip motion along this fault segment. The 80 km long SSE trending South Alfeo fault system is expressed by one or two steeply dipping normal faults, bounding the western side of a 500+ m thick, 5 km wide, elongate, syntectonic Plio-Quaternary sedimentary basin. Both branches of the fault system are mechanically capable of generating magnitude 6-7 earthquakes like those that struck eastern Sicily in 1169, 1542, and 1693.

The Effect of Package Geometry on Moisture Driven Degradation of Polymer Aluminum Capacitors

Polymer aluminum electrolytic capacitors were introduced to provide an alternative to liquid electrolytic capacitors. Polymer electrolytic capacitor electric parameters of capacitance and ESR are less temperature dependent than those of liquid aluminum electrolytic capacitors. Furthermore, the electrical conductivity of the polymer used in these capacitors (poly-3,4ethylenedioxithiophene) is orders of magnitude higher than the electrolytes used in liquid aluminum electrolytic capacitors, resulting in capacitors with much lower equivalent series resistance which are suitable for use in high ripple-current applications. The presence of the moisture-sensitive polymer PEDOT introduces concerns on the reliability of polymer aluminum capacitors in high humidity conditions. Highly accelerated stress testing (or HAST) (110ºC, 85% relative humidity) of polymer aluminum capacitors in which the parts were subjected to unbiased HAST conditions for 700 hours was done to understand the design factors that contribute to the susceptibility to degradation of a polymer aluminum electrolytic capacitor exposed to HAST conditions. A large scale study involving capacitors of different electrical ratings (2.5V – 16V, 100µF – 470 µF), mounting types (surface-mount and through-hole) and manufacturers (6 different manufacturers) was done to determine a relationship between package geometry and reliability in high temperature-humidity conditions. A Geometry-Based HAST test in which the part selection limited variations between capacitor samples to geometric differences only was done to analyze the effect of package geometry on humidity-driven degradation more closely. Raman spectroscopy, x-ray imaging, environmental scanning electron microscopy, and destructive analysis of the capacitors after HAST exposure was done to determine the failure mechanisms of polymer aluminum capacitors under high temperature-humidity conditions.

Oceanic control of multidecadal variability in an idealized coupled GCM

Idealized ocean models are known to develop intrinsic multidecadal oscillations of the meridional overturning circulation (MOC). Here we explore the role of ocean–atmosphere interactions on this low-frequency variability. We use a coupled ocean–atmosphere model set up in a flat-bottom aquaplanet geometry with two meridional boundaries. The model is run at three different horizontal resolutions (4°, 2° and 1°) in both the ocean and atmosphere. At all resolutions, the MOC exhibits spontaneous variability on multidecadal timescales in the range 30–40 years, associated with the propagation of large-scale baroclinic Rossby waves across the Atlantic-like basin. The unstable region of growth of these waves through the long wave limit of baroclinic instability shifts from the eastern boundary at coarse resolution to the western boundary at higher resolution. Increasing the horizontal resolution enhances both intrinsic atmospheric variability and ocean–atmosphere interactions. In particular, the simulated atmospheric annular mode becomes significantly correlated to the MOC variability at 1° resolution. An ocean-only simulation conducted for this specific case underscores the disruptive but not essential influence of air–sea interactions on the low-frequency variability. This study demonstrates that an atmospheric annular mode leading MOC changes by about 2 years (as found at 1° resolution) does not imply that the low-frequency variability originates from air–sea interactions.

Surface acoustic wave streaming in a PDMS microfluidic system: effect of frequency and fluid geometry & A remote ultrasonic glucose sensor

This thesis describes two separate projects. The first is a theoretical and experimental investigation of surface acoustic wave streaming in microfluidics. The second is the development of a novel acoustic glucose sensor. A separate abstract is given for each here. Optimization of acoustic streaming in microfluidic channels by SAWs Surface Acoustic Waves, (SAWs) actuated on flat piezoelectric substrates constitute a convenient and versatile tool for microfluidic manipulation due to the easy and versatile interfacing with microfluidic droplets and channels. The acoustic streaming effect can be exploited to drive fast streaming and pumping of fluids in microchannels and droplets (Shilton et al. 2014; Schmid et al. 2011), as well as size dependant sorting of particles in centrifugal flows and vortices (Franke et al. 2009; Rogers et al. 2010). Although the theory describing acoustic streaming by SAWs is well understood, very little attention has been paid to the optimisation of SAW streaming by the correct selection of frequency. In this thesis a finite element simulation of the fluid streaming in a microfluidic chamber due to a SAW beam was constructed and verified against micro-PIV measurements of the fluid flow in a fabricated device. It was found that there is an optimum frequency that generates the fastest streaming dependent on the height and width of the chamber. It is hoped this will serve as a design tool for those who want to optimally match SAW frequency with a particular microfluidic design. An acoustic glucose sensor Diabetes mellitus is a disease characterised by an inability to properly regulate blood glucose levels. In order to keep glucose levels under control some diabetics require regular injections of insulin. Continuous monitoring of glucose has been demonstrated to improve the management of diabetes (Zick et al. 2007; Heinemann & DeVries 2014), however there is a low patient uptake of continuous glucose monitoring systems due to the invasive nature of the current technology (Ramchandani et al. 2011). In this thesis a novel way of monitoring glucose levels is proposed which would use ultrasonic waves to ‘read’ a subcutaneous glucose sensitive-implant, which is only minimally invasive. The implant is an acoustic analogy of a Bragg stack with a ‘defect’ layer that acts as the sensing layer. A numerical study was performed on how the physical changes in the sensing layer can be deduced by monitoring the reflection amplitude spectrum of ultrasonic waves reflected from the implant. Coupled modes between the skin and the sensing layer were found to be a potential source of error and drift in the measurement. It was found that by increasing the number of layers in the stack that this could be minimized. A laboratory proof of concept system was developed using a glucose sensitive hydrogel as the sensing layer. It was possible to monitor the changing thickness and speed of sound of the hydrogel due to physiological relevant changes in glucose concentration.

The authenticity of resources for the teaching of foreign languages and cultures in France: variable geometry notion

International audience

Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools

We explore the recently developed snapshot-based dynamic mode decomposition (DMD) technique, a matrix-free Arnoldi type method, to predict 3D linear global flow instabilities. We apply the DMD technique to flows confined in an L-shaped cavity and compare the resulting modes to their counterparts issued from classic, matrix forming, linear instability analysis (i.e. BiGlobal approach) and direct numerical simulations. Results show that the DMD technique, which uses snapshots generated by a 3D non-linear incompressible discontinuous Galerkin Navier?Stokes solver, provides very similar results to classical linear instability analysis techniques. In addition, we compare DMD results issued from non-linear and linearised Navier?Stokes solvers, showing that linearisation is not necessary (i.e. base flow not required) to obtain linear modes, as long as the analysis is restricted to the exponential growth regime, that is, flow regime governed by the linearised Navier?Stokes equations, and showing the potential of this type of analysis based on snapshots to general purpose CFD codes, without need of modifications. Finally, this work shows that the DMD technique can provide three-dimensional direct and adjoint modes through snapshots provided by the linearised and adjoint linearised Navier?Stokes equations advanced in time. Subsequently, these modes are used to provide structural sensitivity maps and sensitivity to base flow modification information for 3D flows and complex geometries, at an affordable computational cost. The information provided by the sensitivity study is used to modify the L-shaped geometry and control the most unstable 3D mode.

Visual Insight in Geometry

According to a traditional rationalist proposal, it is possible to attain knowledge of certain necessary truths by means of insight—an epistemic mental act that combines the 'presentational' character of perception with the a priori status usually reserved for discursive reasoning. In this dissertation, I defend the insight proposal in relation to a specific subject matter: elementary Euclidean plane geometry, as set out in Book I of Euclid's Elements. In particular, I argue that visualizations and visual experiences of diagrams allow human subjects to grasp truths of geometry by means of visual insight. In the first two chapters, I provide an initial defense of the geometrical insight proposal, drawing on a novel interpretation of Plato's Meno to motivate the view and to reply to some objections. In the remaining three chapters, I provide an account of the psychological underpinnings of geometrical insight, a task that requires considering the psychology of visual imagery alongside the details of Euclid's geometrical system. One important challenge is to explain how basic features of human visual representations can serve to ground our intuitive grasp of Euclid's postulates and other initial assumptions. A second challenge is to explain how we are able to grasp general theorems by considering diagrams that depict only special cases. I argue that both of these challenges can be met by an account that regards geometrical insight as based in visual experiences involving the combined deployment of two varieties of 'dynamic' visual imagery: one that allows the subject to visually rehearse spatial transformations of a figure's parts, and another that allows the subject to entertain alternative ways of structurally integrating the figure as a whole. It is the interplay between these two forms of dynamic imagery that enables a visual experience of a diagram, suitably animated in visual imagination, to justify belief in the propositions of Euclid’s geometry. The upshot is a novel dynamic imagery account that explains how intuitive knowledge of elementary Euclidean plane geometry can be understood as grounded in visual insight.

The microbiological signature of human cutaneous leishmaniasis lesions exhibits restricted bacterial diversity compared to healthy skin

Localised cutaneous leishmaniasis (LCL) is the most common form of cutaneous leishmaniasis characterised by single or multiple painless chronic ulcers, which commonly presents with secondary bacterial infection. Previous culture- based studies have found staphylococci, streptococci, and opportunistic pathogenic bacteria in LCL lesions, but there have been no comparisons to normal skin. In addition, this approach has strong bias for determining bacterial composition. The present study tested the hypothesis that bacterial communities in LCL lesions differ from those found on healthy skin (HS). Using a high throughput amplicon sequencing approach, which allows for better populational evaluation due to greater depth coverage and the Quantitative Insights Into Microbial Ecology pipeline, we compared the microbiological signature of LCL lesions with that of contralateral HS from the same individuals. Streptococcus , Staphylococcus , Fusobacterium and other strict or facultative anaerobic bacteria composed the LCL microbiome. Aerobic and facultative anaerobic bacteria found in HS, including environmental bacteria, were significantly decreased in LCL lesions (p < 0.01). This paper presents the first comprehensive microbiome identification from LCL lesions with next generation sequence methodology and shows a marked reduction of bacterial diversity in the lesions.

On roof geometry for urban wind energy exploitation in high-rise buildings

The European program HORIZON2020 aims to have 20% of electricity produced by renewable sources. The building sector represents 40% of the European Union energy consumption. Reducing energy consumption in buildings is therefore a priority for energy efficiency. The present investigation explores the most adequate roof shapes compatible with the placement of different types of small wind energy generators on high-rise buildings for urban wind energy exploitation. The wind flow around traditional state-of-the-art roof shapes is considered. In addition, the influence of the roof edge on the wind flow on high-rise buildings is analyzed. These geometries are investigated, both qualitatively and quantitatively, and the turbulence intensity threshold for horizontal axis wind turbines is considered. The most adequate shapes for wind energy exploitation are identified, studying vertical profiles of velocity, turbulent kinetic energy and turbulence intensity. Curved shapes are the most interesting building roof shapes from the wind energy exploitation point of view, leading to the highest speed-up and the lowest turbulence intensity.

Paleoenvironments and Geochemical Signals from the Late Barremian to the Middle Aptian in a Tethyan Marginal Basin, Northeast Spain: Implications for Carbon Sequestration in Restricted Basins

The hallmark of oceanic anoxic event 1a (OAE1a) (early Aptian ~125 Ma) corresponds to worldwide deposition of black shales with total organic carbon (TOC) content > 2% and a d13C positive excursion up to ~5‰. OAE1a has been related to large igneous province volcanism and dissociation of methane hydrates during the Lower Cretaceous. However, the occurrence of atypical, coeval and diachronous organic-rich deposits associated with OAE1a, which are also characterized by positive spikes of the d13C in epicontinental to restricted marine environments of the Tethys Ocean, indicates localized responses decoupled from complex global forcing factors. The present research is a high-resolution, multiproxy approach to assess the paleoenvironmental conditions that led to enhanced carbon sequestration from the late Barremian to the middle Aptian in a restricted, Tethyan marginal basin prior to and during OAE1a. I studied the lower 240 m of the El Pui section, Organyà Basin, Spanish Pyrenees. The basin developed as the result of extensional tectonism linked to the opening of the Atlantic Ocean. At the field scale the section consists of a sequence of alternating beds of cm – m-scale, medium-gray to grayish-black limestones and marlstones with TOC up to ~4%. The results indicate that the lowest 85 m of the section, from latest Barremian –earliest Aptian, characterize a deepening phase of the basin concomitant with sustained riverine flux and intensified primary productivity. These changes induced a shift in the sedimentation pattern and decreased the oxygen levels in the water column through organic matter respiration and limited ventilation of the basin. The upper 155 m comprising the earliest – late-early Aptian document the occurrence of OAE1a and its associated geochemical signatures (TOC up to 3% and a positive shift in d13C of ~5‰). However, a low enrichment of redox-sensitive trace elements indicates that the basin did not achieve anoxic conditions. The results also suggest that a shallower-phase of the basin, coeval with platform progradation, may have increased ventilation of the basin at the same time that heightened sedimentation rates and additional input of organic matter from terrestrial sources increased the burial and preservation rate of TOC in the sediment.

The Students’ Perspective of Geometry Teaching and Learning in High School

The purpose of this article is to present the results obtained from a questionnaire applied to Costa Rican high school students, in order to know their perspectives about geometry teaching and learning. The results show that geometry classes in high school education have been based on a traditional system of teaching, where the teacher presents the theory; he presents examples and exercises that should be solved by students, which emphasize in the application and memorization of formulas. As a consequence, visualization processes, argumentation and justification don’t have a preponderant role. Geometry is presented to students like a group of definitions, formulas, and theorems completely far from their reality and, where the examples and exercises don’t possess any relationship with their context. As a result, it is considered not important, because it is not applicable to real life situations. Also, the students consider that, to be successful in geometry, it is necessary to know how to use the calculator, to carry out calculations, to have capacity to memorize definitions, formulas and theorems, to possess capacity to understand the geometric drawings and to carry out clever exercises to develop a practical ability.

Restricted intake and lipid inclusion: effects on ovarian follicular development in Santa Inês ewe lambs.

The reproductive efficiency is directly related to the nutritional management. The diet lipid inclusion, especially with enhanced sources of omega 6 and omega 3 fatty acids, is positively associated to the ovarian follicular development of ruminants. The objective of this study was to evaluate the effects of toasted soybean grain addition on restricted or ad libitum feeding on ovarian follicular development of Santa Inês ewe lambs In conclusion, the diameter of the largest follicle and the number of >5 mm follicles were not influenced by the restricted intake diet nor the lipid inclusion; however, they increased in a direct relationship with the age of the animals.

Restricted intake and lipid inclusion in Santa Inês ewe lambs diet: age, weight and progesterone concentration at first ovulation.

The age at first ovulation is influenced by several factors, and nutrition has an essential role on it. Lipids provide essential fatty acids that are positively associated to reproductive aspects. The aims of this study were to evaluate the effects of lipid inclusion and restricted intake on age and weight at the first ovulation and the serum progesterone (P4) concentration at the sixth day after first ovulation. The restricted intake imposed in this study did not delay the age at fist ovulation. The greater lipid intake did not favor reproductive parameters. Serum P4 did not increase with the soybean inclusion in the die.