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C*-Algebras for Quantum Solids
No full textGiven a decorated point set which describes the arrangement of the atoms in a solid, we describe two -algebras, one specified as discrete and the other as continuous. The discrete algebra is adapted to the description of the particles in the solid with the help of tight binding models, the continuous one to the description by differential operators. A key concept is that of the hull of the solid, a compact topological space which also comes in a discrete and in a continuous form. We give a more detailed description in the cases that our point set has finite local complexity or comes from a substitution tiling. We also mention the modification needed if there are external magnetic fields
Alpha-case promotes fatigue cracks initiation from the surface in heat treated Ti-6Al-4V fabricated by Laser Powder Bed Fusion
No full textInternational audienceThis research investigates the effect of the formation of an oxygen-stabilised titanium alpha layer – called alpha-case at the surface – on the fatigue properties of Ti-6Al-4V (Ti64) alloy components produced by Laser Powder Bed Fusion (L-PBF). Three post processing heat treatments with different controlled atmospheres were carried out on samples with as-built surfaces to evaluate how differences in alpha-case layer thickness and hardness affect the material’s susceptibility to surface embrittlement and its overall fatigue performance. The investigation includes bulk and subsurface microstructural analysis, surface characterisation by X-ray computed tomography (XCT), and fatigue testing. Key findings show that alpha-case layers can reduce the fatigue resistance of L-PBF fabricated Ti64. The presence of a 70±3 µm thick alpha-case layer was found to promote crack initiation. This is emphasised by a higher density of initiated cracks, thus leading to a reduction in fatigue life. Conversely, thinner alpha-case layers were found to have a reduced impact on the fatigue performance, highlighting the critical role of post processing heat treatments in modulating the fatigue resistance of the material. The use of XCT to characterise the surfaces of the specimens in 3D confirms that fatigue cracks primarily initiate at surface notches, highlighting the predominance of as-built surfaces over microstructure in determining the fatigue resistance of L-PBF Ti64 components
Magnetic tracking for catheterization procedure, using giant-magnetoresistance and space-varying magnetic field free point
No full textInternational audienceX-ray fluoroscopic imaging is the standard method for obtaining catheter position and monitoring the patient's vascular network during catheterization procedures. However, this method exposes both patients and doctors to ionizing radiation. To address this issue, we propose an alternative method for tracking the catheter inside the human body by integrating a magnetic sensor at the catheter tip and generating a known magnetic field (MF) around the operative zone. The catheter's position can then be determined by measuring this MF. Due to the mandatory small size of the catheter, we utilized giant-magnetoresistance (GMR) sensors for this tracking system. GMR sensors require only two wires for connection, have a wide bandwidth that allows flexibility in selecting the working frequency and can detect low-intensity MFs down to the nano Tesla range. Our method is based on the time detection of a moving null MF, known as the Field-Free Point (FFP) for MF generation. This approach requires only a single sensor smaller than 300 µm², making it suitable for any catheter. We constructed an experimental setup to demonstrate the feasibility of this method in one dimension and obtained promising performance results
Global stability of perturbed chemostat systems
No full textInternational audienceThis paper is devoted to the analysis of global stability of the chemostat system with a perturbation term representing any type of exchange between species. This conversion term depends on species and substrate concentrations but also on a positive perturbation parameter. After having written the invariant manifold as a union of a family of compact subsets, our main result states that for each subset in this family, there is a positive threshold for the perturbation parameter below which, the system is globally asymptotically stable in the corresponding subset. Our approach relies on the Malkin-Gorshin Theorem and on a Theorem by Smith and Waltman about perturbations of a globally stable steady state. Properties of steady-states and numerical simulations of the system's asymptotic behavior complete this study for two types of perturbation term between species
Stability of acoustic streaming jets confined in cylindrical cavities
No full textWe study the stability of a steady Eckart streaming jet flowing in a closed cylindrical cavity. This configuration is a generic representation of industrial processes where driving flows in cavity by means of acoustic forcing offers a contactless way of stirring or controling flows. Successfully doing so however requires sufficient insight into the topology induced by the acoustic beam. This, in turn, raises the more fundamental question of whether the basic jet topology is stable and, when it is not, of the alternative states that end up being acoustically forced. To answer these questions we consider a flow forced by an axisymmetric diffracting beam of attenuated sound waves emitted by a plane circular transducer at one cavity end. At the opposite end, the jet impingement drives recirculating structures spanning nearly the entire cavity radius. We rely on Linear Stability Analysis (LSA) together with three-dimensional nonlinear simulations to identify the flow destabilisation mechanisms and to determine the bifurcation criticalities. We show that flow destabilisation is closely related to the impingement-driven recirculating structures, and that the ratio CR between the cavity and the maximum beam radii plays a key role on the flow stability. In total, we identified four mode types destabilising the flow. For 4 ⩽ CR ⩽ 6, a non-oscillatory perturbation rooted in the jet impingement triggers a supercritical bifurcation. For CR = 3, the flow destabilises through a subcritical non-oscillatory bifurcation, and we explain the topological change of the unstable perturbation by analysing its critical points. Further reducing CR increases the shear within the flow, and gradually moves the instability origin to the shear layer between impingement-induced vortices: for CR = 2, an unstable travelling wave grows out of a subcritical bifurcation, which becomes supercritical for CR = 1. For each geometry, the nonlinear 3D simulations confirm both the topology and the growth rate of the unstable perturbation returned by LSA. This study offers fundamental insight into the stability of acoustically-driven flows in general but also opens possible pathways to either induce turbulence acoustically, or to avoid it in realistic configurations
An Online Analytical Solution for Multi-Sector Bearingless Machine Current Reference Calculation
No full textInternational audienceIn this paper, an online analytical current reference calculation for minimizing Joule losses in Multi-Sector Bearingless Synchronous Machine with power-sharing capabilities is presented. In this study, the optimization problem of determining the current references as a function of torque and radial forces, is solved analytically and compared with previously proposed numerical solutions. The proposed method significantly reduces the required data storage and computational burden, making it more suitable for real-time applications. Additionally, it improves the precision of current reference calculations, ensuring more efficient and balanced power distribution among multiple sectors. This advancement contributes to the overall reliability and performance of bearingless machine systems in high-speed and high-precision applications
EEG–Metabolic Coupling and Time Limit at VO2max During Constant-Load Exercise
No full textInternational audienceBackground: Exercise duration at maximum oxygen uptake (V˙O2max) appears to be influenced not only by metabolic factors but also by the interplay between brain dynamics and ventilatory regulation. This study examined how cortical activity, assessed via electroencephalography (EEG), relates to performance and acute fatigue regulation during a constant-load cycling test. We hypothesized that oscillatory activity in the theta, alpha, and beta bands would be associated with ventilatory coordination and endurance capacity. Methods: Thirty trained participants performed a cycling test to exhaustion at 90% maximal aerobic power. EEG and gas exchange were continuously recorded; ratings of perceived exertion were assessed immediately after exhaustion. Results: Beta power was negatively correlated with time spent at V˙O2max (r = −0.542, p = 0.002). Theta and Alpha power alone showed no direct associations with endurance, but EEG–metabolic ratios revealed significant correlations. Specifically, the time to reach V˙O2max correlated with Alpha/V˙O2 (p < 0.001), Alpha/V˙CO2 (p < 0.001), and Beta/V˙CO2 (p = 0.002). The time spent at V˙O2max correlated with Theta/V˙O2 (p = 0.002) and Theta/V˙CO2 (p < 0.001). The time-to-exhaustion was correlated with Theta/V˙CO2 (p < 0.001) and Alpha/V˙CO2 (p < 0.001). Conclusions: These findings indicate that cortical oscillations were associated with different aspects of acute fatigue regulation. Beta activity was associated with fatigue-related neural strain, whereas Theta and Alpha bands, when normalized to metabolic load, were consistent with a role in ventilatory coordination and motor control. EEG–metabolic ratios may provide exploratory indicators of brain–metabolism interplay during high-intensity exercise and could help guide future brain-body interactions in endurance performance
HKKN-stratifications in a non-compact framework
No full textIn this latest version, we have clarified certain mathematical notations and added a few remarks on the fact that algebraic and analytic stratifications coincide on the variety V x P(E).The aim of this paper is twofold. First, we study HKKN stratifications, both algebraically and analytically, for a Cartesian product between a vector space and a compact Kähler manifold. We then use these stratifications to prove convexity properties of the moment map for non-compact analytic subsets invariant under a Borel subgroup
Large-eddy simulations of screeching jets interacting with a flat plate parallel or perpendicular to the jet axis
No full textInternational audienceLarge-eddy simulations of round screeching jets at a Mach number equal to 1.15 and a diameter-based Reynolds number equal to 4 x 105, with or without a flat plate, are performed, in order to study the effects of a plate parallel or perpendicular to the jet axis on the flow development and on tonal noise. The nozzle-to-plate distance is equal to 8r0 for the perpendicular plate and the plate-to-jet axis distance is equal to 14r0 for the parallel plate, where r0 is the nozzle radius. For the jet impinging on the perpendicular plate, the closure of the potential core is prevented and a wall jet develops along the plate. In the parallel-plate case, the presence of the plate induces a longer potential core as well as downstream shock cells that are more intense. In this case, a boundary layer also develops over the plate. Tonal noise components are radiated in the upstream direction in all cases. For the free and impinging jets, a tone is strongly dominant and its frequency is similar for the two jets. In the latter case, secondary tones are found
Computation and stability analysis of periodic orbits using finite differences, Fourier or Chebyshev spectral expansions in time
No full textInternational audienceWe analyse and compare several algorithms to compute numerically periodic solutions of high-dimensional dynamical systems and investigate their Floquet stability without building the monodromy matrix. The solution and its perturbation are discretised in time either using finite differences, Fourier-Galerkin or Chebyshev expansions. The resulting nonlinear set of equations describing the periodic orbit is solved using a Newton-Raphson algorithm. The linearised equations determining the stability lead to a generalised eigenvalue problem. Unlike the Fourier-Galerkin method, the use of Chebyshev polynomials or finite differences has the advantage that the relevant Floquet exponents are directly given without the well known issue of having to sort out the eigenvalues. The speed of convergence of these three methods is illustrated with examples from the Lorenz system, the Langford system and a two-dimensional thermal convection flow inside a differentially heated cavity. This last example demonstrates the potential of the newly proposed Chebyshev expansion for large-scale problems arising from the discretisation of the incompressible Navier-Stokes equations