HAL-INSA Toulouse
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The N-link model for slender rods in a viscous fluid: well-posedness and convergence to classical elastohydrodynamics equations
No full textFlexible fibers at the microscopic scale, such as flagella and cilia, play essential roles in biological and synthetic systems. The dynamics of these slender filaments in viscous flows involve intricate interactions between their mechanical properties and hydrodynamic drag. In this paper, considering a 1D, planar, inextensible Euler-Bernoulli rod in a viscous fluid modeled by Resistive Force Theory, we establish the existence and uniqueness of solutions for the -link model, a mechanical model, designed to approximate the continuous filament with rigid segments. Then, we prove the convergence of the -link model's solutions towards the solutions to classical elastohydrodynamics equations of a flexible slender rod. This provides an existence result for the limit model, comparable to those by Mori and Ohm [Nonlinearity, 2023], in a different functional context and with different methods. Due to its mechanical foundation, the discrete system satisfies an energy dissipation law, which serves as one of the main ingredients in our proofs. Our results provide mathematical validation for the discretization strategy that consists in approximating a continuous filament by the mechanical -link model, which does not correspond to a classical approximation of the underlying PDE
Totally Real Points in the Mandelbrot Set
No full textThe {\em postcritically finite} parameters in the Mandelbrot set are special algebraic integers for which has finite orbit under the polynomial . Recently, Noytaptim and Petsche proved that the only totally real parameters that are postcritically finite are , and . In this note, we study another distinguished algebraic subset of , the {\em parabolic} parameters. A parameter is parabolic provided that possesses a parabolic cycle. We show that the only totally real parameters that are parabolic are , , and
Numerical modeling and experimental study of self-propagating flame fronts in Al/CuO thermite reactions
No full textInternational audienceNanothermites are promising energetic materials as their high-temperature reaction driven by the oxidation of a metallic fuel associated with the reduction of an oxidizer, can exhibit extremely fast burning rates, exceeding hundreds of m s -1 . In addition, by modifying reactant size, stoichiometry and compaction conditions, reaction properties (temperature, intermediate reactions, by-products) and combustion rates can be tailored, making it possible to customize combustion properties for each application. Unfortunately, in spite of three decades of research in the field of thermites, there is no predictive physical models able to provide design guidelines to experimentalists. The reason of this is that the complex multiphasic physics governing thermite combustion, where combustion gases interact with burning particles, is still poorly understood and documented, while being the key step to depict the dynamics of the flame front. The purpose of this work is to propose a first one-dimensional (1D) model that describes the dynamics of the reaction front propagation in Al/CuO powdered thermite considering the reacting flow combined with heat transfer, chemistry and fluid flow. CuO was chosen as it is the widest used metallic oxidizer, that decomposes below the flame temperature, leading to a gas phase driven reaction. Separate mass, momentum and energy transport equations for the three phases, namely Al, CuO particles and gas mixture, are written in the frame of an Euler-Euler approach for multiphase reactive flows. These equations are coupled by modeled interphase transfer terms. The theoretical formulation and numerical methods are detailed. After validating the model with experimental case studies -specifically, the combustion of Al/CuO powder in open glass tubes -numerical experiments are performed to demonstrate the utility of the code in (i) analyzing the multiphase flow dynamics at the thermite flame front, and (ii) examining the critical powder characteristics that affect the burn rate
Integral points on elliptic curves with -invariant over
No full textWe consider elliptic curves defined by an equation of the form , where has coefficients in a perfect field of characteristic not or . By performing and -descent, we obtain, under suitable assumptions on the factorization of , bounds for the number of integral points on these curves. These bounds improve on a general result by Hindry and Silverman. When has degree at most , we give exact expressions for the number of integral points of small height in terms of certain subgroups of Picard groups of the -curves corresponding to the and -torsion of our curve. This allows us to recover explicit results by Bremner, and gives new insight into Pillai's equation
The Parabolic Mandelbrot Set
No full textThis revised version has 80 pages, 26 illustrationsWe solve the longstanding conjecture by Milnor (1993) concerning the connectedness locus of the family of quadratic rational maps tangent to the identity at . We prove that this locus in homeomorphic to the Mandelbrot set and that the homeomorphism is unique, provided it identifies maps that are "hybridly" conjugate on their filled-in Julia set. Moreover this homeomorphism from to is nowhere H\"older on the boundary and so can not have even locally a quasi-conformal extension to complements
Development and validation of a 1D gas–liquid model for dissolved Mn(II) removal by oxidation process in a square bubble column
No full textInternational audienceModeling multiphase reactors requires an in-depth multidisciplinary analysis of various phenomena including the chemical kinetics, oxygen mass transfer, as well as the simulation of flows within these contactors. In this study, a 1D model of two-phase flow for Mn(II) removal from drinking water by aeration process is developed and validated. This model is based on the Eulerian description of two-phase gas-liquid flow with the comparison between a one-medium bubble size and a two-bubble class description to represent the bubble population in the heterogeneous flow regime. All the relevant chemical species are simulated by coupling hydrodynamics, gas-liquid mass transfer, and reaction kinetic. A pseudo-first-order model accounting for homogeneous and heterogeneous kinetics is considered for Mn(II) oxidation. The performance of the developed 1D model is compared and validated with experimental data. The 1D model was able to predict quantitatively Mn oxidation as a function of pH, initial Mn(II) and initial Mn(IV) concentrations
Ecodesign of 3D volumetric fiber-composite structures with topology optimization
No full textInternational audienceDesign for composite material additive manufacturing is governed by multiple process variables that can be computationally expensive to optimize. This is especially true when considering discrete variables, such as the material type to be used, which lead to a lot of possible solutions that have to be evaluated. Here, we propose a workflow for optimizing topology and fiber placement of 3D volumetric structures based on mechanical performance under multiple load cases and environmental impact. An eco-informed material selection from a set fibers and polymers is followed by a methodology to optimize the manufacturing setting. By performing these two steps sequentially, the number of input parameter sets to be tested is reduced in a combinatorial scale, along with the computational cost. The framework can be easily extended by adapting the analyses and holds significant promise for the design of additive manufactured sustainable structures.<br /
Discrete ply modelling of aeronautical intermediate-scale notched carbon fibre reinforced thermoplastic specimens subjected to multiaxial loading
No full textInternational audienceSeveral finite element models developed at the mesoscale level are available for predicting the strength andfailure progression of composite materials. However, this kind of damage models are commonly validatedby comparing with typical coupon-scale testing specimens under uniaxial loading, which are not fullyrepresentative of aeronautical structures subjected to complex multiaxial loads. In this work, the DiscretePly Model (DPM) is employed to reproduce intermediate-scale experimental tests carried out on carbonfibre reinforced thermoplastic samples, with a sharp central notch of 100 mm, tested in the VERTEX rigunder tension, shear, and combined tension and shear loading. The tests show early buckling (particularlyfor the shear and combined cases) and development of post-buckling for almost the entire loading. Thenumerical results obtained demonstrate that the strengths, the fluxes as a function of the applied strains,deformed shapes, buckling modes, crack propagations and failure patterns are predicted with reasonableaccuracy