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Derivation of nonlinear shell models combining shear and flexure: application to biological membranes
No full textInternational audienceBiological membranes are often idealized as incompressible elastic surfaces whose strain energy only depends on their mean curvature and pos-sibly on their shear. We show that this type of model can be derived using a formal asymptotic method by considering biological membranes to be thin, strongly anisotropic, elastic, locally homogeneous bodies
A Gradient Flow Approach to Quantization of Measures
No full text45 pages.International audienceIn this paper we study a gradient flow approach to the problem of quantization of measures in one dimension. By embedding our problem in , we find a continuous version of it that corresponds to the limit as the number of particles tends to infinity. Under some suitable regularity assumptions on the density, we prove uniform stability and quantitative convergence result for the discrete and continuous dynamics
Displacement Reconstructions in Ultrasound Elastography
No full textInternational audienceWe consider the reconstruction of internal elastic displacements from ultrasound measurements , which finds applications in the medical imaging modality called elastography. By appropriate interferometry and windowed Fourier transforms of the ultrasound measurements, we propose a reconstruction procedure of the vectorial structure of spatially varying elastic displacements in biological tissues. This provides a modeling and generalization of scalar reconstruction procedures routinely used in elastography. The proposed algorithm is justified using a single scattering approximation and local asymptotic analysis. Its validity is assessed by numerical simulations
A Luenberger observer for reaction-diffusion models with front position data
No full textInternational audienceWe propose a Luenberger observer for reaction-diffusion models with propagating front features, and for data associated with the location of the front over time. Such models are considered in various application fields, such as electrophysiology, wild-land fire propagation and tumor growth modeling. Drawing our inspiration from image processing methods, we start by proposing an observer for the eikonal-curvature equation that can be derived from the reaction-diffusion model by an asymptotic expansion. We then carry over this observer to the underlying reaction-diffusion equation by an "inverse asymptotic analysis", and we show that the associated correction in the dynamics has a stabilizing effect for the linearized estimation error. We also discuss the extension to joint state-parameter estimation by using the earlier-proposed ROUKF strategy. We then illustrate and assess our proposed observer method with test problems pertaining to electrophysiology modeling, including with a realistic model of cardiac atria. Our numerical trials show that state estimation is directly very effective with the proposed Luenberger observer, while specific strategies are needed to accurately perform parameter estimation – as is usual with Kalman filtering used in a nonlinear setting – and we demonstrate two such successful strategies
Limiting Data Exposure in Multi-Label Classification Processes
No full textInternational audienceAdministrative services such social care, tax reduction, and many others using complex decision processes, request individuals to provide large amounts of private data items, in order to calibrate their proposal to the specific situation of the applicant. This data is subsequently processed and stored by the organization. However, all the requested information is not needed to reach the same decision. We have recently proposed an approach, termed Minimum Exposure, to reduce the quantity of information provided by the users, in order to protect her privacy, reduce processing costs for the organization, and financial lost in the case of a data breach. In this paper, we address the case of decision making processes based on sets of classifiers, typically multi-label classifiers. We propose a practical implementation using state of the art multi-label classifiers, and analyze the effectiveness of our solution on several real multi-label data sets
In situ determination of collagen fibrils size via absolute measurements of second harmonic generation signals
No full textInternational audienceWe correlated SHG and Electron Microscopies to calibrate SHG signals as a function of collagen fibril diameter, down to 30 nm. We observed a fourth power dependence, in agreement with analytical and numerical calculations. We applied this calibration to abnormal fibrils in the Descemet’s membrane of intact unfixed rat corneas
Ultrafast Dynamics of Carboxy-Hemoglobin: Two-Dimensional Infrared Spectroscopy Experiments and Simulations
No full textInternational audienceThis Letter presents a comparison between experimental and simulated 2D mid-infrared spectra of carboxy-hemoglobin in the spectral region of the carbon monoxide stretching mode. The simulations rely on a fluctuating potential energy surface that includes both the effect of heme and the protein surroundings computed from molecular dynamics simulations. A very good agreement between theory and experiment is obtained with no adjustable parameters. The simulations show that the effect of the distal histidine through the hydrogen bond is strong and is directly responsible for the slow decay of the frequency–frequency correlation function on a 10 ps time scale. This study confirms that fluctuations in carboxy-hemoglobin are more inhomogeneous than those in the more frequently studied carboxy-myoglobin. The comparison between simulations and experiments brings valuable information on the complex relation between protein structure and spectral diffusion
Laser beam self-symmetrization in air in the multifilamentation regime
No full textInternational audienceWe show experimental and numerical evidence of spontaneous self-symmetrization of focused laser beams experiencing multi-filamentation in air. The symmetrization effect is observed as the multiple filaments generated prior to focus approach the focal volume. This phenomenon is attributed to the nonlinear interactions amongst the different parts of the beam mediated by the optical Kerr effect, which leads to a symmetric redistribution of the wave vectors even when the beam consists of a bundle of many filaments
Influence of bending resistance on the dynamics of a spherical capsule in shear flow
No full textInternational audienceThe objective of the paper is to study the effect of wall bending resistance on the motion of an initially spherical capsule freely suspended in shear flow. We consider a capsule with a given thickness made of a three–dimensional homogeneous elastic material. A numerical method is used to model the fluid–structure interactions cou- pling a boundary integral method for the fluids with a shell finite element method for the capsule envelope. For a given wall material, the capsule deformability strongly decreases when the wall bending resistance increases. But, if one expresses the same results as a function of the two–dimensional mechanical properties of the mid–surface, which is how the capsule wall is modeled in the thin–shell model, the capsule deformed shape is identical to the one predicted for a capsule devoid of bending resistance. The bending rigidity is found to have a negligible influence on the overall deformation of an initially spherical capsule, which therefore depends only on the elastic stretching of the mid–surface. Still, the bending resistance of the wall must be accounted for to model the buckling phenomenon, which is observed locally at low flow strength. We show that the wrinkle wavelength is only a function of the wall bending resistance and provide the correlation law. Such results can then be used to infer values of the bending modulus and wall thickness from experiments on spherical capsules in simple shear flow