Search

This paper concerns the development of a new Cartesian grid / immersed boundary (IB) method for the computation of incompressible viscous flows in irregular geometries. In IB methods, the computational grid is not aligned with the irregular boundary, and of upmost importance for accuracy and stability is the discretization in cells which are “cut" by the boundary. In this paper, we present an IB method (the LS-STAG method) based on the Cartesian MAC method where the irregular boundary is represented by its level-set function. This implicit representation of the immersed boundary enables us to discretize efficiently the fluxes in the cut-cells by imposing the strict conservation of total kinetic energy at the discrete level. The accuracy and robustness of our method are assessed on benchmark flows.

In his 1983 paper [3], R. F. Gundy introduced a new functional related to the Littlewood-Paley theory, called the density of the area integral. In this paper, we prove that this functional (although highly non-linear) can be expressed as the principal value of an explicit singular integral. This result provides us with a new and precise connection between the density of the area integral and the theory of Calderón-Zygmund operators. It does not seem to be a consequence of the standard Calderón-Zygmund-Cotlar theory, because the sign of a harmonic function in the half-space fails to have, in some appropriate sense, boundary limits.

In a previous paper we proved that a necessary and sufficient condition for all martingales of a given filtration $(\mathscr{F}_t)$ to be continuous is that, for every stopping time $T$ and every $\mathscr{F}_T$-measurable random variable $X$, there exists a continuous local martingale $M$ with $M_T = X$ a.s. The aim of this paper is to study the following question: Can we choose $M \geq 0$ whenever $X \geq 0$? We also give a negative answer to Conjecture 7.1 of Harrison and Pliska.

In this paper we prove a convexity property of the relative entropy along entropic interpolations (solutions of the Schrödinger problem), and a regularity property of the entropic cost along the heat flow. Then we derive a dimensional EVI inequality and a contraction property for the entropic cost along the heat flow. As a consequence, we recover the equivalent results in the Wasserstein space, proved by Erbar, Kuwada and Sturm Résumé Dans cet article nous démontrons une propriété de convexité de l'entropie relative le long des interpolations entropiques (solutions duprobì eme de Schrödinger), et une propriété de régularité du coût entropique le long du flot de la chaleur. Ensuite, nous en déduisons une inégalité EVI dimensionnelle et une propriété de contraction pour le coût entropique le long du flot de la chaleur. En conséquence, nous retrouvons les résultatsrésultatséquivalents dans l'espace de Wasserstein, démontrés par Erbar, Kuwada et Sturm.

In this paper, we study an inverse scattering problem on Liouville surfaces having two asymptotically hyperbolic ends. The main property of Liouville surfaces consists in the complete separability of the Hamilton-Jacobi equations for the geodesic flow. An important related consequence is the fact that the stationary wave equation can be separated into a system of a radial and angular ODEs. The full scattering matrix at fixed energy associated to a scalar wave equation on asymptotically hyperbolic Liouville surfaces can be thus simplified by considering its restrictions onto the generalized harmonics corresponding to the angular separated ODE. The resulting partial scattering matrices consists in a countable set of $2 \times 2$ matrices whose coefficients are the so called transmission and reflection coefficients. It is shown that the reflection coefficients are nothing but generalized Weyl-Titchmarsh functions for the radial ODE in which the generalized angular momentum is seen as the spectral parameter. Using the Complex Angular Momentum method and recent results on 1D inverse problem from generalized Weyl-Titchmarsh functions, we show that the knowledge of the reflection operators at a fixed non zero energy is enough to determine uniquely the metric of the asymptotically hyperbolic Liouville surface under consideration., 39 pp

cote interne IRCAM: Helie08a; None / None; International audience; This paper proposes to solve and simulate various Kirchhoff models of nonlinear strings using Volterra series. Two nonlinearities are studied: the string tension is supposed to depend either on the global elongation of the string (first model), or on the local strain located at $x$ (second, and more precise, model). The boundary conditions are simple Dirichlet homogeneous ones or general dynamic conditions (allowing the string to be connected to any system; typically a bridge). For each model, a Volterra series is used to represent the displacement as a functional of excitation forces. The Volterra kernels are solved using a modal decomposition: the first kernel of the series yields the standard modes of the linearized problem while the next kernels introduce the nonlinear dynamics. As a last step, systematic identification of the kernels lead to a structure composed of linear filters, sums, and products which are well-suited to the sound synthesis, using standard signal processing techniques. The nonlinear dynamic introduced through this simulation is significant and perceptible in sound results for sufficiently large excitations.

cote interne IRCAM: Helie08b; None / None; National audience; In this paper, the Volterra series decomposition of a class of quadratic, time invariant single-input finite dimensional systems is analyzed. The kernels are given by a recursive sequence of linear PDEs in the time domain, and an equivalent algebraic recursion in the Laplace domain. This is used to prove the convergence of the Volterra series to a (possibly weak) trajectory of the system, to provide a practicable value for the radius of convergence of the input in L^oo(R+) and to compute a guaranteed error bound in L^oo(R+) for the truncated series. The result is then extended to MIMO systems. A numerical simulation is performed on an academic SISO example, to illustrate how easily the truncated Volterra series can be implemented.

This paper deals with a new Hilbert- type inequality by introducing a parameter and the Beta function. As applications, the equivalent form, the reversions and some particular results are considered. All the theorems provide some new estimates on this type of inequalities.

In this paper we use the twistor theory in order to build non standard complex structures (with a meaning which we define) on products of 4-manifolds with the sphere of dimension two. To that end, we enumerate the set of complex surfaces whose twistor space is topologically trivial. Among these surfaces, we determine those which admit a spin structure or an anti-selfdual riemannian metric.

21 pages; Let $\wh K$ be the field of formal Laurent series in $X^{-1}$ over the finite field $k$, and let $A$ be the ring of polynomials in $X$ over $k$. One of the main results of the paper is to give a particularly nice coding of the geodesic flow on the quotient of the Bruhat-Tits tree $\TT$ of ${\rm PGL}_2(\wh K)$ by ${\rm PGL}_2(A)$, by using the continued fraction expansion of the endpoints of the geodesic lines in $\TT$ (the space of ends of $\TT$ identifies with $\PP_1(\wh K)$). This allows in particular to prove in a dynamical way the invariance of the Haar measure by the Artin map.

International audience; In this paper, a closed-form solution minimizing the Godard or constant modulus (CM) cost function under the practical conditions of finite SNR and finite equalizer length is derived. While previous work has been reported by Zeng et al., IEEE Trans. Information Theory, 1998, to establish the link between the constant modulus and Wiener receivers, we show that under the Gaussian approximation of intersymbol interference at the output of the equalizer, the CM finite-length receiver is equivalent to the nonblind MMSE equalizer up to a complex gain factor. Some simulation results are provided to support the Gaussian approximation assumption

The extended finite element method (X-FEM) was used with success in the past few years for linear elastic fracture mechanics (LEFM). In the case of elastic–plastic fracture mechanics (EPFM), this method cannot be used without adequate asymptotic solutions to enrich the shape function basis. In this paper, we propose to use the well-known Hutchinson–Rice–Rosengren (HRR) fields to represent the singularities in EPFM. The analysis we are presenting is done in the context of confined plasticity, and shall be used to predict fatigue crack growth without remeshing. A Fourier analysis of the HRR fields is done in order to extract a proper elastic–plastic enrichment basis. Several strategies of enrichment, based on the Fourier analysis results, are compared and a six-enrichment-functions basis is proposed. This new tip enrichment basis is coupled with a Newton like iteration scheme and a radial return method for plastic flow. Numerical comparisons with and without unloading of fracture parameters are made with classical finite element results and show good agreements.

This paper deals with the numerical simulation of acoustic wave propagation in axisymmetric waveguides with varying cross-section using a Webster-Lokshin model. Splitting the pipe into pieces on which the model coefficients are nearly constant, analytical solutions are derived in the Laplace domain, enabling for the realization of the propagation by concatenating scattering matrices of transfer functions (§2). These functions involve standard differential and delay operators, as well as pseudo-differential operators of diffusive type, induced by both the viscothermal losses and the curvature. These operators are explicitly decomposed thanks to an asymptotic expansion, and the diffusive ones may be defined and classified (§3). Various equivalent diffusive realizations may be proposed, that are deeply linked to choices of cuts in the complex analysis of the transfer functions. Then, finite order approximations are given for their simulation (§4).

National audience; In this paper we study the asymptotic limit of the solutions of Landau-Lifschitz equations as the exchange coefficient goes to zero. In order to perform this limit in regular spaces, we have to take into account the singularity induced by a boundary layer term.; On étudie le comportement asymptotique des solutions des équations de Landau-Lifschitz lorsque le coefficient d'échange tend vers zéro. Une couche limite se forme alors au bord du matériau, et on décrit cette couche limite.

International audience; We propose in this paper a three-dimensional cohesive zone model, coupling surfacic damage, Coulomb friction and unilateral contact. This model is devoted to the fracture of solids and to the debonding of interfaces. The thermodynamical formulation of the model is given. We focus our attention on the jumps of solution, which could appear with such softening surfacic models. A dynamical formulation allows to overcome these problems of nonsmooth solutions. A particular mathematical and numerical framework is used to solve dynamical problems submitted to unilateral constraints. The ability of the associated numerical tool is underlined on a buckling-driven fracture of a square plate.; Nous présentons dans ce papier un modèle de zone cohésive tridimensionnel couplant endommagement surfacique, frottement de Coulomb et contact unilatéral. Ce modèle permet la simulation de la fissuration des solides ainsi que celle des interfaces qui les lient. La formulation thermodynamique de ce modèle est donnée. Une attention particulière est portée aux problèmes de solutions à sauts inhérents aux modèles de comportement surfacique adoucissant : une formulation dynamique permet de s'affranchir de cette difficulté. Un cadre mathématique et numérique adéquat est utilisé pour la résolution des problèmes dynamiques en présence de contraintes unilatérales. La pertinence de l'outil numérique associé est soulignée sur un exemple de fissuration par flambement d'une plaque.

cote interne IRCAM: Helie99b; National audience; In this paper, we deal with the inversion of a physical model of a trumpet, i.e. how should the model be controled in order to obtain a given sound. It is shown that this problem is ill-posed since an infinity of inputs can produce the same sound. Then, a criterion based on the slowness of the musician's gestures compared to the sound signal evolution is used: this leads to a physically pertinent solution. Finally, we present some simulation results.

In this paper we consider the nonlinear Dirichlet problem: A(u)=T in Ω0 on ∂Ω, where the right hand side belongs to a “large” Sobolev space W1.q(Ω), 1 < q < 2, for some q, and A is a strongly monotone operator acting from W1.20(Ω) into W1.2(Ω), defined by: A(υ)=-div (a(x,▽υ)). If the differential operator A is linear, the existence of solutions in a “large” Sobolev space has been obtained by N. G. Meyers (see [8]), using a duality method and a regularity theorem. In the case where in the previous differential problem the right hand side is zero, but with non-zero boundary conditions, the existence of solutions can be found in [7]. Other nonlinear boundary value problems with weak solutions in “large” Sobolev spaces are studied in [2] and [1], where the right hand side is a bounded measure.

This paper presents an extension of a model presented by the same authors in the previous CFA [1]. The model allows fast computations of the acoustical impulse-response of the problem of the radiation of ultrasonic pulses by realistic transducers, their scattering by immersed targets and their reception. In the previous version, the model was restricted to the case of small targets centered on the transducer axis. Here, it is shown that a more general formula can be derived allowing the computation of the echo-responses from begets not necessarely centered on axis which can be of arbitrary size. It is shown that the present model may be considered as an extension to the transient case of the well-known Freedman's model which derived from a CW theory. Basically, the idea is to restrict the computation to the contributions arising from the only parts of the target where interferences are constructive

A waveguide finite element theory is applied to the propagation pheneomena in rails. In the first part of the paper the waveguide finite element computation technique is briefly presented. The propagative wavenumbers and corresponding modes of a rail are computed as function of the exctation frequency. The results of finite element computation are compared with those obtained by the simple Euler-Bernoulli beam theory for the flexion. The sound radiation and the distribution of the energy transmitted through the cross-section by the computed propagative modes are analysed. The present analysis gives the valuable informations on the participation of different propagative modes to vibro-acustical response of rails

The signals with an instantaneous frequency following an hyperbolic low are common in many fields of the signal processing, and particularly in the study of biologicals SONARS. In this paper we describe an harmonic analysis adapted to this kind of signals. The problem of stationnarity of stochastic processes will be adressed within the frame of the previous harmonic analysis. This allow us to define a power spectral density for second-order stationnary processes using the Bochner theorem. Some simulation results are presented showing the interest of the adapted harmonic analysis

The aim of this paper is to investigate the interest of a perturbation method to describe a screen effect in a room. The screen is described as an elastic plate and can vibrate. First, the sound pressure in the room is computed by using a boundary element method. Then, a perturbation method is developed taking advantage of a small parameter related to the ratio of the densities of the fluid and the plate. Numerical simulations are presented to examine the convergence of the method

This paper presents a mathematical model for the calculating of sound fields in inclosed areas, even where the internal dimensions are disproportionate: particular reference is made to the diffusive effect of walls. The model is based on a classical ray tracing method. However, not all of the reflected energy necessarily follows the specular path; some of it can be scattered, forming, as it were new sources. The coefficient of diffusion associated with the sample of wall involved in the reflection regulates the sharing of the reflected energy. In order to determine this diffusion coefficient, we have developed a method that allows the measuring of the diffusion of a sample of wall. We have measured the sound propagation curves in several factory halls and compared the results to the previously calculated values. The high degree of correlation between the theoretical and experimental results validates the model and our approach of the coefficient of diffusion

The measurement of the velocity of propagation of ultrasonic pulse in dispersive media gives a quantity which physical meaning is ambiguous. In this paper we simulate a dispersive medium using the Kramers-Kronig relationship which expresses the causality of a linear system. We develope an appropriate signal processing such as Hilbert transform and cross-correlation to measure the time of flight of an ultrasonic impulse propagating in such a medium. This allows to deduce from this simulation the physical significance of the two informations given by two methods. Then these two methods are applied to several categories of graphites with dispersif character. Thus the differences between the measured velocities by Hilbert transform and cross-correlation are correlated to several microstructural properties of the material such as grain size, porosity and to thermal elaboration treatement

The purpose of the present paper is to measure the transfer matrix of acoustical, reciprocal elements of wave guides by using two microphones and several terminal tubes, by mean of the least mean square method. We apply this method for the case of a lateral chimney. The results are satisfactory, but the accuracy is not large enough to determine the anti symmetrical field in the chimney

The aim of this paper is to better understand the correspondence between the classical plane waves propagating in each layer of an anisotropic periodically multilayered medium and the Floquet waves. The last are linear combinations of the classical plane waves. Their wave number is obtained from the eigenvalues of the transfer matrix of one cell of the medium. We have defined a Floquet polarisation which varies with its position in the periodically multilayered medium. This allows us to define a Floquet waves displacement by analogy with the one of the classical plan waves, and to verify the equality of the two displacements at any interface separating two layers. The periodically multilayered medium is then equivalent to a dummy material, and one can draw dispersion curves. In low frequencies range, when the relation between the Floquet wave numbers and the frequency is linear, the multilayered medium can be homogenised; the Floquet polarisation at different interfaces tends to a limit which is the polarisation of the classical plane wave in the homogenised medium

In a previous paper we have shown that, using the differential equations of the trajectories of Jacobi constant J in the restricted problem, we could demonstrate the existence of periodic solutions of the first and the second kind, symmetric and asymmetric, and quasi-periodic solutions of the second kind, for sufficiently small eccentricities, in the neighbourhood of one of the primaries. Some of the intermediate equations have to be corrected, but the conclusions remain unchanged. Those conclusions are now compared to the known existence demonstrations. Finally we show that Uno's demonstration of non-existence of asymmetric periodic solutions of the second kind does not apply to the cases we are studying., Sergysels Roland, Sergysels-Lamy Anne. Solutions périodiques et quasi-périodiques du problème restreint (II). In: Bulletin de la Classe des sciences, tome 60, 1974. pp. 436-443.

In this paper, we propose a purely macroscopic theory of the complex refractive index based on dielectric models defined by constitutive equations which are linear differential equations in the electric field, the polarization vector and their time derivatives up to the orders m and n respectively. Meixner's thermodynamics restrictions impose 0 ≤ n — m ≤ 2 and a set of inequalities on the constitutive coefficients. In the special case m = 2, n — 4, the expression of the complex refractive index shows the existence of two optical resonances. In the general case, it seems that the number of resonance frequencies is the greater integer contained in n/2, Boulanger Philippe, Mayné Georges. Modèles intégro-différentiels en électrodynamique linéaire des continus. In: Bulletin de la Classe des sciences, tome 64, 1978. pp. 153-168.

This paper deals with predictable representation and time changed processes. Let $(M^i)_{i\geq 0}$ be a sequence of independent local martingales. Suppose that each $M^i$ has the property of predictable representation with respect to its natural filtration. Suppose also that $(A^i)_{i\geq 1}$ is a sequence of continuous, increasing, $(\mathscr{F}^{M^0}_t)$ adapted processes. We study sufficient conditions in order that $M = M^0 + \sum M^i_{A^i}$ be a local martingale and $M$ have the property of predictable representation with respect to the filtration $(\mathscr{F}^{M^0}_t) \vee (\mathscr{F}^{M^1_{A^1}}_t \vee (\mathscr{F}^{M^2_{A^2}}_t \vee \cdots$. Such problems arise in the modeling of a security market with continuous trading [1].

We consider in this paper the linear stability problem of an isentropic, one-dimensional flow of a perfect fluid. In particular, we investigate the stability of the simple rarefaction and compression wave. We prove the instability of the compression wave when dissipative effects are disregarded. We follow the method formerly established by one of us and Prigogine on the stability of non equilibrium states (Physica 46, 344, 1970). The example treated, belongs to the class of time dependent stability problems., Glansdorff Paul, Banaï Nozar. Sur la stabilité des ondes simples de compression et de raréfaction. In: Bulletin de la Classe des sciences, tome 56, 1970. pp. 1352-1366.