Subgrid models preserving the symmetry group of the Navier–Stokes equations

In order to preserve the physical properties of the flow (scaling laws, conservation laws, …) during the simulation, a class of subgrid models respecting the symmetry group of the Navier–Stokes equations is built. The class is then refined such that models satisfy the second law of thermodynamics and are suited to take into account the inverse energy cascade. A simple model belonging to the class is tested and a better result than those provided by Smagorinsky and dynamic models is obtained. To cite this article: D. Razafindralandy, A. Hamdouni, C. R. Mecanique 333 (2005).     

Diffusion in isotropic and anisotropic porous systems: Three-dimensional calculations

Effective diffusion coefficients were calculated numerically for three-dimensional unit cells representative of different unconsolidated porous media. These numerical results were compared with the experimental results of Kim for packed beds of glass spheres, mica particles, and an artificial porous medium composed of mylar disks. These three-dimensional numerical results confirm that the porosity is the essential parameter for the determination of the effective diffusion coefficient in the case of unconsolidated isotropic systems. In the case of anisotropic systems, better agreement is obtained between numerical predictions and actual data when the unit cell is three-dimensional rather than twodimensional. This emphasizes the fact that three-dimensional unit cells feature more realistic geometrical properties which are needed to accurately describe anisotropic systems.     

Experimental dynamic analysis of elastic-plastic shear frames with secondary structures

Various experimental models are developed to study the influence of lightweight secondary structures on the dynamic response of elastic and elastic-plastic shear frames. Small-scale two-story model frames, with an elastic single-degree-of-freedom secondary structure attached, are considered for sinusoidal and random in-plane support excitation. Both elastic and elastic-plastic responses are recorded by varying the material properties of the columns of a distinguished floor. Parametric studies are performed by varying the secondary structure's fundamental frequency and damping. Experimental results are compared with those obtained by computational simulations. Experimental and numerical results are in excellent agreement, however they show that the material properties have to be determined very carefully. The statistic response of randomly excited elastic-plastic structures is not much affected by the motion of tuned secondary structures. However, this dynamic behavior is not true for elastic main structures. In this case, an optimally tuned secondary structure decreases the structural response up to 25%.     

Elastic instabilities for strain-stiffening rubber-like spherical and cylindrical thin shells under inflation

This paper is concerned with investigation of the effects of strain-stiffening on the classical limit point instability that is well-known to occur in the inflation of internally pressurized rubber-like spherical thin shells (balloons) and circular cylindrical thin tubes composed of incompressible isotropic non-linearly elastic materials. For a variety of specific strain-energy densities that give rise to strain-stiffening in the stress-stretch response, the inflation pressure versus stretch relations are given explicitly and the non-monotonic character of the inflation curves is examined. While such results are known for constitutive models that exhibit a gradual stiffening (e.g. exponential and power-law models), our primary focus is on materials that undergo severe strain-stiffening in the stress-stretch response. In particular, we consider two phenomenological constitutive models that reflect limiting chain extensibility at the molecular level. It is shown that for materials with sufficiently low extensibility no limit point instability occurs and so stable inflation is then predicted for such materials. Potential applications of the results to the biomechanics of soft tissues are indicated.     

Synthesis of voiced sounds using low-dimensional models of the vocal cords and time-varying subglottal pressure

The vocal cords play an important role on voice production. Air coming from the lungs is forced through the narrow space between the two vocal cords that are set in motion in a frequency that is governed by the tension of the attached muscles. The motion of the vocal cords changes the type of flow, that comes from the lungs, to pulses of air, and as the flow passes through the oral and nasal cavities, it is amplified and further modified until it is radiated from the mouth. This complex process can be modeled by a system of integral-differential equations. This paper considers two mechanical models previously used for explaining the dynamics of the vocal cords. It shows that the level of naturalness of the sound generated by these models is rather poor, and it proposes temporal variations of the parameters of the models to increase such level. Examples of synthetic vowels and diphthongs are given to assess the models. In general, the results show that, although the system of voice production is complex, we can achieve satisfactory results with relatively simple low-dimensional models, by suitable temporal variations of the aerodynamic parameters.     

A linearization technique for multi-species transport problems

We study a one-dimensional multi-species system of dispersive-advective contaminant transport equations coupled by nonlinear biological (kinetic reactions) and physical (adsorption) processes. To deal with the nonlinearities and the coupling, and to avoid additional computational costs, we propose a linearization technique based on first-order Taylor’s series expansions. A stabilized finite element in space, combined with an Euler implicit finite difference discretization in time, is used to approximate the dispersive-advective transport problem. Three computational tests are performed with different boundary conditions, retardation factors and kinetic parameters for a nonlinear reactive multi-species transport model. The proposed methodology is shown to be accurate and decrease computational costs in the numerical implementation of nonlinear reactive transport problems.     

Near-Wall Modification of an Explicit Algebraic Reynolds Stress Model Using Elliptic Blending

The elliptic blending approach is used in order to modify an Explicit Algebraic Reynolds Stress Model so as to reproduce the correct near wall behaviour of the turbulent stresses. The anisotropy stress tensor is expressed as a linear combination of tensor bases whose coefficients are sensitised to the non-local wall-blocking effect through the elliptic blending parameter γ. This parameter is obtained from a separate elliptic equation. The model does not use the distance from the wall thus it can be easily applied to complex geometries. It is validated against detailed DNS data for mean and turbulence quantities for the case of flow and heat transfer between parallel flat plates at three Reynolds numbers as well as against experimental data for the flow in a backward facing step at Re _H = 28,000. The comparison with DNS results or experiments is quite satisfactory and shows the validity of the approach.     

Nonstationarity and related measures for time‐dependent hartree–fock and multiconfigurational models

Based on an earlier article (Eberly and Singh, Phys. Rev. D 1973 , 7, 359) and related works on short‐time evolution, this article proposes a many‐electron formulation for the nonstationarity degree which can be assigned to quantum system at each time point. The key measure introduced, , is a nonstationarity index that can be thought of as an inverse nominal lifetime at each instance of time. The index is directly computed from the time derivative of one‐electron density matrix and is a size‐consistent quantity. In this article, the approach is developed for the time‐dependent Hartree–Fock (TDHF), single‐excitation (TDCIS), and time‐dependent full configuration interaction (TDFCI) models. As a rule, nonstationarity effects are more pronounced in correlated electron systems, and a joint analysis of and the multiconfigurational character of wave functions apparently provide a deeper insight into dynamical molecular processes. The performed calculations on small molecules in laser fields show a preference for the TDCIS model when comparing TDCIS and TDHF with the “exact” TDFCI model. © 2013 Wiley Periodicals, Inc.     

Collective risk models with dependence

In actuarial science, collective risk models, in which the aggregate claim amount of a portfolio is defined in terms of random sums, play a crucial role. In these models, it is common to assume that the number of claims and their amounts are independent, even if this might not always be the case. We consider collective risk models with different dependence structures. Due to the importance of such risk models in an actuarial setting, we first investigate a collective risk model with dependence involving the family of multivariate mixed Erlang distributions. Other models based on mixtures involving bivariate and multivariate copulas in a more general setting are then presented. These different structures allow to link the number of claims to each claim amount, and to quantify the aggregate claim loss. Then, we use Archimedean and hierarchical Archimedean copulas in collective risk models, to model the dependence between the claim number random variable and the claim amount random variables involved in the random sum. Such dependence structures allow us to derive a computational methodology for the assessment of the aggregate claim amount. While being very flexible, this methodology is easy to implement, and can easily fit more complicated hierarchical structures.