On Tollmien–Schlichting-like waves in streaky boundary layers

The linear stability of the boundary layer developing on a flat plate in the presence of finite-amplitude, steady and spanwise periodic streamwise streaks is investigated. The streak amplitudes considered here are below the threshold for onset of the inviscid inflectional instability of sinuous perturbations. It is found that, as the amplitude of the streaks is increased, the most unstable viscous waves evolve from two-dimensional Tollmien–Schlichting waves into three-dimensional varicose fundamental modes which compare well with early experimental findings. The analysis of the growth rates of these modes confirms the stabilising effect of the streaks on the viscous instability and that this stabilising effect increases with the streak amplitude. Varicose subharmonic modes are also found to be unstable but they have growth rates which typically are an order of magnitude lower than those of fundamental modes. The perturbation kinetic energy production associated with the spanwise shear of the streaky flow is found to play an essential role in the observed stabilisation. The possible relevance of the streak stabilising role for applications in boundary layer transition delay is discussed.     

Modified fixed point algorithm in fluid–structure interactionAccélération avec des conditions de transpiration d'un algorithme de point fixe en interaction fluide–structure

In this work, we address the numerical solution of some non-linear problems arising in the time discretization of fluid–structure interaction problems with fully implicit schemes. At each time step, we have to solve a highly non-linear coupled system, since the fluid domain depends on the unknown displacement of the structure. We propose a modified fixed-point algorithm which combines the Block-Gauss–Seidel iterations with a transpiration formulation. Numerical experiments show the great improvement in computing time with respect to the standard method. To cite this article: S. Deparis et al., C. R. Mecanique 331 (2003).     

Azimuthal instability in an impinging jet: adiabatic wall temperature distribution

The present work has been aimed at gaining some new insights into instability phenomena arising when an air jet impinges on a flat plate under certain conditions. At a critical Mach number, depending on the impingement distance, the jet loses its circumferential appearance with the formation of evenly equidistant azimuthal structures, whose number and location depend on the nozzle geometry and on the flow conditions. The instability is investigated in terms of pressure and adiabatic wall temperature; the latter is measured by means of an infrared scanning radiometer. Entrainment effects are found to play a key role in the priming and evolution of the instability.     

Newtonian drop in a Newtonian matrix subjected to large amplitude oscillatory shear flows

The dynamics of a single Newtonian drop immersed in a Newtonian matrix subjected to large-amplitude oscillatory shear flow is investigated. The ratio of the drop and matrix viscosity is above criticality, and thus break-up is absent under constant shear flow. At small forcing amplitudes the drop shape follows a regular oscillation. As the forcing amplitude increases, multipeaked oscillations of drop shape and orientation are observed. Experimental results are compared with predictions obtained with a phenomenological model. Model predictions are in qualitative good agreement with experimental data. The model suggests that the appearance of higher harmonics in the drop response is mainly due to flow nonaffinity.     

Identification of Material Damage Model Parameters: an Inverse Approach Using Digital Image Processing

A reliable prediction of ductile failure in metals is still a wide-open matter of research. Several models are available in the literature, ranging from empirical criteria, porosity-based models and continuum damage mechanics (CDM). One major issue is the accurate identification of parameters which describe material behavior. For some damage models, parameter identification is more or less straightforward, being possible to perform experiments for their evaluation. For the others, direct calibration from laboratory tests is not possible, so that the approach of inverse methods is required for a proper identification. In material model calibration, the inverse approach consists in a non-linear iterative fitting of a parameter-dependent load–displacement curve (coming from a FEM simulation) on the experimental specimen response. The test is usually a tensile test on a round-notched cylindrical bar. The present paper shows a novel inverse procedure aimed to estimate the material parameters of the Gurson–Tvergaard–Needleman (GTN) porosity-based plastic damage model by means of experimental data collected using image analysis. The use of digital image processing allows to substitute the load–displacement curve with other global quantities resulting from the measuring of specimen profile during loading. The advantage of this analysis is that more data are available for calibration thus allowing a greater level of confidence and accuracy in model parameter evaluation.     

Dislocation Patterns and Work-Hardening in Crystalline Plasticity

We propose a continuum model for the evolution of the total dislocation densities in fcc crystals, in the framework of rate-independent plasticity. The basic physical features which are taken into account are: (i) the role of dislocations in hardening; (ii) the relations between the slip velocity and dislocation mobility; (iii) the energetics of self and mutual interactions between dislocations; (iv) nonlocal effects in the interaction between dislocations. A set of reaction–diffusion equations is obtained, with mobilities depending on the slip velocities, which is able to describe the formation of dislocation walls and cells. To this effect, the results of numerical simulations in two special cases are presented. Mathematics Subject Classifications (2000) 74C15, 74C20.     

A High-Field EPR Study of the Accelerated Dynamics of the Amorphous Fraction of Semicrystalline Poly(dimethylsiloxane) at the Melting Point

The reorientation of a small paramagnetic tracer in poly(dimethylsiloxane) (PDMS) has been investigated by high-field electron paramagnetic resonance spectroscopy at a Larmor frequency of 285 GHz. The tracer is confined in the disordered phase of the semicrystalline PDMS. A sudden change of the rotational dynamics is observed close to the melting point (213 K) of the crystallites. This points to strong coupling between the crystalline and the disordered fractions of PDMS. Below the glass transition ( \(T_\mathrm{g} \sim 150 \mathrm{K}\) ), the tracer reorientation occurs via small angle jumps, with no apparent distribution of the correlation times. Above \(T_\mathrm{g}\) , a power-law distribution of correlation times is evidenced.     

Supertwistors and massive particles

In the (super)twistor formulation of massless (super)particle mechanics, the mass-shell constraint is replaced by a “spin-shell” constraint from which the spin content can be read off. We extend this formalism to massive (super)particles (with N$N$-extended space–time supersymmetry) in three and four space–time dimensions, explaining how the spin-shell constraints are related to spin, and we use it to prove equivalence of the massive N=1$N=1$ and BPS-saturated N=2$N=2$ superparticle actions. We also find the supertwistor form of the action for “spinning particles” with N$N$-extended worldline supersymmetry, massless in four dimensions and massive in three dimensions, and we show how this simplifies special features of the N=2$N=2$ case.     

On the Geometry of the Dirac Matter with the Fermionic Potentials and its Quantum Properties

We consider the torsional completion of gravity with electrodynamics for Dirac matter fields; we will see that these Dirac matter field equations will develop torsionally-induced non-linear interactions, which can be manipulated in order to be rearranged in the form of self-fermion potentials of a specific structure: we will see that this structure is formally equivalent to the one arising from quantum properties.     

X-ray single-crystal structural characterization of MgCr2O4, a post-spinel phase synthesized at 23 GPa and 1600 °C

The crystal structure and chemical composition of a crystal of MgCr₂O₄ post-spinel phase synthesized in the model system Mg₃Cr₂Si₃O₁₂–Mg₄Si₄O₁₂ at 23 GPa and 1600 °C have been investigated. Electron microprobe analysis confirmed the MgCr₂O₄ stochiometry of the studied phase. The compound was found to crystallize with the orthorhombic calcium-titanate (CaTi₂O₄) structure type, space group Bbmm, with lattice parameters a=9.468(1), b=9.670(1), c=2.845(1) Å, V=260.5(1) Å³, and Z=4. The structure was refined to R1=0.046 using 286 independent reflections. Magnesium was found to fully occupy the eightfold-coordinated A site (with a mean bond distance of 2.289 Å) and Cr the octahedral B site (mean: 1.986 Å). The successful synthesis of MgCr₂O₄ with (CaTi₂O₄)-type structure and its structural characterization demonstrate the stability of the new post-spinel phase. The absence of MgCr₂O₄ compounds with spinel structure coexisting with the post-spinel phase in the investigated run is discussed.