Superdiffusion in nearly stratified flows

In classical work, Mathéron and the Marsilly showed that superdiffusive scaling of mean-square displacements occurs in transport diffusion for stratified flows with steady simple shear layers and long-range spatial correlations. More recently the authors have calculated a formula for the non-Gaussian large-scale long-time renormalized Green function for these problems. Here the scaling laws and renormalized Green functions for diffusion in nearly stratified flows are studied; in such flows the simple shear layer with long-range correlations is perturbed by incompressible flows with short-range correlations. Here it is established that these flows belong to the same universality class as the simple shear layers, with a renormalized Green function with a similar structure but reflecting homogenization by the transverse displacements. The tools in the analysis involve a modification of homogenization theory and also rigorous diagrammatic perturbation theory.     

Mathematical models with exact renormalization for turbulent transport,II: Fractal interfaces,non-Gaussian statistics and the sweeping effect

This paper continues the study of a model for turbulent transport with an exact renormalization theory which has recently been proposed and developed by the authors. Three important topics are analyzed with complete mathematical rigor for this model: (1) Renormalized higher order statistics of a passively advected scalar such as the pair distance distribution and the fractal dimension of interfaces, (2) the effect of non-Gaussian turbulent velocity statistics on renormalization theory, (3) the sweeping effect of additional large scale mean velocities. A special emphasis is placed on renormalization theory in the vicinity of the value of the analogue of the Kolmogorov-spectrum in the model. In the authors' earlier paper, it was established that the Kolmogorov value is at a phase transition boundary in the exact renormalization theory. It is found here that the qualitative model, despite its simplicity contains, in the vicinity of the Kolmogorov value, a remarkable amount of the qualitative behavior of turbulent transport which has been uncovered in recent experiments and proposed in phenomenological theories. In particular, the Richardson 4/3-law for pair dispersion and interfaces with fractal dimension defect of 2/3 occur in the model rigorously as limits when the Kolmogorov spectrum is approached as a limit from one side of the phase transition boundary; alternative corrections to the Richardson law with the same form as those proposed heuristically in the recent literature and interfaces with fractal dimension defect 1/3, occur in the model when the Kolmogorov spectrum is approached from the other side of the phase transition. It is very interesting that fractal dimension defects of roughly the value either 1/3 or 2/3 for level sets and interfaces of passive scalars have been ubiquitous in recent turbulence experiments. As regards non-Gaussian the asymptotic normality of normalized integrals (B.56) corresponding to compactly supported blobs with mean zero. The proof of this latter fact is done in the same way as Step 2, Proposition B.3, using the fact that the corresponding random processes have finite domain of dependence. This concludes the proof of Proposition B.4.Research partially supported by NSF-DMS-9005799, ARO-DAAL03-89-K-0039 and AFOSR 90-0090Research partially supported by grants NSF-DMS-90-01805, ARO-DAAL03-89-K-0013, and ONR-N00014-89-J-1014     

Direct structural identification of polysaccharides from red algae by FTIR microspectrometry II: Identification of the constituents ofGracilaria verrucosa

The use of the infrared microspectrometry analytical technique as a new tool for the identification of the polysaccharides contained in the red algaeGracilaria verrucosa has demonstrated that in addition to agar spectra, features of the other coexisting constituents can also be obtained. Indeed, the infrared spectra recorded previously, all exhibit two important bands at about 1645 and 1530cm^–1. These two bands were not present in the infrared spectra of the extracted agars and they are expected to be due to the amide I and amide II protein vibrations. In order to confirm this supposition, we have applied some enzymatic treatments, firstly on the whole algae and secondly on the ground algae (the algae has been previously depigmented and then dehydrated). Agarase, xylanase and cellulase were successively carried out on the algae. The last resulting spectrum, i.e. the spectrum obtained from the fraction which has undergone the three treatments, has been identified to be characteristic of proteins. This spectrum contained, both the amide I and II vibrations and in addition, weak absorption at 1230 cm^–1 due probably to the amide III, was observed. Additional weak bands in the 1400–1300 cm^–1 due to the different skeletal modes of the proteins were also present in this spectrum.The infrared spectra also revealed that the use of the enzymatic treatments on the ground algae is more efficient than when it is carried out on the whole algae.     

Flame retardant activity of SiO2-coated regenerated cellulose fibres

An alternative route to lower the flammability of viscose fibres is presented. Instead of adding a flame retardant to the viscose dope chemically, we have grown a layer of silica (SiO₂) on the surface of a regenerated cellulose fibre via a sol-gel process. One set of samples was used as-received, while the other was pre-treated in an 18% NaOH solution, giving a rough, etched surface to the fibre. The different surface morphology of both fibre types triggered a different growth of silica layers. On an untreated fibre, silica formed a 300-400 nm thick surface layer containing a high density of cracks and holes. Conversely, on a NaOH pre-treated fibre, the silica layer intruded into fibre interior, adhered more tightly to the fibre structure and formed an almost defect-free, thin (100 nm) layer on the outer fibre surface. This type of silica layer increased the temperature at which the fibre started to decompose by 20 °C. It also hindered significantly the flow of oxygen to the generated volatiles during the thermal decomposition, and increased the temperature of glowing combustion of the residual char; the temperature of the corresponding exothermic peaks increased by ca. 20 °C and 40 °C. In contrast, the thermal effects of silica coatings that grew on an untreated fibre were much smaller.     

Nonlinear instability of elementary stratified flows at large Richardson number

Elementary stably stratified flows with linear instability at all large Richardson numbers have been introduced recently by the authors [J. Fluid Mech. 376, 319-350 (1998)]. These elementary stratified flows have spatially constant but time varying gradients for velocity and density. Here the nonlinear stability of such flows in two space dimensions is studied through a combination of numerical simulations and theory. The elementary flows that are linearly unstable at large Richardson numbers are purely vortical flows; here it is established that from random initial data, linearized instability spontaneously generates local shears on buoyancy time scales near a specific angle of inclination that nonlinearly saturates into localized regions of strong mixing with density overturning resembling Kelvin-Helmholtz instability. It is also established here that the phase of these unstable waves does not satisfy the dispersion relation of linear gravity waves. The vortical flows are one family of stably stratified flows with uniform shear layers at the other extreme and elementary stably stratified flows with a mixture of vorticity and strain exhibiting behavior between these two extremes. The concept of effective shear is introduced for these general elementary flows; for each large Richardson number there is a critical effective shear with strong nonlinear instability, density overturning, and mixing for elementary flows with effective shear below this critical value. The analysis is facilitated by rewriting the equations for nonlinear perturbations in vorticity-stream form in a mean Lagrangian reference frame. (c) 2000 American Institute of Physics.     

Rationalizing Aggregate Structures with Orbital Contributions to the Exchange-Repulsion Energy**

It is shown that repulsive interactions have a crucial influence on the structure of prototypical non-covalently bonded systems. To explain this, we propose a molecular orbital-based model for the exchange-repulsion contribution to the total interaction energy. As a central result, our model shows that energetically preferred aggregate structures frequently exhibit reduced exchange repulsion, which can be deduced from the nodal structure of certain occupied orbitals. This is used to explain key features of the intermolecular potentials of the Cl₂-He, benzene-benzene, and benzene-hexafluorobenzene aggregates, which are not correctly reproduced by commonly applied electrostatic models.     

Mathematical test criteria for filtering complex systems: Plentiful observations

An important emerging scientific issue is the real time filtering through observations of noisy turbulent signals for complex systems as well as the statistical accuracy of spatio-temporal discretizations for such systems. These issues are addressed here in detail for the setting with plentiful observations for a scalar field through explicit mathematical test criteria utilizing a recent theory [A.J. Majda, M.J. Grote, Explicit off-line criteria for stable accurate time filtering of strongly unstable spatially extended systems, Proceedings of the National Academy of Sciences 104 (4) (2007) 1124–1129]. For plentiful observations, the number of observations equals the number of mesh points. These test criteria involve much simpler decoupled complex scalar filtering test problems with explicit formulas and elementary numerical experiments which are developed here as guidelines for filter performance. The theory includes information criteria to avoid filter divergence with large model errors, asymptotic Kalman gain, filter stability, and accurate filtering with small ensemble size as well as rigorous results delineating the role of various turbulent spectra for filtering under mesh refinement. These guidelines are also applied to discrete approximations for filtering the stochastically forced dissipative advection equation with very turbulent and noisy signals with either an equipartition of energy or ?5/3 turbulent spectrum with infrequent observations as severe test problems. The theory and companion simulations demonstrate accurate statistical filtering in this context with implicit schemes with large time step with very small ensemble sizes and even with unstable explicit schemes under appropriate circumstances provided the filtering strategies are guided by the off-line theoretical criteria. The surprising failure of other strongly stable filtering strategies is also explained through these off-line criteria.