Bad behavior of Godunov mixed methods for strongly anisotropic advection–dispersion equations

We study the performance of Godunov mixed methods, which combine a mixed-hybrid finite element solver and a Godunov-like shock-capturing solver, for the numerical treatment of the advection–dispersion equation with strong anisotropic tensor coefficients. It turns out that a mesh locking phenomenon may cause ill-conditioning and reduce the accuracy of the numerical approximation especially on coarse meshes. This problem may be partially alleviated by substituting the mixed-hybrid finite element solver used in the discretization of the dispersive (diffusive) term with a linear Galerkin finite element solver, which does not display such a strong ill conditioning. To illustrate the different mechanisms that come into play, we investigate the spectral properties of such numerical discretizations when applied to a strongly anisotropic diffusive term on a small regular mesh. A thorough comparison of the stiffness matrix eigenvalues reveals that the accuracy loss of the Godunov mixed method is a structural feature of the mixed-hybrid method. In fact, the varied response of the two methods is due to the different way the smallest and largest eigenvalues of the dispersion (diffusion) tensor influence the diagonal and off-diagonal terms of the final stiffness matrix. One and two dimensional test cases support our findings.     

A global existence and uniqueness result for a class of hyperbolic operators

In this paper a global existence and uniqueness theorem for the Cauchy problem related to the class of hyperbolic operators with double characteristics \(P=D^2_{t} - D^2_{x_1} - (t+ \lambda - \alpha (x_1))^2 D^2_{x_2},\) depending on the parameter \(\lambda \) in the half-space \(\Omega = \mathbb {R}^2 \times ]0, + \infty [\) is proved. In the first part of the paper, a priori estimates in Sobolev spaces \(W^{r,2}\), with \(r\) negative, have been established. Then, the regularity is studied by using these spaces and by constructing a Green’s function in the half-plane for the operator of the waves.     

Nanofibrillated cellulose: surface modification and potential applications

Interest in nanofibrillated cellulose has been increasing exponentially because of its relatively ease of preparation in high yield, high specific surface area, high strength and stiffness, low weight and biodegradability etc. This bio-based nanomaterial has been used mainly in nanocomposites due to its outstanding reinforcing potential. Solvent casting, melt mixing, in situ polymerization and electrospinning are important techniques for the fabrication of nanofibrillated cellulose-based nanocomposites. Due to hydrophilic character along with inherent tendency to form strong network held through hydrogen-bonding, nanofibrillated cellulose cannot uniformly be dispersed in most non-polar polymer matrices. Therefore, surface modification based on polymer grafting, coupling agents, acetylation and cationic modification was used in order to improve compatibility and homogeneous dispersion within polymer matrices. Nanofibrillated cellulose opens the way towards intense and promising research with expanding area of potential applications, including nanocomposite materials, paper and paperboard additive, biomedical applications and as adsorbent.     

FTIR imaging investigation in MIR and in an enlarged MIR-NIR spectral range

The study of polished cross sections is a well-assessed and practical method to investigate the stratigraphy of paintings and multilayer polychromies on works of art, in general. Analyses on cross sections allow us to characterize, at once, all the layers in the stratigraphy, giving information about the artists technique, the number of layers and their composition and sometimes about the conservation history of the artefact. In this paper, the application of an imaging detector focal plane array (FPA) coupled to an infrared (IR) microscope has been studied, focusing on the characteristics and potential of the different working methodologies (attenuated total reflectance (ATR) and total reflection). FPA detector coupled with ATR crystal can “localize” IR information coming from a 30 × 30μm sample area, in a 64 × 64 dot matrix detector. In particular, an innovative analysis methodology has been tested for the total reflectance measurements in order to obtain maximum information with single measurements. Micro-infrared total reflection measurements have been carried out in an extended IR range (from 1,000 to 5,266 cm⁻¹) exploiting the broad spectral response of mercury cadmium telluride detector in order to include overtones and combination bands from near-infrared spectral range without any modification of the standard mid-infrared micro-FT instrumentation. The potentialities of this new approach have been successfully transferred in the imaging/mapping investigations with a minimal tuning of the apparatus. Results obtained on a polished cross section coming from a modern painting and on a micro-sample of a wood polychromy from an undated historic polyptic are shown for demonstration.     

A study of the microstructural and diffusion properties of poly(vinyl alcohol) cryogels containing surfactant supramolecular aggregates

Surfactant-containing poly(vinyl alcohol) (PVA) cryogels have been prepared by drying and reswelling hydrogel patches, previously obtained by the freeze/thaw procedure, in decyltrimethylammonium bromide (C10TAB) aqueous solutions. The microstructural and diffusive properties of the resulting material have been characterized by a combined experimental strategy. Gravimetric measurements show that the cryogel maximum swelling is not affected by the surfactant. The surfactant concentration within the cryogel, measured by ion chromatography, is the same as that in the rehydrating surfactant solution. Electron paramagnetic resonance (EPR) spin-probe and small-angle neutron scattering (SANS) measurements show that surfactant self-aggregation in the gel is similar to that in water, occurring at the same critical concentration and resulting in the formation of micellar aggregates whose structure is not affected by the cryogel polymeric scaffold. However, both the micelle intradiffusion coefficients, measured by PGSE-NMR, and the spin-probe correlation times, measured by EPR, indicate that dynamic processes in the hydrogel are much slower than in bulk water. A quantitative analysis of these results suggests that the cryogel polymer-poor domains, in which surfactant molecules are solubilized, have an average dimension of approximately 0.1 microm. Interestingly the experimental data also show that the polymer-poor phase contains more polymer than expected, suggesting that the spinodal decomposition, which occurs during the freezing step of cryogel preparation, is not complete or prevented by ice formation.