General criterion to discern between coherent and incoherent synthesis of broadband coherent anti‐Stokes Raman spectra

Recently, the ordinary qualitative criterion on how to distinguish between coherent and incoherent convolutions of broadband coherent anti‐Stokes Raman (CARS) signals generated by degenerate pump lasers has been revised in view of a quantitative analysis. The revision has established that incoherent CARS approach can be justified as unitary limit of the function ] erfc(Γ/σ₁)/σ₁, where Γ and σ₁ are respectively the spectral widths of the Raman line and the degenerate pump lasers. The result was, however, limited to nonoverlapping Raman lines. In this work, the extension to a more common situation of closely spaced Raman transitions is considered. For large overlap between adjacent Raman lines, the new analysis suggests significant deviations from the previous result. Weak line mixing is also taken into consideration. Nonetheless, all types of deviations are characterized by a common tendency toward the incoherent limit. Copyright © 2007 John Wiley & Sons, Ltd.     

Transition wave in a supported heavy beam

We consider a heavy, uniform, elastic beam rested on periodically distributed supports as a simplified model of a bridge. The supports are subjected to a partial destruction propagating as a failure wave along the beam. Three related models are examined and compared: (a) a uniform elastic beam on a distributed elastic foundation, (b) an elastic beam in which the mass is concentrated at a discrete set of points corresponding to the discrete set of the elastic supports and (c) a uniform elastic beam on a set of discrete elastic supports. Stiffness of the support is assumed to drop when the stress reaches a critical value. In the formulation, it is also assumed that, at the moment of the support damage, the value of the ‘added mass’, which reflects the dynamic response of the support, is dropped too. Strong similarities in the behavior of the continuous and discrete-continuous models are detected. Three speed regimes, subsonic, intersonic and supersonic, where the failure wave is or is not accompanied by elastic waves excited by the moving jump in the support stiffness, are considered and related characteristic speeds are determined. With respect to these continuous and discrete-continuous models, the conditions are found for the failure wave to exist, to propagate uniformly or to accelerate. It is also found that such beam-related transition wave can propagate steadily only at the intersonic speeds. It is remarkable that the steady-state speed appears to decrease as the jump of the stiffness increases.     

Nanoparticle debonding strength: A comprehensive study on interfacial effects

The most appealing feature of nanofilled polymers is the perspective of obtaining surprisingly high mechanical properties at low nanofiller volume fractions. The knowledge of nanostructure–property relationships is however essential for the design of these materials.In the present work, a model for the critical hydrostatic tension related to nanoparticle debonding is presented. The model accounts for some important issues inherently related to the nanoscale with particular reference to surface elastic stresses on the nanoparticle periphery and the emergence of a zone of altered chemistry surrounding the nanoparticle. The analytical solution suggests that the range of nanoparticle radii where interfacial effects do affect the solution is limited to the nanometer scale. In more details, considering the interphase and surface elastic properties used in the analysis, it has been found that for stiff particles with radius between 10 nm and 100 nm (silica, alumina and other metal oxide nanoparticles) the prominent role is played by the interphase elastic properties. Surface elastic constants were found to have, instead, only a negligible effect.     

Reciprocity in elastic media with rheology

The classic reciprocity theorem of Betti (Nuovo Cimento 2(VII–VIII):69–97, 1872) for perfectly elasto-static media has been extended to the dynamic fields by Graffi (Ann. Mat. Pura Appl. IV(18):173–200, 1939) for isotropic media with variable density. In this note the theorem is extended to a wide class of media with rheology.     

Phantom Chain Simulations of Realistically Sized Polymer‐Based Nanocomposites

Summary: Phantom chain MC simulations have been performed for realistically sized systems of polymer chains filled with solid nanoparticles. The results of the simulations and simple theoretical considerations are used to rationalize a number of parameters relevant to the characterization of these systems. Even when the average number of nanoparticles in contact with a chain is very small (much less than unity), the nanoparticles are nodes of highly interconnected transient networks bridged by the polymer chains.

     

Synthesis of Tailored Perfluoro Unsaturated Monomers for Potential Applications in Proton Exchange Membrane Preparation

The aim of the present work is the synthesis and characterization of new perfluorinated monomers bearing, similarly to Nafion^®, acidic groups for proton transport for potential and future applications in proton exchange membrane (PEM) fuel cells. To this end, we focused our attention on the synthesis of various molecules with (i) sufficient volatility to be used in vacuum polymerization techniques (e.g., PECVD)), (ii) sulfonic, phosphonic, or carboxylic acid functionalities for proton transport capacity of the resulting membrane, (iii) both aliphatic and aromatic perfluorinated tags to diversify the membrane polarity with respect to Nafion^®, and (iv) a double bond to facilitate the polymerization under vacuum giving a preferential way for the chain growth of the polymer. A retrosynthetic approach persuaded us to attempt three main synthetic strategies: (a) organometallic Heck-type cross-coupling, (b) nucleophilic displacement, and (c) Wittig–Horner reaction (carbanion approach). Preliminary results on the plasma deposition of a polymeric film are also presented. The variation of plasma conditions allowed us to point out that the film prepared in the mildest settings (20 W) shows the maximum monomer retention in its structure. In this condition, plasma polymerization likely occurs mainly by rupture of the π bond in the monomer molecule.     

One, no one, and one hundred thousand crack propagation laws: A generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth

Barenblatt and Botvina with elegant dimensional analysis arguments have elucidated that Paris’ power-law is a weak form of scaling, so that the Paris’ parameters C and m should not be taken as material constants. On the contrary, they are expected to depend on all the dimensionless parameters of the problem, and are really “constants” only within some specific ranges of all these. In the present paper, the dimensional analysis approach by Barenblatt and Botvina is generalized to explore the functional dependencies of m and C on more dimensionless parameters than the original Barenblatt and Botvina, and experimental results are interpreted for a wider range of materials including both metals and concrete. In particular, we find that the size-scale dependencies of m and C and the resulting correlation between C and m are quite different for metals and for quasi-brittle materials, as it is already suggested from the fact the fatigue crack propagation processes lead to m=2-5 in metals and m=10-50 in quasi-brittle materials. Therefore, according to the concepts of complete and incomplete self-similarities, the experimentally observed breakdowns of the classical Paris’ law are discussed and interpreted within a unified theoretical framework. Finally, we show that most attempts to address the deviations from the Paris’ law or the empirical correlations between the constants can be explained with this approach. We also suggest that “incomplete similarity” corresponds to the difficulties encountered so far by the “damage tolerant” approach which, after nearly 50 years since the introduction of Paris’ law, is still not a reliable calculation of damage, as Paris himself admits in a recent review.     

Asymptotic interface models in magneto-electro-thermo-elastic composites

We study the quasi-static behavior of a magneto-electro-thermo-elastic composite constituted by a thin magneto-electro-thermo-elastic plate-like layer inserted between two generic magneto-electro-thermo-elastic bodies by means of an asymptotic analysis. After defining a small dimensionless parameter \(\varepsilon\), which will tend to zero, we characterize two different limit models and their associated limit problems, the so-called weak and strong magneto-electro-thermo-elastic interface models, respectively. Moreover, we identify the non classical magneto-electro-thermo-elastic transmission conditions at the interface between the two three-dimensional bodies and we prove a weak convergence result.