A deformation theory of strain gradient crystal plasticity that accounts for geometrically necessary dislocations

We propose a deformation theory of strain gradient crystal plasticity that accounts for the density of geometrically necessary dislocations by including, as an independent kinematic variable, Nye's dislocation density tensor [1953. Acta Metallurgica 1, 153-162]. This is accomplished in the same fashion as proposed by Gurtin and co-workers (see, for instance, Gurtin and Needleman [2005. J. Mech. Phys. Solids 53, 1-31]) in the context of a flow theory of crystal plasticity, by introducing the so-called defect energy. Moreover, in order to better describe the strengthening accompanied by diminishing size, we propose that the classical part of the plastic potential may be dependent on both the plastic slip vector and its gradient; for single crystals, this also makes it easier to deal with the “higher-order” boundary conditions. We develop both the kinematic formulation and its static dual and apply the theory to the simple shear of a constrained strip (example already exploited in Shu et al. [2001. J. Mech. Phys. Solids 49, 1361-1395], Bittencourt et al. [2003. J. Mech. Phys. Solids 51, 281-310], Niordson and Hutchinson [2003. Euro J. Mech. Phys. Solids 22, 771-778], Evers et al. [2004. J. Mech. Phys. Solids 52, 2379-2401], and Anand et al. [2005. J. Mech. Phys. Solids 53, 1789-1826]) to investigate what sort of behaviour the new model predicts. The availability of the total potential energy functional and its static dual allows us to easily solve this simple boundary value problem by resorting to the Ritz method.     

Rigid and Compact Binuclear Bis-hydrated Gd-complexes as High Relaxivity MRI Agents

The first binuclear Gd-complex of the 12-membered pyridine-based polyaminocarboxylate macrocyclic ligand PCTA was synthesized by C−C connection of the pyridine units through two different synthetic procedures. A dimeric AAZTA-ligand was also synthesized with the aim to compare the relaxometric results or the two ditopic Gd-complexes. Thus, the ¹H relaxometric study on [Gd₂PCTA₂(H₂O)₄] and on [Gd₂AAZTA₂(H₂O)₄]²⁻ highlighted the remarkable rigidity and compactness of the two binuclear complexes, which results in molar relaxivities (per Gd), at 1.5 T and 298 K of ca. 12–12.6 mM⁻¹ s⁻¹ with an increase of ca. 80 % at 1.5 T and 298 K (+70 % at 310 K) with respect to the corresponding mononuclear complexes.     

Flavonoids in Lemon and Grapefruit IntegroPectin**

Following the analysis of terpenes present in new lemon and grapefruit “IntegroPectin” pectins obtained via the hydrodynamic cavitation of industrial lemon and grapefruit processing waste, the HPLC-MS analysis of flavonoid and other phenolic compounds reveals the presence of eriocitrin, naringin, hesperidin and kaempferol typical of the respective citrus fruits. The pectic fibers rich in rhamnogalacturonan-I regions act as chemical sponges adsorbing and concentrating at their outer surface highly bioactive citrus flavonoids and terpenes. These findings, together with the unique molecular structure of these new whole citrus pectins, provide preliminary insight into the broad-scope biological activity of these new biomaterials. Numerous new biomedical applications are anticipated, including likely use in the prevention and treatment of microbial infections and neurodegenerative disease.     

Plant Secondary Metabolites: An Opportunity for Circular Economy

Moving toward a more sustainable development, a pivotal role is played by circular economy and a smarter waste management. Industrial wastes from plants offer a wide spectrum of possibilities for their valorization, still being enriched in high added-value molecules, such as secondary metabolites (SMs). The current review provides an overview of the most common SM classes (chemical structures, classification, biological activities) present in different plant waste/by-products and their potential use in various fields. A bibliographic survey was carried out, taking into account 99 research articles (from 2006 to 2020), summarizing all the information about waste type, its plant source, industrial sector of provenience, contained SMs, reported bioactivities, and proposals for its valorization. This survey highlighted that a great deal of the current publications are focused on the exploitation of plant wastes in human healthcare and food (including cosmetic, pharmaceutical, nutraceutical and food additives). However, as summarized in this review, plant SMs also possess an enormous potential for further uses. Accordingly, an increasing number of investigations on neglected plant matrices and their use in areas such as veterinary science or agriculture are expected, considering also the need to implement “greener” practices in the latter sector.     

Adsorption of Crystal Violet Dye Using Activated Carbon of Lemon Wood and Activated Carbon/Fe3O4 Magnetic Nanocomposite from Aqueous Solutions: A Kinetic,Equilibrium and Thermodynamic Study

Activated carbon prepared from lemon (Citrus limon) wood (ACL) and ACL/Fe₃O₄ magnetic nanocomposite were effectively used to remove the cationic dye of crystal violet (CV) from aqueous solutions. The results showed that Fe₃O₄ nanoparticles were successfully placed in the structure of ACL and the produced nanocomposites showed superior magnetic properties. It was found that pH was the most effective parameter in the CV dye adsorption and pH of 9 gave the maximum adsorption efficiency of 93.5% and 98.3% for ACL and ACL/Fe₃O₄, respectively. The Dubinin–Radushkevich (D-R) and Langmuir models were selected to investigate the CV dye adsorption equilibrium behavior for ACL and ACL/Fe₃O₄, respectively. A maximum adsorption capacity of 23.6 and 35.3 mg/g was obtained for ACL and ACL/Fe₃O₄, respectively indicating superior adsorption capacity of Fe₃O₄ nanoparticles. The kinetic data of the adsorption process followed the pseudo-second order (PSO) kinetic model, indicating that chemical mechanisms may have an effect on the CV dye adsorption. The negative values obtained for Gibb’s free energy parameter (−20 < ΔG < 0 kJ/mol) showed that the adsorption process using both types of the adsorbents was physical. Moreover, the CV dye adsorption enthalpy (ΔH) values of −45.4 for ACL and −56.9 kJ/mol for ACL/Fe₃O₄ were obtained indicating that the adsorption process was exothermic. Overall, ACL and ACL/Fe₃O₄ magnetic nanocomposites provide a novel and effective type of adsorbents to remove CV dye from the aqueous solutions.     

ZnS nanoparticles capped with watermelon rind extract and their potential application in dye degradation

We report fabrication of stable ZnS nanoparticles (NPs) using a green chemistry concept with watermelon rind extract as capping and stabilizing agent. The cubic structure of the NPs was evidenced by X-ray powder diffraction analysis and electron diffraction studies. Dynamic light scattering and high-resolution transmission electron microscopy studies revealed that the average size of the ZnS NPs was <12 nm. The bandgap of the ZnS nanocrystals was found to be 3.42 eV using ultraviolet–visible (UV–Vis) spectroscopy studies. The energy-dispersive X-ray spectrum of the fabricated ZnS NPs confirmed the elemental Zn and S signals without peaks from any impurities. The biomolecular capping of the ZnS NPs was analyzed using Fourier-transform infrared spectroscopy. An illustrative stabilization mechanism for the ZnS NPs is given using citrulline, a major phytochemical in watermelon rind extract. The obtained ZnS NPs showed good photocatalytic activity towards methylene blue dye degradation.     

Optimal waiting time bounds for some flux-saturated diffusion equations

We consider the Cauchy problem for two prototypes of flux-saturated diffusion equations. In arbitrary space dimension, we give an optimal condition on the growth of the initial datum which discriminates between occurrence or nonoccurrence of a waiting time phenomenon. We also prove optimal upper bounds on the waiting time. Our argument is based on the introduction of suitable families of subsolutions and on a comparison result for a general class of flux-saturated diffusion equations.     

The category of Colombeau algebras

Since the beginning of Colombeau’s the theory of algebras of generalized functions, the role of its characteristic polynomial growth versus a more general condition has been explored. Recently, we introduced the notion of asymptotic gauge (AG), and we used it to study Colombeau AG-algebras. This construction concurrently generalizes many different algebras used in Colombeau’s theory and, at the same time, allows for more general growth scales. In this paper, we study the categorical properties of Colombeau AG-algebras with respect to the choice of the AG. The main aim of the paper is to study suitable functors to relate differential equations framed in algebras having different growth scales.