Some extremum theorems for the elastoplastic boundary value problem in the presence of large displacements

Summary The incremental boundary value problem for elastoplastic work-hardening continua, is discussed in the presence of large displacements but small strains, and allowing for distributed dislocations.Associated flow laws are assumed, as is the occurrence of interaction between yielding modes in singular points of the yield surface.Four extremum theorems are proved which reduce the problem to the optimization, under linear constraints, of convex quadratic forms (of a non linear form for the third theorem).Finally some results are specialized to small displacements and perfectly plastic (non hardening) cases.

---

Sommario Si discute della soluzione incrementale del problema elastoplastico con incrudimento nel campo dei grandi spostamenti (ma con piccole deformazioni intrinseche), ed in presenza di distorsioni distribuite.Si assumono leggi costitutive del tipo associato, ammettendo la possibilità di interazione tra i modi plastici in corrispondenza dei punti singolari della superficie di snervamento.Si dimostrano quattro proprietà di minimo della soluzione; esse riconducono il problema alla ottimizzazione di funzionali convessi (quadratici tranne che nel caso del terzo teorema) vincolata da equazioni e diseguaglianze lineari.Si specializzano infine alcuni risultati al caso dei piccoli spostamenti e della elastoplasticità senza incrudimento.

---

---

This study forms part of a research programme supported by the National (Italian) Research Council (C.N.R., Gruppo Plasticità).     

On a supplementary conservation law for the energy equation in a rigid heat conductor

We consider a rigid heat conductor with specified constitutive equations and show that the internal energy equation may be written in the form of a symmetric and conservative hyperbolic system of first order quasi-linear equations for which the Cauchy problem is well-posed. Moreover, such a system is useful to study shocks. Several particular cases are examined.     

On the crucial importance of the pH for the formation and self-stabilization of protein microgels and strands

Stable suspensions of protein microgels are formed by heating salt-free β-lactoglobulin solutions at concentrations up to about C = 50 g·L(-1) if the pH is set within a narrow range between 5.75 and 6.1. The internal protein concentration of these spherical particles is about 150 g·L(-1) and the average hydrodynamic radius decreases with increasing pH from 200 to 75 nm. The formation of the microgels leads to an increase of the pH, which is a necessary condition to obtain stable suspensions. The spontaneous increase of the pH during microgel formation leads to an increase of their surface charge density and inhibits secondary aggregation. This self-stabilization mechanism is not sufficient if the initial pH is below 5.75 in which case secondary aggregation leads to precipitation. Microgels are no longer formed above a critical initial pH, but instead short, curved protein strands are obtained with a hydrodynamic radius of about 15-20 nm.     

Spectroscopic, morphological, and mechanistic investigation of the solvent-promoted aggregation of porphyrins modified in meso-positions by glucosylated steroids

Solvent-driven aggregation of a series of porphyrin derivatives was studied by UV/Vis and circular dichroism spectroscopy. The porphyrins are characterised by the presence in the meso positions of steroidal moieties further conjugated with glucosyl groups. The presence of these groups makes the investigated macrocycles amphiphilic and soluble in aqueous solvent, namely, dimethyl acetamide/water. Aggregation of the macrocycles is triggered by a change in bulk solvent composition leading to formation of large architectures that express supramolecular chirality, steered by the presence of the stereogenic centres on the periphery of the macrocycles. The aggregation behaviour and chiroptical features of the aggregates are strongly dependent on the number of moieties decorating the periphery of the porphyrin framework. In particular, experimental evidence indicates that the structure of the steroid linker dictates the overall chirality of the supramolecular architectures. Moreover, the porphyrin concentration strongly affects the aggregation mechanism and the CD intensities of the spectra. Notably, AFM investigations reveal strong differences in aggregate morphology that are dependent on the nature of the appended functional groups, and closely in line with the changes in aggregation mechanism. The suprastructures formed at lower concentration show a network of long fibrous structures spanning over tens of micrometres, whereas the aggregates formed at higher concentration have smaller rod-shaped structures that can be recognised as the result of coalescence of smaller globular structures. The fully steroid substituted derivative forms globular structures over the whole concentration range explored. Finally, a rationale for the aggregation phenomena was given by semiempirical calculations at the PM6 level.     

Determination of phospholipids in milk samples by means of hydrophilic interaction liquid chromatography coupled to evaporative light scattering and mass spectrometry detection

The combined use of the state-of-the-art hybrid mass spectrometers together with high efficient liquid chromatography could surely be a useful tool for such a challenging task, as phospholipids (PLs) analysis. In this research, we used hydrophilic interaction liquid chromatography (150 mm×2.1 mm I.D., 2.7 μm d.p. partially porous column) to achieve the separation of major PLs classes in cow's and donkey's milk samples. Solid-phase extraction (SPE) was performed in order to pre-concentrate minor PLs from non polar lipids (triacylglycerols) and the recovery for the extraction method was assayed on a milk sample, fortified with 5 μg/mL of SM pure standard, and analyzed in triplicate. A value of 89.99% was calculated, with a coefficient of variation (CV%) of 1.93. A 70-min long stepwise gradient of water/acetonitrile afforded baseline separation of PLs classes, at 50 μL/min flow rate. Accurate detection by an ion trap-time of flight (IT-TOF) mass spectrometer (in both positive and negative ionization mode) allowed to fully characterize the distinctive phospholipid profile and fatty acid composition of cow's and donkey's milk, the latter being analyzed for the first time. Evaporative light scattering detection was further employed to attain the quantitative evaluation of major PLs classes identified, by the external calibration method using reference material solutions in the 5-200 μg/mL concentration range. Major difference between the two analyzed samples consisted in the total PLs amount, which in cow's milk was determined as over 20-fold higher than the donkey's.     

Chemical composition and in vitro activity of plant extracts from Ferula communis and Dittrichia viscosa against postharvest fungi

F. communis and D. viscosa are perennial Mediterranean weeds that have been used for different therapeutic purposes in traditional pharmacopeia. Plant extracts were obtained from air dried D. viscosa young shoots (DvA) and F. communis aerial part (FcA) and roots (FcR) with n-hexane. The chemical compositions of the extracts were analyzed by HPLC-DAD, LC-MS (ESI) and LC-Q-TOF techniques. Two sesquiterpene lactones (inuviscolide, tomentosin) and three sesquiterpene acids (costic acid, hydroxycostic acid, ilicic acid) were identified from the D. viscosa extract, while in F. communis extracts three daucane sesquiterpenes (acetoxyferutinin, oxojaeskeanadioyl anisate, fertidin) and one coumarin (ferulenol) derivates were found. Biological activities of plant extracts were studied in in vitro experiments on the colonies and conidia of Botryotinia fuckeliana, Penicillium digitatum, P. expansum, Monilinia laxa, M. fructigena and Aspergillus spp. Extracts showed varying degree of antifungal activities on colony growth and conidia germination. The extract from FcA showed the least effect, while DvA extract had the strongest fungitoxic effects. FcR extract presented a fungitoxic effect on the colony growth, but it was not able to inhibit the conidia germination. These distinctions can be attributed to the differences in chemical composition of plant extracts.     

Generation of Chaotic Beats in a Modified Chua's Circuit Part I: Dynamic Behaviour

This paper and the companion one [Cafagna, D. and Grassi, G., Nonlinear Dynamics, this issue] present the new phenomenon of chaotic beats in non-autonomous Chua's circuit, driven by two sinusoidal inputs with slightly different frequencies. In particular, in this paper the behaviour of the proposed circuit is analyzed both in time-domain and state-space, confirming the chaotic nature of the phenomenon and the effectiveness of the design.     

Modeling the Adsorption of CO on Small Pt,Fe and Co Clusters for the Fischer–Tropsch Synthesis

The adsorption of CO on Fe, Pt and Co clusters was modeled by the DFT approach using the B3LYP and the BPW91 functionals together with the LANL2DZ and the 6-31G(d) basis set. These calculations show that although CO adsorbs more strongly on Pt than on either Fe or Co, the dissociation energy on Fe and on Co is lower than the corresponding dissociation energy on Pt. Therefore, the activation energy for dissociation is not determined by the adsorption energy. Additionaly, the CO bond distances also do not show any correlation to the adsorption energy.