Stability,buckling, and postbuckling of elastic structures

Summary This paper is the continuation of a research on the stability and postbuckling behaviour of elastic structures; in the first Part [n. 4, Vol. X, 1975 of this Journal], the potential energy of elastic tridimensional bodies has been defined in a suitable configuration space, and its properties of regularity have been studied. According to the program given in the previous Paper, we examine now the potential energy functional for some monodimensional and bidimensional structural models. Then the Part II of this research is developed so that the Liapunov stability of the equilibrium configuration of continuous elastic structures is analyzed by means of suitable energy criteria.

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Sommario Questo lavoro costituisce il proseguimento di uno studio sulle stabilità e comportamento postcritico delle strutture elastiche; nel precedente lavoro, pubblicato sul n. 4, vol. X, 1975 di questa rivista, è stato esaminato il problema della definizione dell'energia potenziale di un corpo elastico tridimensionale in un opportuno spazio funzionale delle configurazioni, e sono state esaminate le proprietà di regolarità di questo funzionale. Proseguendo il programma formulato nel lavoro precedente, viene ora innanzitutto completato lo studio del funzionale energia potenziale con riferimento a modelli strutturali mono e bidimensionali. Viene poi sviluppata la Parte II e cioè l'analisi della stabilità secondo Liapunov di una configurazione di equilibrio attraverso opportune formulazioni dei criteri dell'energia.

     

Post processing of solution and flux for the nodal mimetic finite difference method

We develop and analyze a post processing technique for the family of low‐order mimetic discretizations based on vertex unknowns for the numerical treatment of diffusion problems on unstructured polygonal and polyhedral meshes. The post processing works in two steps. First, from the nodal degrees of freedom, we reconstruct an elemental‐based vector field that approximates the gradient of the exact solution. Second, we solve a local problem for each mesh vertex associated with a scheme degree of freedom to determine a post processed normal flux that is conservative and divergence preserving. Theoretical results and numerical experiments for two‐dimensional (2D) and 3D benchmark problems show optimal convergence rates. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 336–363, 2015     

Indifference pricing for CRRA utilities

We study utility indifference pricing of claim streams with intertemporal consumption and constant relative risk aversion utilities. We derive explicit formulas for the derivatives of the utility indifference price with respect to claims and wealth. The elegant structure of these formulas is a reflection of surprising algebraic identities for the derivatives of the optimal consumption stream. Namely, the partial derivative of the optimal consumption stream with respect to the endowment is always a projection. Furthermore, it is an orthogonal projection with respect to a natural “economic inner product”. These algebraic identities generate cancellations between the terms entering derivatives of the indifference price and allow us to prove sharp global bounds for the indifference price that become exact when the claims to wealth ratio is large and risk aversion is between one and two. For general risk aversion, we show that, in the large claims to wealth ratio limit, the asymptotic expansion of the indifference price is given in terms of fractional powers of the wealth, depending on risk aversion. When risk aversion is equal to one, the fractional power depends on the underlying claim.     

Improved Heinz inequalities via the Jensen functional

By virtue of convexity of Heinz means, in this paper we derive several refinements of Heinz norm inequalities with the help of the Jensen functional and its properties. In addition, we discuss another approach to Heinz operator means which is more convenient for obtaining the corresponding operator inequalities for positive invertible operators.     

On the barometric formula inside the Earth

The assumptions leading to the barometric formula are discussed, with remarks on the influence of temperature, gravitational field, Earth rotation, and non-equilibrium conditions. A generalization of the barometric formula for negative heights, e.g., for pressure inside shafts and deep tunnels, is also presented, and some surprising conclusions obtained. Related historical aspects are also discussed.     

Biodiesel Production from Integration Between Reaction and Separation System: Reactive Distillation Process

Biodiesel is a clean burning fuel derived from a renewable feedstock such as vegetable oil or animal fat. It is biodegradable, non-inflammable, non-toxic, and produces lesser carbon monoxide, sulfur dioxide, and unburned hydrocarbons than petroleum-based fuel. The purpose of the present work is to present an efficient process using reactive distillation columns applied to biodiesel production. Reactive distillation is the simultaneous implementation of reaction and separation within a single unit of column. Nowadays, it is appropriately called “Intensified Process”. This combined operation is especially suited for the chemical reaction limited by equilibrium constraints, since one or more of the products of the reaction are continuously separated from the reactants. This work presents the biodiesel production from soybean oil and bioethanol by reactive distillation. Different variables affect the conventional biodiesel production process such as: catalyst concentration, reaction temperature, level of agitation, ethanol/soybean oil molar ratio, reaction time, and raw material type. In this study, the experimental design was used to optimize the following process variables: the catalyst concentration (from 0.5 wt.% to 1.5 wt.%), the ethanol/soybean oil molar ratio (from 3:1 to 9:1). The reactive column reflux rate was 83 ml/min, and the reaction time was 6 min.     

Reversible dispersion of single-walled carbon nanotubes based on a CO2-responsive dispersant

A CO(2)-responsive dispersant, N,N-dimethyl-N'-(pyren-1-ylmethyl) acetimidamidinium (PyAH(+)), which bears both a pyrene moiety and an amidinium cation, has been successfully synthesized. Through strong π-π interaction between the pyrene moiety and single-walled carbon nanotubes (SWNTs), we have demonstrated that PyAH(+) can be modified onto SWNT surfaces to promote the dispersion of SWNTs in water. Furthermore, taking advantage of gas triggered interconversions between the amidinium cation and amidine, reversible control on the solubility of SWNTs has been achieved simply through alternated bubbling of CO(2) and Ar. This work has demonstrated a new method for controlled dispersion and aggregation of SWNTs, and it may contribute to the development of gas responsive carbon materials.     

Cholesterol slows down the lateral mobility of an oxidized phospholipid in a supported lipid bilayer

We investigated the mobility and phase-partitioning of the fluorescent oxidized phospholipid analogue 1-palmitoyl-2-glutaroyl-sn-glycero-3-phospho-N-Alexa647-ethanolamine (PGPE-Alexa647) in supported lipid bilayers. Compared to the conventional phospholipid dihexadecanoylphosphoethanolamine (DHPE)-Bodipy we found consistently higher diffusion constants. The effect became dramatic when immobile obstacles were inserted into the bilayer, which essentially blocked the diffusion of DHPE-Bodipy but hardly influenced the movements of PGPE-Alexa647. In a supported lipid bilayer made of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), the differences in probe mobility leveled off with increasing cholesterol content. Using coarse-grained molecular dynamics simulations, we could ascribe this effect to increased interactions between the oxidized phospholipid and the membrane matrix, concomitant with a translation in the headgroup position of the oxidized phospholipid: at zero cholesterol content, its headgroup is shifted to the outside of the DOPC headgroup region, whereas increasing cholesterol concentrations pulls the headgroup into the bilayer plane.