Sui Coefficienti di Fattoriali

Sunto. Si pongono in relazione le trasformazioni delle potenze in fattoriali, e viceversa, con proprietà di operatori funzionali lineari dipendenti dal simbolo di derivazione.     

Agronomic,metabolomic and lipidomic characterisation of Sicilian Origanum vulgare (L.) ecotypes

Although Origanum vulgare (L.) has been deeply analysed at phytochemical level, poor knowledge is available regarding non-volatile compounds such as lipids. The aim of this work was to characterise five wild Sicilian Origanum ecotypes from an agronomic, metabolomic and lipidomic perspective. Serradifalco presented higher dry weight and inflorescences/plant than the others while Favara had a significantly higher number of branches per plant and more extensive flowered stratum. Metabolomic analysis, performed with LC-MS-TOF, allowed a preliminary characterisation of the non-volatile metabolome of the five oregano ecotypes Origanum vulgare ssp. hirtum. Twenty-five metabolites were identified belonging to organic acids, amino acids, lysophosphatidylcholines, carnithines, nucleic bases and lysophosphatidylethanolamines. Lipidomic analysis identified 115 polar plant membrane glycerolipid species. Thirteen of them were differentially present in the two chosen ecotypes. The role of these metabolites in plant physiology from a qualitative and pharmacological point of view was discussed.     

Discrimination of almonds (Prunus dulcis) geographical origin by minerals and fatty acids profiling

Twenty-one almond samples from three different geographical origins (Sicily, Spain and California) were investigated by determining minerals and fatty acids compositions. Data were used to discriminate by chemometry almond origin by linear discriminant analysis. With respect to previous PCA profiling studies, this work provides a simpler analytical protocol for the identification of almonds geographical origin. Classification by using mineral contents data only was correct in 77% of the samples, while, by using fatty acid profiles, the percentages of samples correctly classified reached 82%. The coupling of mineral contents and fatty acid profiles lead to an increased efficiency of the classification with 87% of samples correctly classified.     

On the well-posedness of the equilibrium problem for linear elasticity in unbounded regions

In this paper we establish some continuous dependence and uniqueness theorems for equilibrium solutions of the equations of general anisotropic linear elasticity in exterior domains. The method we employ is that of the weight function which we introduced in previous papers. However, this is the first example where the method is applied to a static problem. The above theorems are obtained by allowing the strain to be unbounded at large spatial distances. In some cases, no growth condition is assumed. Moreover, the displacement and the elasticities are also possibly allowed to grow.     

On the elastic problem of the orthotropic thick plate

Summary Equilibrium equations for orthotropic media are written taking the displacement components as unknowns; these equations are integrated with operational methods by separation of the variables.The unknown quantities are six « initial funcitons » that is, displacements and their partial derivatives with respect toz, calculated on the planez=0.Following a method of structural mechanics, the cases of symmetrical and nonsymmetrical loading of plate, namely compression and flexion, are considered separately.The separation of the variables allows us to resolve in two successive stages the problem of the boundary conditions: the Cauchy conditions on the surfacesz=± h become differential equations to which we associate the condition on the cylindrical surface.The process leads to a symbolic solution of the problem from which we construct the resolvent equations in the form of power series of operators. If terms of a higher order are retained in these equations, a more accurate theory is obtained; it is shown that if only the first term is assumed, the equation for the ortho tropic plate in the Kirchhoff-Love sense is obtained.The method is applied in order to resolve a problem numerically; the results are compared with those deduced by the usual theory.

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Sommario Si scrivono le equazioni indefinite dell'equilibrio dei mezzi ortotropi assumendo come incognite le componenti di spostamento; se ne effettua l'integrazione con metodi operazionali per separazione delle variabili. Le incognite risultano esplicitate attraverso sei « funzioni iniziali », cioè spostamenti e loro derivate rispetto a z calcolate sul piano medio.In relazione ad una decomposizione dei carichi si individuano due problemi distinti, di compressione e di flessione, che vengono trattati parallelamente.La separazione delle variabili permette di risolvere in due fasi successive il problema dei valori al contorno: le condizioni di Cauchy sulle facce parallele al piano medio si traducono di fatto in equazioni differenziali cui vanno associate le condizioni sulla superficie cilindrica.Il procedimento conduce ad una soluzione simbolica del problema, a partire dalla quale si costruiscono le equazioni risolventi sotto forma di sviluppi in serie di potenze di operatori. L'ordine delle equazioni risolventi, e quindi il numero di condizioni che si possono soddisfare sulla superficie laterale, è fissato dal numero di termini che si considerano in questi sviluppi; si dimostra che il solo primo termine conduce all'equazione della piastra ortotropa ricavata sotto le ipotesi di Kirchhoff-Love.Il metodo è applicato alla soluzione di un problema concreto; i risultati sono messi a confronto con quelli dedotti dalla teoria ordinaria.

     

An a priori assessment of the Partially Stirred Reactor (PaSR) model for MILD combustion

Moderate or Intense Low-oxygen Dilution (MILD) combustion has drawn increasing attention as it allows to avoid the thermo-chemical conditions prone to the formation of pollutant species while ensuring high energy efficiency and fuel flexibility. MILD combustion is characterized by a strong competition between turbulent mixing and chemical kinetics so that turbulence-chemistry interactions are naturally strengthened and unsteady phenomena such as local extinction and re-ignition may occur. The underlying physical mechanisms are not fully understood yet and the validation of combustion models featuring enhanced predictive capabilities is required. Within this context, high-fidelity data from Direct Numerical Simulation (DNS) represent a great opportunity for the assessment and the validation of combustion closure formulations. In this study, the performance of the Partially Stirred Reactor (PaSR) combustion model in MILD conditions is a priori assessed on Direct Numerical Simulations (DNS) of turbulent combustion of MILD mixtures in a cubical domain. Modeled quantities of interest, such as heat release rate and reaction rates of major and minor species, are compared to the corresponding filtered quantities extracted from the DNS. Different submodels for the key model parameters, i.e., the chemical time scale τ_c and the mixing time scale τ_mix, are considered and their influence on the results is evaluated. The results show that the mixing time scale is the leading scale in the investigated cases. The best agreement with the DNS data regarding the prediction of heat release rate and chemical source terms is achieved by the PaSR model that employs a local dynamic approach for the estimation of the mixing time scale. An overestimation of the OH species source terms occurs in limited zones of the computational domain, characterized by low heat release rates.     

Plateau's Problem as a Singular Limit of Capillarity Problems

Soap films at equilibrium are modeled, rather than as surfaces, as regions of small total volume through the introduction of a capillarity problem with a homotopic spanning condition. This point of view introduces a length scale in the classical Plateau's problem, which is in turn recovered in the vanishing volume limit. This approximation of area minimizing hypersurfaces leads to an energy based selection principle for Plateau's problem, points at physical features of soap films that are unaccessible by simply looking at minimal surfaces, and opens several challenging questions. © 2020 Wiley Periodicals LLC.     

Theoretical and experimental determination of the aerodynamic characteristics of a helicopter rotor

Summary A fairly simple theory which can determine the aerodynamic characteristics of a freely hinged rotor in any condition of forward flight is discussed in the present work.Theoretical results are compared with NASA experimental data and with data from tests on a helicopter model in the wind tunnel of Istituto di Meccanica Applicata alle Macchine, Aerodinamica e Gasdinamica (Politecnico of Torino).The agreement between theoretical and experimental results is well suited for practical purpose.

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Sommario Nella nota viene presentata una teoria relativamente semplice per la determinazione delle caratteristiche aerodinamiche di un rotore di elicottero completamente incernierato o basculante nelle condizioni di volo in avanti a regime. I risultati numerici vengono confrontati con dati sperimentali ottenuti dalla NASA e con misure sperimentali effettuate su di un modello di elicottero nella galleria del vento dell'Istituto di Meccanica Applicata alle Macchine, Aerodinamica e Gasdinamica (Politecnico di Torino).L'accordo tra i risultati teorici e i risultati sperimentali è giudicato valido nelle applicazioni pratiche.

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Research supported by the National Research Council (C.N.R.) of Italy.