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.     

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.

     

Simultaneous determination of citrulline and arginine in human blood plasma by capillary electrophoresis with ultraviolet absorption detection

A new capillary electrophoresis method to measure human blood plasma arginine and citrulline levels in a single run without derivatization was established. After adding homoarginine as internal standard, plasma proteins were removed by a 90:10 v/v acetonitrile/ammonia mixture. Arginine and citrulline were detected by an ultraviolet detector at 190 nm and separated in 11.65 and 20.43 min, respectively, by using a 75 mmol/L Tris phosphate solution at pH 1.2 as a background electrolyte. Limits of detection were 0.8 and 5 μmol/L for arginine and citrulline, respectively. Precision tests indicated a good repeatability of migration times and of peak area both for citrulline (CV% = 0.82 and 3.19) and arginine (CV% = 0.65 and 2.79). The CV% for intra‐ and interassay tests were, respectively, 1.84 and 3.23 for citrulline and 1.25 and 1.50 for arginine. Mean recovery was 101.5 and 98.5% for citrulline and arginine, respectively. The performance of the developed method was assessed by measuring plasma arginine levels in 52 subjects and the data were compared with those obtained by our previous assay. The new method was then applied to assess plasma citrulline and arginine in ten chronic kidney disease patients under hypolipidemic therapy with statin.     

CNN Pincer Ruthenium Catalysts for Hydrogenation and Transfer Hydrogenation of Ketones: Experimental and Computational Studies

Reaction of [RuCl(CNN)(dppb)] ( 1‐Cl ) (HCNN=2‐aminomethyl‐6‐(4‐methylphenyl)pyridine; dppb=Ph₂P(CH₂)₄PPh₂) with NaOCH₂CF₃ leads to the amine‐alkoxide [Ru(CNN)(OCH₂CF₃)(dppb)] ( 1‐OCH₂CF₃ ), whose neutron diffraction study reveals a short RuO ??? HN bond length. Treatment of 1‐Cl with NaOEt and EtOH affords the alkoxide [Ru(CNN)(OEt)(dppb)] ? (EtOH)_n ( 1‐OEt?n EtOH ), which equilibrates with the hydride [RuH(CNN)(dppb)] ( 1‐H ) and acetaldehyde. Compound 1‐OEt?n EtOH reacts reversibly with H₂ leading to 1‐H and EtOH through dihydrogen splitting. NMR spectroscopic studies on 1‐OEt?n EtOH and 1‐H reveal hydrogen bond interactions and exchange processes. The chloride 1‐Cl catalyzes the hydrogenation (5 atm of H₂) of ketones to alcohols (turnover frequency (TOF) up to 6.5×10⁴ h^?1, 40 °C). DFT calculations were performed on the reaction of [RuH(CNN′)(dmpb)] ( 2‐H ) (HCNN′=2‐aminomethyl‐6‐(phenyl)pyridine; dmpb=Me₂P(CH₂)₄PMe₂) with acetone and with one molecule of 2‐propanol, in alcohol, with the alkoxide complex being the most stable species. In the first step, the Ru‐hydride transfers one hydrogen atom to the carbon of the ketone, whereas the second hydrogen transfer from NH₂ is mediated by the alcohol and leads to the key “amide” intermediate. Regeneration of the hydride complex may occur by reaction with 2‐propanol or with H₂; both pathways have low barriers and are alcohol assisted.     

Optimal bounds from below of the critical load for elastic solids subject to uniaxial compression

In the recent papers [1,2] we studied a new procedure based on the Korn inequality for determining sufficient conditions for the Hadamard stability, aimed at determining optimal lower bound estimates for the critical load in bifurcation problems. Here, we discuss the effectiveness of our approach for the classical representative problem of uniaxial compression of a Mooney-Rivlin circular cylinder. We find that our lower bound estimate is effective and advantageous for applications, since it is easily implementable in numerical codes. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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.     

Clustering and classification via cluster-weighted factor analyzers

In model-based clustering and classification, the cluster-weighted model is a convenient approach when the random vector of interest is constituted by a response variable $Y$ and by a vector ${\varvec{X}}$ of $p$ covariates. However, its applicability may be limited when $p$ is high. To overcome this problem, this paper assumes a latent factor structure for ${\varvec{X}}$ in each mixture component, under Gaussian assumptions. This leads to the cluster-weighted factor analyzers (CWFA) model. By imposing constraints on the variance of $Y$ and the covariance matrix of ${\varvec{X}}$ , a novel family of sixteen CWFA models is introduced for model-based clustering and classification. The alternating expectation-conditional maximization algorithm, for maximum likelihood estimation of the parameters of all models in the family, is described; to initialize the algorithm, a 5-step hierarchical procedure is proposed, which uses the nested structures of the models within the family and thus guarantees the natural ranking among the sixteen likelihoods. Artificial and real data show that these models have very good clustering and classification performance and that the algorithm is able to recover the parameters very well.