A remark on the junction in a thin multi-domain: the non convex case

Our aim consists of studying, in the spirit of Gamma convergence, a dimension reduction problem for a multi-domain filled of either an hyperelastic material or a non simple grade-two one. We derive asymptotically the limit energy density starting from a sample described trough non convex bulk energy densities, depending either on the first or second order derivative of the displacement.      

Triple point measurements for alternative refrigerants

Triple point data are important in the refrigerating industry, defining the lowest temperature limit at which a refrigerant may circulate in a fluid state. For several refrigerants, triple point data present in the literature are extremely scarce or inaccurate. A recently developed Solid–Liquid Equilibria (SLE) apparatus was used to measure the triple point temperature of 16 of the most widely applied alternative refrigerants, namely three methane derivatives (fluoromethane, R41; difluoromethane, R32; trifluoromethane, R23), four ethane derivatives (pentafluoroethane, R125; 1,1,1,2-tetrafluoroethane, R134a; 1,1,1-trifluoroethane, R143a; 1,1-difluoroethane, R152a), five propane derivatives [1,1,1,2,3,3,3-heptafluoropropane, R227ea; 1,1,2,3,3,3-hexafluoropropane, R236ea; 1,1,1,3,3-Pentafluoropropane, R245fa; 1,1,2,2,3-pentafluoropropane, R245ca; 1,1,1,3,3,3-hexafluoropropane, R236fa), and four hydrofluoro-olefines (2,3,3,3-tetrafluoroprop-1-ene, R1234yf; trans-1,3,3,3 tetrafluoropropene, R1234ze(E); 3,3,3-trifluoropropene, R1243zf; 1,2,3,3,3-pentafluoropropene, 1225ye(Z)]. The experimental setup, that was recently adopted for the SLE estimation of binary systems containing carbon dioxide (J Therm Anal Calorim 105:489–493, 2011), comprises a measuring cell and a system for drawing the liquid nitrogen directly from its insulated tank with the aid of compressed air: the carrier fluid circulating in the circuit is thus the refrigerant itself. The measurements were performed both in the heating and in the cooling mode. In order to confirm the functional efficiency and fine adjustment of the apparatus, the already available triple point literature data for carbon dioxide, dimethyl ether, and nitrous oxide were also compared with the ones measured by the present setup, confirming the validity of the setup. The measured triple point data for the refrigerants revealed generally good agreement with the literature, excepting a few fluids that revealed some discrepancies.     

Estimation of structural element sizes in sand and compacted blocks of ground calcium carbonate using a void network model

An algorithm has been developed for the calculation of the size of the effective structural or skeletal elements which make up the solid phase of an unconsolidated or consolidated porous block. It is based on a previously presented algorithm, but it has now been validated on unconsolidated samples and tested on consolidated samples. It also includes a virtual reality representation of the structures. First, a network model named Pore-Cor is made to reproduce the percolation behaviour of the experimental sample, by matching its simulated percolation characteristics to an experimental mercury intrusion curve. The algorithm then grows skeletal elements between the cubic pores and cylindrical throats of the void network model until they touch up to four of the adjacent void features. The size distributions of the simulated solid elements are compared with each other and with experimentally determined particle size distributions, using a Mann–Whitney test. The algorithm was shown to simulate skeletal elements with the correct trends in size distribution for two different sand samples, provided the sand packed itself optimally under the applied mercury pressure. It was also applied to two samples of variously compressed calcium carbonate powder, having fine and coarse particle size distributions respectively. The simulation demonstrated that on compressing the powder at the minimum force, the skeletal elements differed from the constituent particle sizes, as expected. The average size of the skeletal elements increased as the compression force was increased on the calcium carbonate powders. The results suggest that the method could be useful as a tool for probing the effect of compaction on aggregation or sintering, and for studying other effects such as cementation in geological samples, where other more direct techniques cannot be applied.     

Investigation of alkyl metal intermediate formation in the rhodium-catalyzed hydroformylation: Experimental and theoretical approaches

This review describes experimental results obtained for regioselectivities and diastereoselectivities in rhodium-catalyzed hydroformylations and deuterioformylations of a variety of unsaturated substrates with unmodified Rh catalysts and compares them with values computed in the density functional theory (DFT) framework. Deuterioformylation experiments pointed out that under mild reaction conditions isomeric alkyl metal intermediate formation is non-reversible; hence the selectivity for alkyls reflects the selectivity for the aldehydes. The stability of the relevant alkyl rhodium transition states (TS) has been determined with computational methods at the B3P86/6-31G* level (employing effective core potentials for Rh in the LanL2DZ valence basis set). Theoretical results turn out to be in good agreement with the experimental ones obtained under mild reaction conditions. Significant differences between theory and experiment are conversely obtained for hydroformylations of vinylidenic olefins, such as 1,1-diphenylethene, carried out at high temperature, where β-hydride elimination takes place. To clarify the reaction mechanism under those reaction conditions, it was necessary to compute the whole reaction mechanism, including zero point and thermal corrections also. The calculations, performed on the hydroformylation of 1,1-diphenylethene (yielding almost exclusively linear aldehydes), allowed us to put forward a novel explanation for that behavior: the addition of the fourth CO group to the tricarbonyl intermediate to give the tetracarbonyl one is prevented in the branched isomer, but not in the linear isomer.     

Simple Synthetic Approach to Arylacetic Nsaias via TosMIC Procedure

Preparation of 1-methylpyrrole-2-acetonitrile, 1-methyl-5-(4-methylbenzoyl) pyrrole-2-acetonitrile and 2-(6-methoxy-2-naphthyl)propionitrile by treatment of 1-methylpyrrole-2-carboxaldehyde, 1-methyl-5-(4-methylbenzoyl)pyrrole-2-carboxaldehyde and, respectively, 6-methoxy-2-acetylnaphthalene with tosylmethylisocyanide (TosMIC) is described. This one-step synthetic procedure is very useful to obtain the nitrile precursors of tolmetin and naproxen, two clinically important non-steroidal antiinflammatory agents (NSAIAs).     

On the connection between energy velocity, reverberation time and angular momentum

The decay of a steady acoustic field in an enclosure is studied both theoretically and experimentally. Our main result is that the initial part of any local sound decay is driven by an exponential function of time whose rate constant is equal in modulus to the inverse of the mean energy velocity divergence. This is empirically demonstrated by experimental analysis of both 1-D and 3-D case studies, thus showing that the reverberation time is strictly connected with the sound energy velocity field and can be determined from its differential properties. A further property of the mean energy velocity is found: it is related not only with the reverberation time, but also with the angular momentum density and with the non-uniform distribution of energy.