Discrete Homogenization in Graphene Sheet Modeling

Graphene sheets can be considered as lattices consisting of atoms and of interatomic bonds. Their bond lengths are smaller than one nanometer. Simple models describe their behavior by an energy that takes into account both the interatomic lengths and the angles between bonds. We make use of their periodic structure and we construct an equivalent macroscopic model by means of a discrete homogenization technique. Large three-dimensional deformations of graphene sheets are thus governed by a membrane model whose constitutive law is implicit. By linearizing around a prestressed configuration, we obtain linear membrane models that are valid for small displacements and whose constitutive laws are explicit. When restricting to two-dimensional deformations, we can linearize around a rest configuration and we provide explicit macroscopical mechanical constants expressed in terms of the interatomic tension and bending stiffnesses.     

Further prenylated flavonols from Platanus acerifolia’s unripe buds

In addition to the methylated and prenylated flavonoids previously reported from Platanus acerifolia, the multistep chromatographic processing of the toluene extract of defatted fresh unripe buds resulted in the isolation of 8 metabolites. They corresponded to 5,7-dihydroxychromone, strobopinin [(2S)-5,7-dihydroxy-6-C-methylflavanone] as well as to six prenylated flavonols. Divided into two groups of three isomers, these C₅-substituted flavonols are derived from either galangin (5,7-dihydroxyflavonol) or kaempferide (5,7-dihydroxy-4′-methoxyflavonol). Four of them, unknown in the plant kingdom and with either open or cyclized C₅ chain, are discussed for the ¹³C NMR chemical shift variations when going from the open side C₅ chain to the cyclized chain isomers.     

Scheduling: Agreement graph vs resource constraints

We investigate two scheduling problems. The first is scheduling with agreements (SWA) that consists in scheduling a set of jobs non-preemptively on identical machines in a minimum time, subject to constraints that only some specific jobs can be scheduled concurrently. These constraints are represented by an agreement graph. We extend the NP-hardness of SWA with three distinct values of processing times to only two values and this definitely closes the complexity status of SWA on two machines with two fixed processing times. The second problem is the so-called resource-constrained scheduling. We prove that SWA is polynomially equivalent to a special case of the resource-constrained scheduling and deduce new complexity results of the latter.     

A New Investigation of Aqueous Orthophosphoric Acid Speciation Using Raman Spectroscopy

The Raman spectrum of aqueous phosphoric acid has been investigated at apparentconcentrations of 0.3 to 9.7 mol-dm^–3 at 25°C. A quantitative analysis hasbeen made over this concentration range after the determination of the responsecoefficients of the H₂PO^– ₄ and H₃PO₄ species. In the first step, the spectra wereinterpreted assuming that only two species (H₂PO^– ₄ and H₃PO₄) were present inthe system. The dissociation of phosphoric acid obtained in this case is consistentwith the values Preston and Adams⁽¹⁾ obtained, and which was also found fromRaman spectroscopy. However, a discrepancy exists between the representationsfrom spectra and experimental ones. This discrepancy can be removed if anotherspecies, the anionic dimer H₅P₂O^– ₈ is taken into account. Therefore, in the secondstep, a modified interpretation of the spectra, was used to determine theconcentrations of the H₂PO^– ₄, H₅P₂O^– ₈, and H₃PO₄ species and to deduce the correspondingdegree of dissociation of the acid, as well as the speciation of the solutions as afunction of the apparent concentration of phosphoric acid. As in the results Elmoreand co-workers,² which were deduced from pH measurements, the degree ofdissociation reaches a minimum and then increases significantly for apparentphosphoric acid concentrations greater than 1 mol-dm^–3.     

Pyridazine Derivatives and Related Compounds,Part 221: Synthesis,Reactions, and Insecticidal Activity of 3-Amino-5,6-diaryl-1H-pyrazolo[3,4-c]pyridazines

Starting with 3-amino-5,6-diaryl-1H-pyrazolo[3,4-c]pyridazine, the syntheses of thiourea derivatives, dithiocarbamates, ethyl carbamate, phosphoranylidene amino, and substituted acetamido derivatives are described. The products were screened for their insecticidal activity against Mucsa, domestica, and Aphid, Macrosiphum pisi.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.     

Stability of the determination of the surface impedance of an obstacle from the scattering amplitude

We prove a stability estimate of logarithmic type for the inverse problem consisting in the determination of the surface impedance of an obstacle from the scattering amplitude. We present a simple and direct proof, which is essentially based on an elliptic Carleman inequality. Copyright © 2013 John Wiley & Sons, Ltd.     

A fast and robust fictitious domain method for modelling viscous flows in complex mixers: The example of propellant make‐down

This work deals with the development of a fast three‐dimensional numerical strategy for the simulation of viscous fluid flow in complex mixing systems. The proposed method is based on a distributed Lagrange multiplier fictitious domain method and the use of the low‐cost MINI finite element. Contrary to the previous fictitious domain method developed by our group a few years ago, the underlying partial differential equations are solved here in a coupled manner using a consistent penalty technique. The method is discussed in detail and its precision is assessed by means of experimental data in the case of an agitated vessel. A comparison made with our existing fictitious domain method and its decoupled Uzawa‐based solver clearly shows the advantages of resorting to the MINI finite element and fully coupled solution strategy. The new technique is then applied to the simulation of the flow of a Newtonian viscous fluid in a three‐blade planetary mixer in the context of the production of solid propellants. Copyright © 2008 John Wiley & Sons, Ltd.     

A necklace model for vesicles simulations in 2D

The aim of this paper is to propose a new numerical model to simulate 2D vesicles interacting with a Newtonian fluid. The inextensible membrane is modeled by a chain of circular rigid particles, which are maintained in cohesion by using two different types of forces. First, a spring force is imposed between neighboring particles in the chain. Second, in order to model the bending of the membrane, each triplet of successive particles is submitted to an angular force. Numerical simulations of vesicles in shear flow have been run using FEM and the FreeFem++ software. Exploring different ratios of inner and outer viscosities, we recover the well‐known ‘tank‐treading’ and ‘tumbling’ motions predicted by a theory and experiments. Moreover, for the first time, 2D simulations of the ‘vacillating‐breathing’ regime without special ingredient such as thermal fluctuations are recovered. Copyright © 2014 John Wiley & Sons, Ltd.