Stable two-layer flows at all Re; visco-plastic lubrication of shear-thinning and viscoelastic fluids

Multi-fluid flows are frequently thought of as being less stable than single phase flows. Consideration of different non-Newtonian models can give rise to different types of hydrodynamic instability. Here we show that with careful choice of fluid rheologies and flow paradigm, one can achieve multi-layer flows that are linearly stable for Re = ∞. The basic methodology consists of two steps. First we eliminate interfacial instabilities by using a yield stress fluid in one fluid layer and ensuring that for the base flow configurations studied we maintain an unyielded plug region at the interface. Secondly we eliminate linear shear instabilities by ensuring a strong enough Couette component in the second fluid layer, imposed via the moving interface. We show that this technique can be applied to both shear-thinning and visco-elastic fluids.     

Guest Editorial: A path through quantum crystallography: a short tribute to Professor Lou Massa

Professor Lou Massa’s contributions since the late 1960s to the founding of the field now known as “Quantum Crystallography” (QCr) are briefly described. The term itself has been coined in 1995 by L. Huang, L. Massa, and J. Karle (1985 Nobel Laureate in Chemistry). Originally, QCr referred to the Clinton-Massa’s iterative approach that, for the first time, delivered N-representable electron densities that are consistent with the observed structure factors. These densities satisfy, at once, experimental observation and the necessarily underlying quantum mechanical requirement of being derived from an antisymmetric wavefunction. The single-determinantal quantum mechanical structure Huang, Massa, and Karle (HMK) imposed in their original work can be extended to any method that uses MOs including CI or DFT, as they demonstrate in their papers. HMK use the Clinton-Massa method to reconstruct approximations to the first order reduced density matrix of large molecules in a piecemeal manner from computationally-tractable fragments. The idea was also adapted by J. Hernández Trujillo and R. F. W. Bader in the context of the Quantum Theory of Atoms in Molecules (QTAIM). Massa et al. simplified and generalized this fragmentation method into what came to be known as the “Kernel Energy Method” (KEM) which delivers the properties of large molecules accurately, at a fraction of the computational time, and within any model chemistry as applications to DNA, tRNA, the proto-ribosome, insulin, and graphene, amply demonstrate. Lou Massa has also pushed the envelope in other directions as well. In 1992, he and W. Lipscomb (1976 Nobel Laureate in Chemistry) published several papers predicting the structure and stability of Boron nanotubes and boron fullurene 12 years before they were eventually synthesized in laboratories at Yale and at Brookhaven. More recently, in 2006 L. Massa, J. Karle, and A. Yonath (2009 Nobel Laureate in Chemistry) (MKY) proposed a startling alternative to the then widely-accepted mechanism of the peptide bond formation in the active site of the ribosome. In sharp contrast with the accepted “shuttle mechanism”, MKY’s “direct” mechanism is simpler and, importantly, reproduces the measured thermodynamic and kinetic parameters. Massa has also contributed to other domains, for example interstellar chemistry, and to the policy, history, and philosophy of science. His TV program and Oxford University Press book (both titled “Science and the Written Word”) represent an invaluable and candid documentation of some of the key discoveries in the words of a dozen Nobel Laureates and a constellation of scholars representing the Who’s Who of current science. It is with both admiration and affection that this paper (and this issue) is dedicated to Lou Massa, the person and the scientist.     

Relativistic-consistent electron densities of the coinage metal clusters M2, M4, M4(2-), and M4Na2 (M = Cu, Ag, Au): a QTAIM study

We employ second-order M?ller-Plesset perturbation theory level in combination with recently developed pseudopotential-based correlation consistent basis sets to obtain accurate relativistic-consistent electron densities for small coinage metal clusters. Using calculated electron densities, we employ Bader's quantum theory of atoms in molecules (QTAIM) to gain insights into the nature of metal-metal bonding in the clusters M(2), M(4), M(4)(2-), and M(4)Na(2) (M = Cu, Ag, Au). For the simplest case of the metal dimer, M(2), we correlate the strength of the metal-metal bond with the value of the electron density at the bond critical point, the total energy density at the bond critical point, the sharing (delocalization) index, and the values of the two principle negative curvatures. We then consider changes to the metal-metal bonding and charge density distribution upon the addition of two metal atoms to form the metal tetramer, M(4), and then followed by the addition of an electron pair to form M(4)(2-) and finally followed by the addition of two alkali metal (sodium) ions to form M(4)Na(2). Using topological properties of the electron density, we present evidence for the existence of σ-aromaticity in Au(4)(2-). We also report the existence of two non-nuclear attractors in the molecular graph of Cu(4)(2-) and large negative charge accumulation in the nonbonded Cu basins of this cluster.     

Very weak solutions for the Stokes problem in an exterior domain

In this paper, we study the Stokes problem in exterior domain of ${\mathbb{R}^{3}}$ . We are interested in the existence and the uniqueness of very weak solutions. Here, we extend a result proved by Farwig et al. (J Math Soc Japan 59(1):127–150, 2007) and we prove the existence and the uniqueness of a second type of very weak solution.     

Structure, magnetic properties and M?ssbauer spectra of La0.67Sr0.33FexMn1???xO3 manganites oxide prepared by mechanical ball milling method

La_0.67Sr_0.33Fe_xMn_1-xO₃, with x = 0.0, 0.1, 0.2 and 1 have been elaborated by mechanical system. X-ray diffraction, Scanning electron microscopy, Magnetic measurements and M?ssbauer spectroscopy for the systems have been investigated. Rietveld analysis of the X-ray powder diffraction show that the samples crystallise in the orthorhombic perovskite system with Pnma space group. The average particle size of about 60 nanometre was obtained from scanning electron microscopy and X-ray diffraction. The investigated samples exhibit a ferromagnetic to paramagnetic transition with increasing temperature. The presence of manganese in the structure leads to an increase of the Curie temperature as well as to spontaneous magnetization. The magnetization versus applied magnetic field shows a small coercive field and an unsaturated magnetization which indicates that the nanoparticles of all samples are superparamagnetic at around room temperature. Room temperature M?ssbauer spectra show that the samples with x = 0.1 and x = 1.0 contain minority α-Fe₂O₃ and other spinel ferrite species. Also, they indicate that Fe^3?+? ions are present in slightly distorted octahedral sites in the samples with x = 0.1 and 0.2, while mixed Fe valency was observed for the sample with x = 1.0.     

Identical parallel-machine scheduling under availability constraints to minimize the sum of completion times

In this paper, we study the identical parallel machine scheduling problem with a planned maintenance period on each machine to minimize the sum of completion times. This paper is a first approach for this problem. We propose three exact methods to solve the problem at hand: mixed integer linear programming methods, a dynamic programming based method and a branch-and-bound method. Several constructive heuristics are proposed. A lower bound, dominance properties and two branching schemes for the branch-and-bound method are presented. Experimental results show that the methods can give satisfactory solutions.     

Biharmonic problem in exterior domains

We study here a biharmonic equation in an exterior domain of $\text{R}{}^{\mathrm{n}}$. We give in L^p theory, with 1<p<∞ existence, uniqueness and regularity results. To cite this article: C. Amrouche, M. Fontes, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Fast quantum crystallography

Typical contemporary X-ray crystallography delivers the geometries and, at best, the electron densities of molecules or periodic systems in the crystalline phase. Energies, electron momentum densities, and information relating to the pair density such as electron delocalization measures—all crucial to chemistry—are simply missed. Quantum crystallography (QCr) is an emerging line of research aimed at filling this gap by solving the crystallographic problem under the constraints of quantum mechanics. In this way, not only geometries and electron densities become experimentally accessible but also the entire panoply of quantum mechanical properties that are in the output of any quantum chemical software package. However, QCr remains limited to smaller systems (small molecules or small unit cells) due to the exponential bottleneck that plagues quantum mechanical calculations. When combined with a fragmentation technique, termed the “kernel energy method (KEM)”, QCr's reach to larger molecules is extended considerably to almost “any size”, that is, systems of up to many hundreds of thousands of atoms. KEM has made this doable with any chemical model and is capable of providing the entire quantum mechanics of large molecular systems. The smallness of the R-factor adjudicates the accuracy of the quantum mechanics extracted from the crystallography.