The Zintl ion As-7](2-): an example of an electron-deficient As-x radical anion

K(2,2,2-crypt)](2)As-7]center dot THF, 1 (2,2,2-crypt = 4,7,13,16,21,24-hexaoxa-1,10-diazabicyclo8.8.8]hexacosane) is the first well characterized seven-atom radical anion of group 15. UV-Vis spectroscopy confirms the presence and electronic structure of As-7](2-). Cyclic voltammetry in DMF solution shows the As-7(3) /As-7(2) redox couple as a one-electron reversible process. Theoretical investigations explore the bonding and properties of compound 1.

Social selection and the evolution of cooperative groups: The example of the cellular slime moulds

In social selection the phenotype of an individual depends on its own genotype as well as on the phenotypes, and so genotypes, of other individuals. This makes it impossible to associate an invariant phenotype with a genotype: the social context is crucial. Descriptions of metazoan development, which often is viewed as the acme of cooperative social behaviour, ignore or downplay this fact. The implicit justification for doing so is based on a group-selectionist point of view. Namely, embryos are clones, therefore all cells have the same evolutionary interest, and the visible differences between cells result from a common strategy. The reasoning is flawed, because phenotypic heterogeneity within groups can result from contingent choices made by cells from a flexible repertoire as in multicellular development. What makes that possible is phenotypic plasticity, namely the ability of a genotype to exhibit different phenotypes. However, co-operative social behaviour with division of labour requires that different phenotypes interact appropriately, not that they belong to the same genotype, or have overlapping genetic interests. We sketch a possible route to the evolution of social groups that involves many steps: (a) individuals that happen to be in spatial proximity benefit simply by virtue of their number; (b) traits that are already present act as preadaptations and improve the efficiency of the group; and (c) new adaptations evolve under selection in the social context-that is, via interactions between individuals-and further strengthen group behaviour. The Dictyostelid or cellular slime mould amoebae (CSMs) become multicellular in an unusual way, by the aggregation of free-living cells. In nature the resulting group can be genetically homogeneous (clonal) or heterogeneous (polyclonal); in either case its development, which displays strong cooperation between cells (to the extent of so-called altruism) is not affected. This makes the CSMs exemplars for the study of social behaviour.

A characteristic based numerical method with tracking for nonlinear wave equations

Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function, Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver. Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.

A numerical study of division of flow in open channels

A two-dimensional numerical model which employs the depth-averaged forms of continuity and momentum equations along with k-e turbulence closure scheme is used to simulate the flow at the open channel divisions. The model is generalised to flows of arbitrary geometries and MacCormack finite volume method is used for solving governing equations. Application of cartesian version of the model to analyse the flow at right-angled junction is presented. The numerical predictions are compared with experimental data of earlier investigators and measurements made as part of the present study. Performance of the model in predicting discharge distribution, surface profiles, separation zone parameters and energy losses is evaluated and discussed in detail. To illustrate the application of the numerical model to analyse the flow in acute angled offtakes and streamlined branch entries, a few computational results are presented.

Dynamic stiffness matrix of a general cable element

A computational scheme for determining the dynamic stiffness coefficients of a linear, inclined, translating and viscously/hysteretically damped cable element is outlined. Also taken into account is the coupling between inplane transverse and longitudinal forms of cable vibration. The scheme is based on conversion of the governing set of quasistatic boundary value problems into a larger equivalent set of initial value problems, which are subsequently numerically integrated in a spatial domain using marching algorithms. Numerical results which bring out the nature of the dynamic stiffness coefficients are presented. A specific example of random vibration analysis of a long span cable subjected to earthquake support motions modeled as vector gaussian random processes is also discussed. The approach presented is versatile and capable of handling many complicating effects in cable dynamics in a unified manner.

The unusual formation of methyl alpha-(5,6-dimethoxycarbonyl-2,3-dimethoxyazepin-7-ylidene)-alpha-[5-methoxycarbonyl-2,3-dimethoxypyrid-6-yl)acetate during the pyrolysis of ''azido-meta-hemipinate'' - First example of a reaction involving a concomitant ring expansion and ring extrusion

he ortho methoxycarbonyl substituent constitutes a sole exception in the ring closure reactions of ortho substituted aryl azides, as it provides no rate acceleration to this reaction. Pyrolysis of ''azido-meta-hemipinate'', an aryl azide containing such a substituent, led us to the title compound, a new azepinylidenepyridylacetic ester, whose structure has been established unambiguously by a single crystal X-ray diffraction study. This is the first report of a reaction involving both a ring expansion to an azaheptafulvalene and a ring extrusion to a pyridyl ring residue.

Evaluation of strain-rate effects in transitional round jets using direct numerical simulation

The coherent flame model uses the strain rate to predict reaction rate per unit flame surface area and some procedure that solves for the dynamics of flame surfaces to predict species distributions. The strainrate formula for the reaction rate is obtained from the analytical solution for a flame in a laminar, plane stagnation point flow. Here, the formula's effectiveness is examined by comparisons with data from a direct numerical simulation (DNS) of a round jetlike flow that undergoes transition to turbulence. Significant differences due to general flow features can be understood qualitatively: Model predictions are good in the braids between vortex rings, which are present in the near field of round jets, as the strain rate is extensional and reaction surfaces are isolated. In several other regions, the strain rate is compressive or flame surfaces are folded close together. There, the predictions are poor as the local flow no longer resembles the model flow. Quantitative comparisons showed some discrepancies. A modified, consistent application of the strain-rate solution did not show significant changes in the prediction of mean reaction rate distributions.

Role of indenter angle on the plastic deformation underneath a sharp indenter and on representative strains: An experimental and numerical study

The subsurface microhardness mapping technique of Chaudhri was utilized to determine the shape, size and distribution of plastic strain underneath conical indenters of varying semi-apex angles, alpha (55 degrees, 65 degrees and 75 degrees). Results show that the elastic-plastic boundary under the indenters is elliptical in nature, contradicting the expanding cavity model, and the ellipticity increases with alpha. The maximum plastic strain immediately under the indenter was found to decrease with increasing alpha. Complementary finite-element analysis was conducted to examine the ability of simulations to capture the experimental observations. A comparison of computational and experimental results indicates that the plastic strain distributions as well as the maximum strains immediately beneath the indenter do not match, suggesting that simulation of sharp indentation requires further detailed studies for complete comprehension. Representative strains, epsilon(r), evaluated as the volume-average strains within the elastic-plastic boundary, decrease with increasing alpha and are in agreement with those estimated by using the dimensional analysis. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Numerical simulations of fracture initiation in ductile solids under mode I, dynamic loading

In this paper, an overview of some recent computational studies by the authors on ductile crack initiation under mode I, dynamic loading is presented. In these studies, a large deformation finite element procedure is employed along with the viscoplastic version of the Gurson constitutive model that accounts for the micro-mechanical processes of void nucleation, growth and coalescence. A three-point bend fracture specimen subjected to impact, and a single edge notched specimen loaded by a tensile stress pulse are analysed. Several loading rates are simulated by varying the impact speed or the rise time and magnitude of the stress pulse. A simple model involving a semi-circular notch with a pre-nucleated circular hole situated ahead of it is considered. The growth of the hole and its interaction with the notch tip, which leads to plastic strain and porosity localization in the ligament connecting them, is simulated. The role of strain-rate dependence on ductile crack initiation at high loading rates, and the specimen geometry effect on the variation of dynamic fracture toughness with loading rate are Investigated.

Sensing of delaminations in composite laminates using embedded magnetostrictive particle layers

This is an exploratory study to illustrate the feasibility of detecting delamination type of damage in polymeric laminates with one layer of magnetostrictive particles. One such beam encircled with excitation and sensing coils is used for this study. The change in stress gradient of the magnetostrictive layer in the vicinity of delamination shows up as a change in induced voltage in the sensing coil, and therefore provides a means to sense the presence of delamination. Recognizing the constitutive behavior of the Terfenol-D material is highly nonlinear, analytical expressions for the constitutive relations are developed by using curve fitting techniques to the experimental data. Analytical expressions that relate the applied excitation field with the stress and magnetic flux densities induced in the magnetostrictive layer are developed. Numerical methods are used to find the relative change in the induced voltage in the sensing coil due to the presence of delamination. A typical example of unidirectional laminate, with embedded delaminations, is used for the simulation purposes. This exploratory study illustrates that the open-circuit voltage induced in the sensing coil changes significantly (as large of 68 millivolts) with the occurrence of delamination. This feature can be exploited for device off-line inspection techniques and/or linking monitoring procedures for practical applications.

Numerical modeling of heat and mass transfer in laser surface alloying: Non-equilibrium solidification effects

A transient macroscopic model is developed for studying heat and mass transfer in a single-pass laser surface alloying process, with particular emphasis on non-equilibrium solidification considerations. The solution for species concentration distribution requires suitable treatment of non-equilibrium mass transfer conditions. In this context, microscopic features pertaining to non-equilibrium effects on account of solutal undercooling are incorporated through the formulation of a modified partition-coefficient. The effective partition-coefficient is numerically modeled by Means of a number of macroscopically observable parameters related to the solidifying domain. The numerical model is so developed that the modifications on account of non-equilibrium solidification considerations can be conveniently implemented in existing numerical codes based on equilibrium solidification considerations.

An economical method for direct numerical simulation studies of transitional round jets

A pseudo-spectral method based on Fourier expansions in a Cartesian coordinate system is shown to be an economical method for direct numerical simulation studies of transitional round jets, Several characteristics of the solutions are presented to establish the validity of the solutions in spite of the unnatural choices. We show that neither periodicity, nor the use of a Cartesian system have adversely affected the simulations, Instead, there are benefits in terms of ease of computing and lack of the usual restrictions due to grid structure near the jet axis. By computing the simultaneous evolution of passive scalers, the process of reaction in round jet burners, between a fuel-laden jet and an ambient oxidizer, was also simulated. Some typical solutions are shown and then the results of analysis of these data are summarized. (C) 2001 Elsevier Science Ltd, All rights reserved.

Direct numerical simulation of turbulent spots

A group of high-order finite-difference schemes for incompressible flow was implemented to simulate the evolution of turbulent spots in channel flows. The long-time accuracy of these schemes was tested by comparing the evolution of small disturbances to a plane channel flow against the growth rate predicted by linear theory. When the perturbation is the unstable eigenfunction at a Reynolds number of 7500, the solution grows only if there are a comparatively large number of (equispaced) grid points across the channel. Fifth-order upwind biasing of convection terms is found to be worse than second-order central differencing. But, for a decaying mode at a Reynolds number of 1000, about a fourth of the points suffice to obtain the correct decay rate. We show that this is due to the comparatively high gradients in the unstable eigenfunction near the walls. So, high-wave-number dissipation of the high-order upwind biasing degrades the solution especially. But for a well-resolved calculation, the weak dissipation does not degrade solutions even over the very long times (O(100)) computed in these tests. Some new solutions of spot evolution in Couette flows with pressure gradients are presented. The approach to self-similarity at long times can be seen readily in contour plots.