Network topology of deeply supercooled water

Empirical potential structure refinements have been made to recent high-energy x-ray diffraction data, providing molecular models of deeply supercooled water. The average O-O coordination number is found to drop from 5.13 at 293?K to 4.85 at 244?K, within 3.5?Å. Triplet O-O-O bond angle distributions reveal a broad peak centred at 96.4° at 293?K which shifts to 100.0° at 244?K, indicative of the local geometry becoming increasingly tetrahedral with decreasing temperature. However, although the number of non-bonded interstitial molecules between the first and second shells is depleted upon cooling, the number of interstitial molecules forming triplets that are embedded within the hydrogen bonded tetrahedral network at θ_OOO?=?53°, remains constant. This is consistent with previous observations of an invariant O-O coordination number with temperature (4.24 out to 3.3?Å) and corresponds to non-bonded molecules positioned at close to half the ideal tetrahedral angle. Both -O-O-O- and hydrogen-bonded -O-H-O- ring length distributions show increases in 6 and 7-membered rings upon supercooling. This is concomitant with a shift and increase in intensity of peaks at r₄ ～8.7?Å and r₅ ～10.8?Å in the oxygen-oxygen pair distribution function, which in the models correspond to correlations between adjacent and next-nearest-neighbour hydrogen-bonded rings.     

Time‐dependent finite element simulations of a shear‐thinning viscoelastic fluid with application to blood flow

A new finite element method is developed to simulate time‐dependent viscoelastic shear‐thinning flows characterized by the generalized Oldroyd‐B model. The focus of the algorithm is improved stability through a free‐energy dissipative scheme by using low‐order piecewise‐constant finite element approximations for stress. The algorithm is further modified by incorporating a pressure‐projection method, a DG‐upwinding scheme, a symmetric interior penalty DG method to solve the elliptic pressure‐update equation and a geometric multigrid preconditioner. The improved stability and cost to accuracy is compared when using higher order discontinuous bilinear approximation, where in addition, we consider the influence of a slope limiter for these elements. The algorithm is applied to the 2D start‐up‐driven cavity problem, and the stability of the free energy is illustrated and compared between element choices. An application of the model to modelling blood in small arterioles and channels is considered by simulating pulsatile blood flow through a stenotic arteriole. The individual influences of viscoelasticity and shear‐thinning within the generalized Oldroyd‐B model are investigated by comparing results to the Newtonian, generalized Newtonian and Oldroyd‐B models. Copyright © 2014 John Wiley & Sons, Ltd.     

Evaluation of RBFs for volume data interpolation in CFD

A greedy method for choosing an optimum reduced set of control points is integrated with RBF interpolation and evaluated for the purpose of interpolating large‐volume data sets in CFD. Given a function defined at a set of points, the greedy method selects a small subset of these points that is sufficient to keep the interpolation error at all the remaining points below a chosen bound. This is equivalent to a type of data compression and would have useful storage, post‐processing, and computational applications in CFD. To test the method in terms of both the point selection scheme and the suitability of reduced control point volume interpolation, a trial application of the interpolation to velocity fields in CFD volume meshes is considered. To optimise the point selection process, and attempt to be able to capture multiple length scales, a variable support radius formulation has also been included. Structured and unstructured mesh cases are considered for aerofoils, a wing case and a wing‐body case. For smooth volume functions, the method is shown to work well, producing accurate velocity interpolations using a very small number of the cells in the mesh. For general complex fields including large gradients, the method is still shown to be effective, although large gradients require more interpolation points to be used.Copyright © 2013 John Wiley & Sons, Ltd.     

关于极限理论的学习经验

分析极限理论在数学分析学习中的重要性，介绍学习极限理论的三点经验与体会，即充分理解基本内容；加强基本功训练；试着多问自己一些问题，学会举出各种各样的例子。     

Glutamine: fructose-6-phosphate amidotransferase (GFAT): homology modelling and designing of new inhibitors using pharmacophore and docking based hierarchical virtual screening protocol

Glutamine: fructose-6-phosphate amidotransferase (GFAT), also termed GFPT1 and GFAT1, catalyzes the first committed step of the hexosamine biosynthesis pathway in mammals and consequently plays an important role in type 2 diabetes. In the present study, a combination of pharmacophore modelling, homology modelling, and molecular docking analysis was performed to design new glutamine competitive inhibitors of human GFAT, and to investigate important interaction details of inhibitor molecules. A pharmacophore model of GFAT inhibitors was developed, subsequently validated, and utilized for the screening by the PHASE database to identify new molecules. Afterwards, homology modelling was performed to construct the glutamine-binding site of the GFAT protein. The modelled active site was utilized to dock the studied molecules to investigate important receptor-ligand interactions and to scrutinize database-screened molecules on the basis of essential interactions. This systematic in silico protocol helped us to identify new molecules that would be explored for the treatment of type 2 diabetes and its complications.     

Viscosity Mixing Rules for Binary Systems Containing One Ionic Liquid

In this work the applicability of four of the most commonly used viscosity mixing rules to [ionic liquid (IL)+molecular solvent (MS)] systems is assessed. More than one hundred (IL+MS) binary mixtures were selected from the literature to test the viscosity mixing rules proposed by 1) Hind (Hi), 2) Grunberg and Nissan (G–N), 3) Herric (He) and 4) Katti and Chaudhri (K–C). The analyses were performed by estimating the average (absolute or relative) deviations, AADs and ARDs, between the available experimental data and the predicted ideal mixture viscosity values obtained by means of each rule. The interaction terms corresponding to the adjustable parameters inherent to each rule were also calculated and their trends discussed.     

Accessing Extended Fused Isoindolinones Via Sequential Anionic Intramolecular Cyclizations

Sequential anionic intramolecular cyclizations and modelling were used for the first time to access unusual fused heterocyclic frameworks in excellent yields. 5-Exo-dig cyclizations yielded isoindolinone motifs and a subsequent 6-exo- and 7-endo-dig cyclization was directed to provide either fused isoquinoline or azepine frameworks. Regioselectivities were controlled by exploiting stereoelectronic effects via n_C−→π*_(Ph) interactions, and modelling studies provided reaction scope.     

Case Studies With Mathematical Modeling of Free-Radical Multi-Component Bulk/Solution Polymerizations: Part 1

In part 1 of this series of two extensive overviews of multi-component polymerization case studies, we present mathematical modelling results with experimental confirmations. The case studies are from free-radical, bulk and/or solution polymerizations, covering the range from homo- to hexa-polymerization at both regular and elevated temperature levels, i.e., without and with possible depropagation steps. The model eventually tackles complex polymerization features, ranging from conversion-time histories to more esoteric multi-component composition and/or sequence length profiles. Part 2 of the series will describe more complicated situations with depropagation and composition control policies, all relying solely on a unique monomer/polymer database of physico-chemical properties and other characteristics, with no further parameter adjustment. These database items will be cited in tables in part 2 of the series.