Simulation of local ion transport in lamellar block copolymer electrolytes based on electron micrographs

A method is presented to relate local morphology and ionic conductivity in a solid, lamellar block copolymer electrolyte for lithium batteries, by simulating conductivity through transmission electron micrographs. The electrolyte consists of polystyrene‐block‐poly(ethylene oxide) mixed with lithium bis(trifluoromethanesulfonyl) imide salt (SEO/LiTFSI), where the polystyrene phase is structural phase and the poly(ethylene oxide)/LiTFSI phase is ionically conductive. The electric potential distribution is simulated in binarized micrographs by solving the Laplace equation with constant potential boundary conditions. A morphology factor, f, is reported for each image by calculating the effective conductivity relative to a homogenous conductor. Images from two samples are examined, one annealed with large lamellar grains and one unannealed with small grains. The average value of f is 0.45 ± 0.04 for the annealed sample, and 0.37 ± 0.03 for the unannealed sample, both close to the value predicted by effective medium theory, 1/2. Simulated conductivities are compared to published experimental conductivities. The value of f_Unannealed/f_Annealed is 0.82 for simulations and 6.2 for experiments. Simulation results correspond well to predictions by effective medium theory but do not explain the experimental measurements. Observation of nanoscale morphology over length scales greater than the size of the micrographs (～1 μm) may be required to explain the experimental results. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 266–274     

Stocking and quality decisions for deteriorating perishable products under competition

In this study, we address the joint inventory and quality management in a Cournot duopoly, for a seasonally produced, perishable product whose quality deteriorates over time. The sales of the product occur over two periods, namely the season (first period) and the off-season (second period). Apart from the stocking quantities for the two periods, firms must decide the quality levels of the units to stock for the second selling period. Firms incur a cost to maintain particular quality levels. The equilibrium policies of the firms are characterized, and we discuss the impact of the firms’ quality costs on their inventory and quality decisions. We identify the conditions of the quality costs when competition ceases to exist in the second period, and analyse the impact of the quality costs on inter-temporal price fluctuations and product availability. Using the unconstrained equilibrium policy, we frame the firms’ inventory disposal policies when production yields are exogenous.     

Embedding theorems on hyperelliptic varieties

In this paper, we investigate linear systems on hyperelliptic varieties. We prove analogues of well-known theorems on abelian varieties, like Lefschetz’s embedding theorem and higher k-jet embedding theorems. Syzygy or \(N_p\) -properties are also deduced for appropriate powers of ample line bundles. This is a first result on linear series, on hyperelliptic varieties.     

Closed loop folding units from structural alignments: Experimental foldons revisited

Nonoverlapping closed loops of around 25–35 amino acids formed via nonlocal interactions at the loop ends have been proposed as an important unit of protein structure. This hypothesis is significant as such short loops can fold quickly and so would not be bound by the Leventhal paradox, giving insight into the possible nature of the funnel in protein folding. Previously, these closed loops have been identified either by sequence analysis (conservation and autocorrelation) or studies of the geometry of individual proteins. Given the potential significance of the closed loop hypothesis, we have explored a new strategy for determining closed loops from the insertions identified by the structural alignment of proteins sharing the same overall fold. We determined the locations of the closed loops in 37 pairs of proteins and obtained excellent agreement with previously published closed loops. The relevance of NMR structures to closed loop determination is briefly discussed. For cytochrome c, cytochrome b₅₆₂ and triosephophate isomerase, independent folding units have been determined on the basis of hydrogen exchange experiments and misincorporation proton‐alkyl exchange experiments. The correspondence between these experimentally derived foldons and the theoretically derived closed loops indicates that the closed loop hypothesis may provide a useful framework for analyzing such experimental data. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

On syzygies of projective bundles over abelian varieties

Syzygies or $N_p$-property of an ample line bundles on abelian varieties are well known. In this paper, we study defining equations and syzygies among them of projective bundles over abelian varieties. We prove an analogue of Pareschi's theorem (or Lazarsfeld's conjecture) on abelian varieties, extended to projective bundles over an abelian variety.     

Semistability of Logarithmic Cotangent Bundle on Some Projective Manifolds

In this article, we investigate the semistability of logarithmic de Rham sheaves on a smooth projective variety (X, D), under suitable conditions. This is related to existence of Kähler–Einstein metric on the open variety. We investigate this problem when the Picard number is one. Fix a normal crossing divisor D on X and consider the logarithmic de Rham sheaf Ω _X (log D) on X. We prove semistability of this sheaf, when the log canonical sheaf K _X  + D is ample or trivial, or when ?K _X  ? D is ample, i.e., when X is a log Fano n-fold of dimension n ≤ 6. We also extend the semistability result for Kawamata coverings, and this gives examples whose Picard number can be greater than one.     

A reaction cell with sample laser heating for in situ soft X‐ray absorption spectroscopy studies under environmental conditions

A miniature (1 ml volume) reaction cell with transparent X‐ray windows and laser heating of the sample has been designed to conduct X‐ray absorption spectroscopy studies of materials in the presence of gases at atmospheric pressures. Heating by laser solves the problems associated with the presence of reactive gases interacting with hot filaments used in resistive heating methods. It also facilitates collection of a small total electron yield signal by eliminating interference with heating current leakage and ground loops. The excellent operation of the cell is demonstrated with examples of CO and H₂ Fischer–Tropsch reactions on Co nanoparticles.