Combinatorics,graph theory,and computing

Journal of Algebraic Combinatorics -     

Optimizing the monomer structure of polyhedral oligomeric silsesquioxane for ion transport in hybrid organic–inorganic block copolymers

Poly(ethylene oxide)-b-polyhedral oligomeric silsesquioxane (PEO–POSS) mixed with lithium bis(trifluoromethanesulfonyl)imide salt is a nanostructured hybrid organic–inorganic block copolymer electrolyte that may enable lithium metal batteries. The synthesis and characteristics of three PEO–POSS block copolymer electrolytes which only differ by their POSS silica cage substituents (ethyl, isobutyl, and isooctyl) is reported. Changing the POSS monomer structure results in differences in both thermodynamics and ion transport. All three neat polymers exhibit lamellar morphologies. Adding salt results in the formation of a disordered window which closes and gives way to lamellae at higher salt concentrations. The width of disordered window decreases with increasing length of the POSS alkyl chain substituent from ethyl to isobutyl and is absent in the isooctyl sample. Rheological measurements demonstrate good mechanical rigidity when compared with similar all-organic block copolymers. While salt diffusion coefficient and current ratio are unaffected by substituent length, ionic conductivity increases as the length of the alkyl chain substituent decreases: the ethyl substituent is optimal for ion transport. This is surprising because conventional wisdom suggests that ion transport occurs primarily in the PEO-rich domains, that is, ion transport should be unaffected by substituent length after accounting for the minor change in conducting phase volume fraction. © 2020 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2020 © 2020 Wiley Periodicals, Inc. J. Polym. Sci. 2020 , 58, 363–371     

Detection efficiency calculations using Geant4 for a broad-energy germanium gamma spectrometer

In assistance of radionuclide measurements at Canada’s Comprehensive Nuclear-Test-Ban Treaty (CTBT) laboratory, a Geant4 Monte Carlo application has been developed in simulating a broad-energy germanium detector and calculating detection efficiencies. The detector model was optimized in a reliable and non-biased manner through simultaneous tuning on gap distance and detector dimension, and was validated over various realistic measurement scenarios. All work is based on a series of experiments which covers the typical energy range of gamma radiation in environmental analysis, and considers the variety of the CTBT sample type, dimension and distance-to-detector. In all cases, the predicted efficiencies are consistent with the empirical ones within 5%, with a typical deviation of 3% in majority.     

Pattern‐avoiding permutations and Brownian excursion part I: Shapes and fluctuations

Permutations that avoid given patterns are among the most classical objects in combinatorics and have strong connections to many fields of mathematics, computer science and biology. In this paper we study the scaling limits of a random permutation avoiding a pattern of length 3 and their relations to Brownian excursion. Exploring this connection to Brownian excursion allows us to strengthen the recent results of Madras and Pehlivan [25] and Miner and Pak [29] as well as to understand many of the interesting phenomena that had previously gone unexplained. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 394–419, 2017     

Development of a prototype high-current low-energy ion implanter

A high current-low energy implant system for the processing of semiconductor devices at medium-high dopant levels is described. Criteria for selection and design of ion beam components such as ion beam optics, vacuum requirements and reliability are discussed. Variations in wafer uniformities for within wafer, wafer-to-wafer and run-to-run are presented.     

A proof of zelevinski’s structure theorem for psh algebras 1

We give a new proof of the structure theorem for PSH—algebras, and of a formula for primitives