Maximum of the Characteristic Polynomial for a Random Permutation Matrix

Let P_N be a uniform random N × N permutation matrix and let χ_N(z) = det(zI_N − P_N) denote its characteristic polynomial. We prove a law of large numbers for the maximum modulus of χ_N on the unit circle, specifically, with probability tending to 1 as N → ∞ , for a numerical constant x₀ ≈ 0.652 . The main idea of the proof is to uncover a logarithmic correlation structure for the distribution of (the logarithm of) χ_N , viewed as a random field on the circle, and to adapt a well-known second-moment argument for the maximum of the branching random walk. Unlike the well-studied CUE field in which P_N is replaced with a Haar unitary, the distribution of χ_N(e^2πit) is sensitive to Diophantine properties of the point t . To deal with this we borrow tools from the Hardy-Littlewood circle method. © 2020 Wiley Periodicals LLC     

Long-lived charge carrier generation in ordered films of a covalent perylenediimide–diketopyrrolopyrrole–perylenediimide molecule

The photophysics of a covalently linked perylenediimide–diketopyrrolopyrrole–perylenediimide acceptor–donor–acceptor molecule (PDI–DPP–PDI, 1) were investigated and found to be markedly different in solution versus in unannealed and solvent annealed films. Photoexcitation of 1 in toluene results in quantitative charge separation in τ = 3.1 ± 0.2 ps, with charge recombination in τ = 340 ± 10 ps, while in unannealed/disordered films of 1, charge separation occurs in τ < 250 fs, while charge recombination displays a multiexponential decay in ∼6 ns. The absence of long-lived, charge separation in the disordered film suggests that few free charge carriers are generated. In contrast, upon CH₂Cl₂ vapor annealing films of 1, grazing-incidence X-ray scattering shows that the molecules form a more ordered structure. Photoexcitation of the ordered films results in initial formation of a spin-correlated radical ion pair (electron–hole pair) as indicated by magnetic field effects on the formation of free charge carriers which live for ∼4 μs. This result has significant implications for the design of organic solar cells based on covalent donor–acceptor systems and shows that long-lived, charge-separated states can be achieved by controlling intramolecular charge separation dynamics in well-ordered systems.     

Measurements of anisotropic elastic constants of type 308 stainless-steel electroslag welds

In austenitic-stainless-steel weld metal, mechanical anisotropy is caused by preferred local orientation of elongated subgrains and preferred crystallographic orientation. Ultrasonic and static tensile-test methods used to determine elastic stiffness and compliance matrices, respectively, demonstrated that orthotropic symmetry exists. Inversion of this compliance matrix gave a stiffness matrix which showed general agreement between the two methods. It is suggested that the data can be used directly in finite-element analyses of weldments containing Type 308 stainless steel.     

Silyl trifluoromethanesulfonate-activated para-methoxybenzyl methyl ether as an alkylating agent for thiols and aryl ketones

para-Methoxybenzyl methyl ether acts as an alkylating agent for thiols in the presence of trimethylsilyl trifluoromethanesulfonate and trialkylamine base in good yields (58–96%). Aryl ketones are alkylated under similar conditions, probably through an enol silane intermediate, also in high yields (67–95%). The active alkylating species is likely a p-methoxybenzyl cation.     

The structure of poly-2,5-benzoxazole (ABPBO) and poly-2,6-benzothiazole (ABPBT) fibers by X-ray diffraction

The determination of the crystalline structure of oriented fibers of poly-2,5-benzoxazole (ABPBO) and poly-2,6-ben-zothiazole (ABPBT) is described. Both unit cells are metrically orthorhombic, with the parameters: a = 6.061 (17), b = 3.384 (13), c (fiber axis) = 11.575 (6) Å for ABPBO; and a = 6.044 (6), b = 3.417 (7), c (fiber axis) = 12.194 (18) Å for ABPBT. The fiber repeat consists in each structure of two fused ring groups arranged in a planar, zigzag conformation. The conformational torsion angle and orientation of chains within the unit cells are derived from a linked-atom least squares refinement technique. Polymer chains pack laterally through van der Waals interactions. A plausible disorder model which involves defects in chain direction is presented. Refinement of a static disorder model for ABPBO in which 50% of the chains have their chain directions reversed leads to a lower R residual and sum of constraints.