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.     

Electron spin resonance of an irradiated single crystal of maleic acid

Electron spin resonance spectroscopy has been used to investigate radiation damage in an irradiated single crystal of maleic acid. At least two stable radicals are produced by the radiation. One of these radicals is probably HOOC-H₂C-CH-COOH. Another species, possibly of the form HOOC-RCH-CH-COOH, has also been observed.

Radical yields have been measured for the isomeric maleic and fumaric acids. The G-values are 0.1 for maleic acid and 0.06 for fumaric acid.