Estimation,dependence and stability of solutions of an iterative equation

Aequationes mathematicae - In this paper we study estimation, continuous dependence and Hyers–Ulam stability for continuous solutions of a second order iterative equation. First we give an...     

On the Optimal Design of Wall-to-Wall Heat Transport

We consider the problem of optimizing heat transport through an incompressible fluid layer. Modeling passive scalar transport by advection-diffusion, we maximize the mean rate of total transport by a divergence-free velocity field. Subject to various boundary conditions and intensity constraints, we prove that the maximal rate of transport scales linearly in the r.m.s. kinetic energy and, up to possible logarithmic corrections, as the one-third power of the mean enstrophy in the advective regime. This makes rigorous a previous prediction on the near optimality of convection rolls for energy-constrained transport. On the other hand, optimal designs for enstrophy-constrained transport are significantly more difficult to describe: we introduce a “branching” flow design with an unbounded number of degrees of freedom and prove it achieves nearly optimal transport. The main technical tool behind these results is a variational principle for evaluating the transport of candidate designs. The principle admits dual formulations for bounding transport from above and below. While the upper bound is closely related to the “background method,” the lower bound reveals a connection between the optimal design problems considered herein and other apparently related model problems from mathematical materials science. These connections serve to motivate designs. © 2019 Wiley Periodicals, Inc.     

Editorial

Journal of Elasticity -     

How do molecular interactions affect fluorescence behavior of AIEgens in solution and aggregate states?

Molecular interactions are crucial in diverse fields of protein folding,material science,nanotechnology,and life origins.Although mounting experimental research controls luminescent behavior by adjusting molecular interactions in light-emitting materials,it remains elusive to correlate microscopic molecular interactions with macroscopic luminescent behavior directly.Here,we synthesized three red luminogens with subtle structural variation and investigated the influence of molecular interactions on their luminescent behavior in solution and aggregate states.Our results indicate that strongπ-πand D-A interactions in both dilute solution(between luminogen and solvent molecules)and aggregate(between luminogens)states cause the redshift in emission,while weak interactions(e.g.,Van der Waals,C–H…π,and C–H…F interactions)enhance the quantum yield.This work provides a thoughtful investigation into the complicated influence of various molecular interactions on luminescent behavior.     

Self‐assembled polyurea macromer nanodispersion and resulting hybrid polyurea‐acrylic emulsions and films

A polyurea macromer (PUM) was synthesized and dispersed in basic conditions to form self‐assembled nanoparticles (<20 nm dispersions, up to 30 wt % aq. soln.). These nanoparticles enabled surfactant‐free emulsion polymerization to form hybrid polyurea‐acrylic particles despite the absence of a measureable water‐soluble fraction. The T_g of the starting PUM material was a strong function of the PUM's extent of neutralization and hydration (varying between 100 °C and >175 °C) due to changes in hydrogen and ionic bonding. Two separate hybrid polyurea‐acrylic emulsion systems were prepared: one by direct polymerization of (meth)acrylic monomers in the presence of the nanodispersion and a second by a physical blend of PUM nanodispersion with an acrylic latex control. The direct polymerization method resulted in a hybrid emulsion particle size that developed by a mechanism resembling conventional emulsion polymerization and was unlike that described for seeded polyurethane dispersion systems. Film hardness was shown to increase with increasing coating thickness for the hybrid film prepared by direct polymerization. The resulting mechanical properties could be explained by applying mechanical models for a composite foam structure. These results were unprecedented for normal elastomer films. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1373–1388     

SIMS of organic layers with unknown matrix parameters: Locating the interface in dual beam argon gas cluster depth profiles

Four simple methods are evaluated to determine their accuracies for establishing the interface location in secondary ion mass spectrometry intensity depth profiles of organic layers where matrix effects have not been measured. Accurate location requires the separate measurement of each ion's matrix factor. This is often not possible, and so estimates using matrix-less methods are required. Six pure organic material interfaces are measured using many secondary ions to compare their locations from the four methods with those from full evaluation with matrix terms. For different secondary ions, matrix effects cause the apparent interface positions to vary over 20 nm. The shifts in the intensity profiles on going from a layer of P into a layer of Q are in the opposite direction to that for going from Q into P, so doubling layer thickness errors. The four methods are as follows: M1, use of the median interface position in the intensity profiles for the five lightest ions for 15 ≤ m/z ≤ 150; M2, extrapolation of the position for each ion to m/z = 0 for ions with m/z ≤ 150; M3, as M2 but for m/z ≤ 300; and M4, the extreme positions for all m/z ≤ 100. Comparison with the location using matrix terms shows their ranking, from best to worst, to be M4, M3, M1, and M2 with average errors of 10%, 12%, 14%, and 17%, respectively, of the profile interface full widths at half maximum. Use of pseudo-molecular ions is very much poorer, exceeding 50%, and should be avoided.     

Redox‐Active NOx Ligands in Palladium‐Mediated Processes

This Minireview highlights the redox and non‐innocent behavior of NO_x ligands (x=1, 2, or 3) in selected Pd‐mediated processes, for example, alkene and aromatic oxidation processes. A focus is placed on mechanistic understanding and linking recent transformations, such as C? H bond activation/functionalization and Wacker oxidation, with previous work on the functionalization of aromatics and alkenes by Pd^II salts.