Combinatorics,graph theory,and computing

Journal of Algebraic Combinatorics -     

A comparison of the structure and bonding in the donor–acceptor complexes H3N → BR(OH)2 and H3N → BRH(OH) (R = H; NH2, OH,and F): a computational investigation

Structural Chemistry - Boronic acids, R–B(OH)2, play an important role in synthetic, biological, medicinal, and materials chemistry. Borinic acids, R–BH(OH), find relevance in similar...     

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.     

Synthesis and structural characterization of (η5-Dp)Ru(PPh3)2H (Dp = C8H9−, 1,2-dihydropentalenyl)

Transition Metal Chemistry - (η5-Dp)Ru(PPh3)2H (Dp?=?C8H9?, 1,2-dihydropentalenyl) was synthesized in 90% yield by reaction of (η5-Dp)Ru(PPh3)2Cl with sodium formate....     

Distorted Phthalocyanines by Click Chemistry: Photoacoustic,Photothermal, and Surface-Enhanced Resonance Raman Studies

Distortion of nominally planar phthalocyanine macrocycles affects the excited state dynamics in that most of the excited-state energy decays through internal conversion. A click-type annulation reaction on a perfluorophthalocyanine platform appending a seven-membered ring to the β-positions on one or more of the isoindoles distorts the macrocycle and modulates solubility. The distorted derivative enables photoacoustic imaging, photothermal effects, and strong surface-enhanced resonance Raman signals.     

A door to model reduction in high-dimensional parameter space

Model reduction techniques such as Proper Generalized Decomposition (PGD) are decision-making tools that are about to revolutionize many domains. Unfortunately, their computation is still problematic for problems involving many parameters, for which one has to face the “curse of dimensionality”. An answer to this challenge is given in solid mechanics by the so-called “parameter-multiscale PGD”, which is based on Saint-Venant's principle. In this article, a model problem composed of up to a thousand parameters is presented, showing that the method is able to overcome the “curse of dimensionality”.     

Rational design of methacrylate monomers containing oxadiazole moieties for single‐layer organic light emitting devices

Methacrylate derived monomers functionalized with pendant oxadiazole moieties were synthesized and copolymerized with carbazole containing monomers to form polymers with electron and hole transporting fragments in the same molecule. Substituents on the oxidazole moiety were varied with the purpose of bandgap tuning and performance optimization when employed in single‐layer organic light emitting devices (OLED). Quantum mechanical calculations of the HOMO‐LUMO levels of the oxidazole derivatives were used to down‐select promising candidates for chemical synthesis and testing in single‐layer OLEDs. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1663–1673     

Influences of hyperbranched polyethylenimine on the reactive compatibilization of polycarbonate/polyamide blends

The influences of hyperbranched polyethylenimine(h PEI), which possesses many reactive amino end-groups, on the blending properties of bisphenol-A polycarbonate(PC) and amorphous polyamide(a PA) were systematically investigated. Scanning electron microscopy(SEM) and differential scanning calorimetry(DSC) were used to observe the effect of h PEI on morphologies of PC and a PA phases in bulk blends. While the interfacial fracture toughness between planar PC and a PA layers with and without h PEI was studied by using augmented double cantilever beam(ADCB) method. Results show that the compatibility in PC/a PA blends can be significantly improved by adding a small amount of h PEI, mainly due to the interchange reactions between the polymers leading to the formation of block copolymers, cross-linked polymers and molecules with other constitutions. The augmented double cantilever beam experiments showed that the reactive process drastically reinforced the interfacial adhesion between planar layers of PC and a PA. However, degradation takes place during annealing at 180 °C, which was responsible for the production of small molar mass species of PC.