Dyck paths with a first return decomposition constrained by height

We study the enumeration of Dyck paths having a first return decomposition with special properties based on a height constraint. We exhibit new restricted sets of Dyck paths counted by the Motzkin numbers, and we give a constructive bijection between these objects and Motzkin paths. As a byproduct, we provide a generating function for the number of Motzkin paths of height $k$ with a flat (resp. with no flats) at the maximal height.     

Phase Separation in the Advective Cahn–Hilliard Equation

The Cahn–Hilliard equation is a classic model of phase separation in binary mixtures that exhibits spontaneous coarsening of the phases. We study the Cahn–Hilliard equation with an imposed advection term in order to model the stirring and eventual mixing of the phases. The main result is that if the imposed advection is sufficiently mixing, then no phase separation occurs, and the solution instead converges exponentially to a homogeneous mixed state. The mixing effectiveness of the imposed drift is quantified in terms of the dissipation time of the associated advection–hyperdiffusion equation, and we produce examples of velocity fields with a small dissipation time. We also study the relationship between this quantity and the dissipation time of the standard advection–diffusion equation.

     

A tether controlled exo-selective trans-annular Diels-Alder (TADA) reaction

[reaction: see text] A fully substrate controlled stereoselective route to construct cis-hexahydronaphthalene 4 is described starting from nonracemic butenolide 6. The key step is an exo-selective transannular Diels-Alder reaction (TADA) of tetraene 5, whose intrinsic constraint allows selective formation of one stereodefined product. Compound 4 is a key intermediate in the synthesis of the novel antibiotic branimycin (1).     

Interface energetics and level alignment at covalent metal-molecule junctions: pi-conjugated thiols on gold

The energetics at the interfaces between metal and monolayers of covalently bound organic molecules is studied theoretically. Despite the molecules under consideration displaying very different frontier orbital energies, the highest occupied molecular levels are found to be pinned at a constant energy offset with respect to the metal Fermi level. In contrast, the molecular properties strongly impact the metal work function. These interfacial phenomena are rationalized in terms of charge fluctuations and electrostatics at the atomic length scale as determined by first-principles calculations.     

Equivalance de marita relative

We define a relative Morita equivalence and we extend the Morita—invariance of cyclic and Hochschild homology to the relative'case.     

Turnpike Property in Optimal Microbial Metabolite Production

Journal of Optimization Theory and Applications - We consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP)....     

Theoretical description of the geometric and electronic structures of organic-organic interfaces in organic solar cells: a brief review

We review some of the computational methodologies used in our research group to develop a better understanding of the geometric and electronic structures of organic-organic interfaces present in the active layer of organic solar cells. We focus in particular on the exciton-dissociation and charge-transfer processes at the pentacene-fullerene interface. We also discuss the local morphology at this interface on the basis of molecular dynamics simulations.     

Impact of Imine Bond Orientations on the Geometric and Electronic Structures of Imine-based Covalent Organic Frameworks

Many efforts are currently devoted to improving the stability and crystallinity of imine-based two-dimensional (2D) covalent organic frameworks (COFs) given their wide range of potential applications. The variation in the relative orientations of the imine bonds has been found to be a critical factor that impacts the stacking of the 2D COF layers, leads to the formation of isomer structures, and influences the crystallinity of the final product. Most investigations to date have focused only on the structural properties, while the role of the imine orientations on the electronic properties has not been studied systematically. Here, we explore this effect by examining how the electronic band structures, electronic couplings, and effective masses evolve when considering four isomeric structures of an imine-linked tetraphenyl-pyrene naphthalene-diimide COF. Our results provide an understanding of the impact of the imine orientations and how they need to be controlled to realize COF inter-layer stackings that can lead to efficient cross-plane electron transport. They can be used to guide the design and synthesis of imine-based COFs for applications where charge transport needs to be optimized.     

Allylic phosphinates via palladium-catalyzed allylation of H-phosphinic acids with allylic alcohols

A novel catalytic allylation of H-phosphinic acids is described. Using Pd/xantphos (2 mol %), H-phosphinic acids react directly with allylic alcohols to produce P-allylated disubstituted phosphinic acids.