Homogenization of random degenerated nonlinear monotone operators

This paper deals with homogenization of random nonlinear monotone operators in divergence form. We assume that the structure conditions (strict monotonicity and continuity conditions) degenerate and are given in terms of a weight function. Under proper integrability assumptions on the weight function we construct the effective operator and prove the homogenization result

Homogenization of Biomechanical Models for Plant Tissues

In this paper homogenization of a mathematical model for plant tissue biomechanics is presented. The microscopic model constitutes a strongly coupled system of reaction-diffusion-convection equations for chemical processes in plant cells, the equations of poroelasticity for elastic deformations of plant cell walls and middle lamella, and Stokes equations for fluid flow inside the cells. The chemical process in cells and the elastic properties of cell walls and middle lamella are coupled because elastic moduli depend on densities involved in chemical reactions, whereas chemical reactions depend on mechanical stresses. Using homogenization techniques we derive rigorously a macroscopic model for plant biomechanics. To pass to the limit in the nonlinear reaction terms, which depend on elastic strain, we prove the strong two-scale convergence of the displacement gradient and velocity field

Polymorphic Signature of the Anti-inflammatory Activity of 2,2′- {[1,2-Phenylenebis(methylene)]bis(sulfanediyl)}bis(4,6- dimethylnicotinonitrile)

Weak noncovalent interactions are the basic forces in crystal engineering. Polymorphism in flexible molecules is very common, leading to the development of the crystals of same organic compounds with different medicinal and material properties. Crystallization of 2,2′- {[1,2-phenylenebis(methylene)]bis(sulfanediyl)}bis(4,6-dimethylnicotinonitrile) by evaporation at room temperature from ethyl acetate and hexane and from methanol and ethyl acetate gave stable polymorphs 4a and 4b, respectively, while in acetic acid, it gave metastable polymorph 4c. The polymorphic behavior of the compound has been visualized through singlecrystal X-ray and Hirshfeld analysis. These polymorphs are tested for anti-inflammatory activity via the complete Freund’s adjuvant-induced rat paw model, and compounds have exhibited moderate activities. Studies of docking in the catalytic site of cyclooxygenase-2 were used to identify potential anti-inflammatory lead compounds. These results suggest that the supramolecular aggregate structure, which is formed in solution, influences the solid state structure and the biological activity obtained upon crystallization

Homogenization of a nonlinear random parabolic partial differential equation

The aim of this work is to show how to homogenize a semilinear parabolic second-order partial differential equation, whose coefficients are periodic functions of the space variable, and are perturbed by an ergodic diffusion process, the nonlinear term being highly oscillatory. Our homogenized equation is a parabolic stochastic partial differential equation.Homogenization of periodic PDEs Homogenization of random PDEs Stochastic partial differential equations

Kiloscale Buchwald–Hartwig Amination: Optimized Coupling of Base-Sensitive 6‑Bromoisoquinoline-1-carbonitrile with (<i>S</i>)‑3-Amino-2-methylpropan-1-ol

This work describes the optimization and scale-up of a Buchwald–Hartwig amination reaction for the preparation of a pharmaceutical intermediate. This C–N bond formation is challenged by the use of a chiral primary amine, which both adds cost and favors formation of biaryl byproducts. In order to develop a scalable process, a number of factors had to be investigated including catalyst selection and stoichiometry of the chiral amine. These all needed to be optimized while maintaining low palladium levels in the isolated product. The reaction was found to be most effective using Pd­(dba)₂ with BINAP and Cs₂CO₃ in THF. When executed on 2.5 kg scale, these conditions provided 2.06 kg of the desired product in 80% yield with only 73 ppm residual palladium. To date, this process has been successfully executed to produce more than 12 kg of compound <b>(</b><i><b>S</b></i><b>)-3</b>