This paper proposes a biologically inspired ‘molecular assembly line’ — an externally programmable polymeric chain along which molecules are shuttled between chain sites along an arbitrary pathway. Our hope is to construct a scaffold that mimics biological enzymes known as polyketide synthases in their ability to physically hand-off molecules between assembly sites or domains, thereby making al...

We consider a model of self-avoiding walks on the lattice Zd with different weights for steps in each of the 2d lattice directions. We find that the directiondependent mass for the two-point function of this model has three phases: mass positive in all directions; mass identically −∞; and masses of different signs in different directions. The final possibility can only occur if the weights are ...

We have produced extended series for prudent self-avoiding walks on the square lattice. These are subsets of self-avoiding walks. We conjecture the exact growth constant and critical exponent for the walks, and show that the (anisotropic) generating function is almost certainly not differentiably-finite.

This study aimed to synthesize alumina from an inorganic aluminum nitrate precursor in various binary solvent systems of ethanol and water using the sol-gel self-assembly (SSA) method, employing a triblock copolymer, pluronic P123, as pore-directing agent. The resulting materials were implemented support for cobalt (Co) catalyst methane dry reforming (MDR) reaction at 1073 K under 1 atm. Regard...