Flory approximation for directed branched polymers and directed percolation

Flory approximation for directed branched polymers and directed percolation

Directed polymers versus directed percolation

Universality plays a central role within the rubric of modern statistical mechanics, wherein an insightful continuum formulation rises above irrelevant microscopic details, capturing essential scaling behaviors. Nevertheless, occasions do arise where the lattice or another discrete aspect can constitute a formidable legacy. Directed polymers in random media, along with its close sibling, direct...

Dimensional Reduction for Directed Branched Polymers

Dimensional reduction occurs when the critical behavior of one system can be related to that of another system in a lower dimension. We show that this occurs for directed branched polymers (DBP) by giving an exact relationship between DBP models in D+1 dimensions and repulsive gases at negative activity in D dimensions. This implies relations between exponents of the two models: γ(D + 1) = α(D)...

Renormalized field theory of collapsing directed randomly branched polymers.

We present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition. We develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition. For the swollen phase, we find that by choosing model para...

Template-Directed Synthesis of Structurally Defined Branched Polymers

A grand challenge in materials chemistry is the synthesis of macromolecules and polymers with precise shapes and architectures. In this work, we describe a hybrid synthetic strategy to produce structurally defined branched polymer architectures based on chemically modified DNA. Overall, this approach enables precise control over branch placement, grafting density, and chemical identity of side ...