Scaling and phase transitions – from proteins to ecology

The nature of a phase of matter transcends the microscopic material properties. For example, materials in the liquid phase have certain common properties independent of the chemistry of the constituents: liquids take the shape of the container; they flow; and they can be poured -- alcohol, oil and water as well as a Lennard-Jones computer model exhibit similar behaviour when poised in the liquid phase. I will introduce a simple model of a chain molecule with no spurious symmetries and present the results of computer simulations of its ground state phase diagram. Our calculations on relatively short chains (recall proteins are also much shorter than conventional polymers) reveals a hitherto unstudied “phase” that may have a relationship to proteins, the workhorse molecules of living cells. Our findings may be relevant for understanding proteins as well as for the creation of novel bio-inspired nano-machines.

Scaling ideas are most useful, when one is unable to deal with the full complexity of a problem or more importantly, when many of the details are not essential for the type of information that one is seeking. An important example of scaling arises in the field of ecology, when one wishes to understand the threats of losing bio-diversity. I will describe some recent results on the metabolic scaling of individual trees and a forest comprised of many trees. Our scaling framework unifies seemingly distinct trends in a forest and provides a simple yet promising approach to begin to quantitatively understand a bewilderingly complex many-body system with imperfectly known interactions.

Collaborators: Amos Maritan, Tomasso Anfodillo, Marek Cieplak, Achille Giacometti, Trinh Hoang, Andrea Rinaldo, Tatjana Skrbic, Igor Volkov