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- Mathematical models of chiral symmetry-breaking: a review of general theories, and adiabatic approximations of the APED systemPublication . Diniz, Priscila Costa; Wattis, Jonathan AD; Costa, Fernando Pestana daWe review the literature surrounding chiral symmetry-breaking in chemical systems, with a focus on understanding the mathematical models underlying these chemical processes. We comment in particular on the toy model of Sandars, Viedmaâs crystal grinding systems and the APED model. We include a few new results based on asymptotic analysis of the APED system.
- Long-time behaviour and self-similarity in a coagulation equation with input of monomersPublication . Costa, Fernando Pestana da; Roessel, Henry J. van; Wattis, Jonathan ADFor a coagulation equation with Becker-Doring type interactions and time-independent monomer input we study the detailed long-time behaviour of nonnegative solutions and prove the convergence to a self-similar function
- A hierarchical cluster system based on Horton-Strahler rules for river networksPublication . Costa, Fernando Pestana da; Grinfeld, Michael; Wattis, Jonathan ADWe consider a cluster system in which each cluster is characterized by two parameters: an \order" i; following Horton-Strahler's rules, and a \mass" j following the usual additive rule. Denoting by ci;j (t) the concen- tration of clusters of order i and mass j at time t; we derive a coagulation- like ordinary di erential system for the time dynamics of these clusters. Results about existence and the behaviour of solutions as t ! 1 are ob- tained, in particular we prove that ci;j (t) ! 0 and Ni(c(t)) ! 0 as t ! 1; where the functional Ni( ) measures the total amount of clusters of a given xed order i: Exact and approximate equations for the time evolution of these functionals are derived. We also present numerical results that sug- gest the existence of self-similar solutions to these approximate equations and discuss its possible relevance for an interpretation of Horton's law of river numbers