David Reynolds
Department of Physics. UCSB.
| At the heart of both the renormalization group (RG) and ($\mathcal{H}_{\infty}$) robust control theory is modelling systems with noise and other uncertainties. In its original guise, the RG provides a framework from which to understand how models or theories (linear or nonlinear) of physical systems change when observed on different scales. In the context of dynamical systems, it is related to the theory of averaging and multiple scale analysis. Unfortunately, the standard form of the RG does not work well for heterogeneous systems. In contrast, in robust control theory system realizations are produced from the response of the system and are insensitive to the spatial structure of the system. My recent work has involved marrying these differing ideas. The consequences of this work have been the development of a generalization of the RG that is applicable to heterogeneous systems by placing local and nonlocal coarse graining on the same footing. We treat a $\phi^4$ theory to illustrate what new properties arise from using the generalized RG. |
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