Theodore MacMillan

All Publications

• Spectral energy transfer on complex networks: a filtering approach. Scientific reports MacMillan, T., Ouellette, N. T. 2024; 14 (1): 20691

  Abstract

  The spectral analysis of dynamical systems is a staple technique for analyzing a vast range of systems. But beyond its analytical utility, it is also the primary lens through which many physical phenomena are defined and interpreted. The turbulent energy cascade in fluid mechanics, a dynamical consequence of the three-dimensional Navier-Stokes equations in which energy "cascades" from large injection scales to smaller dissipation scales, is a well-known example that is precisely defined only in reciprocal space. Related techniques in the context of networked dynamical systems have been employed with great success in deriving reduced order models. But what such techniques gain in analytical tractability, they often lose in interpretability and locality, as the lower degree of freedom system frequently contains information from all nodes of the network. Here, we demonstrate that a network of nonlinear oscillators exhibits spectral energy transfer facilitated by an effective force akin to the Reynolds stress in turbulence, an example of an emergent higher order interaction. Then, introducing a filter-based decomposition motivated by large eddy simulation, we show that such higher order interactions can be localized to individual nodes and study the effects of local topology on such interactions.

  View details for DOI 10.1038/s41598-024-71756-x

  View details for PubMedID 39237704

  View details for PubMedCentralID 3497713

• Direct numerical simulation of turbulence and microphysics in the Pi Chamber PHYSICAL REVIEW FLUIDS MacMillan, T., Shaw, R. A., Cantrell, W. H., Richter, D. H. 2022; 7 (2)

  View details for DOI 10.1103/PhysRevFluids.7.020501

  View details for Web of Science ID 000752827200001

• Lagrangian scale decomposition via the graph Fourier transform PHYSICAL REVIEW FLUIDS MacMillan, T., Ouellette, N. T. 2022; 7 (12)

  View details for DOI 10.1103/PhysRevFluids.7.124401

• The most robust representations of flow trajectories are Lagrangian coherent structures JOURNAL OF FLUID MECHANICS MacMillan, T., Richter, D. H. 2021; 927

  View details for DOI 10.1017/jfm.2021.768

  View details for Web of Science ID 000701066600001

• A Lagrangian Cloud Model for the Study of Marine Fog BOUNDARY-LAYER METEOROLOGY Richter, D. H., MacMillan, T., Wainwright, C. 2021

  View details for DOI 10.1007/s10546-020-00595-w

  View details for Web of Science ID 000607776800007

• Detection of evolving Lagrangian coherent structures: A multiple object tracking approach PHYSICAL REVIEW FLUIDS MacMillan, T., Ouellette, N. T., Richter, D. H. 2020; 5 (12)

  View details for DOI 10.1103/PhysRevFluids.5.124401

  View details for Web of Science ID 000600850200004