Transient learning degrees of freedom for introducing function in materials

Varda F. Hagh, Sidney R. Nagel, Andrea J. Liu, M. Lisa Manning, Eric I. Corwin

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


The introduction of transient degrees of freedom into a system can lead to novel material design and training protocols that guide a system into a desired metastable state. In this approach, some degrees of freedom, which were not initially included in the system dynamics, are first introduced and subsequently removed from the energy minimization process once the desired state is reached. Using this conceptual framework, we create stable jammed packings that exist in exceptionally deep energy minima marked by the absence of low-frequency quasilocalized modes; this added stability persists in the thermodynamic limit. The inclusion of particle radii as transient degrees of freedom leads to deeper and much more stable minima than does the inclusion of particle stiffnesses. This is because particle radii couple to the jamming transition, whereas stiffnesses do not. Thus, different choices for the added degrees of freedom can lead to very different training outcomes.

Original languageEnglish (US)
Article numbere2117622119
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number19
StatePublished - May 10 2022


  • degrees of freedom
  • jamming
  • material training
  • mechanical stability
  • metamaterials

ASJC Scopus subject areas

  • General


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