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States of self stress, organizations of internal forces in many-body systemsthat are in equilibrium with an absence of external forces, can be thought ofas the constitutive building blocks of the elastic response of a material. Inoverconstrained disordered packings they have a natural mathematicalcorrespondence with the zero-energy vibrational modes in underconstrainedsystems. While substantial attention in the literature has been paid todiverging length scales associated with zero- and finite-energy vibrationalmodes in jammed systems, less is known about the spatial structure of thestates of self stress. In this work we define a natural way in which a uniquestate of self stress can be associated with each bond in a disordered springnetwork derived from a jammed packing, and then investigate the spatialstructure of these bond-localized states of self stress. This allows for anunderstanding of how the elastic properties of a system would change uponchanging the strength or even existence of any bond in the system.

Spatial structure of states of self stress in jammed systems