Disorder Measures and Non-equilibrium States of Cellular Matter

Cellular materials such as foams, emulsions, or biological tissues in general have a plethora of configurations in mechanical equilibrium. Identifying a global minimum (ground state) in a disordered domain system is a formidable task. However, protocols for lowering total energy through successive topological transitions have been suggested. Through modeling and simulations, we investigate systematic energy variation through a sequence of local equilibrium states, and the parallel changes in various measures of disorder and size-topology correlation in the structure. Statistical measures are identified that allow for quantification of the distance of the current structure from the ground state. This work can be applied as a tool to assess the mechanical state of foam or tissue structures from visual information only, with applications ranging from tissue diagnostics to regenerative medicine.