Jamming: Marginal Stability and Thermodynamic Rigidity
| dc.contributor.advisor | Corwin, Eric | |
| dc.contributor.author | Dennis, Robert | |
| dc.date.accessioned | 2022-02-18T18:13:35Z | |
| dc.date.issued | 2022-02-18 | |
| dc.description.abstract | This dissertation marks a significant step forward in fully understanding glasses and jammed materials as we unify the concept of marginality in amorphous systems, definitively resolve the jamming threshold problem, create new methods for simulating and analyzing polymer packings, and prove a series of salient theorems involving periodic boundary conditions. We shift the discussion of Gardner marginality to include athermal systems and open the door to broader explorations. For the first time, we show that athermal jammed systems in physically relevant spatial dimensions are controlled by the marginal Gardner phase. The set of over-jammed minima form a hierarchical ultrametric space. Understanding the physics of the jamming transition is widely relevant because jamming critical points occur in systems forming a universality class. This work takes important steps toward verifying the critical properties of this transition. While previous works have confirmed the criticality of thermodynamic variables, no such tests have been carried out for the distributions of contact forces and interparticle gaps. We demonstrate that mechanically stable jammed packings of spheres can be made at densities all the way down to zero, not only answering a long-standing question about the lower limit on the density of sphere packings, but demonstrating the shocking result that mechanically rigid packings of spheres can exist at zero density. This result is of widespread importance in materials science research. A system of athermal soft spheres that interact via a one-sided contact potential is an excellent model for jamming and glasses. However, many glasses we interact with on a daily basis consist of molecular chains. By modifying the soft sphere model, I demonstrate how to create polymer packings and examine their properties. Most simulations involving glasses and jamming utilize periodic boundary conditions, a simple choice that drastically reduces finite-size effects. However, we find that sometimes there is a stark difference between systems with periodic boundary conditions and the corresponding infinitely repeated lattice representations. We show a series of proofs that put these differences into perspective, providing a foundation for better understanding when periodic boundary conditions are appropriate. This dissertation includes previously published and unpublished single-authored and co-authored materials. | en_US |
| dc.description.embargo | 2024-01-24 | |
| dc.identifier.uri | https://hdl.handle.net/1794/27081 | |
| dc.language.iso | en_US | |
| dc.publisher | University of Oregon | |
| dc.rights | All Rights Reserved. | |
| dc.subject | glasses | en_US |
| dc.subject | jamming | en_US |
| dc.subject | rigidity | en_US |
| dc.subject | simulation | en_US |
| dc.subject | soft condensed matter | en_US |
| dc.title | Jamming: Marginal Stability and Thermodynamic Rigidity | |
| dc.type | Electronic Thesis or Dissertation | |
| thesis.degree.discipline | Department of Physics | |
| thesis.degree.grantor | University of Oregon | |
| thesis.degree.level | doctoral | |
| thesis.degree.name | Ph.D. |
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