An official website of the United States government
Analysis of quasi-dynamic ordinary differential equations and the quasi-dynamic replicator
- Award ID(s):
- 1814876
- PAR ID:
- 10167537
- Date Published:
- Journal Name:
- Physica A: Statistical Mechanics and its Applications
- Volume:
- 555
- Issue:
- C
- ISSN:
- 0378-4371
- Page Range / eLocation ID:
- 124422
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
Hydrogels prepared from supramolecular cross-linking motifs are appealing for use as biomaterials and drug delivery technologies. The inclusion of macromolecules (e.g., protein therapeutics) in these materials is relevant to many of their intended uses. However, the impact of dynamic network cross-linking on macromolecule diffusion must be better understood. Here, hydrogel networks with identical topology but disparate cross-link dynamics are explored. These materials are prepared from cross-linking with host–guest complexes of the cucurbit[7]uril (CB[7]) macrocycle and two guests of different affinity. Rheology confirms differences in bulk material dynamics arising from differences in cross-link thermodynamics. Fluorescence recovery after photobleaching (FRAP) provides insight into macromolecule diffusion as a function of probe molecular weight and hydrogel network dynamics. Together, both rheology and FRAP enable the estimation of the mean network mesh size, which is then related to the solute hydrodynamic diameters to further understand macromolecule diffusion. Interestingly, the thermodynamics of host–guest cross-linking are correlated with a marked deviation from classical diffusion behavior for higher molecular weight probes, yielding solute aggregation in high-affinity networks. These studies offer insights into fundamental macromolecular transport phenomena as they relate to the association dynamics of supramolecular networks. Translation of these materials from in vitro to in vivo is also assessed by bulk release of an encapsulated macromolecule. Contradictory in vitro to in vivo results with inverse relationships in release between the two hydrogels underscores the caution demanded when translating supramolecular biomaterials into application.more » « less
-
null (Ed.)ABSTRACT Numerical models of rupture dynamics provide great insights into the physics of fault failure. However, resolving stress interactions among multiple faults remains challenging numerically. Here, we derive the elastostatic Green’s functions for stress and displacement caused by arbitrary slip distributions along multiple parallel faults. The equations are derived in the Fourier domain, providing an efficient means to calculate stress interactions with the fast Fourier transform. We demonstrate the relevance of the method for a wide range of applications, by simulating the rupture dynamics of single and multiple parallel faults controlled by a rate- and state-dependent frictional contact, using the spectral boundary integral method and the radiation-damping approximation. Within the antiplane strain approximation, we show seismic cycle simulations with a power-law distribution of rupture sizes and, in a different parameter regime, sequences of seismogenic slow-slip events. Using the in-plane strain approximation, we simulate the rupture dynamics of a restraining stepover. Finally, we describe cycles of large earthquakes along several parallel strike-slip faults in three dimensions. The approach is useful to explore the dynamics of interacting or isolated faults with many degrees of freedom.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.physa.2020.124422
