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Fibrous networks such as collagen are common in physiological systems. One important function of these networks is to provide mechanical stability for cells and tissues. At physiological levels of connectivity, such networks would be mechanically unstable with only central-force interactions. While networks can be stabilized by bending interactions, it has also been shown that they exhibit a critical transition from floppy to rigid as a function of applied strain. Beyond a certain strain threshold, it is predicted that underconstrained networks with only central-force interactions exhibit a discontinuity in the shear modulus. We study the finite-size scaling behavior of this transition and identify both the mechanical discontinuity and critical exponents in the thermodynamic limit. We find both non-mean-field behavior and evidence for a hyperscaling relation for the critical exponents, for which the network stiffness is analogous to the heat capacity for thermal phase transitions. Further evidence for this is also found in the self-averaging properties of fiber networks.
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Inferring phase transitions and critical exponents from limited observations with thermodynamic maps
Phase transitions are ubiquitous across life, yet hard to quantify and describe accurately. In this work, we develop an approach for characterizing generic attributes of phase transitions from very limited observations made deep within different phases’ domains of stability. Our approach is called thermodynamic maps (TM), which combines statistical mechanics and molecular simulations with score-based generative models. TM enable learning the temperature dependence of arbitrary thermodynamic observables across a wide range of temperatures. We show its usefulness by calculating phase transition attributes such as melting temperature, temperature-dependent heat capacities, and critical exponents. For instance, we demonstrate the ability of TM to infer the ferromagnetic phase transition of the Ising model, including temperature-dependent heat capacity and critical exponents, despite never having seen samples from the transition region. In addition, we efficiently characterize the temperature-dependent conformational ensemble and compute melting curves of the two RNA systems: a GCAA tetraloop and the HIV-TAR RNA, which are notoriously hard to sample due to glassy-like energy landscapes.
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- Award ID(s):
- 2044165
- PAR ID:
- 10592494
- Publisher / Repository:
- National Academy of Sciences
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 121
- Issue:
- 52
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1073/pnas.2321971121
