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1. A dislocation-density-based crystal plasticity model for FCC nanocrystalline metals incorporating thermally-activated depinning from grain boundaries

   https://doi.org/10.1016/j.ijplas.2023.103863  

   Cappola, Jonathan; Wang, Jian; Li, Lin (January 2024, International Journal of Plasticity)

   A novel dislocation-density-based crystal plasticity model for nanocrystalline face-centered cubic metals is developed based on the thermally-activated mechanism of dislocations depinning from grain boundaries. Dislocations nucleated from grain boundary dislocation sources are assumed to be the primary carriers of plasticity in the nanocrystals. The evolution of the dislocation density thereby involves a competition between the nucleation of dislocations from grain boundary defect structures, such as ledges, and the absorption of dislocations into the grain boundary via diffusion processes. This model facilitates the simulation of plastic deformation in nanocrystalline metals, with consideration of the initial microstructure resulting from a particular processing method, to be computed as a direct result of dislocation-mediated plasticity only. The exclusion of grain boundary-mediated plasticity mechanisms in the formulation of the crystal plasticity model allows for the exploration of the fundamental role dislocations play in nanocrystalline plasticity. The combined effect of average grain size, grain size distribution shape, and initial dislocation density on the mechanical performance and strain-rate sensitivity are explored with the model. Further, the influence of the grain boundary diffusivity on post-yielding strain-hardening behavior is investigated to discern the impact that the choice of processing route has on the resulting deformation response of the material. 

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2. Effect of a Long-Range Dislocation Pileup on the Atomic-Scale Hydrogen Diffusion near a Grain Boundary in Plastically Deformed bcc Iron

   https://doi.org/10.3390/cryst13081270  

   Peng, Yipeng; Ji, Rigelesaiyin; Phan, Thanh; Chen, Xiang; Zhang, Ning; Xu, Shuozhi; Bastawros, Ashraf; Xiong, Liming (August 2023, Crystals)

   In this paper, we present concurrent atomistic-continuum (CAC) simulations of the hydrogen (H) diffusion along a grain boundary (GB), nearby which a large population of dislocations are piled up, in a plastically deformed bi-crystalline bcc iron sample. With the microscale dislocation slip and the atomic structure evolution at the GB being simultaneously retained, our main findings are: (i) the accumulation of tens of dislocations near the H-charged GB can induce a local internal stress as high as 3 GPa; (ii) the more dislocations piled up at the GB, the slower the H diffusion ahead of the slip–GB intersection; and (iii) H atoms diffuse fast behind the pileup tip, get trapped within the GB, and diffuse slowly ahead of the pileup tip. The CAC simulation-predicted local H diffusivity, Dpileup−tip, and local stresses, σ, are correlated with each other. We then consolidate such correlations into a mechanics model by considering the dislocation pileup as an Eshelby inclusion. These findings will provide researchers with opportunities to: (a) characterize the interplay between plasticity, H diffusion, and crack initiation underlying H-induced cracking (HIC); (b) develop mechanism-based constitutive rules to be used in diffusion–plasticity coupling models for understanding the interplay between mechanical and mass transport in materials at the continuum level; and (c) connect the atomistic deformation physics of polycrystalline materials with their performance in aqueous environments, which is currently difficult to achieve in experiments. 

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3. The combined hydrodynamic and thermodynamic effects of immobilized proteins on the diffusion of mobile transmembrane proteins

   https://doi.org/10.1017/jfm.2019.592  

   Singh, Rohit R.; Sangani, Ashok S.; Daniel, Susan; Koch, Donald L. (October 2019, Journal of Fluid Mechanics)

   The plasma membranes of cells are thin viscous sheets in which some transmembrane proteins have two-dimensional mobility and some are immobilized. Previous studies have shown that immobile proteins retard the short-time diffusivity of mobile particles through hydrodynamic interactions and that steric effects of immobile proteins reduce the long-time diffusivity in a model that neglects hydrodynamic interactions. We present a rigorous derivation of the long-time diffusivity of a single mobile protein interacting hydrodynamically and thermodynamically with an array of immobile proteins subject to periodic boundary conditions. This method is based on a finite element method (FEM) solution of the probability density of the mobile protein diffusing with a position-dependent mobility determined through a multipole solution of Stokes equations. The simulated long-time diffusivity in square arrays decreases as the spacing in the array approaches the particle size in a manner consistent with a lubrication analysis. In random arrays, steric effects lead to a percolation threshold volume fraction above which long-time diffusion is arrested. The FEM/multipole approach is used to compute the long-time diffusivity far away from this threshold. An approximate analysis of mobile protein diffusion through a network of pores connected by bonds with resistances determined by the FEM/multipole calculations is then used to explore higher immobile area fractions and to evaluate the finite simulation cell size scaling behaviour of diffusion near the percolation threshold. Surprisingly, the ratio of the long-time diffusivity to the spatially averaged short-time diffusivity in these two-dimensional fixed arrays is higher in the presence of hydrodynamic interactions than in their absence. Finally, the implications of this work are discussed, including the possibility of using the methods developed here to investigate more complex diffusive phenomena observed in cell membranes. 

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4. An optimization tool for identifying multiple-diffusion domain model parameters

   https://doi.org/10.5194/gchron-6-521-2024  

   Gorin, Andrew L; Gorin, Joshua M; Bergelin, Marie; Shuster, David L (January 2024, Geochronology)

   Abstract. The multiple-diffusion domain (MDD) model empirically describes the diffusive behavior of noble gases in some terrestrial materials and has been commonly used to interpret 40Ar/39Ar stepwise degassing observations in K-feldspar. When applied in this manner, the MDD model can be used to test crustal exhumation scenarios by identifying the permissible thermal paths a rock sample could have undergone over geologic time, assuming the diffusive properties of Ar within the mineral are accurately understood. More generally, the MDD model provides a framework for quantifying the temperature-dependent diffusivity of noble gases in minerals. However, constraining MDD parameters that successfully predict the results of step-heating diffusion experiments is a complex task, and the assumptions made by existing numerical methods used to quantify model parameters can bias the absolute temperatures permitted by thermal modeling. For example, the most commonly used method assumes that no domains lose more than 60 % of their gas during early heating steps (Lovera et al., 1997). This assumption is unverifiable, and we show that the Lovera et al. (1997) procedure may bias predicted temperatures towards lower values when it is violated. To address this potential bias and to provide greater accessibility to the MDD model, we present a new open-source method for constraining MDD parameters from stepwise degassing experimental results, called the “MDD Tool Kit” (https://github.com/dgorin1/mddtoolkit, last access: 11 October 2024). This software optimizes all MDD parameters simultaneously and removes any need for user-defined Ea or regression fitting choices used by other tools. In doing so, this new method eliminates assumptions about the domain size distribution. To test the validity of our thermal predictions, we then use the MDD Tool Kit (https://github.com/dgorin1/mddtoolkit) to interpret 40Ar/39Ar results from the Grayback Fault, AZ, USA. Although the resulting thermal histories are consistently ∼ 60–75 °C higher than those found in previous studies, they agree with independent observations from apatite fission track, zircon fission track, and (U-Th)/He. 

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5. Markov Chain-Based Sampling for Exploring RNA Secondary Structure under the Nearest Neighbor Thermodynamic Model and Extended Applications

   https://doi.org/10.3390/mca25040067  

   Kirkpatrick, Anna; Patton, Kalen; Tetali, Prasad; Mitchell, Cassie (December 2020, Mathematical and Computational Applications)

   null (Ed.)

   Ribonucleic acid (RNA) secondary structures and branching properties are important for determining functional ramifications in biology. While energy minimization of the Nearest Neighbor Thermodynamic Model (NNTM) is commonly used to identify such properties (number of hairpins, maximum ladder distance, etc.), it is difficult to know whether the resultant values fall within expected dispersion thresholds for a given energy function. The goal of this study was to construct a Markov chain capable of examining the dispersion of RNA secondary structures and branching properties obtained from NNTM energy function minimization independent of a specific nucleotide sequence. Plane trees are studied as a model for RNA secondary structure, with energy assigned to each tree based on the NNTM, and a corresponding Gibbs distribution is defined on the trees. Through a bijection between plane trees and 2-Motzkin paths, a Markov chain converging to the Gibbs distribution is constructed, and fast mixing time is established by estimating the spectral gap of the chain. The spectral gap estimate is obtained through a series of decompositions of the chain and also by building on known mixing time results for other chains on Dyck paths. The resulting algorithm can be used as a tool for exploring the branching structure of RNA, especially for long sequences, and to examine branching structure dependence on energy model parameters. Full exposition is provided for the mathematical techniques used with the expectation that these techniques will prove useful in bioinformatics, computational biology, and additional extended applications. 

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