Martensitic Transformations: From Continuum Mechanics to Spin Models and Automata

Abstract

The process of infection of a host is complex, influenced by factors such as microbial variation within and between hosts as well as differences in dose across hosts. This study uses dose-response and microbial growth models to delve into the impact of these factors on infection probability. It is rigorously demonstrated that within-host heterogeneity in microbial infectivity enhances the probability of infection. The effect of infectivity and dose variation between hosts is studied in terms of the expected value of the probability of infection. General analytical findings, derived under the assumption of small infectivity, reveal that both types of heterogeneity reduce the expected infection probability. Interestingly, this trend appears consistent across specific dose-response models, suggesting a limited role for the small infectivity condition. Additionally, the vital dynamics behind heterogeneous infectivity are investigated with a microbial growth model which enhances the biological significance of single-hit dose-response models. Testing these mathematical predictions inspire new and challenging laboratory experiments that could deepen our understanding of infections.

On the critical nature of plastic flow: One and two dimensional models

“…As it has been repeatedly proposed in the literature, the two dimensional models of plasticity may be sufficient to capture the corresponding universality class at least for FCC and hexagonal crystals [53,63,112]. For similar models of criticality associated with transformational plasticity, see [109,110,111]).…”

“…Now u is the lattice field and the function f is periodic with infinite symmetry group [128,111] . The discrete energy f contains information about both the bulk energy φ(∇u) and the surface energy ϕ([u]); the mechanism of such splitting in the continuum limit was discussed in the context of fracture in [129] and in the context of plasticity in [127].…”