Category Ranking
98%
Total Visits
921
Avg Visit Duration
2 minutes
Citations
20
Article Abstract
In this paper we use a formal discrete-to-continuum procedure to derive a continuum variational model for two chains of atoms with slightly incommensurate lattices. The chains represent a cross section of a three-dimensional system consisting of a graphene sheet suspended over a substrate. The continuum model recovers both qualitatively and quantitatively the behavior observed in the corresponding discrete model. The numerical solutions for both models demonstrate the presence of large commensurate regions separated by localized incommensurate domain walls.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevE.96.033003 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
A theoretical model for focal adhesion and cytoskeleton formation in non-motile cells.
J Theor Biol
January 2025
School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QQ, United Kingdom. Electronic address:
To function and survive cells need to be able to sense and respond to their local environment through mechanotransduction. Crucially, mechanical and biochemical perturbations initiate cell signalling cascades, which can induce responses such as growth, apoptosis, proliferation and differentiation. At the heart of this process are actomyosin stress fibres (SFs), which form part of the cell cytoskeleton, and focal adhesions (FAs), which bind this cytoskeleton to the extra-cellular matrix (ECM).
View Article and Find Full Text PDFA discrete-to-continuum model for the human cornea with application to keratoconus.
R Soc Open Sci
July 2024
Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano 20133, Italy.
We introduce a discrete mathematical model for the mechanical behaviour of a planar slice of human corneal tissue, in equilibrium under the action of physiological intraocular pressure (IOP). The model considers a regular (two-dimensional) network of structural elements mimicking a discrete number of parallel collagen lamellae connected by proteoglycan-based chemical bonds (crosslinks). Since the thickness of each collagen lamella is small compared to the overall corneal thickness, we upscale the discrete force balance into a continuum system of partial differential equations and deduce the corresponding macroscopic stress tensor and strain energy function for the micro-structured corneal tissue.
View Article and Find Full Text PDFMicroscopical Justification of Solid-State Wetting and Dewetting.
J Nonlinear Sci
April 2022
Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, Croatia.
The continuum model related to the , i.e., the problem of determining the equilibrium shape of crystalline drops resting on a substrate, is derived in dimension two by means of a rigorous discrete-to-continuum passage by -convergence of atomistic models taking into consideration the atomic interactions of the drop particles both among themselves and with the fixed substrate atoms.
View Article and Find Full Text PDFA discrete-to-continuum model of protein complexes.
Biomech Model Mechanobiol
June 2022
Department System Analysis, Integrated Assessment and Modelling, EAWAG, Überlandstrasse 133, Ch-8600, Düberdorf, Switzerland.
On the basis of a tensor representation of protein shape, obtained by an affine decomposition of residue velocity, we show how to identify actions at continuum scale for both single proteins and their complexes in terms of power equivalence. The approach constructs and justifies a continuum modeling of protein complexes, which avoids a direct, atomistic-based, simulation of the whole complex, rather it focuses (in a statistical sense) on a single protein and its interactions with the neighbors. In the resulting setting we also prove the existence of equilibrium configurations (native states) under large strains.
View Article and Find Full Text PDFComparative analysis of continuum angiogenesis models.
J Math Biol
February 2021
Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, United Kingdom.
Although discrete approaches are increasingly employed to model biological phenomena, it remains unclear how complex, population-level behaviours in such frameworks arise from the rules used to represent interactions between individuals. Discrete-to-continuum approaches, which are used to derive systems of coarse-grained equations describing the mean-field dynamics of a microscopic model, can provide insight into such emergent behaviour. Coarse-grained models often contain nonlinear terms that depend on the microscopic rules of the discrete framework, however, and such nonlinearities can make a model difficult to mathematically analyse.
View Article and Find Full Text PDF