Type of Publication:  Journal article 
Author:  Franzrahe, Kerstin; Nielaba, Peter; Sengupta, S. 
Year of publication:  2010 
Published in:  Physical Review E ; 82 (2010), 1.  ISSN 15393755 
DOI (citable link):  https://dx.doi.org/10.1103/PhysRevE.82.016112 
Summary: 
In soft matter systems the local displacement field can be accessed directly by video microscopy enabling one to compute local strain fields and hence the elastic moduli in these systems using a coarsegraining procedure. We study this process in detail for a simple triangular, harmonic lattice in two dimensions. Coarsegraining local strains obtained from particle configurations in a Monte Carlo simulation generates nontrivial, nonlocal strain correlations (susceptibilities). These may be understood within a generalized, Landautype elastic Hamiltonian containing up to quartic terms in strain gradients [K. Franzrahe et al., Phys. Rev. E 78, 026106 (2008)]. In order to demonstrate the versatility of the analysis of these correlations and to make our calculations directly relevant for experiments on colloidal solids, we systematically study various parameters such as the choice of statistical ensemble, presence of external pressure and boundary conditions. Crucially, we show that special care needs to be taken for an accurate application of our results to actual experiments, where the analyzed area is embedded within a larger system, to which it is mechanically coupled. Apart from the smooth, affine strain fields, the coarsegraining procedure also gives rise to a noise field (χ) made up of nonaffine displacements. Several properties of χ may be rationalized for the harmonic solid using a simple “cell model” calculation. Furthermore the scaling behavior of the probability distribution of the noise field (χ) is studied. We find that for any inverse temperature β, spring constant f, density ρ and coarsegraining length Λ the probability distribution can be obtained from a master curve of the scaling variable X=χβf/ρΛ2.

PACS Classification:  62.20.F , 62.20.D , 82.70.Dd , 05.10.Ln 
Subject (DDC):  530 Physics 
Bibliography of Konstanz:  Yes 
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FRANZRAHE, Kerstin, Peter NIELABA, S. SENGUPTA, 2010. Coarsegraining microscopic strains in a harmonic, twodimensional solid : elasticity, nonlocal susceptibilities, and nonaffine noise. In: Physical Review E. 82(1). ISSN 15393755. Available under: doi: 10.1103/PhysRevE.82.016112
@article{Franzrahe2010Coars12449, title={Coarsegraining microscopic strains in a harmonic, twodimensional solid : elasticity, nonlocal susceptibilities, and nonaffine noise}, year={2010}, doi={10.1103/PhysRevE.82.016112}, number={1}, volume={82}, issn={15393755}, journal={Physical Review E}, author={Franzrahe, Kerstin and Nielaba, Peter and Sengupta, S.} }
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