Coarse-graining microscopic strains in a harmonic, two-dimensional solid and its implications for elasticity: non-local susceptibilities and non-affine noise

Details Coarse-graining microscopic strains in a harmonic, two-dimensional solid and its implications for elasticity: non-local susceptibilities and non-affine noise Coarse-graining microscopic strains in a harmonic, two-dimensional solid and its implications for elasticity: non-local susceptibilities and non-affine noise

2009-11-07

arxiv.org/abs/0911.1410v1

Physics

Condensed Matter

Soft Condensed Matter

16 pages, 12 figures

Scientific paper

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 using a coarse-graining procedure. We study this process for a simple triangular lattice of particles connected by harmonic springs in two-dimensions. Coarse-graining local strains obtained from particle configurations in a Monte Carlo simulation generates non-trivial, non-local strain correlations (susceptibilities), which may be understood within a generalized, Landau type 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. 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 coarse-graining procedure also gives rise to a noise field made up of non-affine displacements. Several properties of this noise field 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 is studied and a master curve is obtained.

Affiliated with

Also associated with

No associations

Rating

Coarse-graining microscopic strains in a harmonic, two-dimensional solid and its implications for elasticity: non-local susceptibilities and non-affine noise does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Coarse-graining microscopic strains in a harmonic, two-dimensional solid and its implications for elasticity: non-local susceptibilities and non-affine noise, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Coarse-graining microscopic strains in a harmonic, two-dimensional solid and its implications for elasticity: non-local susceptibilities and non-affine noise will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-699589