Elastic Moduli in Nano-Size Samples of Amorphous Solids: System Size Dependence

This Letter is motivated by some recent experiments on pan-cake shaped nano-samples of metallic glass that indicate a decline in the measured shear modulus upon decreasing the sample radius. Similar measurements on crystalline samples of the same dimensions showed a much more modest change. In this Letter we offer a theory of this phenomenon; we argue that such results are generically expected for any amorphous solid, with the main effect being related to the increased contribution of surfaces with respect to bulk when the samples get smaller. We employ exact relations between the shear modulus and the eigenvalues of the system's Hessian matrix to explore the role of surface modes in affecting the elastic moduli

Long-time evolution of sequestered CO2_2 in porous media

CO$_2$ sequestration in subsurface reservoirs is important for limiting atmospheric CO$_2$ concentrations. However, a complete physical picture able to predict the structure developing within the porous medium is lacking. We investigate theoretically reactive transport in the long-time evolution of carbon in the brine-rock environment. As CO$_2$ is injected into a brine-rock environment, a carbonate-rich region is created amid brine. Within the carbonate-rich region minerals dissolve and migrate from regions of high concentration to low concentration, along with other dissolved carbonate species. This causes mineral precipitation at the interface between the two regions. We argue that precipitation in a small layer reduces diffusivity, and eventually causes mechanical trapping of the CO$_2$. Consequently, only a small fraction of the CO$_2$ is converted to solid mineral; the remainder either dissolves in water or is trapped in its original form. We also study the case of a pure CO$_2$ bubble surrounded by brine and suggest a mechanism that may lead to a carbonate-encrusted bubble due to structural diffusion

The dynamics of cracks in torn thin sheets

Motivated by recent experiments, we present a study of the dynamics of cracks in thin sheets. While the equations of elasticity for thin plates are well known, there remains the question of path selection for a propagating crack. We invoke a generalization of the principle of local symmetry to provide a criterion for path selection and demonstrate qualitative agreement with the experimental findings. The nature of the singularity at the crack tip is studied with and without the interference of nonlinear terms.Comment: 7 pages, 11 figure