Conformal Dynamics of Precursors to Fracture

An exact integro-differential equation for the conformal map from the unit circle to the boundary of an evolving cavity in a stressed 2-dimensional solid is derived. This equation provides an accurate description of the dynamics of precursors to fracture when surface diffusion is important. The solution predicts the creation of sharp grooves that eventually lead to material failure via rapid fracture. Solutions of the new equation are demonstrated for the dynamics of an elliptical cavity and the stability of a circular cavity under biaxial stress, including the effects of surface stress.Comment: 4 pages, 3 figure

Nonlinear evolution of surface morphology in InAs/AlAs superlattices via surface diffusion

Continuum simulations of self-organized lateral compositional modulation growth in InAs/AlAs short-period superlattices on InP substrate are presented. Results of the simulations correspond quantitatively to the results of synchrotron x-ray diffraction experiments. The time evolution of the compositional modulation during epitaxial growth can be explained only including a nonlinear dependence of the elastic energy of the growing epitaxial layer on its thickness. From the fit of the experimental data to the growth simulations we have determined the parameters of this nonlinear dependence. It was found that the modulation amplitude don't depend on the values of the surface diffusion constants of particular elements.Comment: 4 pages, 3 figures, published in Phys. Rev. Lett. http://link.aps.org/abstract/PRL/v96/e13610

Phase Field Modeling of Fast Crack Propagation

We present a continuum theory which predicts the steady state propagation of cracks. The theory overcomes the usual problem of a finite time cusp singularity of the Grinfeld instability by the inclusion of elastodynamic effects which restore selection of the steady state tip radius and velocity. We developed a phase field model for elastically induced phase transitions; in the limit of small or vanishing elastic coefficients in the new phase, fracture can be studied. The simulations confirm analytical predictions for fast crack propagation.Comment: 5 pages, 11 figure

Influence of uniaxial stress on the lamellar spacing of eutectics

Directional solidification of lamellar eutectic structures submitted to uniaxial stress is investigated. In the spirit of an approximation first used by Jackson and Hunt, we calculate the stress tensor for a two-dimensional crystal with triangular surface, using a Fourier expansion of the Airy function. crystal with triangular surface in contact with its melt, given that a uniaxial external stress is applied. The effect of the resulting change in chemical potential is introduced into the standard model for directional solidification of a lamellar eutectic. This calculation is motivated by an observation, made recently [I. Cantat, K. Kassner, C. Misbah, and H. M\"uller-Krumbhaar, Phys. Rev. E, in press] that the thermal gradient produces similar effects as a strong gravitational field in the case of dilute-alloy solidification. Therefore, the coupling between the Grinfeld and the Mullins-Sekerka instabilities becomes strong, as the critical wavelength of the former instability gets reduced to a value close to that of the latter. Analogously, in the case of eutectics, the characteristic length scale of the Grinfeld instability should be reduced to a size not extremely far from typical lamellar spacings. In a Jackson-Hunt like approach we average the undercooling, including the stress term, over a pair of lamellae. Following Jackson and Hunt, we assume the selected wavelength to be determined by the minimum undercooling criterion and compute its shift due to the external stress. we realize the shifting of the wavelength by the application of external stress. In addition, we find that in general the volume fraction of the two solid phases is changed by uniaxial stress. Implications for experiments on eutectics are discussed.Comment: 8 pages RevTex, 6 included ps-figures, accepted for Phys. Rev.

Guar gum/borax hydrogel: Rheological, low field NMR and release characterizations

Guar gum (GG) and Guar gum/borax (GGb) hydrogels are studied by means of rheology, Low Field Nuclear Magnetic Resonance (LF NMR) and model drug release tests. These three approaches are used to estimate the mesh size (ζ) of the polymeric network. A comparison with similar Scleroglucan systems is carried out. In the case of GGb, the rheological and Low Field NMR estimations of ζ lead to comparable results, while the drug release approach seems to underestimate ζ. Such discrepancy is attributed to the viscous effect of some polymeric chains that, although bound to the network to one end, can freely fluctuate among meshes. The viscous drag exerted by these chains slows down drug diffusion through the polymeric network. A proof for this hypothesis is given by the case of Scleroglucan gel, where the viscous contribution is not so significant and a good agreement between the rheological and release test approaches was found

Wetting layer thickness and early evolution of epitaxially strained thin films

We propose a physical model which explains the existence of finite thickness wetting layers in epitaxially strained films. The finite wetting layer is shown to be stable due to the variation of the non-linear elastic free energy with film thickness. We show that anisotropic surface tension gives rise to a metastable enlarged wetting layer. The perturbation amplitude needed to destabilize this wetting layer decreases with increasing lattice mismatch. We observe the development of faceted islands in unstable films.Comment: 4 pages, 3 eps figure

Dynamic Potential Intensity: An improved representation of the ocean's impact on tropical cyclones

To incorporate the effects of tropical cyclone (TC)-induced upper ocean mixing and sea surface temperature (SST) cooling on TC intensification, a vertical average of temperature down to a fixed depth was proposed as a replacement for SST within the framework of air-sea coupled Potential Intensity (PI). However, the depth to which TC-induced mixing penetrates may vary substantially with ocean stratification and storm state. To account for these effects, here we develop a “Dynamic Potential Intensity” (DPI) based on considerations of stratified fluid turbulence. For the Argo period 2004–2013 and the three major TC basins of the Northern Hemisphere, we show that the DPI explains 11–32% of the variance in TC intensification, compared to 0–16% using previous methods. The improvement obtained using the DPI is particularly large in the eastern Pacific where the thermocline is shallow and ocean stratification effects are strong.United States. Department of Energy. Office of Science (part of the Regional and Global Climate Modeling Program)Atlantic Oceanographic and Meteorological Laboratory (base funds

A lattice model describing scale effects in nonlinear elasticity of nano-inhomogeneities

We present a procedure to map the constitutive laws of elasticity (both in the linear and nonlinear regime) onto a discrete atomic lattice and we apply the resulting elastic lattice model to investigate the strain field within an embedded nano-inhomogeneity. We prove that its elastic behavior at the nanoscale is governed by relevant atomistic effects. In particular, we demonstrate that such effects on the linear and nonlinear elastic properties are described by the same scaling exponent, in a large range of elastic contrast between the matrix and the nano-inhomogeneity. This suggests that the linear and nonlinear elastic behaviors of the composite system belong to the same universality class (at least within the nanometer length scale here investigated).Comment: Accepted on Phys.Rev.B (2010) (in press

Modeling Elasticity in Crystal Growth

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth.Comment: 4 pages, 10 figure