Autonomy and Singularity in Dynamic Fracture

The recently developed weakly nonlinear theory of dynamic fracture predicts $1/r$ corrections to the standard asymptotic linear elastic $1/\sqrt{r}$ displacement-gradients, where $r$ is measured from the tip of a tensile crack. We show that the $1/r$ singularity does not automatically conform with the notion of autonomy (autonomy means that any crack tip nonlinear solution is uniquely determined by the surrounding linear elastic $1/\sqrt{r}$ fields) and that it does not automatically satisfy the resultant Newton's equation in the crack parallel direction. We show that these two properties are interrelated and that by requiring that the resultant Newton's equation is satisfied, autonomy of the $1/r$ singular solution is retained. We further show that the resultant linear momentum carried by the $1/r$ singular fields vanishes identically. Our results, which reveal the physical and mathematical nature of the new solution, are in favorable agreement with recent near tip measurements.Comment: 4 pages, 2 figures, related papers: arXiv:0902.2121 and arXiv:0807.486

Refining Finite-Time Lyapunov Exponent Ridges and the Challenges of Classifying Them

While more rigorous and sophisticated methods for identifying Lagrangian based coherent structures exist, the finite-time Lyapunov exponent (FTLE) field remains a straightforward and popular method for gaining some insight into transport by complex, time-dependent two-dimensional flows. In light of its enduring appeal, and in support of good practice, we begin by investigating the effects of discretization and noise on two numerical approaches for calculating the FTLE field. A practical method to extract and refine FTLE ridges in two-dimensional flows, which builds on previous methods, is then presented. Seeking to better ascertain the role of a FTLE ridge in flow transport, we adapt an existing classification scheme and provide a thorough treatment of the challenges of classifying the types of deformation represented by a FTLE ridge. As a practical demonstration, the methods are applied to an ocean surface velocity field data set generated by a numerical model. (C) 2015 AIP Publishing LLC.ONR N000141210665Center for Nonlinear Dynamic

Doping and critical-temperature dependence of the energy gaps in Ba(Fe_{1-x}Co_x)_2As_2 thin films

The dependence of the superconducting gaps in epitaxial Ba(Fe_{1-x}Co_{x})_2As_2 thin films on the nominal doping x (0.04 \leq x \leq 0.15) was studied by means of point-contact Andreev-reflection spectroscopy. The normalized conductance curves were well fitted by using the 2D Blonder-Tinkham-Klapwijk model with two nodeless, isotropic gaps -- although the possible presence of gap anisotropies cannot be completely excluded. The amplitudes of the two gaps \Delta_{S} and \Delta_{L} show similar monotonic trends as a function of the local critical temperature T_{c}^{A} (measured in the same point contacts) from 25 K down to 8 K. The dependence of the gaps on x is well correlated to the trend of the critical temperature, i.e. to the shape of the superconducting region in the phase diagram. When analyzed within a simple three-band Eliashberg model, this trend turns out to be compatible with a mechanism of superconducting coupling mediated by spin fluctuations, whose characteristic energy scales with T_{c} according to the empirical law \Omega_{0}= 4.65*k_{B}*T_{c}, and with a total electron-boson coupling strength \lambda_{tot}= 2.22 for x \leq 0.10 (i.e. up to optimal doping) that slightly decreases to \lambda_{tot}= 1.82 in the overdoped samples (x = 0.15).Comment: 8 pages, 5 color figure

Analytical and numerical analyses of the micromechanics of soft fibrous connective tissues

State of the art research and treatment of biological tissues require accurate and efficient methods for describing their mechanical properties. Indeed, micromechanics motivated approaches provide a systematic method for elevating relevant data from the microscopic level to the macroscopic one. In this work the mechanical responses of hyperelastic tissues with one and two families of collagen fibers are analyzed by application of a new variational estimate accounting for their histology and the behaviors of their constituents. The resulting, close form expressions, are used to determine the overall response of the wall of a healthy human coronary artery. To demonstrate the accuracy of the proposed method these predictions are compared with corresponding 3-D finite element simulations of a periodic unit cell of the tissue with two families of fibers. Throughout, the analytical predictions for the highly nonlinear and anisotropic tissue are in agreement with the numerical simulations

Resistivity in Co-doped Ba-122: comparison of thin films and single crystals

The temperature dependence of the resistivity of epitaxial Ba(Fe_(1-x)Co_x)2As2 thin films (with nominal doping x = 0.08, 0.10 and 0.15) has been analyzed and compared with analogous measurements on single crystals taken from literature. The rho(T) of thin films looks different from that of single crystals, even when the cobalt content is the same. All rho(T) curves can be fitted by considering an effective two-band model (with holes and electrons bands) in which the electrons are more strongly coupled with the bosons (spin fluctuations) than holes, while the effect of impurities is mainly concentrated in the hole band. Within this model the mediating boson has the same characteristic energy in single crystals and thin films, but the shape of the transport spectral function at low energy has to be very different, leading to a "hardening" of the electron-boson spectral function in thin films, associated with the strain induced by the substrate.Comment: 13 pages, 4 figure

From nonlinear to linearized elasticity via Γ-convergence: the case of multiwell energies satisfying weak coercivity conditions

Linearized elasticity models are derived, via Γ-convergence, from suitably rescaled non- linear energies when the corresponding energy densities have a multiwell structure and satisfy a weak coercivity condition, in the sense that the typical quadratic bound from below is replaced by a weaker p bound, 1 < p < 2, away from the wells. This study is motivated by, and our results are applied to, energies arising in the modeling of nematic elastomers

Spin excitations in the antiferromagnet NaNiO2

In NaNiO2, Ni3+ ions form a quasi two dimensional triangular lattice of S = 1=2 spins. The magnetic order observed below 20K has been described as an A type antiferromagnet with ferro- magnetic layers weakly coupled antiferromagnetically. We studied the magnetic excitations with the electron spin resonance for frequencies 1-20 cm-1, in magnetic fields up to 14 T. The bulk of the results are interpreted in terms of a phenomenological model involving bi-axial anisotropy for the spins: a strong easy-plane term, and a weaker anisotropy within the plane. The direction of the easy plane is constrained by the collective Jahn-Teller distortion occurring in this material at 480 K

Cosmological Parameter Extraction from the First Season of Observations with DASI

The Degree Angular Scale Interferometer (\dasi) has measured the power spectrum of the Cosmic Microwave Background anisotropy over the range of spherical harmonic multipoles 100<l<900. We compare this data, in combination with the COBE-DMR results, to a seven dimensional grid of adiabatic CDM models. Adopting the priors h>0.45 and 0.0<=tau_c<=0.4, we find that the total density of the Universe Omega_tot=1.04+/-0.06, and the spectral index of the initial scalar fluctuations n_s=1.01+0.08-0.06, in accordance with the predictions of inflationary theory. In addition we find that the physical density of baryons Omega_b.h^2=0.022+0.004-0.003, and the physical density of cold dark matter Omega_cdm.h^2=0.14+/-0.04. This value of Omega_b.h^2 is consistent with that derived from measurements of the primordial abundance ratios of the light elements combined with big bang nucleosynthesis theory. Using the result of the HST Key Project h=0.72+/-0.08 we find that Omega_t=1.00+/-0.04, the matter density Omega_m=0.40+/-0.15, and the vacuum energy density Omega_lambda=0.60+/-0.15. (All 68% confidence limits.)Comment: 7 pages, 4 figures, minor changes in response to referee comment

Highly anisotropic energy gap in superconducting Ba(Fe0.9_{0.9}Co0.1_{0.1})2_{2}As2_{2} from optical conductivity measurements

We have measured the complex dynamical conductivity, $\sigma = \sigma_{1} + i\sigma_{2}$, of superconducting Ba(Fe$_{0.9}$Co$_{0.1}$)$_{2}$As$_{2}$ ($T_{c} = 22$ K) at terahertz frequencies and temperatures 2 - 30 K. In the frequency dependence of $\sigma_{1}$ below $T_{c}$, we observe clear signatures of the superconducting energy gap opening. The temperature dependence of $\sigma_{1}$ demonstrates a pronounced coherence peak at frequencies below 15 cm$^{-1}$ (1.8 meV). The temperature dependence of the penetration depth, calculated from $\sigma_{2}$, shows power-law behavior at the lowest temperatures. Analysis of the conductivity data with a two-gap model, gives the smaller isotropic s-wave gap of $\Delta_{A} = 3$ meV, while the larger gap is highly anisotropic with possible nodes and its rms amplitude is $\Delta_{0} = 8$ meV. Overall, our results are consistent with a two-band superconductor with an $s_{\pm}$ gap symmetry.Comment: 6 pages, 4 figures, discussion on pair-barking scattering and possible lifting of the nodes is adde