Resistance of Structural Materials to Deformation in the Case of Linear and Flat Stresses

Annotation: The deformation resistance properties of structural materials in the case of linear and flat stresses are given on the basis of experimental results. The method of estimating the mechanical properties of the material based on the initial deformation diagrams is described. Keywords: Stress, deformation, longitudinal force, internal pressure, stress state, deformation diagram, initial deformation, Yung modulus, Poisson's ratio, anisotropy, strength, yield strength

S-wave singularities in tilted orthorhombic media

Quasi S-wave propagation in low-symmetry anisotropic media is complicated due to the existence of point singularities (conical points) — points in the phase space at which slowness sheets of the split S-waves touch each other. At these points, two eigenvalues of the Christoffel tensor (associated with the quasi S-waves) degenerate into one and polarization directions of the S-waves, which lay in the plane orthogonal to the polarization of the quasi longitudinal wave, are not uniquely defined. In the vicinity of these points, slowness sheets of the S-waves have complicated shapes, leading to rapid variations in polarization directions, multipathing, and cusps and discontinuities of the shear wavefronts. In a tilted orthorhombic medium, the point singularities can occur close to the vertical, distorting the traveltime parameters that are defined at the zero offset. We have analyzed the influence of the singularities on these parameters by examining the derivatives of the slowness surface up to the fourth order. Using two orthorhombic numerical models of different shear anisotropy strength and with different number of singularity points, we evaluate the complexity of the slowness sheets in the vicinity of the conical points and analyze how the traveltime parameters are affected by the singularities. In particular, we observe that the hyperbolic region associated with the singularity points in a model with moderate to strong shear anisotropy spans over a big portion of the slowness surfaces and the traveltime parameters are strongly affected outside the hyperbolic region. In general, the fast shear mode is less affected by the singularities; however, the effect is still very pronounced. Moreover, the hyperbolic region associated with the singularity points on the slow S-wave affects the slowness surface of the fast mode extensively. In addition, we evaluate a relation between the slowness surface Gaussian curvature and the relative geometric spreading, which has anomalous behavior due to the singularities.

Anisotropy Affecting Dendrite Growth of Fe-C Alloy in a Forced Flow

The phase-field model coupling with the concentration field and flow field was used to simulate the dendrite growth during isothermal solidification of Fe-C alloy in a forced flow. The effects of anisotropy modulus and anisotropy strength on the dendrite growth are studied. The results indicate that the dendrites have four preferential growth orientation and the side-branches growth is not perpendicular to the primary branch while the dendrite along with crystallographic directions. When the dendrite along with crystallographic directions, the dendrites have six preferential growth orientation and the side-branches are parallel to the neighborly primary branch. At a anisotropy strength of 0.01, the crystal have no apparent principal branch and grows into coral shapes.With an increase in anisotropy strength, the tip solute concentration decreases, makes the dendrite growth become fast, the tip velocity increased continuously.

Estimation of permeability anisotropy using seismic inversion for the CO2 geological storage site of Sleipner (North Sea)

Since 1996, more than 11 Mt of CO2 have been injected into a deep saline aquifer, the Utsira Sand formation, at the Norwegian Sleipner field. An unexpected application of the extensive seismic monitoring program over this field leads to the estimation of the depth dependence of the permeability anisotropy (strength and direction). Time-lapse seismic monitoring is used to follow the displacement of the injected CO2, considered as a permeability tracer. The upper half of the Utsira sand formation exhibits large anisotropy, with a ratio ζ between the maximum and minimum horizontal permeabilities larger than six. In contrast, ζ can be as small as two in the lower half. The direction of the maximum horizontal permeability does not exhibit substantial depth dependence and lies between N18°E and N34°E. This is in agreement with previous authors who pointed out a clear CO2 plume structure markedly elongated in the north-northeast–south-southwest direction. The small topographical trap at the top of the Utsira sand formation is a minor extrinsic cause of the measured permeability anisotropy, compared to the intrinsic effect of the formation permeability. This permeability information is crucial for reservoir simulation and for forecasting of the CO2 plume expansion for different scenarios of injection.

Kleinberg Navigation on Anisotropic Lattices

We study the Kleinberg problem of navigation in small-world networks when the underlying lattice is stretched along a preferred direction. Extensive simulations confirm that maximally efficient navigation is attained when the length r of long-range links is taken from the distribution P(r)∼r−α, when the exponent α is equal to 2, the dimension of the underlying lattice, regardless of the amount of anisotropy, but only in the limit of infinite lattice size, L→∞. For finite size lattices we find an optimal α(L) that depends strongly on L. The convergence to α=2 as L→∞ shows interesting power-law dependence on the anisotropy strength.