On DLA's η

In his pioneering 1961 paper on seismic anisotropy in a layered earth, Don L. Anderson (hereafter referred to as DLA) introduced a parameter often referred to in global seismology as η without providing any reasoning. This note hopes to clarify the significance of η in the context of the dependence of body wave velocities in a transversely isotropic system on the angle of incidence, and also its relation with the other well-known anisotropic parameters introduced by Leon Thomsen in 1986

Elastic energy of polyhedral bilayer vesicles

In recent experiments [M. Dubois, B. Dem\'e, T. Gulik-Krzywicki, J.-C. Dedieu, C. Vautrin, S. D\'esert, E. Perez, and T. Zemb, Nature (London) Vol. 411, 672 (2001)] the spontaneous formation of hollow bilayer vesicles with polyhedral symmetry has been observed. On the basis of the experimental phenomenology it was suggested [M. Dubois, V. Lizunov, A. Meister, T. Gulik-Krzywicki, J. M. Verbavatz, E. Perez, J. Zimmerberg, and T. Zemb, Proc. Natl. Acad. Sci. U.S.A. Vol. 101, 15082 (2004)] that the mechanism for the formation of bilayer polyhedra is minimization of elastic bending energy. Motivated by these experiments, we study the elastic bending energy of polyhedral bilayer vesicles. In agreement with experiments, and provided that excess amphiphiles exhibiting spontaneous curvature are present in sufficient quantity, we find that polyhedral bilayer vesicles can indeed be energetically favorable compared to spherical bilayer vesicles. Consistent with experimental observations we also find that the bending energy associated with the vertices of bilayer polyhedra can be locally reduced through the formation of pores. However, the stabilization of polyhedral bilayer vesicles over spherical bilayer vesicles relies crucially on molecular segregation of excess amphiphiles along the ridges rather than the vertices of bilayer polyhedra. Furthermore, our analysis implies that, contrary to what has been suggested on the basis of experiments, the icosahedron does not minimize elastic bending energy among arbitrary polyhedral shapes and sizes. Instead, we find that, for large polyhedron sizes, the snub dodecahedron and the snub cube both have lower total bending energies than the icosahedron

Coarsening Dynamics of a One-Dimensional Driven Cahn-Hilliard System

We study the one-dimensional Cahn-Hilliard equation with an additional driving term representing, say, the effect of gravity. We find that the driving field $E$ has an asymmetric effect on the solution for a single stationary domain wall (or `kink'), the direction of the field determining whether the analytic solutions found by Leung [J.Stat.Phys.{\bf 61}, 345 (1990)] are unique. The dynamics of a kink-antikink pair (`bubble') is then studied. The behaviour of a bubble is dependent on the relative sizes of a characteristic length scale $E^{-1}$, where $E$ is the driving field, and the separation, $L$, of the interfaces. For $EL \gg 1$ the velocities of the interfaces are negligible, while in the opposite limit a travelling-wave solution is found with a velocity $v \propto E/L$. For this latter case ($EL \ll 1$) a set of reduced equations, describing the evolution of the domain lengths, is obtained for a system with a large number of interfaces, and implies a characteristic length scale growing as $(Et)^{1/2}$. Numerical results for the domain-size distribution and structure factor confirm this behavior, and show that the system exhibits dynamical scaling from very early times.Comment: 20 pages, revtex, 10 figures, submitted to Phys. Rev.

Dispersive stabilization of the inverse cascade for the Kolmogorov flow

It is shown by perturbation techniques and numerical simulations that the inverse cascade of kink-antikink annihilations, characteristic of the Kolmogorov flow in the slightly supercritical Reynolds number regime, is halted by the dispersive action of Rossby waves in the beta-plane approximation. For beta tending to zero, the largest excited scale is proportional to the logarithm of one over beta and differs strongly from what is predicted by standard dimensional phenomenology which ignores depletion of nonlinearity.Comment: 4 pages, LATEX, 3 figures. v3: revised version with minor correction

Comparison of P-, SV- and SH-wave velocity models below Japan and Northeast China

The recent deployment of the NECESSArray seismic network in Northeast China has allowed new insights on the velocity structure of this formerly poorly resolved area. This experiment has brought new data to debate about the geodynamical context in this region (stagnant slab, origin of intraplate volcanoes, ...). We use a more efficient method for the measurement of travel time residuals by cross-correlating observed and synthetic waveforms. Synthetic seismograms are convolved with high-frequency source-time functions inverted along with focal depths, following a simulated annealing approach. Thus, resulting modeled waveforms take more accurately account for the source effects. The method is used to perform measurements on direct P, SV and SH phases extracted from, respectively, vertical, radial and transverse band-pass-filtered records from NECESSArray and F-NET seismological networks. We finally invert the resulting datasets in order to obtain P-, SV- and SH-wave velocity models. To do so, we use a fast and efficient inversion method using ray theory. Observed structures in the three tomographic models show a very good geographical coherency. Nevertheless, some differences are observed below Songliao basin and Changbaishan volcanoes between, on the one side, P and SV models, and, on the other side, SH model. By measuring velocity ratios, we discuss anisotropy and thermal/compositional origin of these velocity anomalies

Nanomechanical structures with 91 MHz resonance frequency fabricated by local deposition and dry etching

We report an all-dry, two-step, surface nanoengineering method to fabricate nanomechanical elements without photolithography. It is based on the local deposition through a nanostencil of a well-defined aluminum pattern onto a silicon/silicon-nitride substrate, followed by plasma etching to release the structures. The suspended 100-nm-wide, 2-mum-long, and 300-nm-thick nanolevers and nanobridges have natural resonance frequencies of 50 and 91 MHz, respectively. The fabrication method is scalable to a full wafer and allows for a variety of materials to be structured on arbitrary surfaces, thus opening new types of nanoscale mechanical systems

Phase ordering and shape deformation of two-phase membranes

Within a coupled-field Ginzburg-Landau model we study analytically phase separation and accompanying shape deformation on a two-phase elastic membrane in simple geometries such as cylinders, spheres and tori. Using an exact periodic domain wall solution we solve for the shape and phase ordering field, and estimate the degree of deformation of the membrane. The results are pertinent to a preferential phase separation in regions of differing curvature on a variety of vesicles.Comment: 4 pages, submitted to PR