Topography driven spreading

Roughening a hydrophobic surface enhances its nonwetting properties into superhydrophobicity. For liquids other than water, roughness can induce a complete rollup of a droplet. However, topographic effects can also enhance partial wetting by a given liquid into complete wetting to create superwetting. In this work, a model system of spreading droplets of a nonvolatile liquid on surfaces having lithographically produced pillars is used to show that superwetting also modifies the dynamics of spreading. The edge speed-dynamic contact angle relation is shown to obey a simple power law, and such power laws are shown to apply to naturally occurring surfaces

Statistical mechanics of Fofonoff flows in an oceanic basin

We study the minimization of potential enstrophy at fixed circulation and energy in an oceanic basin with arbitrary topography. For illustration, we consider a rectangular basin and a linear topography h=by which represents either a real bottom topography or the beta-effect appropriate to oceanic situations. Our minimum enstrophy principle is motivated by different arguments of statistical mechanics reviewed in the article. It leads to steady states of the quasigeostrophic (QG) equations characterized by a linear relationship between potential vorticity q and stream function psi. For low values of the energy, we recover Fofonoff flows [J. Mar. Res. 13, 254 (1954)] that display a strong westward jet. For large values of the energy, we obtain geometry induced phase transitions between monopoles and dipoles similar to those found by Chavanis and Sommeria [J. Fluid Mech. 314, 267 (1996)] in the absence of topography. In the presence of topography, we recover and confirm the results obtained by Venaille and Bouchet [Phys. Rev. Lett. 102, 104501 (2009)] using a different formalism. In addition, we introduce relaxation equations towards minimum potential enstrophy states and perform numerical simulations to illustrate the phase transitions in a rectangular oceanic basin with linear topography (or beta-effect).Comment: 26 pages, 28 figure

Efficient Image-Space Extraction and Representation of 3D Surface Topography

Surface topography refers to the geometric micro-structure of a surface and defines its tactile characteristics (typically in the sub-millimeter range). High-resolution 3D scanning techniques developed recently enable the 3D reconstruction of surfaces including their surface topography. In his paper, we present an efficient image-space technique for the extraction of surface topography from high-resolution 3D reconstructions. Additionally, we filter noise and enhance topographic attributes to obtain an improved representation for subsequent topography classification. Comprehensive experiments show that the our representation captures well topographic attributes and significantly improves classification performance compared to alternative 2D and 3D representations.Comment: Initial version of the paper accepted at the IEEE ICIP Conference 201

Topography of (exo)planets

Current technology is not able to map the topography of rocky exoplanets, simply because the objects are too faint and far away to resolve them. Nevertheless, indirect effect of topography should be soon observable thanks to photometry techniques, and the possibility of detecting specular reflections. In addition, topography may have a strong effect on Earth-like exoplanet climates because oceans and mountains affect the distribution of clouds \citep{Houze2012}. Also topography is critical for evaluating surface habitability \citep{Dohm2015}. We propose here a general statistical theory to describe and generate realistic synthetic topographies of rocky exoplanetary bodies. In the solar system, we have examined the best-known bodies: the Earth, Moon, Mars and Mercury. It turns out that despite their differences, they all can be described by multifractral statistics, although with different parameters. Assuming that this property is universal, we propose here a model to simulate 2D spherical random field that mimics a rocky planetary body in a stellar system. We also propose to apply this model to estimate the statistics of oceans and continents to help to better assess the habitability of distant worlds

Curvature sensor for the measurement of the static corneal topography and the dynamic tear film topography in the human eye

A system to measure the topography of the first optical surface of the human eye noninvasively by using a curvature sensor is described. The static corneal topography and the dynamic topography of the tear film can both be measured, and the topographies obtained are presented. The system makes possible the study of the dynamic aberrations introduced by the tear film to determine their contribution to the overall ocular aberrations in healthy eyes, eyes with corneal pathologies, and eyes wearing contact lenses

Topography induced optical spectral shifts and finite size effect of focal spot

We observe topography induced spectral shifts using high resolution grating spectrometers which we attribute to the fact that the focal spot has a finite size. The topography induced spectral shifts depend on spectrometer grating orientation and numerical aperture of the microscope objective. This is demonstrated by spectroscopic imaging trenches in GaAs in directions parallel and perpendicular the spectrometer entrance slit. Differences along the two directions of the LO phonon band show that the spectral shift is due to the variation of the grating angle across the non uniform illuminated focal spot caused by topography. Alignment errors of the optical axis lead to additional spectral shifts. Topography induced spectral shifts can be detected by recording spectra by scanning the sample in two perpendicular orientations with respect to the spectrometer entrance slit.Comment: 9 pages, 3 figure

Effects of Topography on Seismic-Wave Propagation: An Example from Northern Taiwan

Topography influences ground motion and, in general, increases the amplitude of shaking at mountain tops and ridges, whereas valleys have reduced ground motions, as is observed from data recorded during and after real earthquakes and from numerical simulations. However, recent publications have focused mainly on the implications for ground motion in the mountainous regions themselves, whereas the impact on surrounding low-lying areas has received less attention. Here, we develop a new spectral-element mesh implementation to accommodate realistic topography as well as the complex shape of the Taipei sedimentary basin, which is located close to the Central Mountain Range in northern Taiwan. Spectral-element numerical simulations indicate that high-resolution topography can change peak ground velocity (PGV) values in mountainous areas by ±50% compared to a half-space response. We further demonstrate that large-scale topography can affect the propagation of seismic waves in nearby areas. For example, if a shallow earthquake occurs in the I-Lan region of Taiwan, the Central Mountain Range will significantly scatter the surface waves and will in turn reduce the amplitude of ground motion in the Taipei basin. However, as the hypocenter moves deeper, topography scatters body waves, which subsequently propagate as surface waves into the basin. These waves continue to interact with the basin and the surrounding mountains, finally resulting in complex amplification patterns in Taipei City, with an overall PGV increase of more than 50%. For realistic subduction zone earthquake scenarios off the northeast coast of Taiwan, the effects of topography on ground motion in both the mountains and the Taipei basin vary and depend on the rupture process. The complex interactions that can occur between mountains and surrounding areas, especially sedimentary basins, illustrate the fact that topography should be taken into account when assessing seismic hazard

Flow of evaporating, gravity-driven thin liquid films over topography

The effect of topography on the free surface and solvent concentration profiles of an evaporating thin film of liquid flowing down an inclined plane is considered. The liquid is assumed to be composed of a resin dissolved in a volatile solvent with the associated solvent concentration equation derived on the basis of the well-mixed approximation. The dynamics of the film is formulated as a lubrication approximation and the effect of a composition-dependent viscosity is included in the model. The resulting time-dependent, nonlinear, coupled set of governing equations is solved using a full approximation storage multigrid method. The approach is first validated against a closed-form analytical solution for the case of a gravity-driven, evaporating thin film flowing down a flat substrate. Analysis of the results for a range of topography shapes reveal that although a full-width, spanwise topography such as a step-up or a step-down does not affect the composition of the film, the same is no longer true for the case of localized topography, such as a peak or a trough, for which clear nonuniformities of the solvent concentration profile can be observed in the wake of the topography

Bathymetry of the Pacific plate and its implications for thermal evolution of lithosphere and mantle dynamics

A long-standing question in geodynamics is the cause of deviations of ocean depth or seafloor topography from the prediction of a cooling half-space model (HSC). Are the deviations caused entirely by mantle plumes or lithospheric reheating associated with sublithospheric small-scale convection or some other mechanisms? In this study we analyzed the age and geographical dependences of ocean depth for the Pacific plate, and we removed the effects of sediments, seamounts, and large igneous provinces (LIPs), using recently available data sets of high-resolution bathymetry, sediments, seamounts, and LIPs. We found that the removal of seamounts and LIPs results in nearly uniform standard deviations in ocean depth of ∼300 m for all ages. The ocean depth for the Pacific plate with seamounts, LIPs, the Hawaiian swell, and South Pacific super-swell excluded can be fit well with a HSC model till ∼80–85 Ma and a plate model for older seafloor, particularly, with the HSC-Plate depth-age relation recently developed by Hillier and Watts (2005) with an entirely different approach for the North Pacific Ocean. A similar ocean depth-age relation is also observed for the northern region of our study area with no major known mantle plumes. Residual topography with respect to Hillier and Watts' HSC-Plate model shows two distinct topographic highs: the Hawaiian swell and South Pacific super-swell. However, in this residual topography map, the Darwin Rise does not display anomalously high topography except the area with seamounts and LIPs. We also found that the topography estimated from the seismic model of the Pacific lithosphere of Ritzwoller et al. (2004) generally agrees with the observed topography, including the reduced topography at relatively old seafloor. Our analyses show that while mantle plumes may be important in producing the Hawaiian swell and South Pacific super-swell, they cannot be the only cause for the topographic deviations. Other mechanisms, particularly lithospheric reheating associated with “trapped” heat below old lithosphere (Huang and Zhong, 2005), play an essential role in causing the deviations in topography from the HSC model prediction