Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder

We discuss the behavior of partially wetting liquids on a rotating cylinder using a model that takes into account the effects of gravity, viscosity, rotation, surface tension and wettability. Such a system can be considered as a prototype for many other systems where the interplay of spatial heterogeneity and a lateral driving force in the proximity of a first- or second-order phase transition results in intricate behavior. So does a partially wetting drop on a rotating cylinder undergo a depinning transition as the rotation speed is increased, whereas for ideally wetting liquids the behavior \bfuwe{only changes quantitatively. We analyze the bifurcations that occur when the rotation speed is increased for several values of the equilibrium contact angle of the partially wetting liquids. This allows us to discuss how the entire bifurcation structure and the flow behavior it encodes changes with changing wettability. We employ various numerical continuation techniques that allow us to track stable/unstable steady and time-periodic film and drop thickness profiles. We support our findings by time-dependent numerical simulations and asymptotic analyses of steady and time-periodic profiles for large rotation numbers

Sensor systems testbed for telerobotic navigation

A testbed has been developed for the study of sensor systems to be used in telerobotic operations. The program, conducted in conjunction with Johnson Space Center of NASA, addresses the navigational problems associated with target acquisition and rendezvous for teleoperated robotic work stations. The program will utilize a mobile platform which will support various sensor systems during their development and testing in an earth-based environment. The testbed has been developed in support of a program to develop sensor systems that will aid in rendezvous and docking operations to be conducted as a part of the space station program. A mobile platform has been used to permit testing of these components in a conventional laboratory environment with consequent savings in cost and complexity. The sensor systems, while representative of devices currently in use for robotic applications, are not considered prototypical of the ones that will be used in the final applications. The test program provided information that will support the design of system augmentations and will lead to a comprehensive test program for sensor development

Stability analysis of polarized domains

Polarized ferrofluids, lipid monolayers and magnetic bubbles form domains with deformable boundaries. Stability analysis of these domains depends on a family of nontrivial integrals. We present a closed form evaluation of these integrals as a combination of Legendre functions. This result allows exact and explicit formulae for stability thresholds and growth rates of individual modes. We also evaluate asymptotic behavior in several interesting limits.Comment: 12 pages, 3 figures, Late

Depinning of three-dimensional drops from wettability defects

Substrate defects crucially influence the onset of sliding drop motion under lateral driving. A finite force is necessary to overcome the pinning influence even of microscale heterogeneities. The depinning dynamics of three-dimensional drops is studied for hydrophilic and hydrophobic wettability defects using a long-wave evolution equation for the film thickness profile. It is found that the nature of the depinning transition explains the experimentally observed stick-slip motion.Comment: 6 pages, 9 figures, submitted to ep

Rayleigh and depinning instabilities of forced liquid ridges on heterogeneous substrates

Depinning of two-dimensional liquid ridges and three-dimensional drops on an inclined substrate is studied within the lubrication approximation. The structures are pinned to wetting heterogeneities arising from variations of the strength of the short-range polar contribution to the disjoining pressure. The case of a periodic array of hydrophobic stripes transverse to the slope is studied in detail using a combination of direct numerical simulation and branch-following techniques. Under appropriate conditions the ridges may either depin and slide downslope as the slope is increased, or first breakup into drops via a transverse instability, prior to depinning. The different transition scenarios are examined together with the stability properties of the different possible states of the system.Comment: Physics synopsis link: http://physics.aps.org/synopsis-for/10.1103/PhysRevE.83.01630

Concept to analyze the displacement time series of individual persistent scatterers

Persistent Scatterer Interferometry (PSInSAR) exploits a time series of Synthetic Aperture Radar (SAR) images to estimate the mean velocity with which the surface of the earth is deforming. However, most PSInSAR algorithms estimate the mean velocities using a linear regression model. Since some deformation phenomena can exhibit a more complex behavior over time, using a linear regression model leads to potentially wrong estimations for the mean velocity. For example, the velocity of a landslide moving down a steep slope can change depending on the water content of the material of the landslide, or an inactive landslide can reactivate due to an earthquake. Both scenarios would not result in a time series with a constant linear slope but in a piecewise linear time series. This paper presents a Matlab-based tool to analyze an individual Persistent Scatterer (PS) time series. The Persistent Scatterer Deformation Pattern Analysis Tool (PSDefoPAT) aims to build a mathematical model that sufficiently describes the time series trend and seasonal and noise components. The trend component is estimated using polynomial regression and piecewise linear models, while a sine function approximates the seasonal component. The goal is to identify the best fitting model for the displacement time series of a PS. PSDefoPAT is introduced by examine the time series of three different PS located in the region surrounding Patras, Greece. Based on the derived models, we discuss the nature of their deformation patterns

Asymptotic theory for a moving droplet driven by a wettability gradient

An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and the receding side -- to respective solutions of the problem on the microscale. On the microscale the velocity of movement is used as the small parameter of an asymptotic expansion. Matching gives the droplet shape, velocity of movement as a function of the imposed wettability gradient and droplet volume.Comment: 8 fig

Nanocrystalline materials studied by powder diffraction line profile analysis

X-ray powder diffraction is a powerful tool for characterising the microstructure of crystalline materials in terms of size and strain. It is widely applied for nanocrystalline materials, especially since other methods, in particular electron microscopy is, on the one hand tedious and time consuming, on the other hand, due to the often metastable states of nanomaterials it might change their microstructures. It is attempted to overview the applications of microstructure characterization by powder diffraction on nanocrystalline metals, alloys, ceramics and carbon base materials. Whenever opportunity is given, the data provided by the X-ray method are compared and discussed together with results of electron microscopy. Since the topic is vast we do not try to cover the entire field

Effective Magnetic Hamiltonian and Ginzburg Criterion for Fluids

We develop further the approach of Hubbard and Schofield (Phys.Lett., A40 (1972) 245), which maps the fluid Hamiltonian onto a magnetic one. We show that all coefficients of the resulting effective Landau-Ginzburg-Wilson (LGW) Hamiltonian may be expressed in terms of the compressibility of a reference fluid containing only repulsive interactions, and its density derivatives; we calculate the first few coefficients in the case of the hard-core reference fluid. From this LGW-Hamiltonian we deduce approximate mean-field relations between critical parameters and test them on data for Lennard-Jones, square-well and hard-core-Yukawa fluids. We estimate the Ginzburg criterion for these fluids.Comment: 4 pages, LaTeX, To appear in Phys.Rev.

Continuation for thin film hydrodynamics and related scalar problems

This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues