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

Determination of the Thickness and Composition Profiles for a Film of Binary Mixture on a Solid Substrate

We determine the steady-state structures that result from liquid-liquid demixing in a free surface film of binary liquid on a solid substrate. The considered model corresponds to the static limit of the diffuse interface theory describing the phase separation process for a binary liquid (model-H), when supplemented by boundary conditions at the free surface and taking the influence of the solid substrate into account. The resulting variational problem is numerically solved employing a Finite Element Method on an adaptive grid. The developed numerical scheme allows us to obtain the coupled steady-state film thickness profile and the concentration profile inside the film. As an example we determine steady state profiles for a reflection-symmetric two-dimensional droplet for various surface tensions of the film and various preferential attraction strength of one component to the substrate. We discuss the relation of the results of the present diffuse interface theory to the sharp interface limit and determine the effective interface tension of the diffuse interface by several means

Complex geodetic and photogrammetric monitoring of the Kraľovany rock slide

Purpose The complex monitoring of rock slides with the size of 16 ha in order to predict the development of other slides and prevent possible human and material losses. Methods Precise geodetic point measurement, terrestrial laser and image scanning and aerial photogrammetry were used to obtain detailed knowledge about the geometry and behaviour of the rock slide. Except for terrestrial images, the images were taken using an SLR camera (set on a motor paraglide) and a compact camera (set on a remotely piloted system). The state and condition of the locality before the rock slide was taken from archive images taken by a digital large format camera. Results Vectors and velocities of the displacements of discrete points were determined with high precision; the changes in quarry wall surfaces were determined by laser and photogrammetry scanning. Finally, high resolution orthophotomosaics of the site were generated using aerial photogrammetry at each observation point. Practical implications The termination of mining and the design of the remediation works were determined according to the results of the measurements. Also, monitoring was carried out in order to observe any changes due to the implementation of a highway project based in the localisation. Originality/ value Complex geodetic and photogrammetric monitoring of rock slides offers detailed information about slide surfaces and has previously been used in Slovakia on a significant scale

USE OF IMAGE BASED MODELLING FOR DOCUMENTATION OF INTRICATELY SHAPED OBJECTS

In the documentation of cultural heritage, we can encounter three dimensional shapes and structures which are complicated to measure. Such objects are for example spiral staircases, timber roof trusses, historical furniture or folk costume where it is nearly impossible to effectively use the traditional surveying or the terrestrial laser scanning due to the shape of the object, its dimensions and the crowded environment. The actual methods of digital photogrammetry can be very helpful in such cases with the emphasis on the automated processing of the extensive image data. The created high resolution 3D models and 2D orthophotos are very important for the documentation of architectural elements and they can serve as an ideal base for the vectorization and 2D drawing documentation. This contribution wants to describe the various usage of image based modelling in specific interior spaces and specific objects. The advantages and disadvantages of the photogrammetric measurement of such objects in comparison to other surveying methods are reviewed