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Register a new userControl of polymer gel surface pattern formation and its three dimensional measurement method
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We report the controllability of a gelation surface pattern formation. Recently, we have found and studied a novel kind of pattern formation that occurs during a radical polymerization (gelation) process. The pattern formation is observed in an open top boundary of quasi two dimensional gelation. In previous studies, we have used two dimensional photo based image processing to analyze the patterns. However, the actual pattern is a three dimensional surface deformation. Thus we develop a three dimensional measurement system using a line laser displacement sensor and an automatic x-stage. Patterns measured by the system are analyzed and discussed by means of pattern controllability. In particular, we focus on the possibility of the pattern control using an external temperature field. As a result, we reveal that the global structure can be controlled, whereas the characteristic length scales (wavelength and amplitude) are not controllable.
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The surface pattern formation on a gelation surface is analyzed using an effective surface roughness. The spontaneous surface deformation on DiMethylAcrylAmide (DMAA) gelation surface is controlled by temperature, initiator concentration, and ambient oxygen. The effective surface roughness is defined using 2-dimensional photo data to characterize the surface deformation. Parameter dependence of the effective surface roughness is systematically investigated. We find that decrease of ambient oxygen, increase of initiator concentration, and high temperature tend to suppress the surface deformation in almost similar manner. That trend allows us to collapse all the data to a unified master curve. As a result, we finally obtain an empirical scaling form of the effective surface roughness. This scaling is useful to control the degree of surface patterning. However, the actual dynamics of this pattern formation is not still uncovered.
We study wave propagation in two-dimensional granular crystals under the Hertzian contact law consisting of hexagonal packings of spheres under various basin geometries including hexagonal, triangular, and circular basins which can be tiled with hexagons. We find that the basin geometry will influence wave reflection at the boundaries, as expected, and also may result in bottlenecks forming. While exterior strikers the size of a single sphere have been considered in the literature, it is also possible to consider strikers which impact multiple spheres along a boundary, or to have multiple sides being struck simultaneously. It is also possible to consider obstructions or even strikers in the interior of the hexagonally packed granular crystal, as previously considered in the case of square packings, resulting in the basin geometry no longer forming a convex set. We consider various configurations of either boundary or interior strikers. We shall also consider the case where a granular crystal is composed of two separate crystals of differing material, with a single interface between the two distinct materials. Depending on the relative material properties of each type of sphere, this can result in a trapping of most of the wave energy within one of the two regions. While repeated reflections from the boundaries will cause the systems we study to fall into disorder for large time, there are a number of interesting wave structures and patters that emerge as transients at intermediate timescales.
A dynamical theory of geophysical precipitation pattern formation is presented and applied to irreversible calcium carbonate (travertine) deposition. Specific systems studied here are the terraces and domes observed at geothermal hot springs, such as those at Yellowstone National Park, and speleothems, particularly stalactites and stalagmites. The theory couples the precipitation front dynamics with shallow water flow, including corrections for turbulent drag and curvature effects. In the absence of capillarity and with a laminar flow profile, the theory predicts a one-parameter family of steady state solutions to the moving boundary problem describing the precipitation front. These shapes match well the measured shapes near the vent at the top of observed travertine domes. Closer to the base of the dome, the solutions deviate from observations, and circular symmetry is broken by a fluting pattern, which we show is associated with capillary forces causing thin film break-up. We relate our model to that recently proposed for stalactite growth, and calculate the linear stability spectrum of both travertine domes and stalactites. Lastly, we apply the theory to the problem of precipitation pattern formation arising from turbulent flow down an inclined plane, and identify a linear instability that underlies scale-invariant travertine terrace formation at geothermal hot springs.
Growth-induced pattern formations in curved film-substrate structures have attracted extensive attentions recently. In most existing literature, the growth tensor is assumed to be homogeneous or piecewise homogeneous. In this paper, we aim at clarifying the influence of a growth gradient on pattern formation and pattern evolution in bilayered tubular tissues under plane-strain deformation. In the framework of finite elasticity, a bifurcation condition is derived for a general material model and a generic growth function. Then we suppose that both layers are composed of neo-Hookean materials. In particular, the growth function is assumed to decay linearly from the inner surface or from the outer surface. It is found that a gradient in the growth has a weak effect on the critical state, compared to the homogeneous growth type where both layers share the same growth factor. Furthermore, a finite element model is built to validate the theoretical model and to investigate the post-buckling behaviors. It is found that the associated pattern transition is not controlled by the growth gradient but by the ratio of the shear modulus between two layers. Different morphologies can occur when the modulus ratio is varied. The current analysis could provide useful insight into the influence of a growth gradient on surface instabilities and suggests that a homogeneous growth field may provide a good approximation on interpreting complicated morphological formations in multiple systems.
In the present work, we explore the existence, stability and dynamics of single and multiple vortex ring states that can arise in Bose-Einstein condensates. Earlier works have illustrated the bifurcation of such states, in the vicinity of the linear limit, for isotropic or anisotropic three-dimensional harmonic traps. Here, we extend these states to the regime of large chemical potentials, the so-called Thomas-Fermi limit, and explore their properties such as equilibrium radii and inter-ring distance, for multi-ring states, as well as their vibrational spectra and possible instabilities. In this limit, both the existence and stability characteristics can be partially traced to a particle picture that considers the rings as individual particles oscillating within the trap and interacting pairwise with one another. Finally, we examine some representative instability scenarios of the multi-ring dynamics including breakup and reconnections, as well as the transient formation of vortex lines.
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