The nonlinear stability of two-phase core-annular flow in a cylindrical pipe is studied. A constant pressure gradient drives the flow of two immiscible liquids of different viscosities and equal densities, and surface tension acts at the interface separating the phases. Insoluble surfactants are included and we assess their effect on the flow stability and ensuing spatio-temporal dynamics. We achieve this by developing an asymptotic analysis in the limit of a thin annular layer -this is usually the relevant regime in applications -to derive a coupled system of nonlinear evolution equations that govern the dynamics of the interface and the local surfactant concentration on it. In the absence of surfactants the system reduces to the Kuramoto-Sivashinsky (KS) equation and its modifications due to viscosity stratification (present when the phases have unequal viscosities) are derived elsewhere. We report on extensive numerical experiments to evaluate the effect of surfactants on KS dynamics (including chaotic states, for example), both in the absence and presence of viscosity stratification. We find that chaos is suppressed in the absence of viscosity differences and that the new flow consists of successive windows (in parameter space) of steady-state travelling waves separated by time-periodic attractors. The intricate structure of the travelling pulses is also explained physically. When viscosity stratification is present we observe a transition from time-periodic dynamics, for instance, to steady-state travelling wave pulses of increasing amplitudes and speeds. Numerical evidence is presented that indicates that the transition occurs through a reverse Feigenbaum cascade in phase space.
Ultra-lightweight, membrane primary mirrors offer a promising future for space telescope technology. However, the advantages of the lightweight structure of the mirrors are restricted by an extremely high susceptibility to microyield. Hence, careful packaging of the membranes is required when transporting mirrors of this type into space. Four packaging models, a cylindrical roll, an umbrella model, a multi-cut model and a single cut model, are presented and compared with each other. Factors such as curvature of the compressed membrane, stability after deployment, and the size of the launch vehicle are considered. All four packaging models appear to be feasible with certain materials and hence warrant physical testing.
Aloin is one of the secondary metabolites that gives plants of the genus Aloe spp. their healing properties. The concentration of aloin is related to the fresh mass and, its industrial purification involves laboratory processes that add extra costs to its commercialization. The objective of this research was to mathematically modelize the estimation of the aloin concentration in A. vera L. from the fresh mass. The theory of discrete perfect least squares approximations was used, considering linear and exponential approximation functions. For the tabulation of the data, the option of class mark and the average of the values were used. The analyses of the approximations indicate that the exponential curves approximate the data better (with R2 = 75% and 82% for the two options, respectively) than the straight lines (with R2 = 65% and 70% for the two options, respectively). The use of these approximations is recommended to estimate the concentration of aloin in A. vera plants based on their fresh mass, facilitating the measurement of this secondary metabolite, and minimizing costs in the industrialization process.
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