Complexity science is the multidisciplinary study of complex systems. Its marked network orientation lends itself well to transport contexts. Key features of complexity science are introduced and defined, with a specific focus on the application to air traffic management. An overview of complex network theory is presented, with examples of its corresponding metrics and multiple scales. Complexity science is starting to make important contributions to performance assessment and system design: selected, applied air traffic management case studies are explored. The important contexts of uncertainty, resilience and emergent behaviour are discussed, with future research priorities summarised.
Liquid bridges appear in a large variety of industrial processes such as the so-called floating-zone technique, used in recent years in crystal growth and in purification of high-melting-point materials.In this paper the dynamics of axisymmetric, slender, viscous liquid bridges having volume close to the cylindrical one, and subjected to a small gravitational field parallel to the axis of the liquid bridge, is considered within the context of one-dimensional theories. Although the dynamics of liquid bridges has been treated through a numerical analysis in the in viscid case, numerical methods become inappropriate to study configurations close to the static stability limit because the evolution time, and thence the computing time, increases excessively. To avoid this difficulty, the problem of the evolution of these liquid bridges has been attacked through a nonlinear analysis based on the singular perturbation method and. whenever possible, the results obtained are compared with the numerical ones.
The steady streaming flow due to vibration in capillary bridges is considered in the limiting case when both the capillary Reynolds number and the non-dimensional vibration frequency (based on the capillary time) are large. An asymptotic model is obtained that provides the streaming flow in the bulk, outside the thin oscillatory boundary layers near the disks and the interface. Numerical integration of this model shows that several symmetric and non-symmetric streaming flow patterns are obtained for varying valúes of the vibration parameters. As a by-product, the quantitative response of the liquid bridge to high-frequency axial vibrations of the disks is also obtained.
Abstract. The combined effect of thermocapillary stress and steady forcing due to vibrations of the disks in a model-half-zone axisymmetric liquid bridge is considered for low-viscosity liquids (i.e., with a large capillary Reynolds number), and low nondimensional vibration frequencies (i.e., small as compared to the capillary Reynolds number). An asymptotic model is derived for the slowly-varying streaming flow in the bulk (outside the oscillatory boundary layers) resulting from both effects that includes also buoyancy and other thermal expansión effects. This model is used to first analyze the steady streaming flow patterns in isothermal conditions and then to show that mechanical vibrations can annihilate almost completely thermocapillary flows of fairly large Reynolds numbers provided that: (i) the Prandtl number is appropriately small, (ii) both disks are vibrated, and (iii) the vibrating amplitudes, frequency and phases are appropriate (the counterbalancing effect depends crucially on the difference of the vibrating phases of both disks).
Mathematics Subject Classification (1991). Primary 76D05, 76D45; Secondary 76D30, 35Q30, 80A20.
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