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8124 results in Fluid dynamics and solid mechanics

Page 102 of 407

Symmetry, Phase Modulation and Nonlinear Waves
  • Thomas J. Bridges
  • Published online:
    30 June 2017
    Print publication:
    03 July 2017
  • Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.

Vibration of Nearly Periodic Structures and Mistuned Bladed Rotors
  • Alok Sinha
  • Published online:
    22 June 2017
    Print publication:
    16 June 2017
  • This is the first comprehensive volume on nearly periodic structures and mistuned blade vibration. Alok Sinha presents fundamental concepts and state-of-the-art techniques in the analysis of free and forced response of a nearly periodic structure, weaving together his own work (covering thirty-five years of research in this field) with works by other researchers. He also discusses similarities between tools used in bladed rotor analysis and condensed matter physics. Specific subjects covered include the reasons behind mode localization, the reasons behind amplitude amplification of steady-state response, state-of-the-art computational techniques for mistuned bladed rotors including multistage rotors, identification of mistuning from measured response, vibration localization in linear atomic chains, and analysis of two-dimensional periodic structures.

  • EDITORIAL: MATHEMATICAL METHODS FOR APPLICATIONS

  • PHIL BROADBRIDGE, MARK NELSON, JUSTIN WANG
  • Journal:
    The ANZIAM Journal / Volume 58 / Issue 3-4 / April 2017
    Published online by Cambridge University Press:
    19 June 2017, pp. 209-210
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  • ANZ VOLUME 58 ISSUE 3-4 COVER AND BACK MATTER

  • Journal:
    The ANZIAM Journal / Volume 58 / Issue 3-4 / April 2017
    Published online by Cambridge University Press:
    19 June 2017, pp. b1-b15
    • Article
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  • ANZ VOLUME 58 ISSUE 3-4 COVER AND FRONT MATTER

  • Journal:
    The ANZIAM Journal / Volume 58 / Issue 3-4 / April 2017
    Published online by Cambridge University Press:
    19 June 2017, pp. f1-f2
    • Article
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  • 6 - Drop Impacts with Liquid Pools and Layers

  • from Part II - Drop Impacts onto Liquid Surfaces
  • Alexander L. Yarin, University of Illinois, Chicago, Ilia V. Roisman, Technische Universität, Darmstadt, Germany, Cameron Tropea, Technische Universität, Darmstadt, Germany
  • Book:
    Collision Phenomena in Liquids and Solids
    Published online:
    13 July 2017
    Print publication:
    15 June 2017, pp 255-320

  • Summary

    In this chapter drop impacts onto a liquid layer of the same liquid as in the drop are considered. The chapter begins with consideration of such weak drop impacts on a liquid layer that they result only in capillary waves propagating over the surface. An interesting feature of these waves is that they are self-similar (Section 6.1). In the following Section 6.2 crown formation in strong (high-velocity) impacts onto thin liquid films is considered. Normal and oblique impacts of a single drop onto a wet wall are studied, as well as crown–crown interaction in sprays impacting the wall. Also, the evolution of the free rim on top of the crown is described. Then, in Section 6.3 drop impacts onto a thick liquid layer are considered and the dynamics of the crater formation is explained. Drop impacts onto a wet wall leave a residual liquid film on the wall which is addressed in Section 6.4. Drop impacts onto deep liquid pools produce a plethora of interesting morphological structures considered in Section 6.5. In the following Section 6.6 bending instability of a free rim is considered and the splashing mechanism is discussed. Splashing resulting from impacts of drop trains one-by-one is discussed in Section 6.7, where its physical mechanism and the link to splashing of a single drop impacting onto a liquid layer are elucidated. Several other regimes of drop impact are also mentioned.

    Drop Impact onto Thin Liquid Layer on a Wall: Weak Impacts and Self-similar Capillary Waves

    Consider patterns of capillary waves propagating over the free surface of a thin liquid film from the point where it was impacted normally by a tiny droplet or a stick (Fig. 6.1), as an example of a relatively weak (low-velocity) impact. For scales of the order of several millimeters the gravity effect on these waves is negligibly small, and for time scales of the order of several milliseconds viscosity effects can also be neglected.

Page 102 of 407