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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 58 (1996), S. 753-785 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A solution algorithm yielding the pressure and flow-rate distributions for steady flow in an arbitrary, tree-like network is provided. Given the tree topology, the conductance of each segment and the pressure distribution at the boundary nodes, the solution is obtained from a simple recursion based on perfect Gauss elimination. An iterative solution method using this algorithm is suggested to solve for the pressure and flow-rate distributions in an arbitrary diverging-converging (arterial-venous) network consisting of two tree-like networks which are connected to each other at the capillary nodes. A number of special solutions for tree-like networks are obtained for which the general algorithm is either simplified or can be replaced by closed form solutions of the pressure and flow-rate distributions. These special solutions can also be obtained for each tree of diverging-converging networks having particular topologies and conductance distributions. Sample numerical results are provided.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 62 (2000), S. 1035-1059 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model describing the ciliary driven flow and motion of suspended particles in downstream suspension feeders is developed. The quasi-steady Stokes equations for creeping flow are solved numerically in an unbounded fluid domain around cylindrical bodies using a boundary integral formulation. The time-dependent flow is approximated with a continuous sequence of steady state creeping flow fields, where metachronously beating ciliary bands are modelled by linear combinations of singularity solutions to the Stokes equations. Generally, the computed flow fields can be divided into an unsteady region close to the driving ciliary bands and a steady region covering the remaining fluid domain. The size of the unsteady region appears to be comparable to the metachronal wavelength of the ciliary band. A systematic investigation is performed of trajectories of infinitely small (fluid) particles in the simulated unsteady ciliary driven flow. A fraction of particles appear to follow trajectories, that resemble experimentally observed particle capture events in the downstream feeding system of the polycheate Sabella penicillus, indicating that particles can be captured by ciliary systems without mechanical contact between particle and cilia. A local capture efficiency is defined and its value computed for various values of beat frequencies and other parameters. The results indicate that the simulated particle capture process is most effective when the flow field oscillates within timescales comparable to transit timescales of suspended particles passing the unsteady region near the ciliary bands. However, the computed retention efficiencies are found to be much lower than those obtained experimentally.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 293-315 
    ISSN: 0271-2091
    Keywords: Euler equations ; free surface ; gravity waves ; finite volume method ; fractional step method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A fractional step method is developed for solving the time dependent two-dimensional Euler equations with full non-linear free-surface boundary conditions. The geometry of the free surface is described by a height function, and its evolution is tracked by integrating in time the kinematic boundary conditions based on the free-surface volume flux. The fluid domain is discretised by adapting a time-varying curvilinear grid to all boundaries, including the free surface. Mass and momentum equations are discretised by a conservative finite volume formulation, taking into account the time dependency of the grid. A fractional step type method is developed for integrating the fluid motion in time. The method is applied to a non-linear standing wave in a square container, testing for compliance with mass and energy conservation and comparing computed wave period with other results. Non-linear travelling waves are simulated in channels with either constant depth or varying depth and non-linear wave processes involving both triad interactions and quartet interactions are studied. Results are compared with both experimental data and theoretical results and excellent agreement is found. Interaction of waves and currents is studied. The blocking of waves in an opposing current is simulated and found to show good agreement with theoretical results. The method is intended to be a first step towards a full description of wave dynamics interacting with structures and currents. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
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