1,720,992 research outputs found
Effective slip lengths for longitudinal shear flow over partial-slip circular bubble mattresses
No full textAbstract. The problem of longitudinal shear flow over a circular bubble mattress with partial slip and protrusion angle 90 o is solved in a quasi-analytical fashion by a novel transform scheme recently devised by the author. The general approach can be readily adapted to other mixed boundary value problems. From the analysis explicit approximations for the effective slip lengths are found as a function of the Navier-slip parameter and the area fraction of the surface covered by protrusions. These new approximation formulas for the slip lengths both unify and extend those based on empirical polynomial fits to numerical data given recently by Ng & Wang [Fluid Dyn. Res., 43, 065504, (2011)]
Constructing multiply connected quadrature domains
No full textAbstract. Multiply connected bounded quadrature domains, with finite connectivity, are reconstructed from their quadrature data using conformal mappings that are ratios of products of Schottky–Klein prime functions. This method provides the natural generalization of the conformal maps to simply and doubly connected quadrature domains constructed by the first author in a number of physical applications. The efficacy of the method is demonstrated by the explicit construction of a range of examples as well as by comparison with alternative constructive methods recently introduce
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Circulation-induced shape deformations of drops and bubbles: Exact two-dimensional models
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ON A CLASS OF GEOMETRY-DRIVEN FREE BOUNDARY PROBLEMS
No full textAn abstract class of two-dimensional geometry-driven free boundary problems is considered in which the evolution of the Cauchy transform of the time-evolving domain satisfies a partial differential equation of conservation type. This idea generalizes an association between free boundary problems and the inverse gravitational problem. It is shown that this class of free boundary problems admits exact solutions expressible in terms of a finite set of time-evolving parameters. In addition, even when exact solutions are not available, a theorem is established which shows that solutions corresponding to certain initial conditions possess nontrivial conserved quantities. Two distinct problems of physical interest are shown to fall within this abstract class: the evolution of a fluid blob in a rotating Hele–Shaw cell and the evolution of highly viscous fluid under the effects of surface tension. Various aspects of these two problems are discussed
10.1098/rspa.2001.0815 Multipolar vortices and algebraic curves
No full textThis paper demonstrates that analytical solutions to the steady two-dimensional Euler equations possessing all the qualitative properties of multipolar vortices observed experimentally and numerically can be constructed using the theory of algebraic curves and quadrature domains. The solutions consist of a finite set of line vortices superposed on finite-area patches of uniform vorticity. By way of example, new solutions are presented in which the support of the vorticity is a quintuply connected vortex patch with five vorticity maxima modelling a symmetric pentapolar vortex consisting of a central core vortex, four satellite vortices and four enclosed zones of irrotational fluid between the core and the satellite vortices. The method of construction is amenable to the derivation of exact solutions of the two-dimensional Euler equations having vorticity distributions of even greater geometrical complexity
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