844 research outputs found
Explicit excluded volume of cylindrically symmetric convex bodies
We represent explicitly the excluded volume Ve{B1,B2} of two generic
cylindrically symmetric, convex rigid bodies, B1 and B2, in terms of a family
of shape functionals evaluated separately on B1 and B2. We show that Ve{B1,B2}
fails systematically to feature a dipolar component, thus making illusory the
assignment of any shape dipole to a tapered body in this class. The method
proposed here is applied to cones and validated by a shape-reconstruction
algorithm. It is further applied to spheroids (ellipsoids of revolution), for
which it shows how some analytic estimates already regarded as classics should
indeed be emended
Hydrodynamic Flows on Curved Surfaces: Spectral Numerical Methods for Radial Manifold Shapes
We formulate hydrodynamic equations and spectrally accurate numerical methods
for investigating the role of geometry in flows within two-dimensional fluid
interfaces. To achieve numerical approximations having high precision and level
of symmetry for radial manifold shapes, we develop spectral Galerkin methods
based on hyperinterpolation with Lebedev quadratures for -projection to
spherical harmonics. We demonstrate our methods by investigating hydrodynamic
responses as the surface geometry is varied. Relative to the case of a sphere,
we find significant changes can occur in the observed hydrodynamic flow
responses as exhibited by quantitative and topological transitions in the
structure of the flow. We present numerical results based on the
Rayleigh-Dissipation principle to gain further insights into these flow
responses. We investigate the roles played by the geometry especially
concerning the positive and negative Gaussian curvature of the interface. We
provide general approaches for taking geometric effects into account for
investigations of hydrodynamic phenomena within curved fluid interfaces.Comment: 14 figure
- …