It is known that in a certain case, the secondary Bjerknes force, which is a radiation force acting between pulsating bubbles, changes (e.g., from attraction to repulsion) as the bubbles approach each other. In this Letter, a theoretical discussion of this phenomenon for two spherical bubbles is described. The present theory, based on analysis of the transition frequencies of interacting bubble...

Figure 1 compares our mixture of spherical Gaussians (SG) basis to spherical harmonics (SH) and zonal harmonics (ZH) [Sloan et al. 2005]. A simple 2-lobe fit with our basis provides good accuracy; error decreases further with more lobes. Asymptotic error decrease in our model compares favorably with increasing order of spherical harmonics and with increasing order and number of lobes in the ZH ...

A configuration of particles confined to a sphere is balanced if they are in equilibrium under all force laws (that act between pairs of points with strength given by a fixed function of distance). It is straightforward to show that every sufficiently symmetrical configuration is balanced, but the converse is far from obvious. In 1957 Leech completely classified the balanced configurations in R...

In this paper, we study the problem of reconstructing the polyhedral structures and geometric positions of a general nD polyhedral scene from a single 2D line drawing. With the idea of local construction and propagation, we propose several powerful techniques for structural reconstruction (i.e. face identification) and geometric reconstruction (i.e. realizability and parametrization). Our struc...

Archimedes was the first to systematically find the centers of gravity of various solid bodies and to apply this concept in determining stable configurations of floating bodies. In this paper, we discuss an error in a proof developed by Archimedes that involves determining whether a uniform, spherical cap will float stably with its base horizontal in a liquid on a spherical Earth. We present a ...

In April 2010 the International Finance Corporation announced the creation of the African, Latin American, and Caribbean fund, a new co-investment vehicle funded largely with commitments from sovereign wealth and pension funds. The fund’s objective was to draw on the IFC and the World Bank’s strengths in emerging markets to identify and support enterprises that might not otherwise have come to ...

For a bar and joint framework (G, p) with point group C3 which describes 3-fold rotational symmetry in the plane, it was recently shown in (Schulze, Discret. Comp. Geom. 44:946-972) that the standard Laman conditions, together with the condition derived in (Connelly et al., Int. J. Solids Struct. 46:762-773) that no vertices are fixed by the automorphism corresponding to the 3-fold rotation (ge...

Observation of writers producingg non-trivial texts suggests t hat most spendd time generating andd organisingg content prior to draftingg full text. Resear chsuggests a linkk between time spent inn these activities andd the quality of the resulting docume nt. Very little is known, however, about either the nature of the representation that is c reatedd during this planningg phase (the writer's...

By a systematic method we construct general classes of exact and selfconsistent axisymmetric MHD solutions describing flows which originate at the near environment of a central gravitating astrophysical object. The unifying scheme contains two large groups of exact MHD outflow models, (I) meridionally self-similar ones with spherical critical surfaces and (II) radially self-similar models with ...

This paper considers the construction of Reproducing Kernel Hilbert Spaces (RKHS) on the sphere as an alternative to the conventional Hilbert space using the inner product that yields the L(S) function space of finite energy signals. In comparison with wavelet representations, which have multi-resolution properties on L(S), the representations that arise from the RKHS approach, which uses diffe...