[1] The paper investigates the influence of relative bend curvature on secondary flow, energy losses, and turbulence in sharp open-channel bends. These processes are important in natural streams with respect to sediment transport, the bathymetry and planimetry, mixing and spreading of pollutants, heat, oxygen, nutrients and biological species, and the conveyance capacity. Laboratory experiments...

Starting with the S-wave radial equation for an attractive central potential V (r), we give results for the n(principal quantum number) and the μ (reduced mass) dependence of Rn0(0), the S-wave radial waveunction at the origin, for potentials with definite curvature.

We consider the problem of nding a compact starshaped hypresurface in a space form for which the normalized m-th elementary symmetric function of principal curvatures is a prescribed function. In this paper conditions for existence of at least one solution to a nonlinear second order elliptic equation of that problem are established in case of a space form with positive sectional curvature.

The existence of closed hypersurfaces of prescribed scalar curvature in globally hyperbolic Lorentzian manifolds is proved provided there are barriers. 0. Introduction Consider the problem of finding a closed hypersurface of prescribed curvature F in a globally hyperbolic (n+1)-dimensional Lorentzian manifold N having a compact Cauchy hypersurface S0. To be more precise, let Ω be a connected op...

Capillarity can be used to direct anisotropic colloidal particles to precise locations and to orient them by using interface curvature as an applied field. We show this in experiments in which the shape of the interface is molded by pinning to vertical pillars of different cross-sections. These interfaces present well-defined curvature fields that orient and steer particles along complex trajec...

Let G be a Lie groupwith Lie algebra g. On the trivial principal G-bundle over g there is a natural connection whose curvature is the Lie bracket of g. The exponential map of G is given by parallel transport of this connection. If G is the diffeomorphism group of a manifold M , the curvature of the natural connection is the Lie bracket of vectorfields on M . In the case that G = SO(3) the motio...

Abstract In this paper we study biconservative hypersurfaces M in space forms $$\overline{M}^{n+1}(c)$$ M ¯ n + 1 ( c ) ...

We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties of the smooth limit surface and the shape regularity of the discrete net.

We study parabolic linear Weingarten surfaces in hyperbolic space H. In particular, we classify two family of parabolic surfaces: surfaces with constant Gaussian curvature and surfaces that satisfy the relation aκ1 + bκ2 = c, where κi are the principal curvatures, and a, b and c are constant.

A convex surface contracting by a strictly monotone, homogeneous degree one function of curvature remains smooth until it contracts to a point in finite time, and is asymptotically spherical in shape. No assumptions are made on the concavity of the speed as a function of principal curvatures.