A non-linear theory is presented for stretching and inplane-bending of isotropic beams which have constant initial curvature and lie in their plane of symmetry. For the kinematics, the geometrically exact one-dimensional (1-D) measures of deformation are specialized for small strain. The 1-D constitutive law is developed in terms of these measures via an asymptotically correct dimensional reduc...

Regions of high curvature of a material line as they evolve in a chaotic flow are considered. In such a region, the curvature as a function of arclength along the line is found to have a universal form with the peak curvature the only parameter involved. The alignment of the principal axes of the strain tensor with respect to the local tangent vector of the curve and the ratio of the two larges...

We consider a liquid interface with different principal curvatures +/-c and find that the mere presence of a spherical particle leads to a deformation field of quadrupolar symmetry; the corresponding "capillary quadrupole moment" is given by the ratio of the particle size and the curvature radius. The resulting pair interaction of nearby particles is anisotropic and favors the formation of aggr...

In this paper, we prove that any non-flat ancient solution to KählerRicci flow with bounded nonnegative bisectional curvature has asymptotic volume ratio zero. We also classify all complete gradient shrinking solitons with nonnegative bisectional curvature. Both results generalize the corresponding earlier results of Perelman in [P1] and [P2]. The results then are applied to study the geometry ...

We derive explicit and precise formulae for 3 by 3 error matrix of particle transverse momentum, direction and impact parameter. The error matrix elements are expressed as functions of up to fourth order statistical moments of the measured coordinates. The formulae are valid for any curvature and track length in case of negligible multiple scattering. The calculation is compared with formulae d...

Abstract In order to further improve the flight stability of explosively formed projectile, formation method tail EFP was studied based on polygonal liner. Under hexagonal charge structure, fins can be when structural parameters are matched. Through numerical simulation LS-DYNA, influence liner (curvature radius, linear thickness), height and shell thickness velocity, length-diameter ratio, com...

The modification of the curvature moduli due to surface charges in lipid bilayers is analyzed using the nonlinear Poisson-Boltzmann equation for the relationship between the charge density and surface potential. An expansion in a small parameter epsilon, which is the ratio of the Debye length and the radius of curvature, is used. At low charge densities, previous results obtained from the Debye...