After protoplanets have acquired sufficient mass to open partial gaps in their natal protostellar disks, residual gas continues diffuse onto horseshoe streamlines under effect of viscous dissipation, and meander out the planets' Hill sphere. Within sphere, intercept flow circumplanetary disks. The host stars' tidal perturbation induces a barrier across converging streamlines' interface. Viscous...

‎based on a definition for circle in finsler space‎, ‎recently proposed by one of the present authors and z‎. ‎shen‎, ‎a natural definition of extrinsic sphere in finsler geometry is given and it is shown that a connected submanifold of a finsler manifold is totally umbilical and has non-zero parallel mean curvature vector field‎, ‎if and only if its circles coincide with circles of the ambient...

We present a multi-scale model to study the attachment of spherical particles with a rigid core, coated with binding ligands and suspended in the surrounding, quiescent fluid medium. This class of fluid-immersed adhesion is widespread in many natural and engineering settings, particularly in microbial surface adhesion. Our theory highlights how the micro-scale binding kinetics of these ligands,...

In this paper, the flow-field of an incompressible viscous flow past a solid-sphere at low Reynolds numbers (up to 270) is investigated numerically. In order to extend the capabilities of the finite volume method, the boundary (body) fitted coordinates (BFC) method is used. Transformation of the partial differential equations to algebraic relations is based on the finite-volume method with coll...

In this paper, the flow-field of an incompressible viscous flow past a solid-sphere at low Reynolds numbers (up to 270) is investigated numerically. In order to extend the capabilities of the finite volume method, the boundary (body) fitted coordinates (BFC) method is used. Transformation of the partial differential equations to algebraic relations is based on the finite-volume method with coll...

in this paper, by modifying cheng-yau$'$s technique to complete hypersurfaces in $s^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [h. li, hypersurfaces with constant scalar curvature in space forms, {em math. ann.} {305} (1996), 665--672].

We prove Gaussian estimates for heat kernels on semisimple Lie groups by using the method of Bloch wave representation. We also give a large time asymptotic expansion for heat kernels on compact extensions of abelian Lie groups.

This article has three goals. First, we generalize the result of Deuring and Serre on the characterization of supersingular locus to all Shimura varieties given by totally indefinite quaternion algebras over totally real number fields. Second, we generalize the result of Ribet on arithmetic level raising to such Shimura varieties in the inert case. Third, as an application to number theory, we ...

Bloch points in permalloy cylinders are investigated using a micromagnetic framework, where thermal effects are included via the Landau-Lifshitz-Bloch equation of motion. We show that this enables micromagnetic modeling of a Bloch point avoiding the problem of singularities, which have been rep0l1ed in the literature so far. The details of the Bloch point which we reveal are compared with earli...