We study the formulation of bond-orientational order in an arbitrary two dimensional geometry. We find that bond-orientational order is properly formulated within the framework of differential geometry with torsion. The torsion reflects the intrinsic frustration for two-dimensional crystals with arbitrary geometry. Within a DebyeHuckel approximation, torsion may be identified as the density of ...

The initial data of the gravitational field produced by a loop thick string is considered. We show that the loop is not a geodesic on the initial hypersurface, while a loop conical singularity is. This suggests that there is the criteria in the string thickness at which the linear perturbation theory around flat space fails to describe the gravity produced by a loop cosmic string. Because the g...

A finite element analysis is presented for sloshing and impulsive motion of liquid-filled conical tanks during lateral anti-symmetric excitation. The performed analyses led to the development of a number of charts which can be used to identify the natural frequency, the mode shapes of conical tanks for both fundamental and the cos(θ)-modes of vibration. Conical tank geometry was described with ...

Out-of-plane curvature of real submarine slopes imposes limitations on applicability existing planar criteria for catastrophic growth slip surfaces. In this paper, the an initially weakened zone in three-dimensional (3D) convex and concave is investigated using process approach. The geometry problem presented a curvilinear coordinate system which governing equations surface are derived. Solutio...

whenever this limit exists. Here Σk(r) ≡ ∂Bn r (0)/Γk denotes the Euclidean sphere of radius r in the k-th conical end of M , all suband superscripts refer to the standard Euclidean coordinates on Rn, ν is the Euclidean exterior unit normal to Σk(r), and dA is the Euclidean area measure. Bartnik [1] and Chruściel [2] discovered sharp conditions on the decay rate of Φ∗g − g0 ensuring that the li...

We study a two-point free boundary problem for a quasilinear parabolic equation. This problem arises in the model of flame propagation in combustion theory. It also arises in the study of the motion of interface moving with curvature in which the studied problem is confined in the conical region bounded by two straight lines and the interface has prescribed touching angles with these two straig...

The naive approach is to parametrize these deformations as the zero-set of a “mean curvature operator”, then study them using the implicit function theorem. However, this entails a good understanding of the Jacobi operator of the initial submanifold Σ, which in general is not possible. The work of Oh and, more recently, of McLean (cfr. [Oh], [ML]) shows that, in the “right” geometric context, t...

We study the evolution of strictly mean-convex entire graphs over $${{\mathbb {R}}}^n$$ by Inverse Mean Curvature flow. First we establish global existence starshaped with superlinear growth at infinity. The main result in this work concerns critical case asymptotically conical convex graphs. In show that there exists a time $$ T < +\infty , which depends on infinity initial data, such unique s...

The physiological functions of epidermal cells are largely determined by their diverse morphologies. Most flowering plants have special conical-shaped petal epidermal cells that are thought to influence light capture and reflectance, and provide pollinator grips, but the molecular mechanisms controlling conical cell shape remain largely unknown. Here, we developed a live-confocal imaging approa...

Conical queries are a novel type of query with an increasing number of applications. Traditional index structures and retrieval mechanisms, in general, have been optimized for rectangular and circular queries, rather than conical queries. In this paper, we focus on conical queries which can be deened as a multi-dimensional cone in a multi-dimensional data space. We develop a model for expressin...