A (not necessarily convex) object C in the plane is κ-curved for some constant 0 < κ < 1, if it has constant description complexity, and for each pointp on the boundary ofC, one can place a diskB ⊆ C of radius κ ·diam(C) whose boundary passes throughp. We prove that the combinatorial complexity of the boundary of the union of a set C of n κ-curved objects (e.g., fat ellipses or rounded heart-sh...

In this paper we present a surface formulation and curved panel integration method for computing the van der Waals interaction energy between a molecular solute and aqueous solvent. This modeling problem arises in computational drug design, where one wishes to understand the energetic tradeoff between a trial drug’s interactions with solvent and its interactions with the target. We use the dive...

The macaque anterior intraparietal area (AIP) is crucial for visually guided grasping. AIP neurons respond during the visual presentation of real-world objects and encode the depth profile of disparity-defined curved surfaces. We investigated the neural representation of curved surfaces in AIP using a stimulus-reduction approach. The stimuli consisted of three-dimensional (3-D) shapes curved al...

The lattice Boltzmann equation (LBE) is an alternative kinetic method capable of solving hydrodynamics for various systems. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and natural to parallelize. Because the method often uses uniform regular Cartesian lattices in space, curved boundaries are often...

In this research effort, the generalized warping and distortional problem of straight or horizontally curved composite beams of arbitrary cross section, loading and boundary conditions is presented. An inclined plane of curvature is considered. Additionally, the stiffness of diaphragmatic plates has been introduced in the formulation in order to compare with the case where rigid diaphragms are ...

The behaviour of materials under spatial confinement is sensitively dependent on the nature of the confining boundaries. In two dimensions, confinement within a hard circular boundary inhibits the hexagonal ordering observed in bulk systems at high density. Using colloidal experiments and Monte Carlo simulations, we investigate two model systems of quasi hard discs under circularly symmetric co...

We present a method that flattens a curved surface and its neighborhood to create effective, uncluttered visualizations by applying standard flow visualization techniques in the deformed space. Level sets of the distance from the curved surface are mapped to parallel planes. Data fields are mapped accordingly. Our method eases the visual inspection and analysis of a curved surface’s vicinity by...

In this study, an alternative second-order boundary scheme is proposed under the framework of the convection-diffusion lattice Boltzmann (LB) method for both straight and curved geometries. With the proposed scheme, boundary implementations are developed for the Dirichlet, Neumann and linear Robin conditions in a consistent way. The Chapman-Enskog analysis and the Hermite polynomial expansion t...

This paper examines the effect of curved boundary continuity on finite element simulations. Quartic C0 continuous and G1 continuous meshes with curved boundaries are created from CAD geometry. These C0 continuous and G1 continuous surface triangles are constructed using Bézier triangles and triangular Gregory patches respectively. Curved tetrahedra are constructed using a shape blending with te...

The classical Cartan-Hadamard theorem asserts that a closed Riemannian manifold M with non-positive sectional curvature has universal cover M̃ diffeomorphic to R, and a byproduct of the proof is that ∂∞M̃n is homeomorphic to Sn−1. We prove analogues of these two results in the case where M has a non-empty totally geodesic boundary. More precisely, if M 1 ,M n 2 are two negatively curved Riemannia...