We discuss a lubrication approximation model of the interface between two immiscible fluids in a Hele-Shaw cell, derived in [CDG93] and widely studied since. The model consists of a single one dimensional evolution equation for the thickness 2h = 2h(x, t) of a thin neck of fluid, ∂th+ ∂x(h ∂ 3 xh) = 0 , for x ∈ (−1, 1) and t ≥ 0. The boundary conditions fix the neck height and the pressure jump...

This paper investigates convergence of the discontinuous finite volume method (DFVM) underminimal regularity assumptions on solutions of second order elliptic boundary value problems. Conventional analysis requires the solutions to be in Sobolev spacesH1+s, s > 1 2 . Here we assume the solutions are in H1+s, s > 0 and employ the techniques developed in Gudi (2010) [18,20] to derive error estima...

We study hypersurfaces moving under flow that depends on the mean curvature. The approach is based on a numerical technique that embeds the evolving hypersurface as the zero level set of a family of evolving surfaces. In this setting, the resulting partial differential equation for the motion of the level set function φ may be solved by using numerical techniques borrowed from hyperbolic conser...

The closed-loop structure of a parallel robot results in complex kinematic singularities in the workspace of the mobile platform. Singularity analysis become important in design, motion planning, and control of parallel robots. Focusing on the instantaneous velocities of passive joints, a new formulation approach is proposed for the instantaneous kinematics and singularity analysis of a class o...

We provide exact and asymptotic counting formulas for five singular lattice path models in the quarter plane. Furthermore, we prove that these models have a non D-finite generating function. Résumé Nous présentons des résultats énumératives pour les cinq modèles de marches dans le quart de plan dites “singulière”. Nous prouvons que ces modéles sont non-holonome.

this article addresses an efficient and novel method for singularity-free path planning and obstacle avoidance of parallel manipulator based on neural networks. a modified 4-5-6-7 interpolating polynomial is used to plan a trajectory for a spherical parallel manipulator. the polynomial function which is smooth and continuous in displacement, velocity, acceleration and jerk is used to find a pat...

We analyze the use of kinematic constraints for articulated object tracking. Conditions for the occurrence of singularities in 3-D models are presented and their effects on tracking are characterized. We describe a novel 2-D Scaled Prismatic Model (SPM) for figure registration. In contrast to 3-D kinematic models, the SPM has fewer singularity problems and does not require detailed knowledge of...

The leading and the subleading Landau singularities in affine Toda field theories are examined in some detail. Formulae describing the subleading simple pole structure of box diagrams are given explicitly. This leads to a new and nontrivial test of the conjectured exact S-matrices for these theories. We show that to the one-loop level the conjectured S-matrices of the An Toda family reproduce t...

This paper presents a coordinate-invariant differential geometric analysis of kinematic singularities for closed kinematic chains containing both active and passive joints. Using the geometric framework developed in Park and Kim (1996) for closed chain manipulability analysis, we classify closed chain singularities into three basic types: (i) those corresponding to singular points of the joint ...

This paper proposes a systematic algorithm based on the interval analysis concept in order to obtain the maximal singularity-free circle or sphere within the workspace of parallel mechanisms. As case studies the 3-RPR planar and 6-UPS parallel mechanisms are considered to illustrate the relevance of the algorithm for 2D and 3D workspaces. To this end, the main algorithm is divided into four sub...