This article describes a number of velocity-based moving mesh numerical methods for multidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conser...

Cometary ultracompact H II regions have been modelled as the interaction of the hypersonic wind from a moving star with the molecular cloud which surrounds the star. We here show that a similar morphology can ensue even if the star is stationary with respect to the cloud material. We assume that the H II region is within a stellar wind bubble which is strongly mass loaded: the cometary shape re...

In this paper we study, from a control theoretic view point, a 1D model of fluid-particle interaction. More precisely, we consider a point mass moving in a pipe filled with a fluid. The fluid is modelled by the viscous Burgers equation whereas the point mass obeys Newton’s second law. The control variable is a force acting on the mass point. The main result of the paper asserts that for any ini...

Quasistatic multi-legged locomotion consists of a series of postures where the mechanism supports itself against gravity while moving free limbs to new positions. A posture is robust if the contacts can passively support the mechanism against gravity as well as disturbance forces generated by moving limbs of the mechanism. This paper is concerned with identifying and computing robust postures o...

We describe a procedure to identify stars from nearby moving groups and associations out of catalogs of stars with large proper motions. We show that from the mean motion vector of a known or suspected moving group, one can identify additional members of the group based on proper motion data and photometry in the optical and infrared, with minimal contamination from background field stars. We d...

this paper proposes a gait planning approach to reduce the required friction for a biped robot walking on various surfaces. to this end, a humanoid robot with 18 dof is considered to develop a dynamics model for studying various 3d manoeuvres. then, feasible trajectories are developed to alleviate the fluctuations on the upper body to resemble human-like walking. in order to generate feasible w...

The interaction of solitary waves on shallow water is examined to fourth order. At first order the interaction is governed by the Korteweg–de Vries (KdV) equation, and it is shown that the unidirectional assumption, of right-moving waves only, is incompatible with mass conservation at third order. To resolve this, a mass conserving system of KdV equations, involving both rightand left-moving wa...