Applications such as suturing in medical simulations require the modeling of knot tying in physically realistic rope. The paper describes the design and implementation of such a system. Our model uses a spline of linear springs, adaptive subdivision and a dynamics simulation. Collisions are discrete event simulated and follow the impulse model. Although some care must be taken to maintain stabl...

Focus Research dealing with the manipulation of flexible objects has been on for a while. Most of the existing motion-planning algorithms that determine a trajectory from a start to the goal state revolve around traditional sampling-based and feedback control methods. What has not been done so far is the realisation of desired goal states from different initial states through reactive, global p...

This paper describes the "scissor-knot-pusher," an instrument that greatly facilitates the execution of knot tying during laparoscopic operations. The instrument acts in essence as an extension of the surgeon's hand and, given its rigid structure, allows the surgeon full control of the process of knot tying. Additionally, after the knot has been tightened, it is possible to cut the suture witho...

A large number of antitrust investigations in the US and in Europe concern various kinds of tying behavior by firms with market power. This primer analyses factors that make ties more likely either to hurt or to benefit consumers. It argues that: (1) The impact of tying on competition in the tied market ranges from “little impact on the rivals’ ability to compete” to “total exclusion of competi...

We prove the existence of a time evolution for infinite anharmonic crystals for a large class of initial configurations. When there are strong forces tying particles to their equilibrium positions then the class of permissible initial conditions can be specified explicitly; otherwise it can only be shown to have full measure with respect to the appropriate Gibbs state. Uniqueness of the time ev...

We prove the existence of a time evolution for infinite anharmonic crystals for a large class of initial configurations. When there are strong forces tying particles to their equilibrium positions then the class of permissible initial conditions can be specified explicitly; otherwise it can only be shown to have full measure with respect to the appropriate Gibbs state. Uniqueness of the time ev...

We study the two-player, complete information all-pay auction in which a tie ensues if neither player outbids the other by more than a given amount. In the event of a tie, each player receives an identical fraction of the winning prize. Thus players engage in two margins of competition: losing versus tying, and tying versus winning. Two pertinent parameters are the margin required for victory a...