Relativistic Rotation in the Large Radius, Small Angular Velocity Limit
Relativistic rotation is considered in the limit of angular velocity approaching zero and radial distance approaching infinity, such that centrifugal acceleration is immeasurably small while tangent velocity remains close to the speed of light. For this case, the predictions of the traditional approach to relativistic rotation using local co-moving Lorentz frames are compared and contrasted with those of the differential geometry based non-time-orthogonal analysis approach. Different predictions by the two approaches imply that only the non-time-orthogonal approach is valid.
Lengths on rotating platforms
The paper treats the issue of the length of a rotating circumference as seen from on board the moving disk and from an inertial reference frame. It is shown that, properly defining a measuring process, the result is in both cases 2πR thus dissolving the Ehrenfest paradox. The same holds good when considering that, for the rotating observer, the perceived radius coincides with the curvature radius of a space-time helix and a complete round trip corresponds to an angle which differs from the one seen by the inertial observer. The apparent contradiction with the Lorentz contraction is discussed.
Numerical analysis and experimental observation of guidewire motion in a blood vessel model.
We have developed a computer-based system to simulate a guidewire in blood vessels for surgical planning, intra-operative assistance, and to facilitate the design of new guidewires. In this study, we compared simulation results with experimental results for validation of the simulation system. First, we inserted a commercial guidewire into a poly (vinyl alcohol) hydrogel blood vessel model using a two-axis automatic stage and measured the position of the guidewire tip and the contact force between the guidewire and the vessel. The experimental apparatus can be used not only for the validation of numerical analyses, but also as a simulation system. Second, similarly to the experiment, the motion of the guidewire in the blood vessel model was calculated when the proximal part of the guidewire model was pushed and twisted. The model of the guidewire is constructed with viscoelastic springs and segments, and the proximal part of the guidewire model is constrained by the fixed catheter model. Collisions between the guidewire and the vessel are calculated, and the contact forces are determined according to the stiffness of the vessel wall. The same tendency was seen in the trajectories and the contact force of both the experimental and simulated guidewire tips.