ion and classification continues, What's Euclidean On a perfectly flat surface, parallel lines never meet. A triangle drawn on such a plane has interior angles that add up to 1800. A straight line is the shortest distance between two points. These and other postulates and results are part of the geometry first invented by Euclid more than 2,000 years ago. Later mathematicians refined and extend...

We study and report on the class of vacuum Maxwell fields in Minkowski space that possess a non-degenerate, diverging, principle null vector field (null eigenvector field of the Maxwell tensor) that is tangent to a shear-free null geodesics congruence. These congruences can be either surface forming (the tangent vectors being proportional to gradients) or not, i.e., the twisting congruences. In...

This paper proposes a novel adaptive Super-Twisting sliding mode control for a microgyroscope under unknown model uncertainties and external disturbances. In order to improve the convergence rate of reaching the sliding surface and the accuracy of regulating and trajectory tracking, a high order Super-Twisting sliding mode control strategy is employed, which not only can combine the advantages ...

BACKGROUND A continuous running suture is the preferential method for abdominal closure. In this technique the suture is secured with an initial knot and successive tissue bites are taken. At each tissue bite, the needle is rotated through the tissue; in doing so, the suture can twist around the knot which acts as an anchor. OBJECTIVE To determine the effect of axial torsional forces on sutur...

Three dimensional curls (‘‘hemi-helices’’) consisting of multiple, periodic and alternating helical sections of opposite chiralities, separated by perversions, are one of a variety of complex shapes that can be produced by a simple generic process consisting of pre-straining one elastomeric strip, joining it side-by-side to another and then releasing the bi-strip. The initial wavelength of the ...

1 2004 (1) References [1] M. Cho and S. Y. Rhee. Optimization of laminates with free edges under bounded uncertainty subject to extension, bending and twisting. International Journal of Solids and Structures, 41:227–245, 2004. [2] C. Lin and Y. Lee. Stacking sequence optimization of laminated composite structures using genetic algorithm with local improvement. Composite Structures, 63:339–345, ...

This paper proposes a real-time simulation technique for thin shells undergoing large deformation. Shells are thin objects such as leaves and papers that can be abstracted as 2D structures. Development of a satisfactory physical model that runs in real-time but produces visually convincing animation of thin shells has been remaining a challenge in computer graphics. Rather than resorting to she...

Real filaments are not perfectly homogeneous. Most of them have various materials composition and shapes making their stiffnesses not constant along the arclength. We investigate the existence of circular and helical equilibrium solutions of an intrinsically straight rod with varying bending and twisting stiffnesses, within the framework of the Kirchhoff model. The planar ring equilibrium solut...

In this paper, we propose a complete model handling physical simulation of deformable 1D objects. We formulate continuous expressions for stretching, bending and twisting energies. These expressions are mechanically rigorous and geometrically exact. Both elastic and plastic deformations are handled to simulate a wide range of materials. We validate the proposed model on several classical test c...

A numerical study was performed for a T-shaped microchannel to enhance mixing performance through a baffle configuration. The mixing performance was analyzed in terms of the DOM (degree of mixing) and the pressure load between the two inlets and outlet. Four different baffle configurations were designed and simulated to determine how they affect the mixing performance of a T-shaped microchannel...