Direction Curves Associated with Darboux Vectors Fields and Their Characterizations

In this paper, we consider the Darboux frame of a curve α lying on an arbitrary regular surface and we use its unit osculator Darboux vector D ¯ o , unit rectifying Darboux vector D ¯ r , and unit normal Darboux vector D ¯ n to define some direction curves such as D ¯ o -direction curve, D ¯ r -direction curve, and D ¯ n -direction curve, respectively. We prove some relationships between α and these associated curves. Especially, the necessary and sufficient conditions for each direction curve to be a general helix, a spherical curve, and a curve with constant torsion are found. In addition to this, we have seen the cases where the Darboux invariants δ o , δ r , and δ n are, respectively, zero. Finally, we enrich our study by giving some examples.

Binormal Motion of Curves with Constant Torsion in 3-Spaces

We study curve motion by the binormal flow with curvature and torsion depending velocity and sweeping out immersed surfaces. Using the Gauss-Codazzi equations, we obtain filaments evolving with constant torsion which arise from extremal curves of curvature energy functionals. They are “soliton” solutions in the sense that they evolve without changing shape.

Molecular dynamics simulation studies on the plastic behaviors of an iron nanowire under torsion

The plastic deformation mechanism of iron (Fe) nanowires under torsion is studied using the molecular dynamics (MD) method by applying an external driving force at a constant torsion speed.

CYLINDRICAL SOLUTIONS IN MODIFIED f(T) GRAVITY

We investigate static cylindrically symmetric vacuum solutions in Weyl coordinates in the framework of f(T) theory of gravity, where T is the torsion scalar. The set of modified Einstein equations is presented and the forthcoming equations are established. Specific physical expressions are assumed for the algebraic function f(T) and solutions are obtained. Moreover, general solution is obtained with finite values of u(r) on the axis r = 0 and this leads to a constant torsion scalar. Cosmological constant is also introduced and its relation to Linet–Tian solution in GR is commented.

The Dang Van Criterion for Fatigue Design

The present work intends to evaluate, using simple, exemplary cases, the importance of a full elasto-plastic analysis in fatigue design. A strain cycling situation (-ε to ε) was modelled with ABAQUS considering two situations: firstly a linear σ vs. ε relationship was assumed, and secondly, the real cyclic σ vs. ε curve was used to model each cycle, which includes a small plastic deformation. The case of change of cross section in a steel shaft subjected to constant torsion and cyclic bending was analysed through finite element modelling using ABAQUS.