All conjugate-maximal-helicity-violating amplitudes from topological open string theory in twistor space

A torsional pendulum involves the oscillation of a rigid body in which the restoring force is provided by the torsion in the string from which the rigid body is suspended. Ideally, the string should be massless; practically, its mass is much smaller than the rigid body's mass and is neglected.
As long as the rigid body's angular displacement is small, its oscillation can be modeled as a linear angular oscillation. The amplitude of the oscillation is an angle. The role of mass is played by the...

The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as

The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:

Consider a cylindrical shaft with a length denoted by L and a consistent cross-sectional radius referred to as r. This shaft undergoes a torque at the free end. The highest shearing strain within the shaft is directly proportional to the twist angle and the radial distance from the shaft axis. When the shaft behaves elastically, this shearing strain can be articulated using variables such as the applied torque, radial distance, the polar moment of inertia, and the modulus of rigidity. By...

Circular shafts undergoing torsional stress maintain their cross-sectional integrity due to their axisymmetric nature. This symmetry ensures an even distribution of stress, allowing the shaft to withstand torsion without distorting. In contrast, square bars, lacking this axial symmetry, experience significant distortion across their cross-sections when subjected to torsion, with the exception of along their diagonals and at lines connecting midpoints. A detailed examination of a cubic element...

A toy train ascending a winding track that curves and tilts offers an intuitive view of torsion, a key geometric concept in the study of space curves. While curvature measures how sharply a path bends, torsion captures how the path twists out of the plane of bending. This twisting behavior is crucial in understanding three-dimensional motion and is precisely described using the Frenet–Serret framework.At each point along a space curve, the Frenet–Serret frame consists of three orthogonal unit...