catastrophic behaviors

Catastrophe theory is a branch of bifurcation theory in the study of dynamical systems.

Bifurcation theory studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circumstances, analyzing how the qualitative nature of equation solutions depends on the parameters that appear in the equation.

This may lead to sudden and dramatic changes.Small changes in certain parameters of a nonlinear system can cause equilibria to appear or disappear, or to change from attracting to repelling and vice versa, leading to large and sudden changes of the behaviour of the system.

Fracture processes are accompanied  by the emission of particles, including photons, electrons, ions and neutral species, during and following the fracture of materials.

Fracto-emission can serve as an attractive aid to understand atomic scale fracture processes.

Energy impulses may be released during the atomic scale cleavage processes. These energy releases account for the fracto-emissions during and after fracture.

The sudden energy release can be explained with a catastrophe theory for cleavage processes.

Multiwalled carbon nanotubes can be bent repeatedly through large angles using the tip of an atomic force microscope, without undergoing catastrophic failure.

Microtubules are among the principal components of the cytoskeleton, the dynamic structural framework of cells.

Microtubules are cylindrical shells of about 25 nanometer in diameter, formed by a regular helical lattice of tubulin dimers. Microtubule can be treated as a hollow cylindrical shell that can bend, buckle, and collapse.

The mechanics of single microtubules can be probed locally by radial indentation with a scanning force microscope tip.

In a situation when the scanning force microscope tip applies a force from one side while the microtubule is supported by a flat surface from the other side, a nonlinear regime and catastrophic collapse of the microtubule under large loads can be found.