The stability of a rapid dynamic crack in a two-dimensional infinite strip is studied in the framework of linear elastic fracture mechanics supplemented with a modified principle of local symmetry. It is predicted that a single crack becomes unstable by a finite wavelength oscillatory mode at a velocity vc, 0.8cR<vc<0.85cR, where cR is the Rayleigh wave speed. The relevance of this theoretical ...

The intent of this short note is to provide an independent proof of the unpublished discovery of Klaus Kröncke [Kro13] that complex projective space with its canonical Fubini–Study metric is dynamically unstable under Ricci flow in all complex dimensions N ≥ 2. The unstable perturbation is not Kähler. This provides a counterexample to a well known conjecture widely attributed to Hamilton. Moreo...

The dynamic instability of single-walled carbon nanotubes (SWCNT), double-walled carbon nanotubes (DWCNT) and triple-walled carbon nanotubes (TWCNT) embedded in an elastic medium under combined static and periodic axial loads are investigated using Floquet–Lyapunov theory. An elastic multiple-beam model is utilized where the nested slender nanotubes are coupled with each other through the van d...

This brief paper proposes a dynamic data-driven method for stability monitoring of rotorcraft systems, where the underlying concept is built upon the principles of symbolic dynamics. The stability monitoring algorithm involves wavelet-packet-based preprocessing to remove spurious disturbances and to improve the signal-to-noise ratio (SNR) of the sensor time series. A quantified measure, called ...

Note on the dynamic instability of microtubules Abstract If the dynamic instability of microtubules follows a gamma distribution then one can associate to it a Cantor set. Microtubules (MTs), the main protein polymeric filaments of the cell cy-toskeleton, are a well-defined biological system where methods in condensed matter, statistical mechanics and the theory of complex systems have been app...

Dynamic instability, polarity, and spatiotemporal organization are hallmarks of the microtubule cytoskeleton that allow formation of complex structures such as the eukaryotic spindle. No similar structure has been identified in prokaryotes. The bacteriophage-encoded tubulin PhuZ is required to position DNA at mid-cell, without which infectivity is compromised. Here, we show that PhuZ filaments,...

Microtubules switch between growing and shrinking states, a feature known as dynamic instability. The biochemical parameters underlying dynamic instability are modulated by a wide variety of microtubule-associated proteins that enable the strict control of microtubule dynamics in cells. The forces generated by controlled growth and shrinkage of microtubules drive a large range of processes, inc...

The flawless distribution of chromosomes to the daughter cells in mitosis depends in part on unlikely sources microtubule instability and chance events. Equal chromosome distribution results from the regular arrangement of microtubules shown in Fig. 1. The result is attachment of the partner chromosomes to opposite spindle poles and their movement to opposite poles in anaphase, so that each dau...