Nonlinear drillstring dynamics analysis

This paper studies the dynamical response of a rotary drilling system with a drag bit, using a lumped parameter model that takes into consideration the axial and torsional vibration modes of the bit. These vibrations are coupled through a bit-rock interaction law. At the bit-rock interface, the cutting process introduces a state-dependent delay, while the frictional process is responsible for discontinuous right-hand sides in the equations governing the motion of the bit. This complex system is characterized by a fast axial dynamics compared to the slow torsional dynamics. A dimensionless formulation exhibits a large parameter in the axial equation, enabling a two-time-scales analysis that uses a combination of averaging methods and a singular perturbation approach. An approximate model of the decoupled axial dynamics permits us to derive a pseudoanalytical expression of the solution of the axial equation. Its averaged behavior influences the slow torsional dynamics by generating an apparent velocity weakening friction law that has been proposed empirically in earlier work. The analytical expression of the solution of the axial dynamics is used to derive an approximate analytical expression of the velocity weakening friction law related to the physical parameters of the system. This expression can be used to provide recommendations on the operating parameters and the drillstring or the bit design in order to reduce the amplitude of the torsional vibrations. Moreover, it is an appropriate candidate model to replace empirical friction laws encountered in torsional models used for control. © 2009 Society for Industrial and Applied Mathematics.

On high-frequency noise scattering by aerofoils in flow

Abstract A theoretical model is developed for the sound scattered when a sound wave is incident on a cambered aerofoil at non-zero angle of attack. The model is based on the linearization of the Euler equations about a steady subsonic flow, and is an adaptation of previous work which considered incident vortical disturbances. Only high-frequency sound waves are considered. The aerofoil thickness, camber and angle of attack are restricted such that the steady flow past the aerofoil is a small perturbation to a uniform flow. The singular perturbation analysis identifies asymptotic regions around the aerofoil; local 'inner' regions, which scale on the incident wavelength, at the leading and trailing edges of the aerofoil; Fresnel regions emanating from the leading and trailing edges of the aerofoil due to the coalescence of singularities and points of stationary phase; a wake transition region downstream of the aerofoil leading and trailing edge; and an outer region far from the aerofoil and wake. An acoustic boundary layer on the aerofoil surface and within the transition region accounts for the effects of curvature. The final result is a uniformly-valid solution for the far-field sound; the effects of angle of attack, camber and thickness are investigated. © 2013 Cambridge University Press.

Perturbation of the stability of amyloid fibrils through alteration of electrostatic interactions.

The self-assembly of proteins and peptides into polymeric amyloid fibrils is a process that has important implications ranging from the understanding of protein misfolding disorders to the discovery of novel nanobiomaterials. In this study, we probe the stability of fibrils prepared at pH 2.0 and composed of the protein insulin by manipulating electrostatic interactions within the fibril architecture. We demonstrate that strong electrostatic repulsion is sufficient to disrupt the hydrogen-bonded, cross-β network that links insulin molecules and ultimately results in fibril dissociation. The extent of this dissociation correlates well with predictions for colloidal models considering the net global charge of the polypeptide chain, although the kinetics of the process is regulated by the charge state of a single amino acid. We found the fibrils to be maximally stable under their formation conditions. Partial disruption of the cross-β network under conditions where the fibrils remain intact leads to a reduction in their stability. Together, these results support the contention that a major determinant of amyloid stability stems from the interactions in the structured core, and show how the control of electrostatic interactions can be used to characterize the factors that modulate fibril stability.