Instabilities at Frictional Interfaces: Creep Patches, Nucleation and Rupture Fronts

The strength and stability of frictional interfaces, ranging from tribological systems to earthquake faults, are intimately related to the underlying spatially-extended dynamics. Here we provide a comprehensive theoretical account, both analytic and numeric, of spatiotemporal interfacial dynamics in a realistic rate-and-state friction model, featuring both velocity-weakening and strengthening behaviors. Slowly extending, loading-rate dependent, creep patches undergo a linear instability at a critical nucleation size, which is nearly independent of interfacial history, initial stress conditions and velocity-strengthening friction. Nonlinear propagating rupture fronts -- the outcome of instability -- depend sensitively on the stress state and velocity-strengthening friction. Rupture fronts span a wide range of propagation velocities and are related to steady state fronts solutions.Comment: Typos and figures corrected. Supplementary information at: http://www.weizmann.ac.il/chemphys/bouchbinder/frictional_instabilities.htm

Avoiding Geometry Improvement in Derivative-Free Model-Based Methods via Randomization

We present a technique for model-based derivative-free optimization called \emph{basis sketching}. Basis sketching consists of taking random sketches of the Vandermonde matrix employed in constructing an interpolation model. This randomization enables weakening the general requirement in model-based derivative-free methods that interpolation sets contain a full-dimensional set of affinely independent points in every iteration. Practically, this weakening provides a theoretically justified means of avoiding potentially expensive geometry improvement steps in many model-based derivative-free methods. We demonstrate this practicality by extending the nonlinear least squares solver, \texttt{POUNDers} to a variant that employs basis sketching and we observe encouraging results on higher dimensional problems

Transient-mediated fate determination in a transcriptional circuit of HIV

Steady-state behavior and bistability have been proposed as mechanisms for decision-making in gene circuits. However, transient gene expression has also been proposed to control cell fate with the decision arbitrated by the lifetime of the expression transient. Here, we report that transcriptional positive-feedback plays a critical role in determining HIV infected cell-fate by extending the duration of Tat expression transients far beyond what protein half-life modulation can achieve. To directly quantify feedback strength and its effects on the duration of Tat transcriptional pulses, we exploit the noise inherent to gene-expression and measure shifts in the autocorrelation of expression noise. The results indicate that transcriptional positive-feedback extends the single-cell Tat expression lifetime by ~6-fold for both minimal Tat circuits and full-length, actively-replicating HIV-1. Importantly, artificial weakening of Tat positive-feedback shortened the duration of Tat expression transients and biased the probability in favor of latency. Thus, transcriptional positive-feedback appears to modulate transient expression lifetime and thereby control cell-fate in HIV

Torque maximisation of the PMAC motor for high performance, low inertia operation

This paper describes the techniques applied to maximise the torque en- velope of the permanent magnet AC (PMAC) motor operating under current and voltage constraints. Standard steady-state descriptions of the system are often suitable for control purposes when the rotor velocity is varying rela- tively slowly. In low inertia applications such as clutchless gearchange opera- tions, where in the pursuit of driveability, the motor is required to accelerate and decelerate its own rotor inertia as quickly as possible. In this case, the voltage drop due to the current dynamics start to become significant. This paper presents a method to reserve voltage headroom dynamically in the field-weakening region in order to maximise the torque envelope when the effective inertia is low. Experimental results show the effectiveness of this approach