Predicting the outputs of finite deep neural networks trained with noisy gradients.

A recent line of works studied wide deep neural networks (DNNs) by approximating them as Gaussian processes (GPs). A DNN trained with gradient flow was shown to map to a GP governed by the neural tangent kernel (NTK), whereas earlier works showed that a DNN with an i.i.

Static friction coefficient is not a material constant.

The static friction coefficient between two materials is considered to be a material constant. We present experiments demonstrating that the ratio of shear to normal force needed to move contacting bodies can, instead, vary systematically with controllable changes in the external loading configuration. Large variations in both the friction coefficient and consequent stress drop are tightly linked to changes in the rupture dynamics of the rough interface separating the two bodies.

The dynamics of the onset of frictional slip.

The way in which a frictional interface fails is critical to our fundamental understanding of failure processes in fields ranging from engineering to the study of earthquakes. Frictional motion is initiated by rupture fronts that propagate within the thin interface that separates two sheared bodies. By measuring the shear and normal stresses along the interface, together with the subsequent rapid real-contact-area dynamics, we find that the ratio of shear stress to normal stress can locally far exceed the static-friction coefficient without precipitating slip.

Slip-stick and the evolution of frictional strength.

The evolution of frictional strength has great fundamental and practical importance. Applications range from earthquake dynamics to hard-drive read/write cycles. Frictional strength is governed by the resistance to shear of the large ensemble of discrete contacts that forms the interface that separates two sliding bodies.

Oscillations in rapid fracture.

Experiments of pure tensile fracture in thin brittle gels reveal a new dynamic oscillatory instability whose onset occurs at a critical velocity, VC=0.87CS, where CS is the shear wave speed. Until VC, crack dynamics are well described by linear elastic fracture mechanics (LEFM).

Experimental study of parametric autoresonance in Faraday waves.

The excitation of large amplitude nonlinear waves is achieved via parametric autoresonance of Faraday waves. We experimentally demonstrate that phase locking to low amplitude driving can generate persistent high-amplitude growth of nonlinear waves in a dissipative system. The experiments presented are in excellent agreement with theory.