<p>Granular materials are hard to understand due to their discrete and a-thermal nature. The mechanical response of a granular packing under external deformations, although highly relevant in industrial processes, is still poorly understood, partly due to the difficulty to generate a homogeneous granular packing. In this thesis, I present a novel shear apparatus that avoids the formation of inhomogeneities known as shear bands. This apparatus provides quasi-static, quasi-uniform simple shear deformation to a 2D model granular system under fixed packing fraction &phi. The position, orientation and forces for each particle are obtained at each shear step, using the photo-elastic technique. This model granular system exhibits coupling between the shear strain, &gamma, and the pressure, P, which we characterize by the `Reynolds pressure', and a `Reynolds coefficient', R(&phi) = (&partial^2 P/ &partial &gamma^2)/2. Under cyclic shear, this system evolves logarithmically slowly towards limit cycle dynamics, which we characterize in terms of pressure relaxation at cycle n: &Delta P &simeq - &beta ln(n/n_0). &beta depends only on the shear cycle amplitude, suggesting an activated process where &beta plays a temperature-like role. In addition, particles in the sheared system are diffusive. The translational and rotational diffusion, observed under stroboscopic view during cyclic shear, are observed to depend on the packing fraction but not on the stress states of the system. Finally, the structure of the force network, and how that connects to the mechanical behavior, is also briefly discussed.</p> / Dissertation

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In this paper a new equivalent circuit is presented which describes the dynamics of a prototype micro-gyro sensor. The concept takes advantage of the principles employed in vibratory gyro sensors and the ductile attributes of GalFeNOL to target high sensitivity and shock tolerance. The sensor is designed as a tuning fork structure. A GalFeNOL patch attached to the y-z surface of the drive prong causes both prongs to bending the x-z plane (about the y axis) and a patch attached to the x-z surface of the sensing prong detects Coriolis-force induced bending in the y-z plane (about the x axis). A permanent magnet is bonded on top of each prong to give bias magnetic fields. A solenoid coil surrounding the drive prong is used to produce bending in the x-z plane of both prongs. The sensing prong is surrounded by a solenoid coil with N turns in which a voltage proportional to the time rate of change of magnetic flux is induced. The equivalent circuit enables the efficient modeling of a gyro sensor and an electromechanical behavioral simulation using the circuit simulator SPICE. The prongs are modeled as wave guiding bending beams which are coupled to the electromagnetic solenoid coil transducer. In contrast to known network approaches, the proposed equivalent circuit is the first tuning fork model, which takes full account of the fictitious force in a constant rotating frame of reference. The Coriolis force as well as the centrifugal force on a concentrated mass are considered.