Katherine A. Newhall

Projectile-shape dependence of impact craters in loose granular media

We report on the penetration of cylindrical projectiles dropped from rest into a dry, noncohesive granular medium. The cylinder length, diameter, density, and tip shape are all explicitly varied. For deep penetrations, as compared to the cylinder diameter, the data collapse onto a single scaling law that varies as the 1/3 power of the total drop distance, the 1/2 power of cylinder length, and the 1/6 power of cylinder diameter. For shallow penetrations, the projectile shape plays a crucial role with sharper objects penetrating deeper.

Attractive emulsion droplets probe the phase diagram of jammed granular matter.

It remains an open question whether statistical mechanics approaches apply to random packings of athermal particles. Although a jamming phase diagram has recently been proposed for hard spheres with varying friction, here we use a frictionless emulsion system in the presence of depletion forces to sample the available phase space of packing configurations. Using confocal microscopy, we access their packing microstructure and test the theoretical assumptions. As a function of attraction, our packing protocol under gravity leads to well-defined jammed structures in which global density initially increases above random close packing and subsequently decreases monotonically. Microscopically, the fluctuations in parameters describing each particle, such as the coordination number, number of neighbors, and local packing fraction, are for all attractions in excellent agreement with a local stochastic model, indicating that long-range correlations are not important. Furthermore, the distributions of local cell volumes can be collapsed onto a universal curve using the predicted k-gamma distribution, in which the shape parameter k is fixed by the polydispersity while the effect of attraction is captured by rescaling the average cell volume. Within the Edwards statistical mechanics framework, this result measures the decrease in compactivity with global density, which represents a direct experimental test of a jamming phase diagram in athermal systems. The success of these theoretical tools in describing yet another class of materials gives support to the much-debated statistical physics of jammed granular matter.

Averaged equation for energy diffusion on a graph reveals bifurcation diagram and thermally assisted reversal times in spin-torque driven nanomagnets

Driving nanomagnets by spin-polarized currents offers exciting prospects in magnetoelectronics, but the response of the magnets to such currents remains poorly understood. We show that an averaged equation describing the diffusion of energy on a graph captures the low-damping dynamics of these systems. From this equation we obtain the bifurcation diagram of the magnets, including the critical currents to induce stable precessional states and magnetization switching, as well as the mean times of thermally assisted magnetization reversal in situations where the standard reaction rate theory of Kramers is no longer valid. These results match experimental observations and give a theoretical basis for a Neel-Brown-type formula with an effective energy barrier for the reversal times.

Distribution of correlated spiking events in a population-based approach for Integrate-and-Fire networks

Randomly connected populations of spiking neurons display a rich variety of dynamics. However, much of the current modeling and theoretical work has focused on two dynamical extremes: on one hand homogeneous dynamics characterized by weak correlations between neurons, and on the other hand total synchrony characterized by large populations firing in unison. In this paper we address the conceptual issue of how to mathematically characterize the partially synchronous “multiple firing events” (MFEs) which manifest in between these two dynamical extremes. We further develop a geometric method for obtaining the distribution of magnitudes of these MFEs by recasting the cascading firing event process as a first-passage time problem, and deriving an analytical approximation of the first passage time density valid for large neuron populations. Thus, we establish a direct link between the voltage distributions of excitatory and inhibitory neurons and the number of neurons firing in an MFE that can be easily integrated into population–based computational methods, thereby bridging the gap between homogeneous firing regimes and total synchrony.

Skin Friction and the Inner Flow in Pressure Gradient Turbulent Boundary Layers

This investigation will look at multiple methods to determine the wall shear stress for several pressure gradient turbulent boundary layer flows, particularly favorable pressure gradient and zero pressure gradient. These methods include using the slope at the wall, the integrated bounary layer equation, momentum integral equation and the Clauser method. In order to perform this study, 2D Laser Doppler Anemometry, (LDA), measurements of the velocity field near the wall for various streamwise positions have been carried out at the Chalmers L2 wind-tunnel. With the resulting wall shear stress calculations, the effects of pressure gradient and upstream conditions will be investigated on the inner region of the velocity profiles and Reynolds stresses. As will be seen, the integrated boundary layer equation is the most accurate technique to determine the wall shear stress when direct measurements are not available. In addition, the velocity profiles show a mild effect of the pressure gradient. The Reynolds stresses show a large effect of the pressure gradient in inner variables, but not below, y and components changes significantly due to the external pressure gradient, damping them as much as 40%, though the streamwise component exhibits an insignificant amount of change. Introduction The effects of Reynolds number and pressure gradient on the skin friction coefficient, Cf , and the velocity field have long been debated as well as the accuracy ∗MS, Rensselaer Polytechnic Institute, Department of Mechanical, Aeronautical and Nuclear Engineering, Troy, NY 12180 †PhD, Rensselaer Polytechnic Institute, Department of Mechanical, Aeronautical and Nuclear Engineering, Troy, NY 12180 ‡Post-doctoral fellow, The Johns Hopkins University, Department of Mechanical Engineering, Baltimore, MD §Associate Professor, Chalmers Institute of Technology, Gothenburg, Sweden ¶Associate Professor, Rensselaer Polytechnic Institute, Department of Mechanical, Aeronautical and Nuclear Engineering, Troy, NY 12180, also Research Professor at University of Puerto Rico-, Mayaguez, Mayaguez, P.R., Department of Mechanical Eng. Copyright c

The Structure of Global Attractors for Dissipative Zakharov Systems with Forcing on the Torus

The Zakharov system was originally proposed to study the propagation of Langmuir waves in an ionized plasma. In this paper, motivated by the work of the first and third authors in [Anal. Partial Differential Equations, 6 (2013), pp. 723--750], we numerically and analytically investigate the dynamics of the dissipative Zakharov system on the torus in one dimension. We find an interesting family of stable periodic orbits and fixed points and explore bifurcations of those points as we take weaker and weaker dissipation.

Random polarization dynamics in a resonant optical medium

Random optical-pulse polarization switching along an active optical medium in the Λ configuration with spatially disordered occupation numbers of its lower energy sublevel pair is described using the idealized integrable Maxwell-Bloch model. Analytical results describing the light polarization-switching statistics for the single self-induced transparency pulse are compared with statistics obtained from direct Monte Carlo numerical simulations.

Smooth and rough turbulent boundary layers: A look at skin friction, pressure gradient and roughness

The skin friction for a turbulent boundary layer can be measured and calculated in several ways with varying degrees of accuracy. In particular, the methods of the velocity gradient at the wall, the integrated boundary layer equation and the momentum integral equation are evaluated for both smooth and rough surface boundary layers. These methods are compared to the oil film interferometry technique measurements for the case of smooth surface flows. The integrated boundary layer equation is found to be relatively reliable, and the values computed with this technique are used to investigate the effect of increasing external favorable pressure gradient for both smooth and rough surfaces, and increasing roughness parameter for the rough surfaces.Copyright