Granular Impact Model as an Energy-Depth Relation

Velocity-squared drag forces are common in describing an object moving through a granular material. The resulting force law is a nonlinear differential equation, and closed-form solutions of the dynamics are typically obtained by making simplifying assumptions. Here, we consider a generalized version of such a force law which has been used in many studies of granular impact. We show that recasting the force law into an equation for the kinetic energy versus depth, K(z), yields a linear differential equation, and thus general closed-form solutions for the velocity versus depth. This approach also has several advantages in fitting such models to experimental data, which we demonstrate by applying it to data from 2D impact experiments. We also present new experimental results for this model, including shape and depth dependence of the velocity-squared drag force

The Effective Potential And Additional Large Radius Compactified Space-Time Dimensions

The consequences of large radius extra space-time compactified dimensions on the four dimensional one loop effective potential are investigated for a model which includes scalar self interactions and Yukawa coupling to fermions. The Kaluza-Klein tower of states associated with the extra compact dimensions shifts the location of the effective potential minimum and modifies its curvature. The dependence of these effects on the radius of the extra dimension is illustrated for various choices of coupling constants and masses. For large radii, the consequence of twisting the fermion boundary condition on the compactified dimensions is numerically found to produce but a negligible effect on the effective potential.Comment: 14 pages, LaTeX, 6 Postscript figure

Conceptual design studies of 1985 commercial VTOL transports that utilized rotors, Volume 2

Results of conceptual design studies of tilt rotor and tandem helicopter aircraft for a 200 nautical mile commercial short haul transport mission are presented. The trade study data used in selecting the design point aircraft and technology details necessary to support the design conclusions are included