Optimum Land Allocation for Species Protection and Military Training on DoD Installations

Replaced with revised version of poster 8/11/10.Environmental Economics and Policy, Health Economics and Policy, Land Economics/Use,

Extracting the Density Profile of an Electronic Wave Function in a Quantum Dot

We use a model of a one-dimensional nanowire quantum dot to demonstrate the feasibility of a scanning probe microscope (SPM) imaging technique that can extract both the energy of an electron state and the amplitude of its wave function using a single instrument. This imaging technique can probe electrons that are buried beneath the surface of a low-dimensional semiconductor structure and provide valuable information for the design of quantum devices. A conducting SPM tip, acting as a movable gate, measures the energy of an electron state using Coulomb blockade spectroscopy. When the tip is close to the nanowire dot, it dents the wave function $\Psi(x)$ of the quantum state, changing the electron's energy by an amount proportional to $\mid\Psi(x)\mid^2$. By recording the change in energy as the SPM tip is moved along the length of the dot, the density profile of the electronic wave function can be found along the length of the quantum dot.Engineering and Applied Science

Zero Dynamics of Planar Biped Walkers with One Degree of Under Actuation

The zero dynamics of a hybrid model of bipedal walking are introduced and studied for a class of N-link, planar robots with one degree of underactuation and outputs that depend only on the configuration variables. Asymptotically stable solutions of the zero dynamics correspond to asymptotically stabilizable orbits of the full hybrid model of the walker. The Poincaré map of the zero dynamics is computed and proven to be diffeomorphic to a scalar, linear, time-invariant system, thereby rendering transparent the existence and stability properties of periodic orbits. For more information: Kod*La

Hybrid Zero Dynamics of Planar Biped Walkers

Planar, underactuated, biped walkers form an important domain of applications for hybrid dynamical systems. This paper presents the design of exponentially stable walking controllers for general planar bipedal systems that have one degree-of-freedom greater than the number of available actuators. The within-step control action creates an attracting invariant set—a two-dimensional zero dynamics submanifold of the full hybrid model—whose restriction dynamics admits a scalar linear time-invariant return map. Exponentially stable periodic orbits of the zero dynamics correspond to exponentially stabilizable orbits of the full model. A convenient parameterization of the hybrid zero dynamics is imposed through the choice of a class of output functions. Parameter optimization is used to tune the hybrid zero dynamics in order to achieve closed-loop, exponentially stable walking with low energy consumption, while meeting natural kinematic and dynamic constraints. The general theory developed in the paper is illustrated on a five link walker, consisting of a torso and two legs with knees