Existence of nontrivial solutions for periodic Schrodinger equations with new nonlinearities

We study the Schr\"{o}dinger equation: \begin{eqnarray} - \Delta u+V(x)u+f(x,u)=0,\qquad u\in H^{1}(\mathbb{R}^{N}),\nonumber \end{eqnarray} where $V$ is periodic and $f$ is periodic in the $x$-variables, $0$ is in a gap of the spectrum of the operator $-\Delta+V$. We prove that under some new assumptions for $f$, this equation has a nontrivial solution. Our assumptions for the nonlinearity $f$ are very weak and greatly different from the known assumptions in the literature.Comment: arXiv admin note: substantial text overlap with arXiv:1310.239

Co-design of forward-control and force-feedback methods for teleoperation of an unmanned aerial vehicle

The core hypothesis of this ongoing research project is that co-designing haptic-feedback and forward-control methods for shared-control teleoperation will enable the operator to more readily understand the shared-control algorithm, better enabling him or her to work collaboratively with the shared-control technology.} This paper presents a novel method that can be used to co-design forward control and force feedback in unmanned aerial vehicle (UAV) teleoperation. In our method, a potential field is developed to quickly calculate the UAV's risk of collision online. We also create a simple proxy to represent the operator's confidence, using the swiftness with which the operator sends commands the to UAV. We use these two factors to generate both a scale factor for a position-control scheme and the magnitude of the force feedback to the operator. Currently, this methodology is being implemented and refined in a 2D-simulated environment. In the future, we will evaluate our methods with user study experiments using a real UAV in a 3D environment.Accepted manuscrip

Midfield RF Signal Detector

This project is part of a Master’s thesis which looks at alternative ways to measure blood glucose. The Master’s thesis uses mid-field signals in order to match impedance and therefore lose less power as they travel through flesh. The goal of this senior project is to build a receiver for those signals and give accurate RSSI (received signal strength indicator) measurements. Mid-fields were originally explored by Stanford professor Dr. Ada Poon [3] who used the signaling technique to recharge the batteries of deeply implanted devices. Devices implanted near the surface of the skin were able to have their batteries recharged using inductive coupling but when devices were implanted deeper in the body, the drop in energy before the signals reached the devices made wireless recharging impractical. Using inductive coils to transmit energy is a near field application and the near field coupling decays as as from the source [1]. Far field transmission is called radiative mode when it is used for far field power transfer, and the power decays as, which can be used when the implant is much smaller than its distance from the source. Dr. Poon discovered how to match impedances with flesh which allowed signals to travel farther without attenuation. These signals are called mid-field signals and occupy a position between near field and far field signals. Poon et al showed that in the midfield power transfer combines inductive and radiative modes [2] and shows much less attenuation as it travels through the body. The project described in this report is part of the larger glucose sensor project but because the glucose sensor system may be patented in the future, details of the work will not be described here. The glucose sensor system needs to sense the strength of a 1.6GHz mid-field wave at some point in the system and developing a sensor to receive and measure RSSI is what is described in this project