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

Fabrication of bovine serum albumin nanotubes through template assisted layer by layer assembly

One-dimensional nanostructures have offered unique advantages in many fields. Protein based nanotubes, in particular, are desirable for biomedical applications due to their ease of functionlization and intrinsic biocompatibility. Template-assisted methods are widely used to fabricate cylindrical nanostructures like carbon nanotubes, metal nanowires, polymer nanorods, etc. In the fabrication of protein nanostructures, the layer by layer (LbL) technique has long been applied to deposit protein multilayers on planar and spherical substrates. The success in each area led to the conclusion that the combination of these two techniques will potentially bring us the capability of fabricating protein nanotubes in a more controllable fashion. In this work, protein nanotubes have been successfully deposited inside nanoscopic pores by sequential filtration of bovine serum albumin (BSA) solution at pH 3.8 and pH 7.0 through the channels in the anodic aluminum oxide (AAO) template. The morphologies of the obtained nanostructures have been examined using scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Also, a simple analysis from UV/Vis spectroscopy has shown that the solutions used in our experiment will not significantly damage the bioactivity of BSA. Our future work will focus on strengthening the mechanical stability of the protein nanotubes and controlling their morphology more precisely