Airborne mapping of complex obstacles using 2D Splinegon

This paper describes a recently proposed algorithm in mapping the unknown obstacle in a stationary environment where the obstacles are represented as curved in nature. The focus is to achieve a guaranteed performance of sensor based navigation and mapping. The guaranteed performance is quantified by explicit bounds of the position estimate of an autonomous aerial vehicle using an extended Kalman filter and to track the obstacle so as to extract the map of the obstacle. This Dubins path planning algorithm is used to provide a flyable and safe path to the vehicle to fly from one location to another. This description takes into account the fact that the vehicle is made to fly around the obstacle and hence will map the shape of the obstacle using the 2D-Splinegon technique. This splinegon technique, the most efficient and a robust way to estimate the boundary of a curved nature obstacles, can provide mathematically provable performance guarantees that are achievable in practice

Long-Term Bidirectional Neuron Interfaces for Robotic Control, and In Vitro Learning Studies

There are two fundamentally different goals for neural interfacing. On the biology side, to interface living neurons to external electronics allows the observation and manipulation of neural circuits to elucidate their fundamental mechanisms. On the engineering side, neural interfaces in animals, people, or in cell culture have the potential to restore missing functionality, or someday, to enhance existing functionality. At the Laboratory for NeuroEngineering at Georgia Tech, we are developing new technologies to help make both goals attainable. We culture dissociated mammalian neurons on multi-electrode arrays, and use them as the brain of a 'Hybrot', or hybrid neural-robotic system. Distributed neural activity patterns are used to control mobile robots. We have created the hardware and software necessary to feed the robots' sensory inputs back to the cultures in real time, as electrical stimuli. By embodying cultured networks, we study learning and memory at the cellular and network level, using 2-photon laser-scanning microscopy to image plasticity while it happens. We have observed a very rich dynamical landscape of activity patterns in networks of only a few thousand cells. We can alter this landscape via electrical stimuli, and use the hybrot system to study the emergent properties of networks in vitro

Energy extremality in the presence of a black hole

We derive the so-called first law of black hole mechanics for variations about stationary black hole solutions to the Einstein--Maxwell equations in the absence of sources. That is, we prove that $\delta M=\kappa\delta A+\omega\delta J+VdQ$ where the black hole parameters $M, \kappa, A, \omega, J, V$ and $Q$ denote mass, surface gravity, horizon area, angular velocity of the horizon, angular momentum, electric potential of the horizon and charge respectively. The unvaried fields are those of a stationary, charged, rotating black hole and the variation is to an arbitrary `nearby' black hole which is not necessarily stationary. Our approach is 4-dimensional in spirit and uses techniques involving Action variations and Noether operators. We show that the above formula holds on any asymptotically flat spatial 3-slice which extends from an arbitrary cross-section of the (future) horizon to spatial infinity.(Thus, the existence of a bifurcation surface is irrelevant to our demonstration. On the other hand, the derivation assumes without proof that the horizon possesses at least one of the following two (related)properties: ($i$) it cannot be destroyed by arbitrarily small perturbations of the metric and other fields which may be present, ($ii$) the expansion of the null geodesic generators of the perturbed horizon goes to zero in the distant future.)Comment: 30 pages, latex fil

The Two Dimensional Kondo Model with Rashba Spin-Orbit Coupling

We investigate the effect that Rashba spin-orbit coupling has on the low energy behaviour of a two dimensional magnetic impurity system. It is shown that the Kondo effect, the screening of the magnetic impurity at temperatures T < T_K, is robust against such spin-orbit coupling, despite the fact that the spin of the conduction electrons is no longer a conserved quantity. A proposal is made for how the spin-orbit coupling may change the value of the Kondo temperature T_K in such systems and the prospects of measuring this change are discussed. We conclude that many of the assumptions made in our analysis invalidate our results as applied to recent experiments in semi-conductor quantum dots but may apply to measurements made with magnetic atoms placed on metallic surfaces.Comment: 22 pages, 1 figure; reference update

Theory of Scanning Tunneling Spectroscopy of a Magnetic Adatom on a Metallic Surface

A comprehensive theory is presented for the voltage, temperature, and spatial dependence of the tunneling current between a scanning tunneling microscope (STM) tip and a metallic surface with an individual magnetic adatom. Modeling the adatom by a nondegenerate Anderson impurity, a general expression is derived for a weak tunneling current in terms of the dressed impurity Green function, the impurity-free surface Green function, and the tunneling matrix elements. This generalizes Fano's analysis to the interacting case. The differential-conductance lineshapes seen in recent STM experiments with the tip directly over the magnetic adatom are reproduced within our model, as is the rapid decay, \sim 10\AA, of the low-bias structure as one moves the tip away from the adatom. With our simple model for the electronic structure of the surface, there is no dip in the differential conductance at approximately one lattice spacing from the magnetic adatom, but rather we see a resonant enhancement. The formalism for tunneling into small clusters of magnetic adatoms is developed.Comment: 12 pages, 9 figures; to appear in Phys. Rev.

Adsorbed 3d transition metal atoms and clusters on Au(111):Signatures derived from one electron calculations

The spectroscopic characteristics of systems with adsorbed d impurities on noble metal surfaces should depend on the number and geometric arrangement of the adsorbed atoms and also on their d band filling. Recent experiments using scanning tunneling microscopy have probed the electronic structure of all 3d transition metal impurities and also of Co dimers adsorbed on Au(111), providing a rich variety of results. In this contribution we correlate those experimental results with ab-initio calculations and try to establish necessary conditions for observing a Kondo resonance when using the single impurity Anderson model. We find that the relevant orbitals at the STM tip position, when it is on top of an impurity, are the dThe spectroscopic characteristics of systems with adsorbed d impurities on noble metal surfaces should depend on the number and geometric arrangement of the adsorbed atoms and also on their d band filling. Recent experiments using scanning tunneling microscopy have probed the electronic structure of all 3d transition metal impurities and also of Co dimers adsorbed on Au(111), providing a rich variety of results. In this contribution we correlate those experimental results with ab-initio calculations and try to establish necessary conditions for observing a Kondo resonance when using the single impurity Anderson model. We find that the relevant orbitals at the STM tip position, when it is on top of an impurity, are the d orbitals with m=0 and that the energy of these levels with respect to the Fermi energy determines the possibility of observing a spectroscopic feature due to the impurity. orbitals with m=0 and that the energy of these levels with respect to the Fermi energy determines the possibility of observing a spectroscopic feature due to the impurity

Spintronic magnetic anisotropy

An attractive feature of magnetic adatoms and molecules for nanoscale applications is their superparamagnetism, the preferred alignment of their spin along an easy axis preventing undesired spin reversal. The underlying magnetic anisotropy barrier --a quadrupolar energy splitting-- is internally generated by spin-orbit interaction and can nowadays be probed by electronic transport. Here we predict that in a much broader class of quantum-dot systems with spin larger than one-half, superparamagnetism may arise without spin-orbit interaction: by attaching ferromagnets a spintronic exchange field of quadrupolar nature is generated locally. It can be observed in conductance measurements and surprisingly leads to enhanced spin filtering even in a state with zero average spin. Analogously to the spintronic dipolar exchange field, responsible for a local spin torque, the effect is susceptible to electric control and increases with tunnel coupling as well as with spin polarization.Comment: 6 pages with 4 figures + 26 pages of Supplementary Informatio

Noisy Kondo impurities

The anti-ferromagnetic coupling of a magnetic impurity carrying a spin with the conduction electrons spins of a host metal is the basic mechanism responsible for the increase of the resistance of an alloy such as Cu${}_{0.998}$Fe${}_{0.002}$ at low temperature, as originally suggested by Kondo . This coupling has emerged as a very generic property of localized electronic states coupled to a continuum . The possibility to design artificial controllable magnetic impurities in nanoscopic conductors has opened a path to study this many body phenomenon in unusual situations as compared to the initial one and, in particular, in out of equilibrium situations. So far, measurements have focused on the average current. Here, we report on \textit{current fluctuations} (noise) measurements in artificial Kondo impurities made in carbon nanotube devices. We find a striking enhancement of the current noise within the Kondo resonance, in contradiction with simple non-interacting theories. Our findings provide a test bench for one of the most important many-body theories of condensed matter in out of equilibrium situations and shed light on the noise properties of highly conductive molecular devices.Comment: minor differences with published versio

The Kondo Box: A Magnetic Impurity in an Ultrasmall Metallic Grain

We study the Kondo effect generated by a single magnetic impurity embedded in an ultrasmall metallic grain, to be called a ``Kondo box''. We find that the Kondo resonance is strongly affected when the mean level spacing in the grain becomes larger than the Kondo temperature, in a way that depends on the parity of the number of electrons on the grain. We show that the single-electron tunneling conductance through such a grain features Kondo-induced Fano-type resonances of measurable size, with an anomalous dependence on temperature and level spacing.Comment: 4 Latex pages, 4 figures, submitted to Phys. Rev. Let