Small gain theorems for large scale systems and construction of ISS Lyapunov functions

We consider interconnections of n nonlinear subsystems in the input-to-state stability (ISS) framework. For each subsystem an ISS Lyapunov function is given that treats the other subsystems as independent inputs. A gain matrix is used to encode the mutual dependencies of the systems in the network. Under a small gain assumption on the monotone operator induced by the gain matrix, a locally Lipschitz continuous ISS Lyapunov function is obtained constructively for the entire network by appropriately scaling the individual Lyapunov functions for the subsystems. The results are obtained in a general formulation of ISS, the cases of summation, maximization and separation with respect to external gains are obtained as corollaries.Comment: provisionally accepted by SIAM Journal on Control and Optimizatio

Experimental observation of an enhanced anisotropic magnetoresistance in non-local configuration

We compare non-local magnetoresistance measurements in multi-terminal Ni nanostructures with corresponding local experiments. In both configurations, the measured voltages show the characteristic features of anisotropic magnetoresistance (AMR). However, the magnitude of the non-local AMR signal is up to one order of magnitude larger than its local counterpart. Moreover, the non-local AMR increases with increasing degree of non-locality, i.e., with the separation between the region of the main current flow and the voltage measurement region. All experimental observations can be consistently modeled in terms of current spreading in a non-isotropic conductor. Our results show that current spreading can significantly enhance the magnetoresistance signal in non-local experiments

Tunable sub-luminal propagation of narrowband x-ray pulses

Group velocity control is demonstrated for x-ray photons of 14.4 keV energy via a direct measurement of the temporal delay imposed on spectrally narrow x-ray pulses. Sub-luminal light propagation is achieved by inducing a steep positive linear dispersion in the optical response of ${}^{57}$Fe M\"ossbauer nuclei embedded in a thin film planar x-ray cavity. The direct detection of the temporal pulse delay is enabled by generating frequency-tunable spectrally narrow x-ray pulses from broadband pulsed synchrotron radiation. Our theoretical model is in good agreement with the experimental data.Comment: 8 pages, 4 figure

Nonlinear motion and mechanical mixing in as-grown GaAs nanowires

We report nonlinear behavior in the motion of driven nanowire cantilevers. The nonlinearity can be described by the Duffing equation and is used to demonstrate mechanical mixing of two distinct excitation frequencies. Furthermore, we demonstrate that the nonlinearity can be used to amplify a signal at a frequency close to the mechanical resonance of the nanowire oscillator. Up to 26 dB of amplitude gain are demonstrated in this way