Problems for p-Monge-Ampère equations

We consider the homogeneous Dirichlet problem for a class of equations which generalize the p-Laplace equations as well as the Monge- Amp`ere equations in a strictly convex domain Ω ⊂ Rn, n ≥ 2. In the sub-linear case, we study the comparison between quantities involving the solution to this boundary value problem and the corresponding quantities involving the (radial) solution of a problem in a ball having the same η1- mean radius as Ω. Next, we consider the eigenvalue problem for such a p-Monge-Amp`ere equation and study a comparison between its principal eigenvalue (eigenfunction) and the principal eigenvalue (eigenfunction) of the corresponding problem in a ball having the same η1-mean radius as Ω. Symmetrization techniques and comparison principles are the main tools used to get our results

Rain retrieval method for mesoscale convective systems

The analysis of recent high-resolution aircraft observations over the ocean made by radar and passive microwave radiometer reveals significant problems in relating the brightness temperature measurements of the radiometer with the radar-derived rain rates. A predominant cause of this problem is that the information on rain drops contained in the radiometric measurements is contaminated by scattering and emission from other hydrometeors present in the field of view (fov) of the radiometer. Extensive observations of rain rate made by ship-borne radars and by the multichannel Special Sensor Microwave Imager (SSM/I), with a much larger fov, lead to similar conclusions. Considering the variability in the meteorological conditions, and in the hydrometeors spatial distribution, we developed an empirical method to estimate rain rate based on two parameters derived from the SSM/I data, which are related to the convective dynamics. The calibration of this empirical algorithm was performed with radar ground truth for November 1992, available over the TOGA-COARE (Tropical Ocean Global Atmosphere-Coupled Ocean Atmosphere Response Experiment) region. Then the algorithm was applied to the same TOGA-COARE region for the remaining three months available. The comparison between the estimated rain rate and the radar observations gives a correlation coefficient of about 0.85, and the monthly total estimated rainfall has an error of about 13%. This rain retrieval method, tuned for Mesoscale Convective Systems (MCSs), is applicable to the Tropical Rain Measuring Mission (TRMM), where microwave radiometric observations and simultaneous radar observations are available

On the validation of rainfall retrieval algorithms for satellite microwave data

The Algorithm Intercomparison Project utilises rainfall estimates derived from radar data to validate the algorithms developed for rainfall retrievals from satellite microwave data. Since seven minutes are needed in order to have a complete radar scan, while the acquisition of the corresponding satellite microwave image needs only a few seconds, the same pixel can be sensed by radar as much as seven minutes later. Within this time delay the raining cells can be displaced and the consequent mismatch can cause a decrease in the correlation coefficient of the comparison. A method to reveal this time-lag effect is presented and a possible approach to take it into account in the validation process for future missions is suggested

On the validation of rainfall retrieval algorithms for satellite microwave data

The Algorithm Intercomparison Project utilises rainfall estimates derived from radar data to validate the algorithms developed for rainfall retrievals from satellite microwave data. Since seven minutes are needed in order to have a complete radar scan, while the acquisition of the corresponding satellite microwave image needs only a few seconds, the same pixel can be sensed by radar as much as seven minutes later. Within this time delay the raining cells can be displaced and the consequent mismatch can cause a decrease in the correlation coefficient of the comparison. A method to reveal this time-lag effect is presented and a possible approach to take it into account in the validation process for future missions is suggested

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