Noninvasive imaging of three-dimensional micro and nanostructures by topological methods

We present topological derivative and energy based procedures for the imaging of micro and nano structures using one beam of visible light of a single wavelength. Objects with diameters as small as 10 nm can be located and their position tracked with nanometer precision. Multiple objects dis-tributed either on planes perpendicular to the incidence direction or along axial lines in the incidence direction are distinguishable. More precisely, the shape and size of plane sections perpendicular to the incidence direction can be clearly determined, even for asymmetric and nonconvex scatterers. Axial resolution improves as the size of the objects decreases. Initial reconstructions may proceed by gluing together two-dimensional horizontal slices between axial peaks or by locating objects at three-dimensional peaks of topological energies, depending on the effective wavenumber. Below a threshold size, topological derivative based iterative schemes improve initial predictions of the lo-cation, size, and shape of objects by postprocessing fixed measured data. For larger sizes, tracking the peaks of topological energy fields that average information from additional incident light beams seems to be more effective

Detecting Damage in Thin Plates by Processing Infrared Thermographic Data with Topological Derivatives

A thermogram is a color image produced by a thermal camera where each color level represents a different radiation intensity (temperature). In this paper, we study the use of steady and time-harmonic thermograms for structural health monitoring of thin plates. Since conductive heat transfer is short range and the associated signal–to–noise ratio is not much favorable, efficient data processing tools are required to successfully interpret thermograms. We will process thermograms by a mathematical tool called topological derivative, showing its efficiency in very demanding situations where thermograms are highly polluted by noise, and/or when the parameters of the medium fluctuate randomly. An exhaustive gallery of numerical simulations will be presented to assess the performance and limitations of this tool

An analysis of performance in elite young cross-country skiing: classical style vs skate skiing.

Problem statement: The aim of this study was to assess the differences in the skiing performance of two skiing styles (classical style Vs. skate skiing), in a group of young high-level skiers. Approach: Four high-level male junior cross-country skiers from the Centre of Winter Sports of Aragon (Spain), were selected for this study that was developed during two competitions: 10 km free technique and 10 km classical technique performed in the same circuit and under the same conditions (snow quality, temperature, wind and relative humidity). Physiological variables, maximal and medium heart rate, blood lactate concentration (basal, final and during the recovery, after 2, 4, 6, 8 and 10 min) and medium skiing speed, were analyzed with GPS Garmin Forerruner 305® Heart Rate Pulse and Lactate Dr. Lange analyzer®. Normally distributed data (Kolmogorov-Smirnov Test and Shapiro-Wilk) were statistically analyzed with one way ANOVA and t-Test for post-hoc comparisons (p<0.05). No-normally distributed data were analyzed with the Friedman and Wilcoxon Tests (p<0.05). Results: No significant differences have been recorded in the medium skiing speed, maximal and medium heart rate between the two styles. The peak heart rate was the same in both styles (188 bpm), although medium heart rate was lower in skate skiing vs. classical skiing (165 bpm Vs. 175 bpm). Blood lactate concentrations recorded significant differences during 4, 6, 8 and 10 min of recovery, being higher in free technique (12.7±1.7; 11.4±1.8; 10.4±1.4 and 8.9±1.6 mmol L−1 Vs. 8.7±1.3; 7.5±1.6; 6.3±1.3 and 5.6±1.1 mmol L−1, respectively). Conclusion: The results of this study suggest that skate skiing generates a higher impact on the cross-country skier than classical skiing, due to higher blood lactate concentrations during 4, 6, 8 and 10 min of recovery. The own characteristics of the free technique may be the reason of the lower mean heart rate