A dynamical system approach to data assimilation in chaotic models

The Assimilation in the Unstable Subspace (AUS) was introduced by Trevisan and Uboldi in 2004, and developed by Trevisan, Uboldi and Carrassi, to minimize the analysis and forecast errors by exploiting the flow-dependent instabilities of the forecast-analysis cycle system, which may be thought of as a system forced by observations. In the AUS scheme the assimilation is obtained by confining the analysis increment in the unstable subspace of the forecast-analysis cycle system so that it will have the same structure of the dominant instabilities of the system. The unstable subspace is estimated by Breeding on the Data Assimilation System (BDAS). AUS- BDAS has already been tested in realistic models and observational configurations, including a Quasi-Geostrophicmodel and a high dimensional, primitive equation ocean model; the experiments include both fixed and“adaptive”observations. In these contexts, the AUS-BDAS approach greatly reduces the analysis error, with reasonable computational costs for data assimilation with respect, for example, to a prohibitive full Extended Kalman Filter. This is a follow-up study in which we revisit the AUS-BDAS approach in the more basic, highly nonlinear Lorenz 1963 convective model. We run observation system simulation experiments in a perfect model setting, and with two types of model error as well: random and systematic. In the different configurations examined, and in a perfect model setting, AUS once again shows better efficiency than other advanced data assimilation schemes. In the present study, we develop an iterative scheme that leads to a significant improvement of the overall assimilation performance with respect also to standard AUS. In particular, it boosts the efficiency of regime’s changes tracking, with a low computational cost. Other data assimilation schemes need estimates of ad hoc parameters, which have to be tuned for the specific model at hand. In Numerical Weather Prediction models, tuning of parameters — and in particular an estimate of the model error covariance matrix — may turn out to be quite difficult. Our proposed approach, instead, may be easier to implement in operational models.

Assimilation of Meteosat Second Generation (MSG) satellite data in a regional numerical weather prediction model using a one-dimensional variational approach

The quality of temperature and humidity retrievals from the infrared SEVIRI sensors on the geostationary Meteosat Second Generation (MSG) satellites is assessed by means of a one dimensional variational algorithm. The study is performed with the aim of improving the spatial and temporal resolution of available observations to feed analysis systems designed for high resolution regional scale numerical weather prediction (NWP) models. The non-hydrostatic forecast model COSMO (COnsortium for Small scale MOdelling) in the ARPA-SIM operational configuration is used to provide background fields. Only clear sky observations over sea are processed. An optimised 1D–VAR set-up comprising of the two water vapour and the three window channels is selected. It maximises the reduction of errors in the model backgrounds while ensuring ease of operational implementation through accurate bias correction procedures and correct radiative transfer simulations. The 1D–VAR retrieval quality is firstly quantified in relative terms employing statistics to estimate the reduction in the background model errors. Additionally the absolute retrieval accuracy is assessed comparing the analysis with independent radiosonde and satellite observations. The inclusion of satellite data brings a substantial reduction in the warm and dry biases present in the forecast model. Moreover it is shown that the retrieval profiles generated by the 1D–VAR are well correlated with the radiosonde measurements. Subsequently the 1D–VAR technique is applied to two three–dimensional case–studies: a false alarm case–study occurred in Friuli–Venezia–Giulia on the 8th of July 2004 and a heavy precipitation case occurred in Emilia–Romagna region between 9th and 12th of April 2005. The impact of satellite data for these two events is evaluated in terms of increments in the integrated water vapour and saturation water vapour over the column, in the 2 meters temperature and specific humidity and in the surface temperature. To improve the 1D–VAR technique a method to calculate flow–dependent model error covariance matrices is also assessed. The approach employs members from an ensemble forecast system generated by perturbing physical parameterisation schemes inside the model. The improved set–up applied to the case of 8th of July 2004 shows a substantial neutral impact.

Low-dimensional carbon allotropes: an electron microscopy investigation

The research reported in this manuscript concerns the structural characterization of graphene membranes and single-walled carbon nanotubes (SWCNTs). The experimental investigation was performed using a wide range of transmission electron microscopy (TEM) techniques, from conventional imaging and diffraction, to advanced interferometric methods, like electron holography and Geometric Phase Analysis (GPA), using a low-voltage optical set-up, to reduce radiation damage in the samples. Electron holography was used to successfully measure the mean electrostatic potential of an isolated SWCNT and that of a mono-atomically thin graphene crystal. The high accuracy achieved in the phase determination, made it possible to measure, for the first time, the valence-charge redistribution induced by the lattice curvature in an individual SWCNT. A novel methodology for the 3D reconstruction of the waviness of a 2D crystal membrane has been developed. Unlike other available TEM reconstruction techniques, like tomography, this new one requires processing of just a single HREM micrograph. The modulations of the inter-planar distances in the HREM image are measured using Geometric Phase Analysis, and used to recover the waviness of the crystal. The method was applied to the case of a folded FGC, and a height variation of 0.8 nm of the surface was successfully determined with nanometric lateral resolution. The adhesion of SWCNTs to the surface of graphene was studied, mixing shortened SWCNTs of different chiralities and FGC membranes. The spontaneous atomic match of the two lattices was directly imaged using HREM, and we found that graphene membranes act as tangential nano-sieves, preferentially grafting achiral tubes to their surface.

Innovative Homogeneous and Heterogeneous Systems for Electrochemically Generated Luminescence Investigations: Towards One-Dimensional ECL

My research PhD work is focused on the Electrochemically Generated Luminescence (ECL) investigation of several different homogeneous and heterogeneous systems. ECL is a redox induced emission, a process whereby species, generated at electrodes, undergo a high-energy electron transfer reaction to form excited states that emit light. Since its first application, the ECL technique has become a very powerful analytical tool and has widely been used in biosensor transduction. ECL presents an intrinsically low noise and high sensitivity; moreover, the electrochemical generation of the excited state prevents scattering of the light source: for all these characteristics, it is an elective technique for ultrasensitive immunoassay detection. The majority of ECL systems involve species in solution where the emission occurs in the diffusion layer near to the electrode surface. However, over the past few years, an intense research has been focused on the ECL generated from species constrained on the electrode surface. The aim of my work is to study the behavior of ECL-generating molecular systems upon the progressive increase of their spatial constraints, that is, passing from isolated species in solution, to fluorophores embedded within a polymeric film and, finally, to patterned surfaces bearing “one-dimensional” emitting spots. In order to describe these trends, I use different “dimensions” to indicate the different classes of compounds. My thesis was mostly developed in the electrochemistry group of Bologna with the supervision of Prof Francesco Paolucci and Dr Massimo Marcaccio. With their help and also thanks to their long experience in the molecular and supramolecular ECL fields and in the surface investigations using scanning probe microscopy techniques, I was able to obtain the results herein described. Moreover, during my research work, I have established a new collaboration with the group of Nanobiotechnology of Prof. Robert Forster (Dublin City University) where I spent a research period. Prof. Forster has a broad experience in the biomedical field, especially he focuses his research on film surfaces biosensor based on the ECL transduction. This thesis can be divided into three sections described as follows: (i) in the fist section, homogeneous molecular and supramolecular ECL-active systems, either organic or inorganic species (i.e., corannulene, dendrimers and iridium metal complex), are described. Driving force for this kind of studies includes the search for new luminophores that display on one hand higher ECL efficiencies and on the other simple mechanisms for modulating intensity and energy of their emission in view of their effective use in bioconjugation applications. (ii) in the second section, the investigation of some heterogeneous ECL systems is reported. Redox polymers comprising inorganic luminophores were described. In such a context, a new conducting platform, based on carbon nanotubes, was developed aimed to accomplish both the binding of a biological molecule and its electronic wiring to the electrode. This is an essential step for the ECL application in the field of biosensors. (iii) in the third section, different patterns were produced on the electrode surface using a Scanning Electrochemical Microscopy. I developed a new methods for locally functionalizing an inert surface and reacting this surface with a luminescent probe. In this way, I successfully obtained a locally ECL active platform for multi-array application.

Three dimensional seismic imaging and earthquake locations in a complex, segmented fault region in Southern Apennines (Italy)

The southern Apennines of Italy have been experienced several destructive earthquakes both in historic and recent times. The present day seismicity, characterized by small-to-moderate magnitude earthquakes, was used like a probe to obatin a deeper knowledge of the fault structures where the largest earthquakes occurred in the past. With the aim to infer a three dimensional seismic image both the problem of data quality and the selection of a reliable and robust tomographic inversion strategy have been faced. The data quality has been obtained to develop optimized procedures for the measurements of P- and S-wave arrival times, through the use of polarization filtering and to the application of a refined re-picking technique based on cross-correlation of waveforms. A technique of iterative tomographic inversion, linearized, damped combined with a strategy of multiscale inversion type has been adopted. The retrieved P-wave velocity model indicates the presence of a strong velocity variation along a direction orthogonal to the Apenninic chain. This variation defines two domains which are characterized by a relatively low and high velocity values. From the comparison between the inferred P-wave velocity model with a portion of a structural section available in literature, the high velocity body was correlated with the Apulia carbonatic platforms whereas the low velocity bodies was associated to the basinal deposits. The deduced Vp/Vs ratio shows that the ratio is lower than 1.8 in the shallower part of the model, while for depths ranging between 5 km and 12 km the ratio increases up to 2.1 in correspondence to the area of higher seismicity. This confirms that areas characterized by higher values are more prone to generate earthquakes as a response to the presence of fluids and higher pore-pressures.

Local Earthquake Tomography by trans-dimensional Monte Carlo Sampling

In this study a new, fully non-linear, approach to Local Earthquake Tomography is presented. Local Earthquakes Tomography (LET) is a non-linear inversion problem that allows the joint determination of earthquakes parameters and velocity structure from arrival times of waves generated by local sources. Since the early developments of seismic tomography several inversion methods have been developed to solve this problem in a linearized way. In the framework of Monte Carlo sampling, we developed a new code based on the Reversible Jump Markov Chain Monte Carlo sampling method (Rj-McMc). It is a trans-dimensional approach in which the number of unknowns, and thus the model parameterization, is treated as one of the unknowns. I show that our new code allows overcoming major limitations of linearized tomography, opening a new perspective in seismic imaging. Synthetic tests demonstrate that our algorithm is able to produce a robust and reliable tomography without the need to make subjective a-priori assumptions about starting models and parameterization. Moreover it provides a more accurate estimate of uncertainties about the model parameters. Therefore, it is very suitable for investigating the velocity structure in regions that lack of accurate a-priori information. Synthetic tests also reveal that the lack of any regularization constraints allows extracting more information from the observed data and that the velocity structure can be detected also in regions where the density of rays is low and standard linearized codes fails. I also present high-resolution Vp and Vp/Vs models in two widespread investigated regions: the Parkfield segment of the San Andreas Fault (California, USA) and the area around the Alto Tiberina fault (Umbria-Marche, Italy). In both the cases, the models obtained with our code show a substantial improvement in the data fit, if compared with the models obtained from the same data set with the linearized inversion codes.

High-Speed Laser Processing of Thin Single and Multi-Layer Films

Theoretical models are developed for the continuous-wave and pulsed laser incision and cut of thin single and multi-layer films. A one-dimensional steady-state model establishes the theoretical foundations of the problem by combining a power-balance integral with heat flow in the direction of laser motion. In this approach, classical modelling methods for laser processing are extended by introducing multi-layer optical absorption and thermal properties. The calculation domain is consequently divided in correspondence with the progressive removal of individual layers. A second, time-domain numerical model for the short-pulse laser ablation of metals accounts for changes in optical and thermal properties during a single laser pulse. With sufficient fluence, the target surface is heated towards its critical temperature and homogeneous boiling or "phase explosion" takes place. Improvements are seen over previous works with the more accurate calculation of optical absorption and shielding of the incident beam by the ablation products. A third, general time-domain numerical laser processing model combines ablation depth and energy absorption data from the short-pulse model with two-dimensional heat flow in an arbitrary multi-layer structure. Layer removal is the result of both progressive short-pulse ablation and classical vaporisation due to long-term heating of the sample. At low velocity, pulsed laser exposure of multi-layer films comprising aluminium-plastic and aluminium-paper are found to be characterised by short-pulse ablation of the metallic layer and vaporisation or degradation of the others due to thermal conduction from the former. At high velocity, all layers of the two films are ultimately removed by vaporisation or degradation as the average beam power is increased to achieve a complete cut. The transition velocity between the two characteristic removal types is shown to be a function of the pulse repetition rate. An experimental investigation validates the simulation results and provides new laser processing data for some typical packaging materials.

Three-dimensional joint kinematics of swimming using body-worn inertial and magnetic sensors

Wearable inertial and magnetic measurements units (IMMU) are an important tool for underwater motion analysis because they are swimmer-centric, they require only simple measurement set-up and they provide the performance results very quickly. In order to estimate 3D joint kinematics during motion, protocols were developed to transpose the IMMU orientation estimation to a biomechanical model. The aim of the thesis was to validate a protocol originally propositioned to estimate the joint angles of the upper limbs during one-degree-of-freedom movements in dry settings and herein modified to perform 3D kinematics analysis of shoulders, elbows and wrists during swimming. Eight high-level swimmers were assessed in the laboratory by means of an IMMU while simulating the front crawl and breaststroke movements. A stereo-photogrammetric system (SPS) was used as reference. The joint angles (in degrees) of the shoulders (flexion-extension, abduction-adduction and internal-external rotation), the elbows (flexion-extension and pronation-supination), and the wrists (flexion-extension and radial-ulnar deviation) were estimated with the two systems and compared by means of root mean square errors (RMSE), relative RMSE, Pearson’s product-moment coefficient correlation (R) and coefficient of multiple correlation (CMC). Subsequently, the athletes were assessed during pool swimming trials through the IMMU. Considering both swim styles and all joint degrees of freedom modeled, the comparison between the IMMU and the SPS showed median values of RMSE lower than 8°, representing 10% of overall joint range of motion, high median values of CMC (0.97) and R (0.96). These findings suggest that the protocol accurately estimated the 3D orientation of the shoulders, elbows and wrists joint during swimming with accuracy adequate for the purposes of research. In conclusion, the proposed method to evaluate the 3D joint kinematics through IMMU was revealed to be a useful tool for both sport and clinical contexts.