The quantum time-dependent harmonic oscillator

La presente tesi si propone di mostrare che l’oscillatore armonico quantistico dipendente dal tempo è un sistema risolvibile in maniera esatta. La trattazione è articolata in tre capitoli: nel primo viene richiamata la teoria dell’oscillatore armonico quantistico indipendente dal tempo, al fine di recuperare i concetti e le metodologie che sono comuni anche alla sua controparte dipendente dal tempo. Nel secondo capitolo viene fornita una breve introduzione alla teoria degli operatori invarianti dipendenti dal tempo, di cui ci interessa la loro relazione con le soluzioni dell’equazione di Schrödinger. Infine, nel terzo capitolo viene presentato il problema dell’oscillatore armonico quantistico dipendente dal tempo e discussa la sua soluzione esatta. In aggiunta se ne individuano gli stati coerenti.

Towards a Smart Campus Digital Twin: Promoting Awareness and Sustainability Through Wayfinding and Real-Time Environmental Data

The newly inaugurated Navile District of the University of Bologna is a complex created along the Navile canal, that now houses various teaching and research activities for the disciplines of Chemistry, Industrial Chemistry, Pharmacy, Biotechnology and Astronomy. A Building Information Modeling system (BIM) gives staff of the Navile campus several ways to monitor buildings in the complex throughout their life cycle, one of which is the ability to access real-time environmental data such as room temperature, humidity, air composition, and more, thereby simplifying operations like finding faults and optimizing environmental resource usage. But smart features at Navile are not only available to the staff: AlmaMap Navile is a web application, whose development is documented in this thesis, that powers the public touch kiosks available throughout the campus, offering maps of the district and indications on how to reach buildings and spaces. Even if these two systems, BIM and AlmaMap, don't seem to have many similarities, they share the common intent of promoting awareness for informed decision making in the campus, and they do it while relying on web standards for communication. This opens up interesting possibilities, and is the idea behind AlmaMap Navile 2.0, an app that interfaces with the BIM system and combines real-time sensor data with a comfort calculation algorithm, giving users the ability not just to ask for directions to a space, but also to see its comfort level in advance and, should they want to, check environmental measurements coming from each sensor in a granular manner. The end result is a first step towards building a smart campus Digital Twin, that can support all the people who are part of the campus life in their daily activities, improving their efficiency and satisfaction, giving them the ability to make informed decisions, and promoting awareness and sustainability.

Modeling and visualization of medical anesthesiology acts

Dissertação para obtenção do Grau de Mestre em Engenharia Informática

Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

Capillaries within compartments: Microvascular interpretation of dynamic positron emission tomography data

Measurement of exchange of substances between blood and tissue has been a long-lasting challenge to physiologists, and considerable theoretical and experimental accomplishments were achieved before the development of the positron emission tomography (PET). Today, when modeling data from modern PET scanners, little use is made of earlier microvascular research in the compartmental models, which have become the standard model by which the vast majority of dynamic PET data are analysed. However, modern PET scanners provide data with a sufficient temporal resolution and good counting statistics to allow estimation of parameters in models with more physiological realism. We explore the standard compartmental model and find that incorporation of blood flow leads to paradoxes, such as kinetic rate constants being time-dependent, and tracers being cleared from a capillary faster than they can be supplied by blood flow. The inability of the standard model to incorporate blood flow consequently raises a need for models that include more physiology, and we develop microvascular models which remove the inconsistencies. The microvascular models can be regarded as a revision of the input function. Whereas the standard model uses the organ inlet concentration as the concentration throughout the vascular compartment, we consider models that make use of spatial averaging of the concentrations in the capillary volume, which is what the PET scanner actually registers. The microvascular models are developed for both single- and multi-capillary systems and include effects of non-exchanging vessels. They are suitable for analysing dynamic PET data from any capillary bed using either intravascular or diffusible tracers, in terms of physiological parameters which include regional blood flow. (C) 2003 Elsevier Ltd. All rights reserved.

Examining the information content of time-lapse crosshole GPR data collected under different infiltration conditions to estimate unsaturated soil hydraulic properties

Time-lapse geophysical data acquired during transient hydrological experiments are being increasingly employed to estimate subsurface hydraulic properties at the field scale. In particular, crosshole ground-penetrating radar (GPR) data, collected while water infiltrates into the subsurface either by natural or artificial means, have been demonstrated in a number of studies to contain valuable information concerning the hydraulic properties of the unsaturated zone. Previous work in this domain has considered a variety of infiltration conditions and different amounts of time-lapse GPR data in the estimation procedure. However, the particular benefits and drawbacks of these different strategies as well as the impact of a variety of key and common assumptions remain unclear. Using a Bayesian Markov-chain-Monte-Carlo stochastic inversion methodology, we examine in this paper the information content of time-lapse zero-offset-profile (ZOP) GPR traveltime data, collected under three different infiltration conditions, for the estimation of van Genuchten-Mualem (VGM) parameters in a layered subsurface medium. Specifically, we systematically analyze synthetic and field GPR data acquired under natural loading and two rates of forced infiltration, and we consider the value of incorporating different amounts of time-lapse measurements into the estimation procedure. Our results confirm that, for all infiltration scenarios considered, the ZOP GPR traveltime data contain important information about subsurface hydraulic properties as a function of depth, with forced infiltration offering the greatest potential for VGM parameter refinement because of the higher stressing of the hydrological system. Considering greater amounts of time-lapse data in the inversion procedure is also found to help refine VGM parameter estimates. Quite importantly, however, inconsistencies observed in the field results point to the strong possibility that posterior uncertainties are being influenced by model structural errors, which in turn underlines the fundamental importance of a systematic analysis of such errors in future related studies.

Structural joint inversion of time-lapse crosshole ERT and GPR traveltime data

Time-lapse geophysical monitoring and inversion are valuable tools in hydrogeology for monitoring changes in the subsurface due to natural and forced (tracer) dynamics. However, the resulting models may suffer from insufficient resolution, which leads to underestimated variability and poor mass recovery. Structural joint inversion using cross-gradient constraints can provide higher-resolution models compared with individual inversions and we present the first application to time-lapse data. The results from a synthetic and field vadose zone water tracer injection experiment show that joint 3-D time-lapse inversion of crosshole electrical resistance tomography (ERT) and ground penetrating radar (GPR) traveltime data significantly improve the imaged characteristics of the point injected plume, such as lateral spreading and center of mass, as well as the overall consistency between models. The joint inversion method appears to work well for cases when one hydrological state variable (in this case moisture content) controls the time-lapse response of both geophysical methods. Citation: Doetsch, J., N. Linde, and A. Binley (2010), Structural joint inversion of time-lapse crosshole ERT and GPR traveltime data, Geophys. Res. Lett., 37, L24404, doi: 10.1029/2010GL045482.

Time-lapse and probabilistic inversion strategies for plane-wave electromagnetic data.

L'utilisation efficace des systèmes géothermaux, la séquestration du CO2 pour limiter le changement climatique et la prévention de l'intrusion d'eau salée dans les aquifères costaux ne sont que quelques exemples qui démontrent notre besoin en technologies nouvelles pour suivre l'évolution des processus souterrains à partir de la surface. Un défi majeur est d'assurer la caractérisation et l'optimisation des performances de ces technologies à différentes échelles spatiales et temporelles. Les méthodes électromagnétiques (EM) d'ondes planes sont sensibles à la conductivité électrique du sous-sol et, par conséquent, à la conductivité électrique des fluides saturant la roche, à la présence de fractures connectées, à la température et aux matériaux géologiques. Ces méthodes sont régies par des équations valides sur de larges gammes de fréquences, permettant détudier de manières analogues des processus allant de quelques mètres sous la surface jusqu'à plusieurs kilomètres de profondeur. Néanmoins, ces méthodes sont soumises à une perte de résolution avec la profondeur à cause des propriétés diffusives du champ électromagnétique. Pour cette raison, l'estimation des modèles du sous-sol par ces méthodes doit prendre en compte des informations a priori afin de contraindre les modèles autant que possible et de permettre la quantification des incertitudes de ces modèles de façon appropriée. Dans la présente thèse, je développe des approches permettant la caractérisation statique et dynamique du sous-sol à l'aide d'ondes EM planes. Dans une première partie, je présente une approche déterministe permettant de réaliser des inversions répétées dans le temps (time-lapse) de données d'ondes EM planes en deux dimensions. Cette stratégie est basée sur l'incorporation dans l'algorithme d'informations a priori en fonction des changements du modèle de conductivité électrique attendus. Ceci est réalisé en intégrant une régularisation stochastique et des contraintes flexibles par rapport à la gamme des changements attendus en utilisant les multiplicateurs de Lagrange. J'utilise des normes différentes de la norme l2 pour contraindre la structure du modèle et obtenir des transitions abruptes entre les régions du model qui subissent des changements dans le temps et celles qui n'en subissent pas. Aussi, j'incorpore une stratégie afin d'éliminer les erreurs systématiques de données time-lapse. Ce travail a mis en évidence l'amélioration de la caractérisation des changements temporels par rapport aux approches classiques qui réalisent des inversions indépendantes à chaque pas de temps et comparent les modèles. Dans la seconde partie de cette thèse, j'adopte un formalisme bayésien et je teste la possibilité de quantifier les incertitudes sur les paramètres du modèle dans l'inversion d'ondes EM planes. Pour ce faire, je présente une stratégie d'inversion probabiliste basée sur des pixels à deux dimensions pour des inversions de données d'ondes EM planes et de tomographies de résistivité électrique (ERT) séparées et jointes. Je compare les incertitudes des paramètres du modèle en considérant différents types d'information a priori sur la structure du modèle et différentes fonctions de vraisemblance pour décrire les erreurs sur les données. Les résultats indiquent que la régularisation du modèle est nécessaire lorsqu'on a à faire à un large nombre de paramètres car cela permet d'accélérer la convergence des chaînes et d'obtenir des modèles plus réalistes. Cependent, ces contraintes mènent à des incertitudes d'estimations plus faibles, ce qui implique des distributions a posteriori qui ne contiennent pas le vrai modèledans les régions ou` la méthode présente une sensibilité limitée. Cette situation peut être améliorée en combinant des méthodes d'ondes EM planes avec d'autres méthodes complémentaires telles que l'ERT. De plus, je montre que le poids de régularisation des paramètres et l'écart-type des erreurs sur les données peuvent être retrouvés par une inversion probabiliste. Finalement, j'évalue la possibilité de caractériser une distribution tridimensionnelle d'un panache de traceur salin injecté dans le sous-sol en réalisant une inversion probabiliste time-lapse tridimensionnelle d'ondes EM planes. Etant donné que les inversions probabilistes sont très coûteuses en temps de calcul lorsque l'espace des paramètres présente une grande dimension, je propose une stratégie de réduction du modèle ou` les coefficients de décomposition des moments de Legendre du panache de traceur injecté ainsi que sa position sont estimés. Pour ce faire, un modèle de résistivité de base est nécessaire. Il peut être obtenu avant l'expérience time-lapse. Un test synthétique montre que la méthodologie marche bien quand le modèle de résistivité de base est caractérisé correctement. Cette méthodologie est aussi appliquée à un test de trac¸age par injection d'une solution saline et d'acides réalisé dans un système géothermal en Australie, puis comparée à une inversion time-lapse tridimensionnelle réalisée selon une approche déterministe. L'inversion probabiliste permet de mieux contraindre le panache du traceur salin gr^ace à la grande quantité d'informations a priori incluse dans l'algorithme. Néanmoins, les changements de conductivités nécessaires pour expliquer les changements observés dans les données sont plus grands que ce qu'expliquent notre connaissance actuelle des phénomenès physiques. Ce problème peut être lié à la qualité limitée du modèle de résistivité de base utilisé, indiquant ainsi que des efforts plus grands devront être fournis dans le futur pour obtenir des modèles de base de bonne qualité avant de réaliser des expériences dynamiques. Les études décrites dans cette thèse montrent que les méthodes d'ondes EM planes sont très utiles pour caractériser et suivre les variations temporelles du sous-sol sur de larges échelles. Les présentes approches améliorent l'évaluation des modèles obtenus, autant en termes d'incorporation d'informations a priori, qu'en termes de quantification d'incertitudes a posteriori. De plus, les stratégies développées peuvent être appliquées à d'autres méthodes géophysiques, et offrent une grande flexibilité pour l'incorporation d'informations additionnelles lorsqu'elles sont disponibles. -- The efficient use of geothermal systems, the sequestration of CO2 to mitigate climate change, and the prevention of seawater intrusion in coastal aquifers are only some examples that demonstrate the need for novel technologies to monitor subsurface processes from the surface. A main challenge is to assure optimal performance of such technologies at different temporal and spatial scales. Plane-wave electromagnetic (EM) methods are sensitive to subsurface electrical conductivity and consequently to fluid conductivity, fracture connectivity, temperature, and rock mineralogy. These methods have governing equations that are the same over a large range of frequencies, thus allowing to study in an analogous manner processes on scales ranging from few meters close to the surface down to several hundreds of kilometers depth. Unfortunately, they suffer from a significant resolution loss with depth due to the diffusive nature of the electromagnetic fields. Therefore, estimations of subsurface models that use these methods should incorporate a priori information to better constrain the models, and provide appropriate measures of model uncertainty. During my thesis, I have developed approaches to improve the static and dynamic characterization of the subsurface with plane-wave EM methods. In the first part of this thesis, I present a two-dimensional deterministic approach to perform time-lapse inversion of plane-wave EM data. The strategy is based on the incorporation of prior information into the inversion algorithm regarding the expected temporal changes in electrical conductivity. This is done by incorporating a flexible stochastic regularization and constraints regarding the expected ranges of the changes by using Lagrange multipliers. I use non-l2 norms to penalize the model update in order to obtain sharp transitions between regions that experience temporal changes and regions that do not. I also incorporate a time-lapse differencing strategy to remove systematic errors in the time-lapse inversion. This work presents improvements in the characterization of temporal changes with respect to the classical approach of performing separate inversions and computing differences between the models. In the second part of this thesis, I adopt a Bayesian framework and use Markov chain Monte Carlo (MCMC) simulations to quantify model parameter uncertainty in plane-wave EM inversion. For this purpose, I present a two-dimensional pixel-based probabilistic inversion strategy for separate and joint inversions of plane-wave EM and electrical resistivity tomography (ERT) data. I compare the uncertainties of the model parameters when considering different types of prior information on the model structure and different likelihood functions to describe the data errors. The results indicate that model regularization is necessary when dealing with a large number of model parameters because it helps to accelerate the convergence of the chains and leads to more realistic models. These constraints also lead to smaller uncertainty estimates, which imply posterior distributions that do not include the true underlying model in regions where the method has limited sensitivity. This situation can be improved by combining planewave EM methods with complimentary geophysical methods such as ERT. In addition, I show that an appropriate regularization weight and the standard deviation of the data errors can be retrieved by the MCMC inversion. Finally, I evaluate the possibility of characterizing the three-dimensional distribution of an injected water plume by performing three-dimensional time-lapse MCMC inversion of planewave EM data. Since MCMC inversion involves a significant computational burden in high parameter dimensions, I propose a model reduction strategy where the coefficients of a Legendre moment decomposition of the injected water plume and its location are estimated. For this purpose, a base resistivity model is needed which is obtained prior to the time-lapse experiment. A synthetic test shows that the methodology works well when the base resistivity model is correctly characterized. The methodology is also applied to an injection experiment performed in a geothermal system in Australia, and compared to a three-dimensional time-lapse inversion performed within a deterministic framework. The MCMC inversion better constrains the water plumes due to the larger amount of prior information that is included in the algorithm. The conductivity changes needed to explain the time-lapse data are much larger than what is physically possible based on present day understandings. This issue may be related to the base resistivity model used, therefore indicating that more efforts should be given to obtain high-quality base models prior to dynamic experiments. The studies described herein give clear evidence that plane-wave EM methods are useful to characterize and monitor the subsurface at a wide range of scales. The presented approaches contribute to an improved appraisal of the obtained models, both in terms of the incorporation of prior information in the algorithms and the posterior uncertainty quantification. In addition, the developed strategies can be applied to other geophysical methods, and offer great flexibility to incorporate additional information when available.

Frequency-dependent attenuation as a potential indicator of oil saturation

At seismic frequencies, wave-induced fluid flow is a major cause of P-wave attenuation in partially saturated porous rocks. Attenuation is of great importance for the oil industry in the interpretation of seismic field data. Here, the effects on P-wave attenuation resulting from changes in oil saturation are studied for media with coexisting water, oil, and gas. For that, creep experiments are numerically simulated by solving Biot's equations for consolidation of poroelastic media with the finite-element method. The experiments yield time-dependent stress?strain relations that are used to calculate the complex P-wave modulus from which frequency-dependent P-wave attenuation is determined. The models are layered media with periodically alternating triplets of layers. Models consisting of triplets of layers having randomly varying layer thicknesses are also considered. The layers in each triplet are fully saturated with water, oil, and gas. The layer saturated with water has lower porosity and permeability than the layers saturated with oil and gas. These models represent hydrocarbon reservoirs in which water is the wetting fluid preferentially saturating regions of lower porosity. The results from the numerical experiments showed that increasing oil saturation, connected to a decrease in gas saturation, resulted in a significant increase of attenuation at low frequencies (lower than 2 Hz). Furthermore, replacing the oil with water resulted in a distinguishable behavior of the frequency-dependent attenuation. These results imply that, according to the physical mechanism of wave-induced fluid flow, frequency-dependent attenuation in media saturated with water, oil, and gas is a potential indicator of oil saturation.

On the inclusion of channel's time dependence in a hidden Markov model for blind channel estimation

In this paper, the theory of hidden Markov models (HMM) isapplied to the problem of blind (without training sequences) channel estimationand data detection. Within a HMM framework, the Baum–Welch(BW) identification algorithm is frequently used to find out maximum-likelihood (ML) estimates of the corresponding model. However, such a procedureassumes the model (i.e., the channel response) to be static throughoutthe observation sequence. By means of introducing a parametric model fortime-varying channel responses, a version of the algorithm, which is moreappropriate for mobile channels [time-dependent Baum-Welch (TDBW)] isderived. Aiming to compare algorithm behavior, a set of computer simulationsfor a GSM scenario is provided. Results indicate that, in comparisonto other Baum–Welch (BW) versions of the algorithm, the TDBW approachattains a remarkable enhancement in performance. For that purpose, onlya moderate increase in computational complexity is needed.

Significance of Time Scales in Nonlinear Dynamical Analysis of Electroencephalogram Signals

We propose to show in this paper, that the time series obtained from biological systems such as human brain are invariably nonstationary because of different time scales involved in the dynamical process. This makes the invariant parameters time dependent. We made a global analysis of the EEG data obtained from the eight locations on the skull space and studied simultaneously the dynamical characteristics from various parts of the brain. We have proved that the dynamical parameters are sensitive to the time scales and hence in the study of brain one must identify all relevant time scales involved in the process to get an insight in the working of brain.

The point source method for inverse scattering in the time domain

Many recent inverse scattering techniques have been designed for single frequency scattered fields in the frequency domain. In practice, however, the data is collected in the time domain. Frequency domain inverse scattering algorithms obviously apply to time-harmonic scattering, or nearly time-harmonic scattering, through application of the Fourier transform. Fourier transform techniques can also be applied to non-time-harmonic scattering from pulses. Our goal here is twofold: first, to establish conditions on the time-dependent waves that provide a correspondence between time domain and frequency domain inverse scattering via Fourier transforms without recourse to the conventional limiting amplitude principle; secondly, we apply the analysis in the first part of this work toward the extension of a particular scattering technique, namely the point source method, to scattering from the requisite pulses. Numerical examples illustrate the method and suggest that reconstructions from admissible pulses deliver superior reconstructions compared to straight averaging of multi-frequency data. Copyright (C) 2006 John Wiley & Sons, Ltd.

A time-domain probe method for three-dimensional rough surface reconstructions

The task of this paper is to develop a Time-Domain Probe Method for the reconstruction of impenetrable scatterers. The basic idea of the method is to use pulses in the time domain and the time-dependent response of the scatterer to reconstruct its location and shape. The method is based on the basic causality principle of timedependent scattering. The method is independent of the boundary condition and is applicable for limited aperture scattering data. In particular, we discuss the reconstruction of the shape of a rough surface in three dimensions from time-domain measurements of the scattered field. In practise, measurement data is collected where the incident field is given by a pulse. We formulate the time-domain fieeld reconstruction problem equivalently via frequency-domain integral equations or via a retarded boundary integral equation based on results of Bamberger, Ha-Duong, Lubich. In contrast to pure frequency domain methods here we use a time-domain characterization of the unknown shape for its reconstruction. Our paper will describe the Time-Domain Probe Method and relate it to previous frequency-domain approaches on sampling and probe methods by Colton, Kirsch, Ikehata, Potthast, Luke, Sylvester et al. The approach significantly extends recent work of Chandler-Wilde and Lines (2005) and Luke and Potthast (2006) on the timedomain point source method. We provide a complete convergence analysis for the method for the rough surface scattering case and provide numerical simulations and examples.

Modelling the time-evolution of phytoplankton size spectra from satellite remote sensing

A dynamic size-structured model is developed for phytoplankton and nutrients in the oceanic mixed layer and applied to extract phytoplankton biomass at discrete size fractions from remotely sensed, ocean-colour data. General relationships between cell size and biophysical processes (such as sinking, grazing, and primary production) of phytoplankton were included in the model through a bottom–up approach. Time-dependent, mixed-layer depth was used as a forcing variable, and a sequential data-assimilation scheme was implemented to derive model trajectories. From a given time-series, the method produces estimates of size-structured biomass at every observation, so estimates seasonal succession of individual phytoplankton size, derived here from remote sensing for the first time. From these estimates, normalized phytoplankton biomass size spectra over a period of 9 years were calculated for one location in the North Atlantic. Further analysis demonstrated that strong relationships exist between the seasonal trends of the estimated size spectra and the mixed-layer depth, nutrient biomass, and total chlorophyll. The results contain useful information on the time-dependent biomass flux in the pelagic ecosystem.

A Multilevel Model with Time Series Components for the Analysis of Tribal Art Prices

In the present work we perform an econometric analysis of the Tribal art market. To this aim, we use a unique and original database that includes information on Tribal art market auctions worldwide from 1998 to 2011. In Literature, art prices are modelled through the hedonic regression model, a classic fixed-effect model. The main drawback of the hedonic approach is the large number of parameters, since, in general, art data include many categorical variables. In this work, we propose a multilevel model for the analysis of Tribal art prices that takes into account the influence of time on artwork prices. In fact, it is natural to assume that time exerts an influence over the price dynamics in various ways. Nevertheless, since the set of objects change at every auction date, we do not have repeated measurements of the same items over time. Hence, the dataset does not constitute a proper panel; rather, it has a two-level structure in that items, level-1 units, are grouped in time points, level-2 units. The main theoretical contribution is the extension of classical multilevel models to cope with the case described above. In particular, we introduce a model with time dependent random effects at the second level. We propose a novel specification of the model, derive the maximum likelihood estimators and implement them through the E-M algorithm. We test the finite sample properties of the estimators and the validity of the own-written R-code by means of a simulation study. Finally, we show that the new model improves considerably the fit of the Tribal art data with respect to both the hedonic regression model and the classic multilevel model.