Classical limit of the Nelson model

Since the development of quantum mechanics it has been natural to analyze the connection between classical and quantum mechanical descriptions of physical systems. In particular one should expect that in some sense when quantum mechanical effects becomes negligible the system will behave like it is dictated by classical mechanics. One famous relation between classical and quantum theory is due to Ehrenfest. This result was later developed and put on firm mathematical foundations by Hepp. He proved that matrix elements of bounded functions of quantum observables between suitable coherents states (that depend on Planck's constant h) converge to classical values evolving according to the expected classical equations when h goes to zero. His results were later generalized by Ginibre and Velo to bosonic systems with infinite degrees of freedom and scattering theory. In this thesis we study the classical limit of Nelson model, that describes non relativistic particles, whose evolution is dictated by Schrödinger equation, interacting with a scalar relativistic field, whose evolution is dictated by Klein-Gordon equation, by means of a Yukawa-type potential. The classical limit is a mean field and weak coupling limit. We proved that the transition amplitude of a creation or annihilation operator, between suitable coherent states, converges in the classical limit to the solution of the system of differential equations that describes the classical evolution of the theory. The quantum evolution operator converges to the evolution operator of fluctuations around the classical solution. Transition amplitudes of normal ordered products of creation and annihilation operators between coherent states converge to suitable products of the classical solutions. Transition amplitudes of normal ordered products of creation and annihilation operators between fixed particle states converge to an average of products of classical solutions, corresponding to different initial conditions.

Incompressible limit and well-posedness of PDE models of tissue growth

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical aspects of living tissues. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems where saturation holds in the moving domain. Our work aims at investigating the stiff pressure limit of reaction-advection-porous medium equations motivated by tumor development. Our first study concerns the analysis and numerical simulation of a model including the effect of nutrients. A coupled system of equations describes the cell density and the nutrient concentration and the derivation of the pressure equation in the stiff limit was an open problem for which the strong compactness of the pressure gradient is needed. To establish it, we use two new ideas: an L3-version of the celebrated Aronson-Bénilan estimate, and a sharp uniform L4-bound on the pressure gradient. We further investigate the sharpness of this bound through a finite difference upwind scheme, which we prove to be stable and asymptotic preserving. Our second study is centered around porous medium equations including convective effects. We are able to extend the techniques developed for the nutrient case, hence finding the complementarity relation on the limit pressure. Moreover, we provide an estimate of the convergence rate at the incompressible limit. Finally, we study a multi-species system. In particular, we account for phenotypic heterogeneity, including a structured variable into the problem. In this case, a cross-(degenerate)-diffusion system describes the evolution of the phenotypic distributions. Adapting methods recently developed in the context of two-species systems, we prove existence of weak solutions and we pass to the incompressible limit. Furthermore, we prove new regularity results on the total pressure, which is related to the total density by a power law of state.

A high energy perspective of the co-evolution of black holes and their host galaxies

Thanks to the Chandra and XMM–Newton surveys, the hard X-ray sky is now probed down to a flux limit where the bulk of the X-ray background is almost completely resolved into discrete sources, at least in the 2–8 keV band. Extensive programs of multiwavelength follow-up observations showed that the large majority of hard X–ray selected sources are identified with Active Galactic Nuclei (AGN) spanning a broad range of redshifts, luminosities and optical properties. A sizable fraction of relatively luminous X-ray sources hosting an active, presumably obscured, nucleus would not have been easily recognized as such on the basis of optical observations because characterized by “peculiar” optical properties. In my PhD thesis, I will focus the attention on the nature of two classes of hard X-ray selected “elusive” sources: those characterized by high X-ray-to-optical flux ratios and red optical-to-near-infrared colors, a fraction of which associated with Type 2 quasars, and the X-ray bright optically normal galaxies, also known as XBONGs. In order to characterize the properties of these classes of elusive AGN, the datasets of several deep and large-area surveys have been fully exploited. The first class of “elusive” sources is characterized by X-ray-to-optical flux ratios (X/O) significantly higher than what is generally observed from unobscured quasars and Seyfert galaxies. The properties of well defined samples of high X/O sources detected at bright X–ray fluxes suggest that X/O selection is highly efficient in sampling high–redshift obscured quasars. At the limits of deep Chandra surveys (∼10−16 erg cm−2 s−1), high X/O sources are generally characterized by extremely faint optical magnitudes, hence their spectroscopic identification is hardly feasible even with the largest telescopes. In this framework, a detailed investigation of their X-ray properties may provide useful information on the nature of this important component of the X-ray source population. The X-ray data of the deepest X-ray observations ever performed, the Chandra deep fields, allows us to characterize the average X-ray properties of the high X/O population. The results of spectral analysis clearly indicate that the high X/O sources represent the most obscured component of the X–ray background. Their spectra are harder (G ∼ 1) than any other class of sources in the deep fields and also of the XRB spectrum (G ≈ 1.4). In order to better understand the AGN physics and evolution, a much better knowledge of the redshift, luminosity and spectral energy distributions (SEDs) of elusive AGN is of paramount importance. The recent COSMOS survey provides the necessary multiwavelength database to characterize the SEDs of a statistically robust sample of obscured sources. The combination of high X/O and red-colors offers a powerful tool to select obscured luminous objects at high redshift. A large sample of X-ray emitting extremely red objects (R−K >5) has been collected and their optical-infrared properties have been studied. In particular, using an appropriate SED fitting procedure, the nuclear and the host galaxy components have been deconvolved over a large range of wavelengths and ptical nuclear extinctions, black hole masses and Eddington ratios have been estimated. It is important to remark that the combination of hard X-ray selection and extreme red colors is highly efficient in picking up highly obscured, luminous sources at high redshift. Although the XBONGs do not present a new source population, the interest on the nature of these sources has gained a renewed attention after the discovery of several examples from recent Chandra and XMM–Newton surveys. Even though several possibilities were proposed in recent literature to explain why a relatively luminous (LX = 1042 − 1043erg s−1) hard X-ray source does not leave any significant signature of its presence in terms of optical emission lines, the very nature of XBONGs is still subject of debate. Good-quality photometric near-infrared data (ISAAC/VLT) of 4 low-redshift XBONGs from the HELLAS2XMMsurvey have been used to search for the presence of the putative nucleus, applying the surface-brightness decomposition technique. In two out of the four sources, the presence of a nuclear weak component hosted by a bright galaxy has been revealed. The results indicate that moderate amounts of gas and dust, covering a large solid angle (possibly 4p) at the nuclear source, may explain the lack of optical emission lines. A weak nucleus not able to produce suffcient UV photons may provide an alternative or additional explanation. On the basis of an admittedly small sample, we conclude that XBONGs constitute a mixed bag rather than a new source population. When the presence of a nucleus is revealed, it turns out to be mildly absorbed and hosted by a bright galaxy.

Sviluppo di metodologie di localizzazione nel contesto del Comprehensive Nuclear Test-Ban Treaty

Since the first underground nuclear explosion, carried out in 1958, the analysis of seismic signals generated by these sources has allowed seismologists to refine the travel times of seismic waves through the Earth and to verify the accuracy of the location algorithms (the ground truth for these sources was often known). Long international negotiates have been devoted to limit the proliferation and testing of nuclear weapons. In particular the Treaty for the comprehensive nuclear test ban (CTBT), was opened to signatures in 1996, though, even if it has been signed by 178 States, has not yet entered into force, The Treaty underlines the fundamental role of the seismological observations to verify its compliance, by detecting and locating seismic events, and identifying the nature of their sources. A precise definition of the hypocentral parameters represents the first step to discriminate whether a given seismic event is natural or not. In case that a specific event is retained suspicious by the majority of the State Parties, the Treaty contains provisions for conducting an on-site inspection (OSI) in the area surrounding the epicenter of the event, located through the International Monitoring System (IMS) of the CTBT Organization. An OSI is supposed to include the use of passive seismic techniques in the area of the suspected clandestine underground nuclear test. In fact, high quality seismological systems are thought to be capable to detect and locate very weak aftershocks triggered by underground nuclear explosions in the first days or weeks following the test. This PhD thesis deals with the development of two different seismic location techniques: the first one, known as the double difference joint hypocenter determination (DDJHD) technique, is aimed at locating closely spaced events at a global scale. The locations obtained by this method are characterized by a high relative accuracy, although the absolute location of the whole cluster remains uncertain. We eliminate this problem introducing a priori information: the known location of a selected event. The second technique concerns the reliable estimates of back azimuth and apparent velocity of seismic waves from local events of very low magnitude recorded by a trypartite array at a very local scale. For the two above-mentioned techniques, we have used the crosscorrelation technique among digital waveforms in order to minimize the errors linked with incorrect phase picking. The cross-correlation method relies on the similarity between waveforms of a pair of events at the same station, at the global scale, and on the similarity between waveforms of the same event at two different sensors of the try-partite array, at the local scale. After preliminary tests on the reliability of our location techniques based on simulations, we have applied both methodologies to real seismic events. The DDJHD technique has been applied to a seismic sequence occurred in the Turkey-Iran border region, using the data recorded by the IMS. At the beginning, the algorithm was applied to the differences among the original arrival times of the P phases, so the cross-correlation was not used. We have obtained that the relevant geometrical spreading, noticeable in the standard locations (namely the locations produced by the analysts of the International Data Center (IDC) of the CTBT Organization, assumed as our reference), has been considerably reduced by the application of our technique. This is what we expected, since the methodology has been applied to a sequence of events for which we can suppose a real closeness among the hypocenters, belonging to the same seismic structure. Our results point out the main advantage of this methodology: the systematic errors affecting the arrival times have been removed or at least reduced. The introduction of the cross-correlation has not brought evident improvements to our results: the two sets of locations (without and with the application of the cross-correlation technique) are very similar to each other. This can be commented saying that the use of the crosscorrelation has not substantially improved the precision of the manual pickings. Probably the pickings reported by the IDC are good enough to make the random picking error less important than the systematic error on travel times. As a further justification for the scarce quality of the results given by the cross-correlation, it should be remarked that the events included in our data set don’t have generally a good signal to noise ratio (SNR): the selected sequence is composed of weak events ( magnitude 4 or smaller) and the signals are strongly attenuated because of the large distance between the stations and the hypocentral area. In the local scale, in addition to the cross-correlation, we have performed a signal interpolation in order to improve the time resolution. The algorithm so developed has been applied to the data collected during an experiment carried out in Israel between 1998 and 1999. The results pointed out the following relevant conclusions: a) it is necessary to correlate waveform segments corresponding to the same seismic phases; b) it is not essential to select the exact first arrivals; and c) relevant information can be also obtained from the maximum amplitude wavelet of the waveforms (particularly in bad SNR conditions). Another remarkable point of our procedure is that its application doesn’t demand a long time to process the data, and therefore the user can immediately check the results. During a field survey, such feature will make possible a quasi real-time check allowing the immediate optimization of the array geometry, if so suggested by the results at an early stage.

Cooperative communication and distributed detection in wireless sensor networks

Recent progress in microelectronic and wireless communications have enabled the development of low cost, low power, multifunctional sensors, which has allowed the birth of new type of networks named wireless sensor networks (WSNs). The main features of such networks are: the nodes can be positioned randomly over a given field with a high density; each node operates both like sensor (for collection of environmental data) as well as transceiver (for transmission of information to the data retrieval); the nodes have limited energy resources. The use of wireless communications and the small size of nodes, make this type of networks suitable for a large number of applications. For example, sensor nodes can be used to monitor a high risk region, as near a volcano; in a hospital they could be used to monitor physical conditions of patients. For each of these possible application scenarios, it is necessary to guarantee a trade-off between energy consumptions and communication reliability. The thesis investigates the use of WSNs in two possible scenarios and for each of them suggests a solution that permits to solve relating problems considering the trade-off introduced. The first scenario considers a network with a high number of nodes deployed in a given geographical area without detailed planning that have to transmit data toward a coordinator node, named sink, that we assume to be located onboard an unmanned aerial vehicle (UAV). This is a practical example of reachback communication, characterized by the high density of nodes that have to transmit data reliably and efficiently towards a far receiver. It is considered that each node transmits a common shared message directly to the receiver onboard the UAV whenever it receives a broadcast message (triggered for example by the vehicle). We assume that the communication channels between the local nodes and the receiver are subject to fading and noise. The receiver onboard the UAV must be able to fuse the weak and noisy signals in a coherent way to receive the data reliably. It is proposed a cooperative diversity concept as an effective solution to the reachback problem. In particular, it is considered a spread spectrum (SS) transmission scheme in conjunction with a fusion center that can exploit cooperative diversity, without requiring stringent synchronization between nodes. The idea consists of simultaneous transmission of the common message among the nodes and a Rake reception at the fusion center. The proposed solution is mainly motivated by two goals: the necessity to have simple nodes (to this aim we move the computational complexity to the receiver onboard the UAV), and the importance to guarantee high levels of energy efficiency of the network, thus increasing the network lifetime. The proposed scheme is analyzed in order to better understand the effectiveness of the approach presented. The performance metrics considered are both the theoretical limit on the maximum amount of data that can be collected by the receiver, as well as the error probability with a given modulation scheme. Since we deal with a WSN, both of these performance are evaluated taking into consideration the energy efficiency of the network. The second scenario considers the use of a chain network for the detection of fires by using nodes that have a double function of sensors and routers. The first one is relative to the monitoring of a temperature parameter that allows to take a local binary decision of target (fire) absent/present. The second one considers that each node receives a decision made by the previous node of the chain, compares this with that deriving by the observation of the phenomenon, and transmits the final result to the next node. The chain ends at the sink node that transmits the received decision to the user. In this network the goals are to limit throughput in each sensor-to-sensor link and minimize probability of error at the last stage of the chain. This is a typical scenario of distributed detection. To obtain good performance it is necessary to define some fusion rules for each node to summarize local observations and decisions of the previous nodes, to get a final decision that it is transmitted to the next node. WSNs have been studied also under a practical point of view, describing both the main characteristics of IEEE802:15:4 standard and two commercial WSN platforms. By using a commercial WSN platform it is realized an agricultural application that has been tested in a six months on-field experimentation.

Testing future weak lensing surveys through simulations of observations

Weak lensing experiments such as the future ESA-accepted mission Euclid aim to measure cosmological parameters with unprecedented accuracy. It is important to assess the precision that can be obtained in these measurements by applying analysis software on mock images that contain many sources of noise present in the real data. In this Thesis, we show a method to perform simulations of observations, that produce realistic images of the sky according to characteristics of the instrument and of the survey. We then use these images to test the performances of the Euclid mission. In particular, we concentrate on the precision of the photometric redshift measurements, which are key data to perform cosmic shear tomography. We calculate the fraction of the total observed sample that must be discarded to reach the required level of precision, that is equal to 0.05(1+z) for a galaxy with measured redshift z, with different ancillary ground-based observations. The results highlight the importance of u-band observations, especially to discriminate between low (z < 0.5) and high (z ~ 3) redshifts, and the need for good observing sites, with seeing FWHM < 1. arcsec. We then construct an optimal filter to detect galaxy clusters through photometric catalogues of galaxies, and we test it on the COSMOS field, obtaining 27 lensing-confirmed detections. Applying this algorithm on mock Euclid data, we verify the possibility to detect clusters with mass above 10^14.2 solar masses with a low rate of false detections.

Potential Analysis for Hypoelliptic Second Order PDEs with Nonnegative Characteristic Form

In this Thesis we consider a class of second order partial differential operators with non-negative characteristic form and with smooth coefficients. Main assumptions on the relevant operators are hypoellipticity and existence of a well-behaved global fundamental solution. We first make a deep analysis of the L-Green function for arbitrary open sets and of its applications to the Representation Theorems of Riesz-type for L-subharmonic and L-superharmonic functions. Then, we prove an Inverse Mean value Theorem characterizing the superlevel sets of the fundamental solution by means of L-harmonic functions. Furthermore, we establish a Lebesgue-type result showing the role of the mean-integal operator in solving the homogeneus Dirichlet problem related to L in the Perron-Wiener sense. Finally, we compare Perron-Wiener and weak variational solutions of the homogeneous Dirichlet problem, under specific hypothesis on the boundary datum.

New knowledge, diagnostic and control tools to limit the impact of viral nervous necrosis (VNN) in the Mediterranean aquaculture sector

The role of aquaculture in satisfying the global seafood demand is essential. The expansion of the aquaculture sector and the intensification of its activities have enhanced the circulation of infectious agents. Among these, the nervous necrosis virus (NNV) represents the most widespread in the Mediterranean basin. The NNV is responsible for a severe neuropathological condition named viral nervous necrosis (VNN), impacting hugely on fish farms due to the serious disease-associated losses. Therefore, it is fundamental to develop new strategies to limit the impact of VNN in this area, interconnecting several aspects of disease management, diagnosis and prevention. This PhD thesis project, focusing on aquatic animals’ health, deals with these topics. The first two chapters expand the knowledge on VNN epidemiology and distribution, showing the possibility of interspecies transmission, persistent infections and a potential carrier role for invertebrates. The third study expands the horizon of VNN diagnosis, by developing a quick and affordable multiplex RT-PCR able to detect and simultaneously discriminate between NNV variants, reducing considerably the time and costs of genotyping. The fourth study, with the development of a fluorescent in situ hybridization technique and its application to aquatic vertebrates and invertebrates’ tissues, contributes to expand the knowledge on NNV distribution at cellular level, localizing also the replication site of the virus. Finally, the last study dealing with an in vitro evaluation of the NNV susceptibility to a commercial biocide, stress the importance to implement proper disinfectant procedures in fish farms to prevent virus spread and disease outbreaks.

Weak reasoning argumentative theory. A dialogical approach for the discovery of philosophy in high schools

In the literature on philosophical practices, despite the crucial role that argumentation plays in these activities, no specific argumentative theories have ever been proposed to assist the figure of the facilitator in conducting philosophical dialogue and to enhance student’s critical thinking skills. The dissertation starts from a cognitive perspective that challenges the classic Cartesian notion of rationality by focusing on limits and biases of human reasoning. An argumentative model (WRAT – Weak Reasoning Argumentative Theory) is then outlined in order to respond to the needs of philosophical dialogue. After justifying the claim that this learning activity, among other inductive methodologies, is the most suitable for critical thinking education, I inquired into the specific goal of ‘arguing’ within this context by means of the tools provided by Speech Act Theory: the speaker’s intention is to construct new knowledge by questioning her own and other’s beliefs. The model proposed has been theorized on this assumption, starting from which the goals, and, in turn, the related norms, have been pinpointed. In order to include all the epistemic attitudes required to accomplish the complex task of arguing in philosophical dialogue, I needed to integrate two opposed cognitive accounts, Dual Process Theory and Evolutionary Approach, that, although they provide incompatible descriptions of reasoning, can be integrated to provide a normative account of argumentation. The model, apart from offering a theoretical contribution to argumentation studies, is designed to be applied to the Italian educational system, in particular to classes in technical and professional high schools belonging to the newly created network Inventio. This initiative is one of the outcomes of the research project by the same name, which also includes an original Syllabus, research seminars, a monitoring action and publications focused on introducing philosophy, in the form of workshop activities, into technical and professional schools.