Aspetti innovativi per la valutazione e la misura della porosità nei materiali dell'edilizia antica e moderna. La geometria frattale della porosità

New concepts on porosity appraisal in ancient and modern construction materials. The role of Fractal Geometry on porosity characterization and transport phenomena. This work studied the potential of Fractal Geometry to the characterization of porous materials. Besides the descriptive aspects of the pore size distribution, the fractal dimensions have led to the development of rational relations for the prediction of permeability coefficients to fluid and heat transfer. The research considered natural materials used in historical buildings (rock and earth) as well as currently employed materials as hydraulic cement and technologically advanced materials such as silicon carbide or YSZ ceramics. The experimental results of porosity derived from the techniques of mercury intrusion and from the image analysis. Data elaboration was carried out according to established procedures of Fractal Geometry. It was found that certain classes of materials are clearly fractal and respond to simple patterns such as Sierpinski and Menger models. In several cases, however, the fractal character is not recognised because the microstructure of the material is based on different phases at different dimensional scales, and in consequence the “fractal dimensions” calculated from porosimetric data do not come within the standard range (less than 3). Using different type and numbers of fractal units is possible, however, to obtain “virtual” microstructures that have the fraction of voids and pore size distribution equivalent with the experimental ones for almost any material. Thus it was possible to take the expressions for the permeability and the thermal conduction which does not require empirical “constants”, these expressions have also provided values that are generally in agreement with the experimental available data. More problematic has been the fractal discussion of the geometry of the rupture of the material subjected to mechanical stress both external and internal applied. The results achieved on these issues are qualitative and prone to future studies. Keywords: Materials, Microstructure, Porosity, Fractal Geometry, Permeability, Thermal conduction, Mechanical strength.

Per un museo virtuale dell'informatica. Un supporto automatico per creare "visite museali"

The subject of the present research is related to the field of computer technology applied to support intellectual activities such as text translation, screenwriting and content organization of popular and education courses, especially concerning museum visits. The research has started with the deep analysis of the cognitive process which characterizes a screenwriter while working. This choice has been made because a screenplay is not only an aid to the realization of a show but, more in general, it can be considered as the planning of an education, popular and formative intellectual activity. After this analysis, the research has focused on the specific area of the planning, description and introduction of topics related to the history of science, and in particular, of computer science. To focus on this area it has been fundamental to analyse subjects concerning the didactics of museum visits organization. The aim was to find out the guide lines that a teacher should follow when planning the visit of a museum (virtual museum of the history of computer science). The consequent designing and realisation of an automatic support system for the description and the production of a formative, education and popular multimedia product (for the history of computer science), has been possible thanks to the results achieved through this research. The system obtained is provided by the following features: ·management of multimedia slides (such as texts, video, audio or images) which can be classified on the bases of the topic and of the profile of the user; ·automatic creation of a sequence of multimedia slides which introduce the topic; ·management of the interaction with the user to check and give validity to the product. The most innovative aspect of the present research is represented by the fact that the product is realised on the bases of the profile of the user.

Morphological and functional study of cerebral aging in rat

Aging is a physiological process characterized by a progressive decline of the “cellular homeostatic reserve”, refereed as the capability to respond suitably to exogenous and endogenous stressful stimuli. Due to their high energetic requests and post-mitotic nature, neurons are peculiarly susceptible to this phenomenon. However, the aged brain maintains a certain level of adaptive capacities and if properly stimulated may warrant a considerable functional recovery. Aim of the present research was to verify the plastic potentialities of the aging brain of rats subjected to two kind of exogenous stimuli: A) the replacement of the standard diet with a ketogenic regimen (the change forces the brain to use ketone bodies (KB) in alternative to glucose to satisfy the energetic needs) and B) a behavioural task able to induce the formation of inhibitory avoidance memory. A) Fifteen male Wistar rats of 19 months of age were divided into three groups (average body weight pair-matched), and fed for 8 weeks with different dietary regimens: i) diet containing 10% medium chain triglycerides (MCT); ii) diet containing 20% MCT; iii) standard commercial chow. Five young (5 months of age) and five old (26-27 months of age) animals fed with the standard diet were used as further controls. The following morphological parameters reflecting synaptic plasticity were evaluated in the stratum moleculare of the hippocampal CA1 region (SM CA1), in the outer molecular layer of the hippocampal dentate gyrus (OML DG), and in the granule cell layer of the cerebellar cortex (GCL-CCx): average area (S), numeric density (Nvs), and surface density (Sv) of synapses, and average volume (V), numeric density (Nvm), and volume density (Vv) of synaptic mitochondria. Moreover, succinic dehydrogenase (SDH) activity was cytochemically determined in Purkinje cells (PC) and V, Nvm, Vv, and cytochemical precipitate area/mitochondrial area (R) of SDH-positive mitochondria were evaluated. In SM CA1, MCT-KDs induced the early appearance of the morphological patterns typical of old animals: higher S and V, and lower Nvs and Nvm. On the contrary, in OML DG, Sv and Vv of MCT-KDs-fed rats were higher (as a result of higher Nvs and Nvm) vs. controls; these modifications are known to improve synaptic function and metabolic supply. The opposite effects of MCT-KDs might reflect the different susceptibility of these brain regions to the aging processes: OML DG is less vulnerable than SM CA1, and the reactivation of ketone bodies uptake and catabolism might occur more efficiently in this region, allowing the exploitation of their peculiar metabolic properties. In GCL-CCx, the results described a new scenario in comparison to that found in the hippocampal formation: 10%MCT-KD induced the early appearance of senescent patterns (decreased Nvs and Nvm; increased V), whereas 20%MCT-KD caused no changes. Since GCL-CCx is more vulnerable to age than DG, and less than CA1, these data further support the hypothesis that MCT-KDs effects in the aging brain critically depend on neuronal vulnerability to age, besides MCT percentage. Regarding PC, it was decided to evaluate only the metabolic effect of the dietetic regimen (20%MCT-KD) characterized by less side effects. KD counteracted age-related decrease in numeric density of SDH-positive mitochondria, and enhanced their energetic efficiency (R was significantly higher in MCT-KD-fed rats vs. all the controls). Since it is well known that Purkinje and dentate gyrus cells are less vulnerable to aging than CA1 neurons, these results corroborate our previous hypothesis. In conclusion, the A) experimental line provides the first evidence that morphological and functional parameters reflecting synaptic plasticity and mitochondrial metabolic competence may be modulated by MCT-KDs in the pre-senescent central nervous system, and that the effects may be heterogeneous in different brain regions. MCT-KDs seem to supply high energy metabolic intermediates and to be beneficial (“anti-aging”) for those neurons that maintain the capability to exploit them. This implies risks but also promising potentialities for the therapeutic use of these diets during aging B) Morphological parameters of synapses and synaptic mitochondria in SM CA1 were investigated in old (26-27 month-old) female Wistar rats following a single trial inhibitory avoidance task. In this memory protocol animals learn to avoid a dark compartment in which they received a mild, inescapable foot-shock. Rats were tested 3 and 6 or 9 hours after the training, divided into good and bad responders according to their performance (retention times above or below 100 s, respectively) and immediately sacrificed. Nvs, S, Sv, Nvm, V, and Vv were evaluated. In the good responder group, the numeric density of synapses and mitochondria was significantly higher and the average mitochondrial volume was significantly smaller 9 hours vs. 6 hours after the training. No significant differences were observed among bad responders. Thus, better performances in passive avoidance memory task are correlated with more efficient plastic remodeling of synaptic contacts and mitochondria in hippocampal CA1. These findings indicate that maintenance of synaptic plastic reactivity during aging is a critical requirement for preserving long-term memory consolidation.

Design of optical networks for advanced applications

Nowadays, computing is migrating from traditional high performance and distributed computing to pervasive and utility computing based on heterogeneous networks and clients. The current trend suggests that future IT services will rely on distributed resources and on fast communication of heterogeneous contents. The success of this new range of services is directly linked to the effectiveness of the infrastructure in delivering them. The communication infrastructure will be the aggregation of different technologies even though the current trend suggests the emergence of single IP based transport service. Optical networking is a key technology to answer the increasing requests for dynamic bandwidth allocation and configure multiple topologies over the same physical layer infrastructure, optical networks today are still “far” from accessible from directly configure and offer network services and need to be enriched with more “user oriented” functionalities. However, current Control Plane architectures only facilitate efficient end-to-end connectivity provisioning and certainly cannot meet future network service requirements, e.g. the coordinated control of resources. The overall objective of this work is to provide the network with the improved usability and accessibility of the services provided by the Optical Network. More precisely, the definition of a service-oriented architecture is the enable technology to allow user applications to gain benefit of advanced services over an underlying dynamic optical layer. The definition of a service oriented networking architecture based on advanced optical network technologies facilitates users and applications access to abstracted levels of information regarding offered advanced network services. This thesis faces the problem to define a Service Oriented Architecture and its relevant building blocks, protocols and languages. In particular, this work has been focused on the use of the SIP protocol as a inter-layers signalling protocol which defines the Session Plane in conjunction with the Network Resource Description language. On the other hand, an advantage optical network must accommodate high data bandwidth with different granularities. Currently, two main technologies are emerging promoting the development of the future optical transport network, Optical Burst and Packet Switching. Both technologies respectively promise to provide all optical burst or packet switching instead of the current circuit switching. However, the electronic domain is still present in the scheduler forwarding and routing decision. Because of the high optics transmission frequency the burst or packet scheduler faces a difficult challenge, consequentially, high performance and time focused design of both memory and forwarding logic is need. This open issue has been faced in this thesis proposing an high efficiently implementation of burst and packet scheduler. The main novelty of the proposed implementation is that the scheduling problem has turned into simple calculation of a min/max function and the function complexity is almost independent of on the traffic conditions.

X-Ray studies of the physics of matter around super-massive black-holes in nearby Seyfert galaxies

Seyfert galaxies are the closest active galactic nuclei. As such, we can use them to test the physical properties of the entire class of objects. To investigate their general properties, I took advantage of different methods of data analysis. In particular I used three different samples of objects, that, despite frequent overlaps, have been chosen to best tackle different topics: the heterogeneous BeppoS AX sample was thought to be optimized to test the average hard X-ray (E above 10 keV) properties of nearby Seyfert galaxies; the X-CfA was thought the be optimized to compare the properties of low-luminosity sources to the ones of higher luminosity and, thus, it was also used to test the emission mechanism models; finally, the XMM–Newton sample was extracted from the X-CfA sample so as to ensure a truly unbiased and well defined sample of objects to define the average properties of Seyfert galaxies. Taking advantage of the broad-band coverage of the BeppoS AX MECS and PDS instruments (between ~2-100 keV), I infer the average X-ray spectral propertiesof nearby Seyfert galaxies and in particular the photon index (<Gamma>~1.8), the high-energy cut-off (~290 keV), and the relative amount of cold reflection (<R>~1.0). Moreover the unified scheme for active galactic nuclei was positively tested. The distribution of isotropic indicators used here (photon index, relative amount of reflection, high-energy cut-off and narrow FeK energy centroid) are similar in type I and type II objects while the absorbing column and the iron line equivalent width significantly differ between the two classes of sources with type II objects displaying larger absorbing columns. Taking advantage of the XMM–Newton and X–CfA samples I also deduced from measurements that 30 to 50% of type II Seyfert galaxies are Compton thick. Confirming previous results, the narrow FeK line is consistent, in Seyfert 2 galaxies, with being produced in the same matter responsible for the observed obscuration. These results support the basic picture of the unified model. Moreover, the presence of a X-ray Baldwin effect in type I sources has been measured using for the first time the 20-100 keV luminosity (EW proportional to L(20-100)^(−0.22±0.05)). This finding suggests that the torus covering factor may be a function of source luminosity, thereby suggesting a refinement of the baseline version of the unifed model itself. Using the BeppoSAX sample, it has been also recorded a possible correlation between the photon index and the amount of cold reflection in both type I and II sources. At a first glance this confirms the thermal Comptonization as the most likely origin of the high energy emission for the active galactic nuclei. This relation, in fact, naturally emerges supposing that the accretion disk penetrates, depending to the accretion rate, the central corona at different depths (Merloni et al. 2006): the higher accreting systems hosting disks down to the last stable orbit while the lower accreting systems hosting truncated disks. On the contrary, the study of the well defined X–C f A sample of Seyfert galaxies has proved that the intrinsic X-ray luminosity of nearby Seyfert galaxies can span values between 10^(38−43) erg s^−1, i.e. covering a huge range of accretion rates. The less efficient systems have been supposed to host ADAF systems without accretion disk. However, the study of the X–CfA sample has also proved the existence of correlations between optical emission lines and X-ray luminosity in the entire range of L_(X) covered by the sample. These relations are similar to the ones obtained if high-L objects are considered. Thus the emission mechanism must be similar in luminous and weak systems. A possible scenario to reconcile these somehow opposite indications is assuming that the ADAF and the two phase mechanism co-exist with different relative importance moving from low-to-high accretion systems (as suggested by the Gamma vs. R relation). The present data require that no abrupt transition between the two regimes is present. As mentioned above, the possible presence of an accretion disk has been tested using samples of nearby Seyfert galaxies. Here, to deeply investigate the flow patterns close to super-massive black-holes, three case study objects for which enough counts statistics is available have been analysed using deep X-ray observations taken with XMM–Newton. The obtained results have shown that the accretion flow can significantly differ between the objects when it is analyzed with the appropriate detail. For instance the accretion disk is well established down to the last stable orbit in a Kerr system for IRAS 13197-1627 where strong light bending effect have been measured. The accretion disk seems to be formed spiraling in the inner ~10-30 gravitational radii in NGC 3783 where time dependent and recursive modulation have been measured both in the continuum emission and in the broad emission line component. Finally, the accretion disk seems to be only weakly detectable in rk 509, with its weak broad emission line component. Finally, blueshifted resonant absorption lines have been detected in all three objects. This seems to demonstrate that, around super-massive black-holes, there is matter which is not confined in the accretion disk and moves along the line of sight with velocities as large as v~0.01-0.4c (whre c is the speed of light). Wether this matter forms winds or blobs is still matter of debate together with the assessment of the real statistical significance of the measured absorption lines. Nonetheless, if confirmed, these phenomena are of outstanding interest because they offer new potential probes for the dynamics of the innermost regions of accretion flows, to tackle the formation of ejecta/jets and to place constraints on the rate of kinetic energy injected by AGNs into the ISM and IGM. Future high energy missions (such as the planned Simbol-X and IXO) will likely allow an exciting step forward in our understanding of the flow dynamics around black holes and the formation of the highest velocity outflows.

Studio di macromolecole associate alla calcificazione in organismi marini

Lo studio riportato in questa tesi ha come scopo l’osservazione e la comprensione dei processi molecolari associati alla deposizione di CaCO3 nei polimorfi di calcite e aragonite nel mollusco gasteropode Haliotis rufescens. In particolare l’attenzione si è focalizzata sullo strato glicoproteico (green layer) che si trova inserito all’interno dell’ipostraco o strato madreperlaceo. Studi precedenti suggeriscono l’ipotesi che il green layer sia una struttura polifunzionale che svolge un ruolo attivo nell’induzione di crescita dei cristalli di carbonato di calcio nella conchiglia. All’analisi microscopica il green layer si presenta come un foglietto trilaminato. Sugli strati esterni è depositata aragonite nella forma prismatica da una parte e sferulitica dall’altra. All’interno è racchiuso un core proteico, formato da glicoproteine e ricco di chitina. Questa struttura tripartita conferisce al guscio calcareo nuove proprietà meccaniche, come la resistenza alle fratture molto maggiore rispetto al minerale naturale. Il green layer è stato trattato in ambiente alcalino, l’unico in grado di solubilizzarlo. È stato ottenuto del materiale proteico che è stato caratterizzato utilizzando SDS-PAGE, colorato con Blu Comassie e all’argento per visualizzarne la componente peptidica. Il green layer è fluorescente, sono state quindi eseguite analisi spettroscopiche sull’estratto peptidico per determinarne le proprietà chimo fisiche (dipendenza dal pH dell’intensità di fluorescenza). Sono stati eseguiti esperimenti di crescita dei cristalli di CaCO3 in ambiente saturo di CaCl2 in assenza e presenza del peptide e in assenza e presenza di Mg++. I cristalli sono stati osservati al microscopio elettronico a scansione (SEM) e al microscopio confocale. Da un punto di vista spettroscopico si osserva che, eccitando l’estratto alcalino del green layer a 280 nm e 295 nm, lunghezze d’onda caratteristiche degli aminoacidi aromatici, si ottiene uno spettro di emissione che presenta una forte banda centrata a 440 nm e una spalla a circa 350 nm, quest’ultima da ascrivere all’emissione tipica di aminoacidi aromatici. L’emissione di fluorescenza dell’estratto dal green layer dipende dal pH per tutte le bande di emissione; tale effetto è particolarmente visibile per lo spettro di emissione a 440 nm, la cui lunghezza d’onda di emissione e l’intensità dipendono dalla ionizzazione di aminoacidi acidi (pKa = 4) e dell’istidina (pKa = 6.5 L’emissione a 440 nm proviene invece da un’eccitazione il cui massimo di eccitazione è centrato a 350 nm, tipica di una struttura policiclica aromatica. Poiché nessun colorante estrinseco viene isolato dalla matrice del green layer a seguito dei vari trattamenti, tale emissione potrebbe derivare da una modificazione posttraduzionale di aminoacidi le cui proprietà spettrali suggeriscono la formazione di un prodotto di dimerizzazione della tirosina: la ditirosina. Questa struttura potrebbe essere la causa del cross-link che rende resistente il green layer alla degradazione da parte di agenti chimici ed enzimatici. La formazione di ditirosina come fenomeno post-traduzionale è stato recentemente acquisito come un fenomeno di origine perossidativa attraverso la formazione di un radicale Tyr ed è stato osservato anche in altri organismi caratterizzati da esoscheletro di tipo chitinoso, come gli insetti del genere Manduca sexta. Gli esperimenti di cristallizzazione in presenza di estratto di green layer ne hanno provato l’influenza sulla nucleazione dei cristalli. In presenza di CaCl2 avviene la precipitazione di CaCO3 nella fase calcitica, ma la conformazione romboedrica tipica della calcite viene modificata dalla presenza del peptide. Inoltre aumenta la densità dei cristalli che si aggregano a formare strutture sferiche di cristalli incastrati tra loro. Aumentando la concentrazione di peptide, le sfere a loro volta si uniscono tra loro a formare strutture geometriche sovrapposte. In presenza di Mg++, la deposizione di CaCO3 avviene in forma aragonitica. Anche in questo caso la morfologia e la densità dei cristalli dipendono dalla concentrazione dello ione e dalla presenza del peptide. È interessante osservare che, in tutti i casi nei quali si sono ottenute strutture cristalline in presenza dell’estratto alcalino del green layer, i cristalli sono fluorescenti, a significare che il peptide è incluso nella struttura cristallina e ne induce la modificazione strutturale come discusso in precedenza. Si osserva inoltre che le proprietà spettroscopiche del peptide in cristallo ed in soluzione sono molto diverse. In cristallo non si ha assorbimento alla più corta delle lunghezze d’onda disponibili in microscopia confocale (405 nm) bensì a 488 nm, con emissione estesa addirittura sino al rosso. Questa è un’indicazione, anche se preliminare, del fatto che la sua struttura in soluzione e in cristallo è diversa da quella in soluzione. In soluzione, per un peptide il cui peso molecolare è stimato tra 3500D (cut-off della membrana da dialisi) e 6500 D, la struttura è, presumibilmente, totalmente random-coil. In cristallo, attraverso l’interazione con gli ioni Ca++, Mg++ e CO3 -- la sua conformazione può cambiare portando, per esempio, ad una sovrapposizione delle strutture aromatiche, in modo da formare sistemi coniugati non covalenti (ring stacking) in grado di assorbire ed emettere luce ad energia più bassa (red shift).

Materiali Ceramici per Edilizia con Funzionalità Fotocatalitica

This thesis wad aimed at the study and application of titanium dioxide photocatalytic activity on ceramic materials. As a matter of fact, photocatalysis is a very promising method to face most of the problems connected with the increasing environmental pollution. Furthermore, titanium dioxide, in its anatase crystallographic phase, is one of the most investigated photocatalytic material and results to be perfectly compatible with silicate body mixes. That goal was pursued by two different strategies: 1. the addition to a body mix used for heavy clay products of several titania powders, with different mean crystallite size, surface area, morphology and anatase/rutile ratio and a titania nanosuspension as well. The titania addition followed two procedures: bulk and spray addition over the ceramic samples surface. Titania was added in two different percentages: 2.5 and 7.5 wt.% in both of the methods. The ceramic samples were then fired at three maximum temperatures: 900, 950 and 1000 °C. Afterwards, the photocatalytic activity of the prepared ceramic samples was evaluated by following the degradation of an organic compound in aqueous medium, under UV radiation. The influence of titania morphological characteristics on the photoactivity of the fired materials was studied by means of XRD and SEM observations. The ceramic samples, sprayed with a slip containing 7.5 wt.% of titania powder and fired at 900 °C, have the best photoactivity, with a complete photo-decomposition of the organic compound. At 1000 °C no sample acted as a photocatalyst due to the anatase-to-rutile phase transformation and to the reaction between titania and calcium and iron oxides in the raw materials. 2. The second one foresaw the synthesis of TiO2-SiO2 solid solutions, using the following stoichiometry: Ti1-xSixO2 where x = 0, 0.1, 0.3 and 0.5 atoms per formula unit (apfu). The mixtures were then fired following two thermal cycles, each with three maximum temperatures. The effect of SiO2 addition into the TiO2 crystal structure and, consequently, on its photocatalytic activity when fired at high temperature, was thoroughly investigated by means of XRD, XPS, FE-SEM, TEM and BET analysis. The photoactivity of the prepared powders was assessed both in gas and liquid phase. Subsequently, the TiO2-SiO2 solid solutions, previously fired at 900 °C, were sprayed over the ceramic samples surface in the percentage of 7.5 wt.%. The prepared ceramic samples were fired at 900 and 1000 °C. The photocatalytic activity of the ceramic samples was evaluated in liquid phase. Unfortunately, that samples did not show any appreciable photoactivity. In fact, samples fired at 900 °C showed a pretty low photoactivity, while the one fired at 1000 °C showed no photoactivity at all. This was explained by the excessive coarsening of titania particles. To summarise, titania particle size, more than its crystalline phase, seems to have a relevant role in the photocatalytic activity of the ceramic samples.

Numerical and analytical vibro-acoustic modelling of porous materials: the Cell Method for poroelasticity and the case of inclusions

Porous materials are widely used in many fields of industrial applications, to achieve the requirements of noise reduction, that nowadays derive from strict regulations. The modeling of porous materials is still a problematic issue. Numerical simulations are often problematic in case of real complex geometries, especially in terms of computational times and convergence. At the same time, analytical models, even if partly limited by restrictive simplificative hypotheses, represent a powerful instrument to capture quickly the physics of the problem and general trends. In this context, a recently developed numerical method, called the Cell Method, is described, is presented in the case of the Biot's theory and applied for representative cases. The peculiarity of the Cell Method is that it allows for a direct algebraic and geometrical discretization of the field equations, without any reduction to a weak integral form. Then, the second part of the thesis presents the case of interaction between two poroelastic materials under the context of double porosity. The idea of using periodically repeated inclusions of a second porous material into a layer composed by an original material is described. In particular, the problem is addressed considering the efficiency of the analytical method. A analytical procedure for the simulation of heterogeneous layers based is described and validated considering both conditions of absorption and transmission; a comparison with the available numerical methods is performed. ---------------- I materiali porosi sono ampiamente utilizzati per diverse applicazioni industriali, al fine di raggiungere gli obiettivi di riduzione del rumore, che sono resi impegnativi da norme al giorno d'oggi sempre più stringenti. La modellazione dei materiali porori per applicazioni vibro-acustiche rapprensenta un aspetto di una certa complessità. Le simulazioni numeriche sono spesso problematiche quando siano coinvolte geometrie di pezzi reali, in particolare riguardo i tempi computazionali e la convergenza. Allo stesso tempo, i modelli analitici, anche se parzialmente limitati a causa di ipotesi semplificative che ne restringono l'ambito di utilizzo, rappresentano uno strumento molto utile per comprendere rapidamente la fisica del problema e individuare tendenze generali. In questo contesto, un metodo numerico recentemente sviluppato, il Metodo delle Celle, viene descritto, implementato nel caso della teoria di Biot per la poroelasticità e applicato a casi rappresentativi. La peculiarità del Metodo delle Celle consiste nella discretizzazione diretta algebrica e geometrica delle equazioni di campo, senza alcuna riduzione a forme integrali deboli. Successivamente, nella seconda parte della tesi viene presentato il caso delle interazioni tra due materiali poroelastici a contatto, nel contesto dei materiali a doppia porosità. Viene descritta l'idea di utilizzare inclusioni periodicamente ripetute di un secondo materiale poroso all'interno di un layer a sua volta poroso. In particolare, il problema è studiando il metodo analitico e la sua efficienza. Una procedura analitica per il calcolo di strati eterogenei di materiale viene descritta e validata considerando sia condizioni di assorbimento, sia di trasmissione; viene effettuata una comparazione con i metodi numerici a disposizione.