Effective properties evaluation for smart composite materials

The purpose of this article is to present a method which consists in the development of unit cell numerical models for smart composite materials with piezoelectric fibers made of PZT embedded in a non-piezoelectric matrix (epoxy resin). This method evaluates a globally homogeneous medium equivalent to the original composite, using a representative volume element (RVE). The suitable boundary conditions allow the simulation of all modes of the overall deformation arising from any arbitrary combination of mechanical and electrical loading. In the first instance, the unit cell is applied to predict the effective material coefficients of the transversely isotropic piezoelectric composite with circular cross section fibers. The numerical results are compared to other methods reported in the literature and also to results previously published, in order to evaluate the method proposal. In the second step, the method is applied to calculate the equivalent properties for smart composite materials with square cross section fibers. Results of comparison between different combinations of circular and square fiber geometries, observing the influence of the boundary conditions and arrangements are presented.

Mass transport in polymers

The study of mass transport in polymeric membranes has grown in importance due to its potential application in many processes such as separation of gases and vapors, packaging, controlled drug release. The diffusion of a low molecular weight species in a polymer is often accompanied by other phenomena like swelling, reactions, stresses, that have not been investigated in all their aspects yet. Furthermore, novel materials have been developed that include inorganic fillers, reactive functional groups or ions, that make the scenery even more complicated. The present work focused on the experimental study of systems where the diffusion is accompanied by other processes; suitable models were also developed to describe the particular circumstances in order to understand the underlying concepts and be able to design the performances of the material. The effect of solvent-induced deformation in polymeric films during sorption processes was studied since the dilation, especially in constrained membranes, can cause the development of stresses and therefore early failures of the material. The bending beam technique was used to test the effects of the dilation and the stress induced in the polymer by penetrant diffusion. A model based on the laminate theory was developed that accounts for the swelling and is able to predict the stress that raise in the material. The addition of inorganic fillers affects the transport properties of polymeric films. Mixed matrix membranes based on fluorinated, high free volume matrices show attractive performances for separation purposes but there is a need for deeper investigation of the selectivity properties towards gases and vapors. A new procedure based on the NELF model was tested on the experimental data; it allows to predict solubility of every penetrant on the basis of data for one vapor. The method has proved to be useful also for the determination of the diffusion coefficient and for an estimation of the permeability in the composite materials. Oxygen scavenging systems can overcome lack of barrier properties in common polymers that forbids their application in sensitive applications as food packaging. The final goal of obtaining a membrane almost impermeable to oxygen leads to experimental times out of reach. Hence, a simple model was developed in order to describe the transport of oxygen in a membrane with also reactive groups and analyze the experimental data collected on SBS copolymers that show attractive scavenging capacity. Furthermore, a model for predicting the oxygen barrier behavior of a film formed as a blend of OSP in a common packaging material was built, considering particles capable of reactions with oxygen embedded in a non-reactive matrix. Perfluorosulphonic acid ionomers (PFSI) are capturing attention due to a high thermal and chemical resistance coupled with very peculiar transport properties, that make them appropriate to be used in fuel cells. The possible effect of different formation procedure was studied together with the swelling due to water sorption since both water uptake and dilation can dramatically affect the fuel cells performances. The water diffusion and sorption was studied with a FTIR-ATR spectrometer that can give deeper information on the bonds between water molecules and the sulphonic hydrophilic groups and, therefore, on the microstructure of the hydrated ionomer.

Gleichmäßig dünne Basen zweiter Ordnung

Eine Menge B nicht negativer ganzer Zahlen heißt Basis h-ter Ordnung, wenn jede nicht negative ganze Zahl Summe von höchstens h Elementen von B ist. Eine der großen Fragen der additiven Zahlentheorie ist die nach der effektivsten Basis h-ter Ordnung für ein gegebenes h>=2. Im Fokus des Interesses steht dabei der immer noch offene Fall h=2. Bezeichnet B(x) die Anzahl der Elemente b aus B mit 0= af(x), wobei f die Wurzelfunktion bezeichne. Andererseits gibt es Basen B zweiter Ordnung mit B(x) <= cf(x). Daher kann man den Limes superior S(B), den Limes inferior s(B) sowie im Falle der Existenz den Limes d(B) des Quotienten B(x) / f(x) als Dichtefunktionen von Basen zweiter Ordnung betrachten. J. W. S. Cassels konstruierte 1957 eine Basis C zweiter Ordnung mit d(C)=5,196…. G. Hofmeister gab 2001 eine Basis H zweiter Ordnung mit asymptotischer Wurzeldichte d(H)=4,638… an. In der vorliegenden Arbeit wird eine Basis S zweiter Ordnung mit asymptotischer Wurzeldichte d(S)=3,464… konstruiert. Darüber hinaus wird für die von J. W. S. Cassels, für die von G. Hofmeister und für die in dieser Arbeit verwendete Klasse von Basen zweiter Ordnung gezeigt, dass die asymptotische Wurzeldichte innerhalb der jeweiligen Klasse nicht mehr zu verbessern ist. Bisher war die Frage nach möglichen Verbesserungen innerhalb der jeweiligen Konstruktionsprinzipien offen geblieben.

Sensitivity analysis of a parabolic-elliptic problem

We consider the heat flux through a domain with subregions in which the thermal capacity approaches zero. In these subregions the parabolic heat equation degenerates to an elliptic one. We show the well-posedness of such parabolic-elliptic differential equations for general non-negative L-infinity-capacities and study the continuity of the solutions with respect to the capacity, thus giving a rigorous justification for modeling a small thermal capacity by setting it to zero. We also characterize weak directional derivatives of the temperature with respect to capacity as solutions of related parabolic-elliptic problems.

Application of innovative methods of source apportionment in air contamination assessment

In this work, new tools in atmospheric pollutant sampling and analysis were applied in order to go deeper in source apportionment study. The project was developed mainly by the study of atmospheric emission sources in a suburban area influenced by a municipal solid waste incinerator (MSWI), a medium-sized coastal tourist town and a motorway. Two main research lines were followed. For what concerns the first line, the potentiality of the use of PM samplers coupled with a wind select sensor was assessed. Results showed that they may be a valid support in source apportionment studies. However, meteorological and territorial conditions could strongly affect the results. Moreover, new markers were investigated, particularly focusing on the processes of biomass burning. OC revealed a good biomass combustion process indicator, as well as all determined organic compounds. Among metals, lead and aluminium are well related to the biomass combustion. Surprisingly PM was not enriched of potassium during bonfire event. The second research line consists on the application of Positive Matrix factorization (PMF), a new statistical tool in data analysis. This new technique was applied to datasets which refer to different time resolution data. PMF application to atmospheric deposition fluxes identified six main sources affecting the area. The incinerator’s relative contribution seemed to be negligible. PMF analysis was then applied to PM2.5 collected with samplers coupled with a wind select sensor. The higher number of determined environmental indicators allowed to obtain more detailed results on the sources affecting the area. Vehicular traffic revealed the source of greatest concern for the study area. Also in this case, incinerator’s relative contribution seemed to be negligible. Finally, the application of PMF analysis to hourly aerosol data demonstrated that the higher the temporal resolution of the data was, the more the source profiles were close to the real one.

Nanoscopic studies of conjugated polymer blends by (electric) scanning probe microscopy

Conjugated polymers and conjugated polymer blends have attracted great interest due to their potential applications in biosensors and organic electronics. The sub-100 nm morphology of these materials is known to heavily influence their electromechanical properties and the performance of devices they are part of. Electromechanical properties include charge injection, transport, recombination, and trapping, the phase behavior and the mechanical robustness of polymers and blends. Electrical scanning probe microscopy techniques are ideal tools to measure simultaneously electric (conductivity and surface potential) and dielectric (dielectric constant) properties, surface morphology, and mechanical properties of thin films of conjugated polymers and their blends.rnIn this thesis, I first present a combined topography, Kelvin probe force microscopy (KPFM), and scanning conductive torsion mode microscopy (SCTMM) study on a gold/polystyrene model system. This system is a mimic for conjugated polymer blends where conductive domains (gold nanoparticles) are embedded in a non-conductive matrix (polystyrene film), like for polypyrrole:polystyrene sulfonate (PPy:PSS), and poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS). I controlled the nanoscale morphology of the model by varying the distribution of gold nanoparticles in the polystyrene films. I studied the influence of different morphologies on the surface potential measured by KPFM and on the conductivity measured by SCTMM. By the knowledge I gained from analyzing the data of the model system I was able to predict the nanostructure of a homemade PPy:PSS blend.rnThe morphologic, electric, and dielectric properties of water based conjugated polymer blends, e.g. PPy:PSS or PEDOT:PSS, are known to be influenced by their water content. These properties also influence the macroscopic performance when the polymer blends are employed in a device. In the second part I therefore present an in situ humidity-dependence study on PPy:PSS films spin-coated and drop-coated on hydrophobic highly ordered pyrolytic graphite substrates by KPFM. I additionally used a particular KPFM mode that detects the second harmonic electrostatic force. With this, I obtained images of dielectric constants of samples. Upon increasing relative humidity, the surface morphology and composition of the films changed. I also observed that relative humidity affected thermally unannealed and annealed PPy:PSS films differently. rnThe conductivity of a conjugated polymer may change once it is embedded in a non-conductive matrix, like for PPy embedded in PSS. To measure the conductivity of single conjugated polymer particles, in the third part, I present a direct method based on microscopic four-point probes. I started with metal core-shell and metal bulk particles as models, and measured their conductivities. The study could be extended to measure conductivity of single PPy particles (core-shell and bulk) with a diameter of a few micrometers.

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.

Quantum biology. Simulazioni di trasferimento di energia in una struttura dimerica

La quantum biology (QB) è un campo di ricerca emergente che cerca di affronta- re fenomeni quantistici non triviali all’interno dei contesti biologici dotandosi di dati sperimentali di esplorazioni teoriche e tecniche numeriche. I sistemi biologici sono per definizione sistemi aperti, caldi,umidi e rumorosi, e queste condizioni sono per loro imprenscindibili; si pensa sia un sistema soggetto ad una veloce decoerenza che sopprime ogni dinamica quantistica controllata. La QB, tramite i principi di noise assisted transport e di antenna fononica sostiene che la presenza di un adeguato livello di rumore ambientale aumenti l’efficienza di un network di trasporto,inoltre se all’interno dello spettro ambientale vi sono specifici modi vibrazionali persistenti si hanno effetti di risonanza che rigenerano la coerenza quantistica. L’interazione ambiente-sistema è di tipo non Markoviano,non perturbativo e di forte non equi- librio, ed il rumore non è trattato come tradizionale rumore bianco. La tecnica numerica che per prima ha predetto la rigenerazione della coerenza all’interno di questi network proteici è stato il TEBD, Time Evolving Block Decimation, uno schema numerico che permette di simulare sistemi 1-D a molti corpi, caratterizzati da interazioni di primi vicini e leggermente entangled. Tramite gli algoritmi numerici di Orthopol l’hamiltoniana spin-bosone viene proiettata su una catena discreta 1-D, tenendo conto degli effetti di interazione ambiente-sistema contenuti nello spettro(il quale determina la dinamica del sistema).Infine si esegue l’evoluzione dello stato.

T2 mapping in the knee after microfracture at 3.0 T: correlation of global T2 values and clinical outcome - preliminary results

OBJECTIVE: The aim of our study was to correlate global T2 values of microfracture repair tissue (RT) with clinical outcome in the knee joint. METHODS: We assessed 24 patients treated with microfracture in the knee joint. Magnetic resonance (MR) examinations were performed on a 3T MR unit, T2 relaxation times were obtained with a multi-echo spin-echo technique. T2 maps were obtained using a pixel wise, mono-exponential non-negative least squares fit analysis. Slices covering the cartilage RT were selected and region of interest analysis was done. An individual T2 index was calculated with global mean T2 of the RT and global mean T2 of normal, hyaline cartilage. The Lysholm score and the International Knee Documentation Committee (IKDC) knee evaluation forms were used for the assessment of clinical outcome. Bivariate correlation analysis and a paired, two tailed t test were used for statistics. RESULTS: Global T2 values of the RT [mean 49.8ms, standards deviation (SD) 7.5] differed significantly (P<0.001) from global T2 values of normal, hyaline cartilage (mean 58.5ms, SD 7.0). The T2 index ranged from 61.3 to 101.5. We found the T2 index to correlate with outcome of the Lysholm score (r(s)=0.641, P<0.001) and the IKDC subjective knee evaluation form (r(s)=0.549, P=0.005), whereas there was no correlation with the IKDC knee form (r(s)=-0.284, P=0.179). CONCLUSION: These findings indicate that T2 mapping is sensitive to assess RT function and provides additional information to morphologic MRI in the monitoring of microfracture.

Low rank subspace clustering (LRSC)

We consider the problem of fitting a union of subspaces to a collection of data points drawn from one or more subspaces and corrupted by noise and/or gross errors. We pose this problem as a non-convex optimization problem, where the goal is to decompose the corrupted data matrix as the sum of a clean and self-expressive dictionary plus a matrix of noise and/or gross errors. By self-expressive we mean a dictionary whose atoms can be expressed as linear combinations of themselves with low-rank coefficients. In the case of noisy data, our key contribution is to show that this non-convex matrix decomposition problem can be solved in closed form from the SVD of the noisy data matrix. The solution involves a novel polynomial thresholding operator on the singular values of the data matrix, which requires minimal shrinkage. For one subspace, a particular case of our framework leads to classical PCA, which requires no shrinkage. For multiple subspaces, the low-rank coefficients obtained by our framework can be used to construct a data affinity matrix from which the clustering of the data according to the subspaces can be obtained by spectral clustering. In the case of data corrupted by gross errors, we solve the problem using an alternating minimization approach, which combines our polynomial thresholding operator with the more traditional shrinkage-thresholding operator. Experiments on motion segmentation and face clustering show that our framework performs on par with state-of-the-art techniques at a reduced computational cost.

Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

An empirical model to estimate the demand for primary care in urban settings

Objective. To measure the demand for primary care and its associated factors by building and estimating a demand model of primary care in urban settings.^ Data source. Secondary data from 2005 California Health Interview Survey (CHIS 2005), a population-based random-digit dial telephone survey, conducted by the UCLA Center for Health Policy Research in collaboration with the California Department of Health Services, and the Public Health Institute between July 2005 and April 2006.^ Study design. A literature review was done to specify the demand model by identifying relevant predictors and indicators. CHIS 2005 data was utilized for demand estimation.^ Analytical methods. The probit regression was used to estimate the use/non-use equation and the negative binomial regression was applied to the utilization equation with the non-negative integer dependent variable.^ Results. The model included two equations in which the use/non-use equation explained the probability of making a doctor visit in the past twelve months, and the utilization equation estimated the demand for primary conditional on at least one visit. Among independent variables, wage rate and income did not affect the primary care demand whereas age had a negative effect on demand. People with college and graduate educational level were associated with 1.03 (p < 0.05) and 1.58 (p < 0.01) more visits, respectively, compared to those with no formal education. Insurance was significantly and positively related to the demand for primary care (p < 0.01). Need for care variables exhibited positive effects on demand (p < 0.01). Existence of chronic disease was associated with 0.63 more visits, disability status was associated with 1.05 more visits, and people with poor health status had 4.24 more visits than those with excellent health status. ^ Conclusions. The average probability of visiting doctors in the past twelve months was 85% and the average number of visits was 3.45. The study emphasized the importance of need variables in explaining healthcare utilization, as well as the impact of insurance, employment and education on demand. The two-equation model of decision-making, and the probit and negative binomial regression methods, was a useful approach to demand estimation for primary care in urban settings.^

SERBA: a B.I.E. program with linear elements for 2-D elastostatics analysis

The great developments that have occurred during the last few years in the finite element method and its applications has kept hidden other options for computation. The boundary integral element method now appears as a valid alternative and, in certain cases, has significant advantages. This method deals only with the boundary of the domain, while the F.E.M. analyses the whole domain. This has the following advantages: the dimensions of the problem to be studied are reduced by one, consequently simplifying the system of equations and preparation of input data. It is also possible to analyse infinite domains without discretization errors. These simplifications have the drawbacks of having to solve a full and non-symmetric matrix and some difficulties are incurred in the imposition of boundary conditions when complicated variations of the function over the boundary are assumed. In this paper a practical treatment of these problems, in particular boundary conditions imposition, has been carried out using the computer program shown below. Program SERBA solves general elastostatics problems in 2-dimensional continua using the boundary integral equation method. The boundary of the domain is discretized by line or elements over which the functions are assumed to vary linearly. Data (stresses and/or displacements) are introduced in the local co-ordinate system (element co-ordinates). Resulting stresses are obtained in local co-ordinates and displacements in a general system. The program has been written in Fortran ASCII and implemented on a 1108 Univac Computer. For 100 elements the core requirements are about 40 Kwords. Also available is a Fortran IV version (3 segments)implemented on a 21 MX Hewlett-Packard computer,using 15 Kwords.

Mathematical analysis of a model of chemotaxis arising from morphogenesis

We consider non-negative solution of a chemotaxis system with non constant chemotaxis sensitivity function X. This system appears as a limit case of a model formorphogenesis proposed by Bollenbach et al. (Phys. Rev. E. 75, 2007).Under suitable boundary conditions, modeling the presence of a morphogen source at x=0, we prove the existence of a global and bounded weak solution using an approximation by problems where diffusion is introduced in the ordinary differential equation. Moreover,we prove the convergence of the solution to the unique steady state provided that ? is small and ? is large enough. Numerical simulations both illustrate these results and give rise to further conjectures on the solution behavior that go beyond the rigorously proved statements.

Reduction of critical mass in a chemotaxis system by external application of a chemoattractant

In this paper we study non-negative radially symmetric solutions of a parabolic-elliptic Keller-Segel system. The system describes the chemotactic movement of cells under the additional circumstance that an external application of a chemo attractant at a distinguished point is introduced.