Trasmission and Reflection (ATR)Far-Infrared Spectroscopy Applied in the Analysis of Cultural Heritage Materials

FIR spectroscopy is an alternative way of collecting spectra of many inorganic pigments and corrosion products found on art objects, which is not normally observed in the MIR region. Most FIR spectra are traditionally collected in transmission mode but as a real novelty it is now also possible to record FIR spectra in ATR (Attenuated Total Reflectance) mode. In FIR transmission we employ polyethylene (PE) for preparation of pellets by embedding the sample in PE. Unfortunately, the preparation requires heating of the PE in order to produces at transparent pellet. This will affect compounds with low melting points, especially those with structurally incorporated water. Another option in FIR transmission is the use of thin films. We test the use of polyethylene thin film (PETF), both commercial and laboratory-made PETF. ATR collection of samples is possible in both the MIR and FIR region on solid, powdery or liquid samples. Changing from the MIR to the FIR region is easy as it simply requires the change of detector and beamsplitter (which can be performed within a few minutes). No preparation of the sample is necessary, which is a huge advantage over the PE transmission method. The most obvious difference, when comparing transmission with ATR, is the distortion of band shape (which appears asymmetrical in the lower wavenumber region) and intensity differences. However, the biggest difference can be the shift of strong absorbing bands moving to lower wavenumbers in ATR mode. The sometimes huge band shift necessitates the collection of standard library spectra in both FIR transmission and ATR modes, provided these two methods of collecting are to be employed for analyses of unknown samples. Standard samples of 150 pigment and corrosion compounds are thus collected in both FIR transmission and ATR mode in order to build up a digital library of spectra for comparison with unknown samples. XRD, XRF and Raman spectroscopy assists us in confirming the purity or impurity of our standard samples. 24 didactic test tables, with known pigment and binder painted on the surface of a limestone tablet, are used for testing the established library and different ways of collecting in ATR and transmission mode. In ATR, micro samples are scratched from the surface and examined in both the MIR and FIR region. Additionally, direct surface contact of the didactic tablets with the ATR crystal are tested together with water enhanced surface contact. In FIR transmission we compare the powder from our test tablet on the laboratory PETF and embedded in PE. We also compare the PE pellets collected using a 4x beam condenser, focusing the IR beam area from 8 mm to 2 mm. A few samples collected from a mural painting in a Nepalese temple, corrosion products collected from archaeological Chinese bronze objects and samples from a mural paintings in an Italian abbey, are examined by ATR or transmission spectroscopy.

Refined Gelfand models for some finite complex reflection groups

In 'Involutory reflection groups and their models' (F. Caselli, 2010), a uniform Gelfand model is constructed for all complex reflection groups G(r,p,n) satisfying GCD(p,n)=1,2 and for all their quotients modulo a scalar subgroup. The present work provides a refinement for this model. The final decomposition obtained is compatible with the Robinson-Schensted generalized correspondence.

Spectrum reconstruction from a scattering measurement using the adjoint Boltzmann transport equation for photons

Quality control of medical radiological systems is of fundamental importance, and requires efficient methods for accurately determine the X-ray source spectrum. Straightforward measurements of X-ray spectra in standard operating require the limitation of the high photon flux, and therefore the measure has to be performed in a laboratory. However, the optimal quality control requires frequent in situ measurements which can be only performed using a portable system. To reduce the photon flux by 3 magnitude orders an indirect technique based on the scattering of the X-ray source beam by a solid target is used. The measured spectrum presents a lack of information because of transport and detection effects. The solution is then unfolded by solving the matrix equation that represents formally the scattering problem. However, the algebraic system is ill-conditioned and, therefore, it is not possible to obtain a satisfactory solution. Special strategies are necessary to circumvent the ill-conditioning. Numerous attempts have been done to solve this problem by using purely mathematical methods. In this thesis, a more physical point of view is adopted. The proposed method uses both the forward and the adjoint solutions of the Boltzmann transport equation to generate a better conditioned linear algebraic system. The procedure has been tested first on numerical experiments, giving excellent results. Then, the method has been verified with experimental measurements performed at the Operational Unit of Health Physics of the University of Bologna. The reconstructed spectra have been compared with the ones obtained with straightforward measurements, showing very good agreement.

Master Equation: Biological Applications and Thermodynamic Description

It is well known that many realistic mathematical models of biological systems, such as cell growth, cellular development and differentiation, gene expression, gene regulatory networks, enzyme cascades, synaptic plasticity, aging and population growth need to include stochasticity. These systems are not isolated, but rather subject to intrinsic and extrinsic fluctuations, which leads to a quasi equilibrium state (homeostasis). The natural framework is provided by Markov processes and the Master equation (ME) describes the temporal evolution of the probability of each state, specified by the number of units of each species. The ME is a relevant tool for modeling realistic biological systems and allow also to explore the behavior of open systems. These systems may exhibit not only the classical thermodynamic equilibrium states but also the nonequilibrium steady states (NESS). This thesis deals with biological problems that can be treat with the Master equation and also with its thermodynamic consequences. It is organized into six chapters with four new scientific works, which are grouped in two parts: (1) Biological applications of the Master equation: deals with the stochastic properties of a toggle switch, involving a protein compound and a miRNA cluster, known to control the eukaryotic cell cycle and possibly involved in oncogenesis and with the propose of a one parameter family of master equations for the evolution of a population having the logistic equation as mean field limit. (2) Nonequilibrium thermodynamics in terms of the Master equation: where we study the dynamical role of chemical fluxes that characterize the NESS of a chemical network and we propose a one parameter parametrization of BCM learning, that was originally proposed to describe plasticity processes, to study the differences between systems in DB and NESS.