High quality colloidal crystals with different architectures and their optical properties

In this present work high quality PMMA opals with different sphere sizes, silica opals from large size spheres, multilayer opals, and inverse opals were fabricated. Highly monodisperse PMMA spheres were synthesized by surfactant-free emulsion polymerization (polydispersity ~2%). Large-area and well-ordered PMMA crystalline films with a homogenous thickness were produced by the vertical deposition method using a drawing device. Optical experiments have confirmed the high quality of these PMMA photonic crystals, e.g., well resolved high-energy bands of the transmission and reflectance spectra of the opaline films were observed. For fabrication of high quality opaline photonic crystals from large silica spheres (diameter of 890 nm), self-assembled in patterned Si-substrates a novel technique has been developed, in which the crystallization was performed by using a drawing apparatus in combination with stirring. The achievements comprise a spatial selectivity of opal crystallization without special treatment of the wafer surface, the opal lattice was found to match the pattern precisely in width as well as depth, particularly an absence of cracks within the size of the trenches, and finally a good three-dimensional order of the opal lattice even in trenches with a complex confined geometry. Multilayer opals from opaline films with different sphere sizes or different materials were produced by sequential crystallization procedure. Studies of the transmission in triple-layer hetero-opal revealed that its optical properties cannot only be considered as the linear superposition of two independent photonic bandgaps. The remarkable interface effect is the narrowing of the transmission minima. Large-area, high-quality, and robust photonic opal replicas from silicate-based inorganic-organic hybrid polymers (ORMOCER® s) were prepared by using the template-directed method, in which a high quality PMMA opal template was infiltrated with a neat inorganic-organic ORMOCER® oligomer, which can be photopolymerized within the opaline voids leading to a fully-developed replica structure with a filling factor of nearly 100%. This opal replica is structurally homogeneous, thermally and mechanically stable and the large scale (cm2 size) replica films can be handled easily as free films with a pair of tweezers.

Characterization of geothermal reservoirs’ parameters by inverse problem resolution and geostatistical simulations

BTES (borehole thermal energy storage)systems exchange thermal energy by conduction with the surrounding ground through borehole materials. The spatial variability of the geological properties and the space-time variability of hydrogeological conditions affect the real power rate of heat exchangers and, consequently, the amount of energy extracted from / injected into the ground. For this reason, it is not an easy task to identify the underground thermal properties to use when designing. At the current state of technology, Thermal Response Test (TRT) is the in situ test for the characterization of ground thermal properties with the higher degree of accuracy, but it doesn’t fully solve the problem of characterizing the thermal properties of a shallow geothermal reservoir, simply because it characterizes only the neighborhood of the heat exchanger at hand and only for the test duration. Different analytical and numerical models exist for the characterization of shallow geothermal reservoir, but they are still inadequate and not exhaustive: more sophisticated models must be taken into account and a geostatistical approach is needed to tackle natural variability and estimates uncertainty. The approach adopted for reservoir characterization is the “inverse problem”, typical of oil&gas field analysis. Similarly, we create different realizations of thermal properties by direct sequential simulation and we find the best one fitting real production data (fluid temperature along time). The software used to develop heat production simulation is FEFLOW 5.4 (Finite Element subsurface FLOW system). A geostatistical reservoir model has been set up based on literature thermal properties data and spatial variability hypotheses, and a real TRT has been tested. Then we analyzed and used as well two other codes (SA-Geotherm and FV-Geotherm) which are two implementation of the same numerical model of FEFLOW (Al-Khoury model).

Inverse problems in classical and quantum physics

The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A promising result is that one can qualitatively reconstruct the conductivity inside the cross-section of a human chest. Even though the human volunteer is neither two-dimensional nor circular, such reconstructions can be useful in medical applications: monitoring for lung problems such as accumulating fluid or a collapsed lung and noninvasive monitoring of heart function and blood flow.

Inverse size exclusion chromatography (ISEC)

In this work, an improved protocol for inverse size-exclusion chromatography (ISEC) was established to assess important pore structural data of porous silicas as stationary phases in packed chromatographic columns. After the validity of the values generated by ISEC was checked by comparison with data obtained from traditional methods like nitrogen sorption at 77 K (Study A), the method could be successfully employed as valuable tool at the development of bonded poly(methacrylate)-coated silicas, while traditional methods generate partially incorrect pore structural information (Study B). Study A: Different mesoporous silicas were converted by a pseudomorphical transition into ordered MCM-41-type silica while maintaining the particle-size and -shape. The essential parameters like specific surface area, average pore diameter and specific pore volume, the pore connectivity from ISEC remained nearly the same which was reflected by the same course of the theoretical plate height vs. linear velocity curves. Study B: In the development of bonded poly(methacrylate)-coated silicas for the reversed phase separation of biopolymers, ISEC was the only method to generate valid pore structural information of the polymer-coated materials. Synthesis procedures were developed to obtain reproducibly covalently bonded poly(methacrylate) coatings with good thermal stability on different base materials, employing as well particulate and monolithic materials.

Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem

In various imaging problems the task is to use the Cauchy data of the solutions to an elliptic boundary value problem to reconstruct the coefficients of the corresponding partial differential equation. Often the examined object has known background properties but is contaminated by inhomogeneities that cause perturbations of the coefficient functions. The factorization method of Kirsch provides a tool for locating such inclusions. In this paper, the factorization technique is studied in the framework of coercive elliptic partial differential equations of the divergence type: Earlier it has been demonstrated that the factorization algorithm can reconstruct the support of a strictly positive (or negative) definite perturbation of the leading order coefficient, or if that remains unperturbed, the support of a strictly positive (or negative) perturbation of the zeroth order coefficient. In this work we show that these two types of inhomogeneities can, in fact, be located simultaneously. Unlike in the earlier articles on the factorization method, our inclusions may have disconnected complements and we also weaken some other a priori assumptions of the method. Our theoretical findings are complemented by two-dimensional numerical experiments that are presented in the framework of the diffusion approximation of optical tomography.

Investigation of the nuclear matter density distributions of the exotic 12 Be, 14 Be and 8 B nuclei by elastic proton scattering in inverse kinematics

The proton-nucleus elastic scattering at intermediate energies is a well-established method for the investigation of the nuclear matter distribution in stable nuclei and was recently applied also for the investigation of radioactive nuclei using the method of inverse kinematics. In the current experiment, the differential cross sections for proton elastic scattering on the isotopes $^{7,9,10,11,12,14}$Be and $^8$B were measured. The experiment was performed using the fragment separator at GSI, Darmstadt to produce the radioactive beams. The main part of the experimental setup was the time projection ionization chamber IKAR which was simultaneously used as hydrogen target and a detector for the recoil protons. Auxiliary detectors for projectile tracking and isotope identification were also installed. As results from the experiment, the absolute differential cross sections d$sigma$/d$t$ as a function of the four momentum transfer $t$ were obtained. In this work the differential cross sections for elastic p-$^{12}$Be, p-$^{14}$Be and p-$^{8}$B scattering at low $t$ ($t leq$~0.05~(GeV/c)$^2$) are presented. The measured cross sections were analyzed within the Glauber multiple-scattering theory using different density parameterizations, and the nuclear matter density distributions and radii of the investigated isotopes were determined. The analysis of the differential cross section for the isotope $^{14}$Be shows that a good description of the experimental data is obtained when density distributions consisting of separate core and halo components are used. The determined {it rms} matter radius is $3.11 pm 0.04 pm 0.13$~fm. In the case of the $^{12}$Be nucleus the results showed an extended matter distribution as well. For this nucleus a matter radius of $2.82 pm 0.03 pm 0.12$~fm was determined. An interesting result is that the free $^{12}$Be nucleus behaves differently from the core of $^{14}$Be and is much more extended than it. The data were also compared with theoretical densities calculated within the FMD and the few-body models. In the case of $^{14}$Be, the calculated cross sections describe the experimental data well while, in the case of $^{12}$Be there are discrepancies in the region of high momentum transfer. Preliminary experimental results for the isotope $^8$B are also presented. An extended matter distribution was obtained (though much more compact as compared to the neutron halos). A proton halo structure was observed for the first time with the proton elastic scattering method. The deduced matter radius is $2.60pm 0.02pm 0.26$~fm. The data were compared with microscopic calculations in the frame of the FMD model and reasonable agreement was observed. The results obtained in the present analysis are in most cases consistent with the previous experimental studies of the same isotopes with different experimental methods (total interaction and reaction cross section measurements, momentum distribution measurements). For future investigation of the structure of exotic nuclei a universal detector system EXL is being developed. It will be installed at the NESR at the future FAIR facility where higher intensity beams of radioactive ions are expected. The usage of storage ring techniques provides high luminosity and low background experimental conditions. Results from the feasibility studies of the EXL detector setup, performed at the present ESR storage ring, are presented.

Inverse Static Analysis of Massive Parallel Arrays of Three-State Actuators via Artificial Intelligence

Massive parallel robots (MPRs) driven by discrete actuators are force regulated robots that undergo continuous motions despite being commanded through a finite number of states only. Designing a real-time control of such systems requires fast and efficient methods for solving their inverse static analysis (ISA), which is a challenging problem and the subject of this thesis. In particular, five Artificial intelligence methods are proposed to investigate the on-line computation and the generalization error of ISA problem of a class of MPRs featuring three-state force actuators and one degree of revolute motion.

Direct and inverse transient eddy current problems

Die vorliegende Arbeit behandelt Vorwärts- sowie Rückwärtstheorie transienter Wirbelstromprobleme. Transiente Anregungsströme induzieren elektromagnetische Felder, welche sogenannte Wirbelströme in leitfähigen Objekten erzeugen. Im Falle von sich langsam ändernden Feldern kann diese Wechselwirkung durch die Wirbelstromgleichung, einer Approximation an die Maxwell-Gleichungen, beschrieben werden. Diese ist eine lineare partielle Differentialgleichung mit nicht-glatten Koeffizientenfunktionen von gemischt parabolisch-elliptischem Typ. Das Vorwärtsproblem besteht darin, zu gegebener Anregung sowie den umgebungsbeschreibenden Koeffizientenfunktionen das elektrische Feld als distributionelle Lösung der Gleichung zu bestimmen. Umgekehrt können die Felder mit Messspulen gemessen werden. Das Ziel des Rückwärtsproblems ist es, aus diesen Messungen Informationen über leitfähige Objekte, also über die Koeffizientenfunktion, die diese beschreibt, zu gewinnen. In dieser Arbeit wird eine variationelle Lösungstheorie vorgestellt und die Wohlgestelltheit der Gleichung diskutiert. Darauf aufbauend wird das Verhalten der Lösung für verschwindende Leitfähigkeit studiert und die Linearisierbarkeit der Gleichung ohne leitfähiges Objekt in Richtung des Auftauchens eines leitfähigen Objektes gezeigt. Zur Regularisierung der Gleichung werden Modifikationen vorgeschlagen, welche ein voll parabolisches bzw. elliptisches Problem liefern. Diese werden verifiziert, indem die Konvergenz der Lösungen gezeigt wird. Zuletzt wird gezeigt, dass unter der Annahme von sonst homogenen Umgebungsparametern leitfähige Objekte eindeutig durch die Messungen lokalisiert werden können. Hierzu werden die Linear Sampling Methode sowie die Faktorisierungsmethode angewendet.

Inverse and regular phenyl-azole ligands for luminescent Iridium(III) complexes

In the modern society, light is mostly powered by electricity which lead to a significant increase of the global energy consumption. In order to reduce it, different kinds of electric lamps have been developed over the years; it is now accepted that phosphorescence-based OLEDs offer many advantages over existing light technologies. Iridium complexes are considered excellent candidates for bright materials by virtue of the possibility to easily tune the wavelength of the emitted radiation, by appropriate modifications of the nature of the ligands. It is important to note that the synthesis of Ir(III) blue-emitting complexes is a very challenging goal, because of wide HOMO-LUMO gaps needed for produce a deep blue emission. During my thesis I planned the synthesis of two different series of new Ir(III) heteroleptic complexes, the C and the N series, using cyclometalating ligands containing an increasing number of nitrogens in inverse and regular position. I successfully performed in the synthesis of the required four ligands, i.e. 1-methyl-4-phenyl-1H-imidazole (2), 4-phenyl-1-methyl-1,2,3-triazole (3), 1-phenyl-1H-1,2,3-triazole (6) and 1-phenyl-1H-tetrazole (7), that differ in the number of nitrogens present in the heterocyclic ring and in the position of the phenyl ring. Therefore the cyclometalation of the obtained ligands to get the corresponding Ir(III)-complexes was attempted. I succeeded in the synthesis of two Ir(III)-complexes of the C series, and I carried out various attempts to set up the appropriate reaction conditions to get the remaining desired derivatives. The work is still in progress, and once all the desired complexes will be synthesized and characterized, a correlation between their structure and their emitting properties could be formulated analysing and comparing the photophysical data of the real compounds.

Parallel recusive algorithms for inverse discrete Legendre transform and inverse discrete Laguerre transform

This paper presents parallel recursive algorithms for the computation of the inverse discrete Legendre transform (DPT) and the inverse discrete Laguerre transform (IDLT). These recursive algorithms are derived using Clenshaw's recurrence formula, and they are implemented with a set of parallel digital filters with time-varying coefficients.

Equivariant inverse spectral theory and toric orbifolds

Let O-2n be a symplectic toric orbifold with a fixed T-n-action and with a tonic Kahler metric g. In [10] we explored whether, when O is a manifold, the equivariant spectrum of the Laplace Delta(g) operator on C-infinity(O) determines O up to symplectomorphism. In the setting of tonic orbifolds we shmilicantly improve upon our previous results and show that a generic tone orbifold is determined by its equivariant spectrum, up to two possibilities. This involves developing the asymptotic expansion of the heat trace on an orbifold in the presence of an isometry. We also show that the equivariant spectrum determines whether the toric Kahler metric has constant scalar curvature. (C) 2012 Elsevier Inc. All rights reserved.