Two-Dimensional Bin Packing Problem with Guillotine Restrictions

This thesis, after presenting recent advances obtained for the two-dimensional bin packing problem, focuses on the case where guillotine restrictions are imposed. A mathematical characterization of non-guillotine patterns is provided and the relation between the solution value of the two-dimensional problem with guillotine restrictions and the two-dimensional problem unrestricted is being studied from a worst-case perspective. Finally it presents a new heuristic algorithm, for the two-dimensional problem with guillotine restrictions, based on partial enumeration, and computationally evaluates its performance on a large set of instances from the literature. Computational experiments show that the algorithm is able to produce proven optimal solutions for a large number of problems, and gives a tight approximation of the optimum in the remaining cases.

Computer simulations of two-dimensional colloidal crystals under confinement and shear

In this thesis we are presenting a broadly based computer simulation study of two-dimensional colloidal crystals under different external conditions. In order to fully understand the phenomena which occur when the system is being compressed or when the walls are being sheared, it proved necessary to study also the basic motion of the particles and the diffusion processes which occur in the case without these external forces. In the first part of this thesis we investigate the structural transition in the number of rows which occurs when the crystal is being compressed by placing the structured walls closer together. Previous attempts to locate this transition were impeded by huge hysteresis effects. We were able to determine the transition point with higher precision by applying both the Schmid-Schilling thermodynamic integration method and the phase switch Monte Carlo method in order to determine the free energies. These simulations showed not only that the phase switch method can successfully be applied to systems with a few thousand particles and a soft crystalline structure with a superimposed pattern of defects, but also that this method is way more efficient than a thermodynamic integration when free energy differences are to be calculated. Additionally, the phase switch method enabled us to distinguish between several energetically very similar structures and to determine which one of them was actually stable. Another aspect considered in the first result chapter of this thesis is the ensemble inequivalence which can be observed when the structural transition is studied in the NpT and in the NVT ensemble. The second part of this work deals with the basic motion occurring in colloidal crystals confined by structured walls. Several cases are compared where the walls are placed in different positions, thereby introducing an incommensurability into the crystalline structure. Also the movement of the solitons, which are created in the course of the structural transition, is investigated. Furthermore, we will present results showing that not only the well-known mechanism of vacancies and interstitial particles leads to diffusion in our model system, but that also cooperative ring rotation phenomena occur. In this part and the following we applied Langevin dynamics simulations. In the last chapter of this work we will present results on the effect of shear on the colloidal crystal. The shear was implemented by moving the walls with constant velocity. We have observed shear banding and, depending on the shear velocity, that the inner part of the crystal breaks into several domains with different orientations. At very high shear velocities holes are created in the structure, which originate close to the walls, but also diffuse into the inner part of the crystal.

Higher-order molecular properties and excitation energies in single-reference and multireference coupled-cluster theory

Coupled-cluster (CC) theory is one of the most successful approaches in high-accuracy quantum chemistry. The present thesis makes a number of contributions to the determination of molecular properties and excitation energies within the CC framework. The multireference CC (MRCC) method proposed by Mukherjee and coworkers (Mk-MRCC) has been benchmarked within the singles and doubles approximation (Mk-MRCCSD) for molecular equilibrium structures. It is demonstrated that Mk-MRCCSD yields reliable results for multireference cases where single-reference CC methods fail. At the same time, the present work also illustrates that Mk-MRCC still suffers from a number of theoretical problems and sometimes gives rise to results of unsatisfactory accuracy. To determine polarizability tensors and excitation spectra in the MRCC framework, the Mk-MRCC linear-response function has been derived together with the corresponding linear-response equations. Pilot applications show that Mk-MRCC linear-response theory suffers from a severe problem when applied to the calculation of dynamic properties and excitation energies: The Mk-MRCC sufficiency conditions give rise to a redundancy in the Mk-MRCC Jacobian matrix, which entails an artificial splitting of certain excited states. This finding has established a new paradigm in MRCC theory, namely that a convincing method should not only yield accurate energies, but ought to allow for the reliable calculation of dynamic properties as well. In the context of single-reference CC theory, an analytic expression for the dipole Hessian matrix, a third-order quantity relevant to infrared spectroscopy, has been derived and implemented within the CC singles and doubles approximation. The advantages of analytic derivatives over numerical differentiation schemes are demonstrated in some pilot applications.

Two-dimensional relaxation-diffusion analysis to study water compartmentalization in cells by a single-sided NMR device

In questo lavoro di tesi è presentato un metodo per lo studio della compartimentalizzazione dell’acqua in cellule biologiche, mediante lo studio dell’autodiffusione delle molecole d’acqua tramite uno strumento NMR single-sided. Le misure sono state eseguite nel laboratorio NMR all’interno del DIFA di Bologna. Sono stati misurati i coefficienti di autodiffusione di tre campioni in condizione bulk, ottenendo risultati consistenti con la letteratura. È stato poi analizzato un sistema cellulare modello, Saccharomyces cerevisiae, allo stato solido, ottimizzando le procedure per l’ottenimento di mappe di correlazione 2D, aventi come assi il coefficiente di autodiffusione D e il tempo di rilassamento trasversale T2. In questo sistema l’acqua è confinata e l’autodiffusione è ristretta dalle pareti cellulari, si parla quindi di coefficiente di autodiffusione apparente, Dapp. Mediante le mappe sono state individuate due famiglie di nuclei 1H. Il campione è stato poi analizzato in diluizione in acqua distillata, confermando la separazione del segnale in due distinte famiglie. L’utilizzo di un composto chelato, il CuEDTA, ha permesso di affermare che la famiglia con il Dapp maggiore corrisponde all’acqua esterna alle cellule. L’analisi dei dati ottenuti sulle due famiglie al variare del tempo lasciato alle molecole d’acqua per la diffusione hanno portato alla stima del raggio dei due compartimenti: r=2.3±0.2µm per l’acqua extracellulare, r=0.9±0.1µm per quella intracellulare, che è probabilmente acqua scambiata tra gli organelli e il citoplasma. L’incertezza associata a tali stime tiene conto soltanto dell’errore nel calcolo dei parametri liberi del fit dei dati, è pertanto una sottostima, dovuta alle approssimazioni connesse all’utilizzo di equazioni valide per un sistema poroso costituito da pori sferici connessi non permeabili. Gli ordini di grandezza dei raggi calcolati sono invece consistenti con quelli osservabili dalle immagini ottenute con il microscopio ottico.

Two-dimensional linear-combination model fitting of magnetic resonance spectra to define the macromolecule baseline using FiTAID, a Fitting Tool for Arrays of Interrelated Datasets

To propose the determination of the macromolecular baseline (MMBL) in clinical 1H MR spectra based on T(1) and T(2) differentiation using 2D fitting in FiTAID, a general Fitting Tool for Arrays of Interrelated Datasets.

Informatics for cross-sample analysis with comprehensive two-dimensional gas chromatography and high-resolution mass spectrometry (GCxGC-HRMS)

This paper describes informatics for cross-sample analysis with comprehensive two-dimensional gas chromatography (GCxGC) and high-resolution mass spectrometry (HRMS). GCxGC-HRMS analysis produces large data sets that are rich with information, but highly complex. The size of the data and volume of information requires automated processing for comprehensive cross-sample analysis, but the complexity poses a challenge for developing robust methods. The approach developed here analyzes GCxGC-HRMS data from multiple samples to extract a feature template that comprehensively captures the pattern of peaks detected in the retention-times plane. Then, for each sample chromatogram, the template is geometrically transformed to align with the detected peak pattern and generate a set of feature measurements for cross-sample analyses such as sample classification and biomarker discovery. The approach avoids the intractable problem of comprehensive peak matching by using a few reliable peaks for alignment and peak-based retention-plane windows to define comprehensive features that can be reliably matched for cross-sample analysis. The informatics are demonstrated with a set of 18 samples from breast-cancer tumors, each from different individuals, six each for Grades 1-3. The features allow classification that matches grading by a cancer pathologist with 78% success in leave-one-out cross-validation experiments. The HRMS signatures of the features of interest can be examined for determining elemental compositions and identifying compounds.

Two-Dimensional Manganese(II) Coordination Polymer Based on Phthalate and Pyrazine Bridges Exhibiting Antiferromagnetic Porperties

Benzodifuran-functionalised pyrene and anthracene fluorophores 1 and 2 were obtained in reasonable yields. Their single crystal structures, electrochemical, optical absorption, and fluorescence characteristics have been described. They show strong luminescence with high quantum yields of 0.53 for 1 and 0.48 for 2. Magnetic measurements for the 2D coordination polymer [Mn(Pht(Pyz(H2O)2]n (1), in which metal centres are linked together by pyrazine (Pyz) and 1,6-bridging o-phthalate ligand (Pht2-), revealed antiferromagnetic interactions between Mn(II) ions.

Two-dimensional grayscale ultrasound and spectral Doppler waveform evaluation of dogs with chronic enteropathies

Sonography is an important diagnostic tool to examine the gastrointestinal tract of dogs with chronic diarrhea. Two-dimensional grayscale ultrasound parameters to assess for various enteropathies primarily focus on wall thickness and layering. Mild, generalized thickening of the intestinal wall with maintenance of the wall layering is common in inflammatory bowel disease. Quantitative and semi-quantitative spectral Doppler arterial waveform analysis can be utilized for various enteropathies, including inflammatory bowel disease and food allergies. Dogs with inflammatory bowel disease have inadequate hemodynamic responses during digestion of food. Dogs with food allergies have prolonged vasodilation and lower resistive and pulsatility indices after eating allergen-inducing foods.

Development of one-dimensional and two-dimensional computational tools that simulate steady internal condensing flows in terrestrial and zero-gravity environments

This dissertation presents an effective quasi one-dimensional (1-D) computational simulation tool and a full two-dimensional (2-D) computational simulation methodology for steady annular/stratified internal condensing flows of pure vapor. These simulation tools are used to investigate internal condensing flows in both gravity as well as shear driven environments. Through accurate numerical simulations of the full two dimensional governing equations, results for laminar/laminar condensing flows inside mm-scale ducts are presented. The methodology has been developed using MATLAB/COMSOL platform and is currently capable of simulating film-wise condensation for steady (and unsteady flows). Moreover, a novel 1-D solution technique, capable of simulating condensing flows inside rectangular and circular ducts with different thermal boundary conditions is also presented. The results obtained from the 2-D scientific tool and 1-D engineering tool, are validated and synthesized with experimental results for gravity dominated flows inside vertical tube and inclined channel; and, also, for shear/pressure driven flows inside horizontal channels. Furthermore, these simulation tools are employed to demonstrate key differences of physics between gravity dominated and shear/pressure driven flows. A transition map that distinguishes shear driven, gravity driven, and “mixed” driven flow zones within the non-dimensional parameter space that govern these duct flows is presented along with the film thickness and heat transfer correlations that are valid in these zones. It has also been shown that internal condensing flows in a micro-meter scale duct experiences shear driven flow, even in different gravitational environments. The full 2-D steady computational tool has been employed to investigate the length of annularity. The result for a shear driven flow in a horizontal channel shows that in absence of any noise or pressure fluctuation at the inlet, the onset of non-annularity is partly due to insufficient shear at the liquid-vapor interface. This result is being further corroborated/investigated by R. R. Naik with the help of the unsteady simulation tool. The condensing flow results and flow physics understanding developed through these simulation tools will be instrumental in reliable design of modern micro-scale and spacebased thermal systems.