Quasi-Regular Solutions for 3D Equations of Tricomi and Keldish Types

Цветан Д. Христов, Недю Ив. Попиванов, Манфред Шнайдер - Изучени са някои тримерни гранични задачи за уравнения от смесен тип. За уравнения от типа на Трикоми те са формулирани от М. Протер през 1952, като тримерни аналози на задачите на Дарбу или Коши–Гурса в равнината. Добре известно е, че новите задачи са некоректни. Ние формулираме нова гранична задача за уравнения от типа на Келдиш и даваме понятие за квазиругулярно решение на тази задача и на eдна от задачите на Протер. Намерени са достатъчни условия за единственост на такива решения.

Quantization of the Inhomogeneous Bianchi I model:quasi-Heisenberg picture

The quantization scheme is suggested for a spatially inhomogeneous 1+1 Bianchi I model. The scheme consists in quantization of the equations of motion and gives the operator (so called quasi-Heisenberg) equations describing explicit evolution of a system. Some particular gauge suitable for quantization is proposed. The Wheeler-DeWitt equation is considered in the vicinity of zero scale factor and it is used to construct a space where the quasi-Heisenberg operators act. Spatial discretization as a UV regularization procedure is suggested for the equations of motion.

Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two-dimensional Euler equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.

Numerical study of the enlarged O(5) symmetry of the 3D antiferromagnetic RP^(2) spin model

We investigate by means of Monte Carlo simulation and finite-size scaling analysis the critical properties of the three dimensional O (5) non-linear σ model and of the antiferromagnetic RP^(2) model, both of them regularized on a lattice. High accuracy estimates are obtained for the critical exponents, universal dimensionless quantities and critical couplings. It is concluded that both models belong to the same universality class, provided that rather non-standard identifications are made for the momentum-space propagator of the RP^(2) model. We have also investigated the phase diagram of the RP^(2) model extended by a second-neighbor interaction. A rich phase diagram is found, where most of the phase transitions are of the first order.

SCAPHOID AND LUNATE CARPAL MECHANICS OVER THE SPECTRUM OF HEALTHY FUNCTION

When ligaments within the wrist are damaged, the resulting loss in range of motion and grip strength can lead to reduced earning potential and restricted ability to perform important activities of daily living. Left untreated, ligament injuries ultimately lead to arthritis and chronic pain. Surgical repair can mitigate these issues but current procedures are often non-anatomic and unable to completely restore the wrist’s complex network of ligaments. An inability to quantitatively assess wrist function clinically, both before and after surgery, limits the ability to assess the response to clinical intervention. Previous work has shown that bones within the wrist move in a similar pattern across people, but these patterns remain challenging to predict and model. In an effort to quantify and further develop the understanding of normal carpal mechanics, we performed two studies using 3D in vivo carpal bone motion analysis techniques. For the first study, we measured wrist laxity and performed CT scans of the wrist to evaluate 3D carpal bone positions. We found that through mid-range radial-ulnar deviation range of motion the scaphoid and lunate primarily flexed and extended; however, there was a significant relationship between wrist laxity and row-column behaviour. We also found that there was a significant relationship between scaphoid flexion and active radial deviation range of motion. For the second study, an analysis was performed on a publicly available database. We evaluated scapholunate relative motion over a full range of wrist positions, and found that there was a significant amount of variation in the location and orientation of the rotation axis between the two bones. Together the findings from the two studies illustrate the complexity and subject specificity of normal carpal mechanics, and should provide insights that can guide the development of anatomical wrist ligament repair surgeries that restore normal function.

The interaction between two oppositely travelling, horizontally offset, antisymmetric quasi-geostrophic hetons

We investigate numerically the nonlinear interactions between hetons. Hetons are baroclinic structures consisting of two vortices of opposite sign lying at different depths. Hetons are long-lived. They most often translate (they can sometimes rotate) and therefore they can noticeably contribute to the transport of scalar properties in the oceans. Heton interactions can interrupt this translation and thus this transport, by inducing a reconfiguration of interacting hetons into more complex baroclinic multipoles. More specifically, we study here the general case of two hetons, which collide with an offset between their translation axes. For this purpose, we use the point vortex theory, the ellipsoidal vortex model and direct simulations in the three-dimensional quasi-geostrophic contour surgery model. More specifically, this paper shows that there are in general three regimes for the interaction. For small horizontal offsets between the hetons, their vortices recombine as same-depth dipoles which escape at an angle. The angle depends in particular on the horizontal offset. It is a right angle for no offset, and the angle is shallower for small but finite offsets. The second limiting regime is for large horizontal offsets where the two hetons remain the same hetonic structures but are deflected by the weaker mutual interaction. Finally, the intermediate regime is for moderate offsets. This is the regime where the formation of a metastable quadrupole is possible. The formation of this quadrupole greatly restrains transport. Indeed, it constrains the vortices to reside in a closed area. It is shown that the formation of such structures is enhanced by the quasi-periodic deformation of the vortices. Indeed, these structures are nearly unobtainable for singular vortices (point vortices) but may be obtained using deformable, finite-core vortices.

Development and validation of a computationally efficient pseudo 3D model for planar SOFC integrated with a heating furnace

Efficient numerical models facilitate the study and design of solid oxide fuel cells (SOFCs), stacks, and systems. Whilst the accuracy and reliability of the computed results are usually sought by researchers, the corresponding modelling complexities could result in practical difficulties regarding the implementation flexibility and computational costs. The main objective of this article is to adapt a simple but viable numerical tool for evaluation of our experimental rig. Accordingly, a model for a multi-layer SOFC surrounded by a constant temperature furnace is presented, trained and validated against experimental data. The model consists of a four-layer structure including stand, two interconnects, and PEN (Positive electrode-Electrolyte-Negative electrode); each being approximated by a lumped parameter model. The heating process through the surrounding chamber is also considered. We used a set of V-I characteristics data for parameter adjustment followed by model verification against two independent sets of data. The model results show a good agreement with practical data, offering a significant improvement compared to reduced models in which the impact of external heat loss is neglected. Furthermore, thermal analysis for adiabatic and non-adiabatic process is carried out to capture the thermal behaviour of a single cell followed by a polarisation loss assessment. Finally, model-based design of experiment is demonstrated for a case study.

Investigating the mesh dependency and upscaling of 3D grain-based models for the simulation of brittle fracture processes in low-porosity crystalline rock

The application of 3D grain-based modelling techniques is investigated in both small and large scale 3DEC models, in order to simulate brittle fracture processes in low-porosity crystalline rock. Mesh dependency in 3D grain-based models (GBMs) is examined through a number of cases to compare Voronoi and tetrahedral grain assemblages. Various methods are used in the generation of tessellations, each with a number of issues and advantages. A number of comparative UCS test simulations capture the distinct failure mechanisms, strength profiles, and progressive damage development using various Voronoi and tetrahedral GBMs. Relative calibration requirements are outlined to generate similar macro-strength and damage profiles for all the models. The results confirmed a number of inherent model behaviors that arise due to mesh dependency. In Voronoi models, inherent tensile failure mechanisms are produced by internal wedging and rotation of Voronoi grains. This results in a combined dependence on frictional and cohesive strength. In tetrahedral models, increased kinematic freedom of grains and an abundance of straight, connected failure pathways causes a preference for shear failure. This results in an inability to develop significant normal stresses causing cohesional strength dependence. In general, Voronoi models require high relative contact tensile strength values, with lower contact stiffness and contact cohesional strength compared to tetrahedral tessellations. Upscaling of 3D GBMs is investigated for both Voronoi and tetrahedral tessellations using a case study from the AECL’s Mine-by-Experiment at the Underground Research Laboratory. An upscaled tetrahedral model was able to reasonably simulate damage development in the roof forming a notch geometry by adjusting the cohesive strength. An upscaled Voronoi model underestimated the damage development in the roof and floor, and overestimated the damage in the side-walls. This was attributed to the discretization resolution limitations.

Development of a polyplexes-based miRNA delivery system in a 3D-bioplotted osteoarthritis cellular model.

L'osteoartrite (OA) è una patologia infiammatorio/degenerativa ossea per la quale non sono disponibili terapie causali efficaci ma solo approcci palliativi per la riduzione del dolore cronico. E’ quindi giustificato un investimento per individuare nuove strategie di trattamento. In quest’ottica, lo scopo di questa tesi è stato quello di indagare l’efficacia di polyplexi a base di chitosano o di PEI-g-PEG in un modello cellulare 3D in vitro basato su un hydrogel di Gellan Gum Metacrilato (GGMA) con a bordo condrociti in condizioni simulate di OA. Inizialmente sono state studiate la dimensione e il potenziale-Z di un pool di formulazioni di poliplexi. Quindi se ne è valutata la citocompatibilità utilizzando cellule staminali mesenchimali immortalizzate Y201. Infine, una miscela di GGMA, cellule e polyplexi è stata utilizzata per la stampa 3D di campioni che sono stati coltivati fino a 14 giorni. La condizione OA è stata simulata trattando le cellule con una miscela di citochine implicate nello sviluppo della malattia. Tutte le formulazioni a base di chitosano e due basate su PEI-g-PEG si sono dimostrate citocompatibili e sono hanno veicolato i miRNA nelle cellule (come mostrato dai risultati di analisi in fluorescenza). I risultati delle colorazioni H&E e AlcianBlue hanno confermato che il terreno condizionato ha ben ricreato le condizioni di OA. I polyplexi a base di chitosano e PEI-g-PEG hanno controbilanciato gli effetti delle citochine. Risultati incoraggianti, anche se da approfondire ulteriormente, provengono anche dall’analisi di espressione (RT-PCR) di cinque geni specifici della cartilagine. Concludendo, questo modello ha ben riprodotto le condizioni di OA in vitro; il chitosano ha mostrato di essere un adeguato veicolo per un trattamento a base di miRNA; il PEI-g-PEG si propone come un'alternativa più economica e ragionevolmente affidabile, sebbene il rischio di citotossicità alle concentrazioni più elevate richieda una più esteva validazione sperimentale.

The United Nations 'quasi-prosecutorial' investigative mechanisms: assessing a new institutional model in the international criminal justice landscape

This work aims to provide a theoretical examination of three recently created bodies of the United Nations mandated to investigate the alleged international crimes committed in Syria (IIIM), Iraq (UNITAD) and Myanmar (IIMM). Established as a compromise solution in the paralysis of international criminal jurisdictions, these essentially overlapping entities have been depicted as a ‘new generation’ of UN investigative mechanisms. While non-judicial in nature, they depart indeed from traditional commissions of inquiry in several respects due to their increased criminal or ‘quasi-prosecutorial’ character. After clarifying their legal basis and different mandating authorities, a comparative institutional analysis is thus carried out in order to ascertain whether these ‘mechanisms’ can be said to effectively represent a new institutional model. Through an in-depth assessment of their mandates, the thesis is also intended to outline both the strengths and the criticalities of these organs. Given their aim to facilitate criminal proceedings by sharing information and case files, it is suggested that more attention shall be paid to the position of the person under investigation. To this end, some proposals are made in order to enhance the mechanisms’ frameworks, especially from the angle of procedural safeguards. As a third aspect, the cooperation with judicial authorities is explored, in order to shed light on the actors involved, the relevant legal instruments and the possible obstacles, in particular from a human rights perspective. Ultimately, drawing from the detected issues, the thesis seeks to identify some lessons learned which could be taken into account in case of creation of new ad hoc investigative mechanisms or of a permanent institution of this kind.

Study of Bone Biomineralization in 2D and 3D Cultures of a Human Osteosarcoma Cell Line As Osteoblast-like Model

This PhD project focuses on the study of the early stages of bone biomineralization in 2D and 3D cultures of osteoblast-like SaOS-2 osteosarcoma cells, exposed to an osteogenic cocktail. The efficacy of osteogenic treatment was assessed on 2D cell cultures after 7 days. A large calcium minerals production, an overexpression of osteogenic markers and of alkaline phosphatase activity occurred in treated samples. TEM microscopy and cryo-XANES micro-spectroscopy were performed for localizing and characterizing Ca-depositions. These techniques revealed a different localization and chemical composition of Ca-minerals over time and after treatment. Nevertheless, the Mito stress test showed in treated samples a significant increase in maximal respiration levels associated to an upregulation of mitochondrial biogenesis indicative of an ongoing differentiation process. The 3D cell cultures were realized using two different hydrogels: a commercial collagen type I and a mixture of agarose and lactose-modified chitosan (CTL). Both biomaterials showed good biocompatibility with SaOS-2 cells. The gene expression analysis of SaOS-2 cells on collagen scaffolds indicated an osteogenic commitment after treatment. and Alizarin red staining highlighted the presence of Ca-spots in the differentiated samples. In addition, the intracellular magnesium quantification, and the X-ray microscopy on mineral depositions, suggested the incorporation of Mg during the early stages of bone formation process., SaOS-2 cells treated with osteogenic cocktail produced Ca mineral deposits also on CTL/agarose scaffolds, as confirmed by alizarin red staining. Further studies are underway to evaluate the differentiation also at the genetic level. Thanks to the combination of conventional laboratory methods and synchrotron-based techniques, it has been demonstrated that SaOS-2 is a suitable model for the study of biomineralization in vitro. These results have contributed to a deeper knowledge of biomineralization process in osteosarcoma cells and could provide new evidences about a therapeutic strategy acting on the reversibility of tumorigenicity by osteogenic induction.

A 3D biomimetic in vitro model: a novel strategy to investigate glioma biology

Gliomas are one of the most frequent primary malignant brain tumors. Acquisition of stem-like features likely contributes to the malignant nature of high-grade gliomas and may be responsible for the initiation, growth, and recurrence of these tumors. In this regard, although the traditional 2D cell culture system has been widely used in cancer research, it shows limitations in maintaining the stemness properties of cancer and in mimicking the in vivo microenvironment. In order to overcome these limitations, different three-dimensional (3D) culture systems have been developed to mimic better the tumor microenvironment. Cancer cells cultured in 3D structures may represent a more reliable in vitro model due to increased cell-cell and cell-extracellular matrix (ECM) interaction. Several attempts to recreate brain cancer tissue in vitro are described in literature. However, to date, it is still unclear which main characteristics the ideal model should reproduce. The overall goal of this project was the development of a 3D in vitro model able to reproduce the brain ECM microenvironment and to recapitulate pathological condition for the study of tumor stroma interactions, tumor invasion ability, and molecular phenotype of glioma cells. We performed an in silico bioinformatic analysis using GEPIA2 Software to compare the expression level of seven matrix protein in the LGG tumors with healthy tissues. Then, we carried out a FFPE retrospective study in order to evaluate the percentage of expression of selected proteins. Thus, we developed a 3D scaffold composed by Hyaluronic Acid and Collagen IV in a ratio of 50:50. We used two astrocytoma cell lines, HTB-12 and HTB-13. In conclusion, we developed an in vitro 3D model able to reproduce the composition of brain tumor ECM, demonstrating that it is a feasible platform to investigate the interaction between tumor cells and the matrix.

From point cloud to HBIM: an integrated workflow for 3D reconstruction of heritage building with model accuracy evaluation

Modern society is now facing significant difficulties in attempting to preserve its architectural heritage. Numerous challenges arise consequently when it comes to documentation, preservation and restoration. Fortunately, new perspectives on architectural heritage are emerging owing to the rapid development of digitalization. Therefore, this presents new challenges for architects, restorers and specialists. Additionally, this has changed the way they approach the study of existing heritage, changing from conventional 2D drawings in response to the increasing requirement for 3D representations. Recently, Building Information Modelling for historic buildings (HBIM) has escalated as an emerging trend to interconnect geometrical and informational data. Currently, the latest 3D geomatics techniques based on 3D laser scanners with enhanced photogrammetry along with the continuous improvement in the BIM industry allow for an enhanced 3D digital reconstruction of historical and existing buildings. This research study aimed to develop an integrated workflow for the 3D digital reconstruction of heritage buildings starting from a point cloud. The Pieve of San Michele in Acerboli’s Church in Santarcangelo Di Romagna (6th century) served as the test bed. The point cloud was utilized as an essential referential to model the BIM geometry using Autodesk Revit® 2022. To validate the accuracy of the model, Deviation Analysis Method was employed using CloudCompare software to determine the degree of deviation between the HBIM model and the point cloud. The acquired findings showed a very promising outcome in the average distance between the HBIM model and the point cloud. The conducted approach in this study demonstrated the viability of producing a precise BIM geometry from point clouds.

Atomic Charge Transfer-counter Polarization Effects Determine Infrared Ch Intensities Of Hydrocarbons: A Quantum Theory Of Atoms In Molecules Model.

Atomic charge transfer-counter polarization effects determine most of the infrared fundamental CH intensities of simple hydrocarbons, methane, ethylene, ethane, propyne, cyclopropane and allene. The quantum theory of atoms in molecules/charge-charge flux-dipole flux model predicted the values of 30 CH intensities ranging from 0 to 123 km mol(-1) with a root mean square (rms) error of only 4.2 km mol(-1) without including a specific equilibrium atomic charge term. Sums of the contributions from terms involving charge flux and/or dipole flux averaged 20.3 km mol(-1), about ten times larger than the average charge contribution of 2.0 km mol(-1). The only notable exceptions are the CH stretching and bending intensities of acetylene and two of the propyne vibrations for hydrogens bound to sp hybridized carbon atoms. Calculations were carried out at four quantum levels, MP2/6-311++G(3d,3p), MP2/cc-pVTZ, QCISD/6-311++G(3d,3p) and QCISD/cc-pVTZ. The results calculated at the QCISD level are the most accurate among the four with root mean square errors of 4.7 and 5.0 km mol(-1) for the 6-311++G(3d,3p) and cc-pVTZ basis sets. These values are close to the estimated aggregate experimental error of the hydrocarbon intensities, 4.0 km mol(-1). The atomic charge transfer-counter polarization effect is much larger than the charge effect for the results of all four quantum levels. Charge transfer-counter polarization effects are expected to also be important in vibrations of more polar molecules for which equilibrium charge contributions can be large.