Abstract: Möbius bands have been studied extensively, mainly in topology. Generalized Möbius-Listing surfaces and bodies providing a full geometrical generalization, is a quite new field, motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. In general, cutting leads to interlinked and intertwined different surfaces or bodies, resulting in very complex systems. However, under certain conditions, the result of cutting can be a single surface or body, which reduces complexity considerably. Our research is motivated by this reduction of complexity. In the study of cutting Generalized Möbius-Listing bodies with polygons as cross section, the conditions under which a single body results, displaying the Möbius phenomenon of a one-sided body, have been determined for even and odd polygons. These conditions are based on congruence and rotational symmetry of the resulting cross sections after cutting, and on the knife cutting the origin. The Möbius phenomenon is important, since the process of cutting (or separation of zones in a GML body in general) then results in a single body, not in different, intertwined domains. In all previous works it was assumed that the cross section of the GML bodies is constant, but the main result of this paper is that it is sufficient that only one cross section on the whole GML structure meets the conditions for the Möbius phenomenon to occur. Several examples are given to illustrate this.

Abstract: The radiation damage created in silicon materials by Mn-57 -> Fe-57 ion implantation has been studied and characterized by Mossbauer spectroscopy showing four main lines, assigned to: substitutional, interstitial and damaged configuration sites of the implanted ions. Nevertheless, the Mossbauer spectrum of Fe-57 in this materials remains with some ambiguous identification regarding the implantation configurations before and after annealing, specially the damaged configurations and its evolution. In the present work some possible implantation configurations are suggested and evaluated using a multiscale approach by Monte Carlo ion transport and electronic structure calculations within DFT. The proposed implantation environments were evaluated in terms of stability and the Fe-57 hyperfine parameters were calculated to establish the connections with the experimental observations. Good agreement was found between the experimental and the calculated hyperfine parameters for some configurations; suggesting which ones could be the implantation environments before and after sample annealing.

Abstract: Cultural heritage represents the vehicle of our cultural identity, handed over from past to future generations throughout human history. As a repository of fundamental cultural and social values, the preservation of all forms of cultural heritage is a responsibility of every society and of humankind as a whole. When it comes to tangible cultural heritage, preservation of heritage translates into preservation of objects and, therefore, of the materials they are constituted of. This crucial task relies heavily on the application of scientific analytical methods to answer material and conservation-related questions. ​ ​ The fundamental contribution of this analytical approach led, in the past decades, to an ever-deepening understanding of the factors governing the degradation of cultural heritage. However, the extreme complexity of the heritage object-environment system results in a massive research field, which inevitably presents relevant open questions. This is where the present PhD work comes into play, attempting to fill knowledge gaps in literature by starting from specific case studies and un-answered research questions. ​ ​ The multianalytical research conducted during this PhD unraveled fundamental information on the properties governing the reactivity and long-term behavior of different classes of materials, from α-brass in an indoor environment to artists’ pigments in the presence of light, moisture and soluble particulate matter (PM). The paramount importance of the synthesis conditions on the composition, physical properties and reactivity of heritage materials was also demonstrated, in particular for stable lead pyroantimonate and unstable Geranium lake artists’ pigments. Moreover, the study and characterization of specific heritage objects, namely a series of 16th century reliquary altarpieces and the painting L’Arlesienne, by Vincent Van Gogh, allowed to obtain relevant insights into their composition and on potential risks for their conservation. The challenging nature of the samples considered, created the perfect opportunity to test an innovative spectroscopic technique, optical photo-thermal IR (O-PTIR), for the characterization of heritage materials. Striking results were obtained, highlighting a great potential for the application of this non-destructive sub-micron molecular spectroscopy to the analysis of cultural heritage. Finally, in the last section of this work, strategies to implement the continuous monitoring of PM levels in indoor environmental quality studies were also considered, with a particular focus on the identification of environmental hazards for the collections housed in specific conservation environments (War Heritage Institute in Brussels and St. Martin’s church in Aalst, BE).

Abstract: The low-pressure hollow cathode discharge made of a hollow circular tube and an anode is a type of simple structure discharge system. In particular, under the arc discharge mode, hollow cathodes have high plasma density and energy density with a wide range of adaptability of pressure and current. Low-pressure hollow cathode arc (HCA) discharges have been widely used as plasma sources in various fields such as manufacturing, vacuum welding, and aerospace since the 1960s. Despite the early experimental and applied researches on low-pressure HCA discharges, the basic theoretical study was relatively lagged much behind, resulting in many unanswered questions, such as the optimal discharge operating parameters, the power deposition inside the cathode, the causes of plasma instability, and how to effectively reduce cathode erosion and so on. Due to the special discharge structure of the hollow cathode, it is difficult to make an accurate experimental diagnosis, so a reasonable numerical simulation is an effective study method. However, up to now, there is still a lack of complete and effective numerical models which can evaluate various physical fields in the low-pressure hollow cathode discharges. To address the above problems and difficulties, a comprehensive and self-consistent 2D multi-physical coupling numerical model based on a commercial program of finite element method, the COMSOL Multiphysics, was provided in this paper. The model involves plasma transport, arc flow and heat transfer, and cathode thermal equilibrium, and can consider the effect of an applied magnetic field. The processes of secondary electron emission, thermal-field electron emission, ions and backflow high-energy electrons bombardment, and thermal radiation from the cathode surface are considered in the cathode thermal equilibrium process. Based on the above background, this paper works from the following aspects： In Chapter 1, the basic concepts of low-pressure HCA discharge including the hollow cathode effect, the basic characteristics, and operation modes were introduced firstly; Secondly, the application fields, development history, and overseas and domestic research status of hollow cathode discharge were reviewed; finally, the problems were presented and the research background was explained, and the research purpose of this paper was clarified. In Chapter 2, a complete and self-consistent numerical model of low-pressure hollow cathode discharge was proposed based on the fundamental theory and assumptions, and the set of control equations and boundary conditions in the model were elaborated. In addition, the electron energy distribution function, the collision processes, the solving tools of this model, and calculation schemes were introduced in detail. Finally, a validation example was given to test the rationality and applicability of the numerical model. In Chapter 3, the fundamental plasma properties of low-pressure hollow cathode arcs were investigated. Firstly, the ion Joule heating effect was studied. The results showed that the temperature distributions of the arc and cathode are only able to approach the experimental measurements after considering the ion Joule heating, which shows that the Joule heating of ions is crucial for the heating of the arc plasma. Secondly, by comparing the radial distribution of electron and ion density inside the cathode, the structure of the cathode sheath could be simulated well using this model. Finally, it was shown that the thermal radiation from the cathode surface is an important cooling mechanism of the cathode and only under higher surface emissivity can balance the larger heat flow given by the plasma to the cathode, and the temperature distribution of the cathode shows a non-monotonic increasing trend and is consistent with the profile of experimental measurement so that the so-called active zone is formed. In Chapter 4, the power deposition in the low-pressure HCA was studied in simulation. Two main aspects were considered: the power deposition into particles (both electrons and heavy particles) and the power deposition onto the cathode. It was found that the deposited power into particles increases with the rise of discharge current, but there is no effect on the total power deposition onto the cathode. In high-density plasmas, Coulomb collisions between electrons and ions also become very important, especially since a portion of the deposition energy on heavy particles comes mainly from the energy transfer from electrons to ions. It was also found that regardless of external parameters, half of the power deposition onto the cathode always comes from the particle contribution, while the other half is the net contribution of heat transfer and cathode radiation. The HCA model also allows the simulation of multiple discharge modes for low-pressure HCA discharges over a wide range of gas flow rates. It was also shown that the discharge operating conditions and the external magnetic field can change the distribution of the particle flow on the cathode wall. In Chapter 5, the ion sputtering erosion process on the cathode was simulated by coupling the HCA numerical model with the moving grid technique. The results showed that the ion sputtering erosion on the cathode depends on the ion flux and the plasma potential near the cathode wall and that their distribution and magnitude jointly determine the erosion morphology of the cathode. It was also found that the location of the most severe erosion on the cathode is located in the region of the densest ion flux on the cathode wall, rather than in the longitudinal correspondence with the central region of the internal positive column (IPC). The external magnetic fields can mitigate the cathode erosion and reduce the erosion depth, but stronger magnetic fields lead to a concentration of current density at the cathode tip, which can enhance erosion slightly at the cathode outlet end. Finally, the conclusions and innovation highlights were summarized, and prospects for future work were discussed.

Abstract: There is a type of filament that forms dosed contours encircling regions of one polarity of magnetic field, while the surrounding region has the opposite polarity One distribution of ring-filaments has sizes 2R = 40,000 to 160,000 km with the maximum around 100,000 km; the other distribution (with filaments and filament channels) has bigger sizes, with a maximum around 300,000 km. At low and mid latitudes the radial component B-rs (radial for the Sun) in the region outlined by filaments varies from 50 to 100 gauss, while the longitudinal component B-phi varies from 10 to 30 gauss. The total current inside the filament is 10(10) – 10(11) A, the ratio R/a approximate to 5 to 10, the magnetic flux crossing the surface is approximate to 10(21) – 10(22) MX; th, magnetic energy is approximate to 10(29) – 10(31) erg. Polar ring-filaments at latitudes 60 degrees-80 degrees are related to the polar magnetic field reversal and the quasi-flare processes at the poles during the field reversal. Correlation between B-rs and B-phi for the polar filament bands cannot be satisfactorily explained. A theoretical model using the conservation laws is used to study the relations between the various fields, currents, etc, of shrinking polar ring-filaments and their evolution. According to this theory ring-filaments should rise higher above the photosphere when shrinking. However, observations show that the height lowers. Presumably the discrepancy is due to the lack of dissipation in the model.