Inorganic Fullerene-like Nanoparticles and Inorganic Nanotubes

The subjects of the presented papers cover a wide range of challenges in the area of inorganic fullerene-like nanoparticles and nanotubes. However, it can include only a few comprehensive experimental and theoretical efforts, stepwise evaluating the rationalization of the synthesis, and elucidation of the stability, mechanical, electronic and adhesive properties of these nanostructures. We believe that this thematic issue can be helpful, not only for an advanced researcher to grasp the latest developments in this field, but also to permit a beginner to gain a deeper insight into the field of inorganic fullerene-like nanoparticles and nanotubes

A well-posedness framework for inpainting based on coherence transport

Image inpainting is the process of touching-up damaged or unwanted portions of a picture and is an important task in image processing. For this purpose Bornemann and März [J. Math. Imaging Vis. , 28 (2007), pp. 259– 278] introduced a very efficient method called Image Inpainting Based on Coherence Transport which fills the missing region by advecting the image information along integral curves of a coherence vector field from the boundary towards the interior of the hole. The mathematical model behind this method is a first-order functional advection PDE posed on a compact domain with all inflow boundary. We show that this problem is well-posed under certain conditions

The diffeomorphism group of a non-compact orbifold

We endow the diffeomorphism group of a paracompact (reduced) orbifold with the structure of an infinite dimensional Lie group modelled on the space of compactly supported sections of the tangent orbibundle. For a second countable orbifold, we prove that this Lie group is C^0-regular and thus regular in the sense of Milnor. Furthermore an explicit characterization of the Lie algebra associated to the diffeomorphism group of an orbifold is given.Comment: 184 pp, LaTex and TikZ. V4: updated some remarks and literature, corrected typos and minor errors. The results remain unchanged. For the reader's convenience, the appendix contains some definitions and known facts from A. Pohl's preprint arXiv:1001.0668 and H. Glockner's preprint arXiv:math/0408008 which are used in the tex

Methods and Trends in 2D van der Waals Heterostructures

The research here will identify both thermal and electronic trends in 2D heterostructures and develop rigorous methodologies for calculating interface structures. A link will be made between common devices and the materials and interfaces from which they are constructed. A comprehensive presentation of the theories used throughout the thesis will be given, defining density functional theory, the Frozen phonon method and thermal conductivity via the Boltzmann transport equation. The failure of Anderson's rule in 2D heterostructures will be demonstrated and explained. Also demonstrated, will be, how 2D heterostructure bandgap predictions can be improved using two physically based corrections to Anderson's rule ΔE_Γ and ΔE_IF. We will show that ΔE_Γ affects the bandstructure such that for any constructed heterostructure the effective mass will always decrease and will likely exhibit an indirect bandgap. Furthermore, we will provide expressions to give the band alignments in terms of knowable material properties. It is then discussed how theory could be readily extended to other 2D heterostructures by adjustments to corrective terms ΔE_Γ and ΔE_IF. This insight allows for a method which avoids the need for advanced calculation when estimating the properties of TMDC heterostructures. This in turn will expand the possibilities for exploring the optoelectronic properties of various heterostructures to the broader research community. We will follow on by showing that the thermal conductivity of a TMDC heterostructure will be lower than either of its constituents. We will show that this is consistent even when considering a wide range of possible conductivities. Generous parameter allocation will be used to define maximum bounding conductivity values. Such an approach will improve the confidence in the results. This is expected to provide a route for artificially reducing heat flow in 2D layered materials and will demonstrate a clear trend in the thermal transport of 2D heterostructure interfaces. To facilitate methods for heterostructures and interfaces A program, ARTEMIS, well be developed. This software allows for the generation of interfaces by identifying lattice matches between two parent crystal structures. To allow for further exploration of the energetic space of the interface, multiple surface terminations parallel to the Miller plane and interface alignments are used to generate sets of potential interfaces for each lattice match. These interface structures can then be used in atomic simulations to determine the most energetically favourable interface. The software here can help to both drastically reduce the work of generating and exploring interfaces, as well as aid in understanding of how the interface structure influences subsequent properties. Using several test cases, we will demonstrate how ARTEMIS can both identify the location of an interface in existing structures, and also predict an optimum interface separation based upon the parents’ atomic structures, which aims to accelerate and inform the study of interface science. The electronic and mechanical properties of Ba₂TiSi₂O₈, an inter-grain material, will be obtained and compared using the generalised gradient approximation and hybrid functional methods. This will define procedures and limitations for the investigation of inter-grain materials. With no need to adhere to the stoichiometry of the parent crystals procedural generation of inter-grain materials cannot be achived by ARTEMIS. It will be demonstrated that for insulating inter-grain materials hybrid functionals can result in significant change. The hybrid functional corrects the bandgap from 3.79 eV to 5.72 eV and shows overall stronger ionic bonding and weaker covalent bonding within the structure. The calculated value of 131.73 GPa for the bulk modulus sits between the values of its two parent crystals (BaTiO₃ and SiO₂). Using the HSE06 functional, will give a better understanding of the optical and electron transport properties and provide better understanding of the chemical structure making this investigation helpful for further work on similar inter-grain systems. This body of work serves the purpose of identifying general trends across heterostructures and interfaces and developing sound methodologies for the investigation of these structures.Engineering and Physical Sciences Research Council (EPSRC

Maths, Logic and Language

A work on the philosophy of mathematics (2017) ‘Number’, such a simple idea, and yet it fascinated and absorbed the greatest proportion of human geniuses over centuries, not to mention the likes of Pythagoras, Euclid, Newton, Leibniz, Descartes and countless maths giants like Euler, Gauss and Hilbert, etc.. Einstein thought of pure maths as the poetry of logical ideas, the exactitude of which, although independent of experience, strangely seems to benefit the study of the objects of reality. And, interestingly as well as surprisingly we are nowhere near any clear understandings of numbers despite discoveries of many productive usages of numbers. This is - rightly or wrongly - a humble attempt to approach the subject from an angle hitherto unthought-of

Computational modeling of thermal transport in low-dimensional materials

Over the past two decades, controlling thermal transport properties at the nanoscale has become more and more relevant. This is mostly motivated by the need of developing novel energy-harvesting techniques based on thermoelectricity and the necessity to control the heat dissipation in semiconductor devices. In this field, two major research lines can be identified: On one side 'phononics', which aims at developing devices such as thermal diodes, thermal transistors, and thermal logic gates, among others, and on the other side, phonon engineering aiming at controlling heat transport by producing or structurally modifying heterostructures made of novel nanomaterials (e.g., two-dimensional (2D) materials, nanotubes, organic systems). In order to gain insight into the factors controlling nanoscale heat flow and to be able to design highly-efficient thermal devices, the development of new computational approaches is crucial. The primary goal of the present thesis is the implementation of new methodologies addressing classical and quantum thermal transport at the nanoscale. We will focus on three major issues: (i) We will study thermal rectification effect in nanodevices made of novel 2D materials by means of nonequilibrium molecular dynamics simulations. The influence of structural asymmetry and substrate deposition on the thermal rectification will be investigated. (ii) To address quantum ballistic thermal transport in nanoscale systems, we will implement a nonequilibrium Green's functions (NEGF) treatment of transport combined with a density-functional based approach. Here, we will explore the dependence of the thermal transport properties of 2D materials and nanotubes on different intrinsic (structural anisotropy and grain boundaries) and external (molecular functionalization, strain engineering, and doping) factors. Finally, (iii) a time-dependent NEGF formalism will be developed and implemented to probe the transient and steady thermal transport in molecular junctions. In short, our results show that the mechanisms governing the thermal rectification effect in the 2D thermal rectifiers proposed in this work are shape asymmetries, interface material (planar stacking order), and changes in the degree of spatial localization of high-frequency modes (under nonequilibrium heat transport conditions). The rectification effect can be also controlled by substrate engineering. Moreover, we found that quantum ballistic thermal transport in 2D puckered materials displays an anisotropic behavior. The presence of structural disorder in the form of grain boundaries in graphene reduces overall its thermal transport efficiency. Dynamical disorder induced by coupling to a thermostat has however a weaker effect, suggesting that structural defects are playing a major role. External factors have a noticeable influence on the heat transport in new 2D materials and BNC heteronanotubes. On the other hand, we have also been able to characterize, from a quantum point of view, the phonon dynamics in carbon-based molecular junctions. We expect that the results obtained within this thesis will yield new insights into the thermal management of low-dimensional materials, and thus open new routes to the design of thermoelectric and phononic devices.In den letzten zwei Jahrzehnten hat die Kontrolle der thermischen Transporteigenschaften im Nanobereich immer mehr an Bedeutung gewonnen. Dies ist vor allem auf die Notwendigkeit zurückzuführen, neue Energiegewinnungstechniken zu entwickeln, die auf Thermoelektrizität basieren, sowie auf die Problematik, die Wärmeabfuhr in Halbleiterbauelementen kontrollieren zu müssen. In diesem Bereich lassen sich zwei große Forschungslinien identifizieren: Auf der einen Seite 'Phononik', die unter anderem auf die Entwicklung von Bauelementen wie thermischen Dioden, Transistoren und Logikgattern abzielt, und auf der anderen Seite die Phononentechnik, die den Wärmetransport durch Herstellung oder strukturelle Modifikation von Heterostrukturen aus neuartigen Nanomaterialien (z.B. zweidimensionalen (2D) Materialien, Nanoröhren, organischen Systemen) steuert. Um einen Einblick in die Faktoren zu erhalten, die den Wärmefluss im Nanobereich steuern, und um hocheffiziente thermische Bauteile entwickeln zu können, ist die Entwicklung neuer Berechnungsansätze entscheidend. Das Hauptziel der vorliegenden Arbeit ist die Implementierung neuer Methoden, die sich mit dem klassischen und dem quantenthermischen Transport auf der Nanoskala befassen. Wir werden uns auf drei Hauptthemen konzentrieren: (i) Wir werden den thermischen Rektifikationseffekt in Nanobauteilen aus neuartigen 2D-Materialien mit Hilfe von Nichtgleichgewichts-Molekulardynamiksimulationen studieren. Der Einfluss von Strukturasymmetrie und Substratablagerung auf die thermische Rektifikation wird untersucht. (ii) Um den quantenballistischen Wärmetransport in nanoskaligen Systemen anzugehen, werden wir eine NEGF-Behandlung (Nichtgleichgewichts-Greensche Funktionen) des Transports in Kombination mit einem dichtefunktionalen Ansatz implementieren. Hier wird die Abhängigkeit der thermischen Transporteigenschaften von 2D-Materialien und Nanoröhrchen von verschiedenen intrinsischen (strukturelle Anisotropie und Korngrenzen) und externen (molekulare Funktionalisierung, Stammtechnik und Dotierung) Faktoren untersucht. Schließlich wird (iii) ein zeitabhängiger NEGF-Formalismus entwickelt und implementiert, um den transienten und stetigen Wärmetransport in molekularen Verbindungen zu untersuchen. Unsere Ergebnisse zeigen, dass die wesentlichen Mechanismen für die thermische Gleichrichtung in 2D thermischen Gleichrichtern durch Asymmetrien der Bauteilform, das Interface-Material (planare Stapelung Reihenfolge), und änderungen im Grad der räumlichen Lokalisierung von Hochfrequenz-Modi (unter Nicht-Gleichgewicht Wärmetransport-Bedingungen) gegeben sind. Der Gleichrichteffekt kann auch durch die Wahl des Substrats gesteuert werden. Darüber hinaus haben wir festgestellt, dass der quantenballistische Wärmetransport in 2D-Puckered-Materialien ein anisotropes Verhalten zeigt. Das Vorhandensein von strukturellen Störungen in Form von Korngrenzen in Graphen reduziert insgesamt die Effizienz des Wärmetransports. Dynamische Störungen, die durch die Ankopplung an einen Thermostaten hervorgerufen werden, haben jedoch eine schwächere Wirkung, was darauf hindeutet, dass strukturelle Defekte eine große Rolle spielen. Externe Faktoren haben einen nachweislichen Einfluss auf den Wärmetransport in neuen 2D-Materialien und BNC-Heteronanotubes. Weiterhin konnten wir auch die Phononendynamik in kohlenstoffbasierten molekularen Verbindungen quantitativ charakterisieren. Wir erwarten, dass die Ergebnisse dieser Arbeit neue Erkenntnisse über das Wärmemanagement von niedrigdimensionalen Materialien liefern und damit neue Wege für das Design von thermoelektrischen und phononischen Bauelementen eröffnen