The knowledge of the packing behaviour of small organic compounds in crystal lattices is of great importance for industries dealing with solid state materials. The properties of materials depend on how the molecules arrange themselves in a crystalline environment. Crystal structure prediction provides a theoretical approach through the application of computational strategies to seek possible crystal packing arrangements (or polymorphs) a compound may adopt. Based on the chemical diagrams, this thesis investigates polymorphism of several small organic compounds. Plausible crystal packings of those compounds are generated, and their lattice energies are minimised using molecular mechanics and/or quantum mechanics methods. Most of the work presented here is conducted using two software packages commercially available in this field, Polymorph Predictor of Materials Studio 4.0 and GRACE 1.0. In general, the computational techniques implemented in GRACE are very good at reproducing the geometries of the crystal structures corresponding to the experimental observations of the compounds, in addition to describing their solid state energetics correctly. Complementing the CSP results obtained using GRACE with isostructurality offers a route by which new potential polymorphs of the targeted compounds might be crystallised using the existing experimental data. Based on all calculations in this thesis, four new potential polymorphs for four different compounds, which have not yet been determined experimentally, are predicted to exist and may be obtained under the right crystallisation conditions. One polymorph is expected to crystallise under pressure. The remaining three polymorphs might be obtained by using a seeding technique or the utilisation of suitable tailor made additives. / University of Bradford

Polyominoes are two-dimensional objects obtained by joining edge by edge squares of same size. Originally, polyominoes appeared in mathematical recreations, but it turned out that they have applications in various fields, for example, theoretical physics and bio-informatics. Among the most popular topics in combinatorics related to polyominoes one finds enumerating polyominoes of given size, including the asymptotic growth of the numbers of polyominoes, tiling problems, and reconstruction of polyominoes. Recently Qureshi introduced a binomial ideal induced by the geometry of a given polyomino, called polyomino ideal, and its related algebra. From that moment different authors studied algebraic properties and invariants related to this ideal, such as primality, Gröbner bases, Gorensteinnes and Castelnuovo-Mumford regularity. In this thesis, we provide an overview on the results that we obtained about polyomino ideals and its related algebra. In the first part of the thesis, we discuss questions about the primality and the Gröbner bases of the polyomino ideal. In the second part of the thesis, we talk over the Castelnuovo-Mumford regularity, Hilbert series, and Gorensteinnes of the polyomino ideal and its coordinate ring.

Topological states in photonic systems are described by qualitative discrete quantum numbers and feature unique combinations of properties such as robustness to perturbations and dissipationless surface transport of energy and information. Due to the many easily accessible platforms in photonics, topological photonics is one of the spearheads of topological physics that has offered exciting possibilities for investigations of novel topological phenomena and numerous promising technological uses. This master thesis aims at investigating from a theoretical and experimental perspective the properties of topological states of interacting light modes in arrays of coupled waveguides. First, we present a review of recent advances in the recently emerged field of topological physics. Then we review recent work on lattice models that feature topological edge states, and subsequently, we identify the existence of robust corner states on the edge of honeycomb lattices. These states display, similarly to the corner states known in 1D SSH and 2D Kagome lattices, exponential localisation with naturally occurring total destructive interference. Additionally, the corner states share properties with the dynamic transport modes of photonic Floquet topological insulators. However, the origin of the corner localisation is different from the previously studied examples: instead of dimerised coupling strength, the asymmetric and dimerised number of neighbours in the direction of the corner generates the intensity gradient. Motivated by our numerical study, we outline an experimental realisation of the novel honeycomb corner states, by means of waveguide lattices written in glass. The waveguides are 3D written in the bulk of a glass sample, with the lattice pattern orthogonal to the main direction of propagation which acts as a time coordinate in the experiments. Femtosecond direct laser writing enables fabricating truly 3D waveguides. Our experimental preparations cover a study of the effects of fabrication parameters for the relevant structures. We discuss how the localisation and robustness properties of the honeycomb corner states would next be investigated in the prepared experimental setting. / Topologiska tillstånd i fotoniska system beskrivs av särskilda topologiska diskreta kvanttal och har unika kombinationer av egenskaper såsom robusthet mot fluktuationer och förlustfri yttransport av energi och information. Tack vare de många lättillgängliga plattformarna inom fotonik är topologisk fotonik en av spjutspetsarna inom topologisk fysik och har erbjudit unika möjligheter för undersökningar av nya topologiska fenomen och med många lovande tekniska användningsområden. Denna masteruppsats syftar till att undersöka, ur ett teoretiskt och experimentellt perspektiv, egenskaperna hos topologiska tillstånd av interagerande ljusmoder i gitter av kopplade vågledare. Först presenterar vi en översikt av de senaste framstegen inom det nyligen uppkomna området topologisk fysik. Sedan sammanfattar vi det senaste arbetet med gittermodeller som har topologiska kanttillstånd, och därefter identifierar vi förekomsten av robusta hörntillstånd på kanten av bikakegitter. Dessa tillstånd uppvisar, på samma sätt som hörntillstånden som är kända i 1D SSH- och 2D Kagome-gitter, hög kantlokalisering med naturligt förekommande total destruktiv interferens. Dessutom delar hörntillstånden egenskaper med de kända fotoniska Floquet-topologiska isolatorerna som uppvisar topologisk transport. Ursprunget till hörnlokaliseringen skiljer sig dock från de tidigare studerade exemplen: istället för en dimeriserad kopplingsstyrka genererar det asymmetriska och dimeriserade antalet grannar i hörnets riktning intensitetsgradienten. Med motivering i den numeriska studien inleder vi en experimentell realisering av de nya bikakehörntillstånden, med hjälp av vågledargitter skrivna i glas. Vågledarna är 3D-skrivna på insidan av ett glasprov, med gittermönstret ortogonalt mot huvudutbredningsriktningen som fungerar som en tidskoordinat i experimenten. Direkt laserskrivning med femtosekundlaser gör det möjligt att tillverka vågledare i tre dimensioner. Våra experimentella förberedelser omfattar en studie av effekterna av tillverkningsparametrar för de relevanta strukturerna. Vi diskuterar hur lokaliserings- och robusthetsegenskaperna för bikakehörntillstånden sedan skulle undersökas med den experimentella metoden.

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The emergence of metal Additive Manufacturing (AM) over the last two decades has opened venues to mitigate the challenges associated with stochastic open-cell metal foams manufactured through the traditional foaming process. Regular lattices with user-defined unit cell topologies have been reported to exhibit better mechanical properties in comparison to metal foams which extend their applicability to multifunctional heat exchangers subjected to both thermal and mechanical loads. The current study aims at investigating the thermal-hydraulic characteristics of promising novel unit cell topologies realizable through AM technologies. Experimental investigation was conducted on four different topologies, viz (a) Octet, (b) Face-diagonal (FD) cube, (c) Tetrakaidecahedron, and (d) Cube, printed in single-cell thick sandwich type configuration in 420 stainless steel via Binder Jetting technology at same intended porosity. The effective thermal conductivity of the samples was found to be strongly dependent on the lattice porosity, however, no significant dependence on the unit-cell topology was demonstrated. Face-diagonal cube lattice exhibited the highest heat transfer coefficient and pressure drop, and consequently provided the lowest thermal-hydraulic performance. A procedure to incorporate the manufacturing-induced random roughness effects in the samples during numerical modelling is introduced. The numerical simulations were conducted on samples exhibiting the roughness profiles having statistically same mean roughness as the additively manufactured coupons and the results were compared to that obtained from the intended smooth-profiled CAD models that were fed into the printing machines. The analysis showed that inclusion of roughness effects in computational models can significantly improve the thermal performance predictions. Through this study, we demonstrate that additively manufactured ordered lattices exhibit superior thermal transport characteristics and future developmental efforts would require extensive experimentations to characterize their thermal and flow performance as well as local surface quality and AM-induced defect recognition. Experimental findings would also need to be supported by computational efforts where configurations which closely mimic the real AM parts could be modeled. A combined experimental-numerical framework is recommended for advancements in metal additive manufacturing-enabled enhanced heat transfer concepts.

<p dir="ltr">In this work we investigate the existence and experimentally measurable properties of Majorana quasiparticles in a few-body number conserving atomic system.</p>

The investigation into topological phases on non-periodic lattices has recently gained wide interest because of the discovery of never-before seen phenomena lacking a counterpart in periodic lattices. In this thesis, I present the results of my work on the lattice Laughlin state on fractal lattices and that of the BHZ model on quasicrystals. I show that the entanglement spectrum has the same topological fingerprint as in periodic lattices, and thus can be used as a probe of topological order in these new environments, where such probes are severely lacking, especially for interacting topological phases. I also show how the entanglement entropy displays precise oscillations as a function of lattice filling in fractal lattices, and is smooth for periodic lattices. I study the on-site particle densities, and anyonic excitations on different kinds of fractal lattices and show how radically different they are from the 2D case. Finally, I study the BHZ model on the Amman-Beenker tiling and show the different kinds of Bulk Localized Transport(BLT) states, the edge states, and how the latter can be used to pump charge between different kind of BLT states. I couple two layers of the half-BHZ, which are time-reversed partners of each other, with a simple time-reversal symmetric hopping, and show that the BLT and edge states still survive.

Twenty-five muscovites have been systematically studied chemically, optically, and structurally. Multiple linear regressions were performed on these data to determine the correlations of the compositional components with both the optical properties and the unit cell parameters. The results of this study indicate refractive indices increase to the extent Fe and Ti constitute the octahedral cations, and to the extent OH rather than F coordinates to these cations. The optic angle 2VX decreases nearly linearly with the Ti content. The b cell edge follows a near-linear trend with ∑(Mg + Fe(total)), similar to that found by Guidotti (1984). / Master of Science / incomplete_metadata