Dissertations / Theses on the topic 'Non-classical'

This thesis looks at two disparate problems relating to Schottky groups, and in particular what it means for a Schottky group to be classical or non-classical. The first problem focusses ofl the uniformization of R.iemann surfaces using Schottky groups. We extend the retrosection theorem of Koebe by giving conditions on lengths of curves as to when a Riemann surface can be uniformized by a classical Schottky group. The second section of this thesis examines a paper of Yamamoto ([40]), which gives the first example of a non-classical Schottky group. We firstly expand on the detail given in the paper, and then use this to give a second example of a non-classical Schottky group. We then take tIns second example and generalise to a two-variable family of non-classical Schottky groups.

The main objective of this thesis is to understand molecular crystallization as a multistep process with or without polymeric additives, including transient liquid-liquid phase separation, nanocrystal nucleation within the dense phase, and subsequent nanocrystal self-assembly or self-organization in sequence. The thesis starts with a quaternary model system, containing DL-Glutamic acid (Glu), polyethyleneimine (PEI), water, and EtOH, for the understanding of multistep precipitation of Glu with PEI as an additive. The experiments were performed by mixing Glu-PEI aqueous solution with a non-solvent EtOH. First, the phase diagram of the quaternary system is determined, obtaining precipitate, coacervates, or homogeneous mixtures by varying Glu/PEI w/w and water/EtOH v/v. Coacervation is observed to occur over a wide range of Glu/PEI with various volumes. The composition of coacervates is conveniently characterized by nuclear magnetic resonance spectroscopy. The observed coacervates are thermodynamically stable phases rich in solute, which is different from metastable polymer-induced liquid precursors. The combination of atomic force microscopy, small angle scattering, and ξ-potential measurements confirms the coexistence of monomers and Glu/PEI complexes and the aggregation of complexes in Glu-PEI-water systems. This suggests that there might be a direct structural transformation between the Glu-PEI complexes in aqueous solution and the metastable liquid precursors in a water-EtOH mixture. The multistep mechanism of Glu precipitation with PEI as an additive is investigated thereafter. The combination of stopped flow and small angle scattering demonstrates that the initially formed liquid precursors pass through an alteration of growth and coalescence. Combined with results from optical microscopy and scanning electron microscopy, the nucleation of nanoplatelets happens within each liquid precursor droplet, and nanoplatelets reorient themselves and self-organize into a radial orientation in the crystalline microspheres. The recipe was then extended to the precipitation of organics in other oppositely charged amino acid-polyelectrolyte systems. After the success in preparing hierarchical microspheres in solution, the similar recipe can be extended to the preparation of patterned thin films on substrate. By dipping a quaternary DL-Lys·HCl (Lys)–polyacrylic acid (PAA)–water–EtOH dispersion on a hydrophilic slide, the fast evaporation process of the volatile solvent EtOH is responsible for the homogeneous nucleation of NPs. Then, the following complete evaporation causes the mesocrystallization of a continuous spherulitic thin film along the receding line of the liquid, which again transforms into a mesocrystalline thin film. Furthermore, annealing is used to optimize the property of mesocrystalline thin films. As evaporation is a non-equilibrium process, it can be used to tune the kinetics of crystallization. Therefore, hierarchical or periodical thin films are obtainable by starting the evaporation from microspheres recrystallization, obtaining mesocrystalline thin films with 4 hierarchy levels. The results reveal that evaporation provides an easy but effective way for the formation of patterned structures via the positioning of NPs after their fast nucleation, resulting in different kinds of patterns by controlling the concentration of NPs, solvent evaporation rate, and other physical forces. Non-classical crystallization is not limited to crystallizations with polymeric additives. We also observed the nucleation and growth of a new molecular layer on the growing DL-Glu·H2O crystals from a supersaturated mother liquor by using an in-situ atomic force microscopy (AFM), where the nucleation and growth of a molecular layer proceed via amorphous nanoparticle (NP) attachment and relaxation process before the observation of the growth of a newly formed molecular layer. NP attachment to the crystal surface is too fast to observe by using in-situ AFM. The height shrinkage of NPs, combined to the structural transformation from 3D amorphous NPs to 2D crystalline layer, is observed during the relaxation process. The nucleation and growth of a newly formed molecular layer from NP relaxation is contradictory to the classical nucleation theory, which hypothesizes that nuclei show the same crystallographic properties as a bulk crystal. The formation of a molecular layer by NP attachment and relaxation rather than attachment of single molecules provides a different picture from the currently held classical nucleation and growth theory regarding the growth of single crystals from solution.
Das Hauptziel dieser Arbeit ist das Verständnis der molekularen Kristallisation, sowohl mit als auch ohne polymere Additive, als einen mehrstufigen Prozess. Dieser beinhaltet eine transiente flüssig-flüssig Phasentrennung, die Nukleation von Nanokristallen in der dichten flüssigen Precursor-Phase so wie eine anschließende nanokristalline Selbstorganisation. Die Arbeit beginnt mit Untersuchungen an einem quaternären Modelsystem bestehend aus DL-Glutamat (Glu), Polyethylenimin (PEI), Wasser und Ethanol. Das Phasendiagramm dieses quaternären Systems wird durch Variation der Glu/PEI w/w und Wasser/EtOH v/v Verhältnisse bestimmt, wobei Präzpitat aus polymerinduzierten flüssigen Precursor, Koazervate oder homogene Mischungen erhalten werden Das thermodynamisch stabile Koazervat kann als Referenz für das Verständnis von flüssigen Precursorn angesehen werden, welche in der Natur metastabil und transient sind. Der mehrstufige Mechanismus der Glu-Präzipitation mit PEI als Additiv wird dann mittels Neutronen Kleinwinkelstreuung untersucht. Dies zeigt, dass die ursprünglich gebildeten flüssigen Precursor noch vor der Nukleation von Nanokristallen einen Wechsel von Wachstum und Koaleszenz durchlaufen. Die Ergebnisse aus optischer- und Eletronenmikroskopie zeigen, dass sowohl die flüssigen Precursor Superstrukturen ausbilden als auch, dass die Nukleation von Nanoplättchen in jedem einzelnen Precursor Tropfen von statten geht. Dies geschieht noch bevor sich die Nanoplättchen selbst in einer radialen Orientierung ausrichten. Diese Studie liefert die Kinetik der Präzipitation von organischen Stoffen in Gegenwart von polymeren Additiven. Eine ähnliche Vorgehensweise wie für die Herstellung von Mikrokügelchen kann für die Darstellung von gemusterten Filmen angewandt werden. Die homogene Nukleation von Nanopartikeln (NPs) findet während der Verdampfung einer quarternären DL-Lys·HCl-Polyacrylsäure-Wasser-Ethanol Dispersion auf einer hydrophilen Oberfläche statt. Die darauffolgende vollständige Verdampfung löst die Mesokristallisation eines kontinuierlichen sphärolithischen dünnen Films aus, welcher sich wiederum in einen mesokristallinen dünnen Film umwandelt. Mesokristalline Filme mit 4 Hierarchiestufen bzw. auch periodische Filme werden durch die Verdampfung der Mikrokügelchen-Dispersion erhalten. Die Ergebnisse zeigen, dass die Verdampfung eine einfache aber effektive Methode zur Herstellung von verschieden gemusterten hierarchischen Filmen darstellt. Nicht-klassische Kristallisation wird auch in der Abwesenheit von polymeren Additiven beobachtet. Wir verfolgen mittels Rasterkraftmikroskop (AFM) die Nukleation und das Wachstum einer neuen molekularen Schicht auf wachsenden DL-Glu·H2O Kristallen aus übersättigter Mutterlauge. Die Bildung einer neuen molekularen Schicht verläuft durch die Anlagerung von amorphen Nanopartikeln. Das Schrumpfen der NPs zusammen mit der strukturellen Änderung von dreidimensionalen NPs zu 2D Schichten wird während dieses Relaxationsprozesses beobachtet. Schließlich kommt es zu der Ausbildung einer neuen molekularen Schicht. Die Bildung einer molekularen Schicht durch die Anlagerung von Nanopartikeln aus der Lösung und die darauffolgende Relaxation liefert ein abweichendes Bild zu der bisher gängigen klassischen Theorie des Kristallwachstums.

Streptococcus pneumoniae is a common resident of the human nasorpharynx that can cause severe illness, including bacterial meningitis and pneumonia. Ruminococcus gnavus is a commensal resident of the human gastrointestinal tract, present in the vast majority and overrepresented in those with inflammatory bowel disease. Both bacteria exploit very different niches, however both make use of sialidases, a class of enzymes that releases terminal sialic acids from sialoglycoconjugates by hydrolysing the -glycosidic linkage. There are three pneumococcal sialidases: SpNanA, a hydrolytic sialdiase; SpNanB, an intra-molecular trans-sialidase; and SpNanC. The primary reaction product of SpNanC is Neu5Ac2en (2-deoxy-2,3-didehydro-N-acetylneuraminic acid, also known as DANA), a potent inhibitor of hydrolytic bacterial and viral sialidases. The crystal structure of SpNanC in complex with Neu5Ac2en has been solved and a reaction mechanism for its formation proposed. R. gnavus can grow on sialylated substrates however it does not grow on sialic acid. The crystal structure of RgNanH has also been solved, confirming that it is an intra-molecular trans-sialidase, like SpNanB, that produces 2,7-anhydro-Neu5Ac, a sialic acid derivative with an intra- molecular linkage. This suggests a method of partitioning an important carbon source in a competitive environment. These works highlight the importance of thorough structural characterisation of sialidases, because although they may appear superficially very similar, they have significant diversity in their reaction mechanisms and their responses to inhibitors.

This Ph.D. aimed to investigate some of the non-classical features in HD, focusing in detail on weight loss and metabolism by means of whole body indirect calorimetry in both early stage human patients, as well as in the R6/2 transgenic mouse model of HD. In addition, circadian rhythms and sleep disturbances were investigated in the same patient cohort using actigraphy and polysomnography. Pilot studies on zerostomia, cholesterol levels, olfaction, gestation and orthostatic hypotension were also briefly examined in order to identify further, possible non-classical symptoms. I found that patients had a trend towards elevated total energy expenditure, a finding which was significant in 14 week old R6/2 mice. I also found that patients had an overall loss of form and definition in their rest-activity actograms, suggesting a disturbed circadian rhythm. Sleep cycles were poorly consolidated, fragmented and irregular and the majority of patients had longer sleep latencies, reduced sleep efficiency, more time spent awake during the sleep period, frequent arousals and apnoeas, and reduced slow wave and rapid eye movement sleep. Pilot studies revealed that patients also have significant problems of xerostomia, olfaction and gestation. These investigations will help to define the extent and nature of non-classical abnormalities in this condition more thoroughly, thus providing a better profile of problems and deficits in HD. Future longitudinal studies involving pre-symptomatic patients will help to provide possible biomarkers for disease therapy and could ultimately contribute towards reducing morbidity and mortality in patients, as well as to provide insight into common degenerative pathways of other neurodegenerative diseases.

The standard model of knowledge and belief attributes to agents the ability to reason perfectly in classical logic. This is known as the problem of logical omniscience and, in accordance with the requirements of their contexts of use, has led to the development of a number of alternative epistemic logics. Some of these alternatives can, like the standard model, be regarded as presenting for discussion and analysis in a base language a system of reasoning, or consequence relation: the relation under which beliefs are closed. Adopting this perspective with regard to a useful four-valued logic, the resulting extension of the standard model is described and many technical points of comparison with the original model are given.

This thesis comprises two main objectives. The first objective involved the stereochemical studies of chiral 4,6-diamino-1-aryl-1,2-dihydro-s-triazines and an investigation on how the different conformations of these stereoisomers may affect their binding affinity to the enzyme dihydrofolate reductase (DHFR). The ortho-substituted 1-aryl-1,2-dihydro-s-triazines were synthesised by the three component method. An ortho-substitution at the C6' position was observed when meta-azidocycloguanil was decomposed in acid. The ortho-substituent restricts free rotation and this gives rise to atropisomerism. Ortho-substituted 4,6-diamino-1-aryl-2-ethyl-1,2-dihydro-2-methyl-s-triazine contains two elements of chirality and therefore exists as four stereoisomers: (S,aR), (R,aS), (R,aR) and (S,aS). The energy barriers to rotation of these compounds were calculated by a semi-empirical molecular orbital program called MOPAC and they were found to be in excess of 23 kcal/mol. The diastereoisomers were resolved and enriched by C18 reversed phase h.p.l.c. Nuclear overhauser effect experiments revealed that (S,aR) and (R,aS) were the more stable pair of stereoisomers and therefore existed as the major component. The minor diastereoisomers showed greater binding affinity for the rat liver DHFR in in vitro assay. The second objective entailed the investigation into the possibility of retaining DHFR inhibitory activity by replacing the classical diamino heterocyclic moiety with an amidinyl group. 4-Benzylamino-3-nitro-N,N-dimethyl-phenylamidine was synthesised in two steps. One of the two phenylamidines indicated weak inhibition against the rat liver DHFR. This weak activity may be due to the failure of the inhibitor molecule to form strong hydrogen bonds with residue Glu-30 at the active site of the enzyme.

Staphylococcus aureus is a highly problematic human pathogen due to its ability to cause devastating infections, paired with a capacity to withstand the action of a large fraction of available antibiotics. Both pathogenicity and antibiotic resistance are encoded by numerous genomic elements, though the expression of these factors is energetically costly and not always beneficial for cellular survival. Therefore, S. aureus has developed sophisticated regulatory networks to integrate a multitude of signals, enabling it to navigate the delicate balance between its pathogenic lifestyle and baseline needs for cellular energy homeostasis. It is thus imperative to study S. aureus behavior and its underlying regulatory circuits not as isolated entities, but rather holistically as part of an optimized, highly interconnected system. To do so, we must seek to achieve a comprehensive understanding of all encoded regulators, that is, not only historically well defined elements like transcription factors, two-component systems and σ factors, but also the lesser studied ’non-classical’ regulators like small regulatory RNAs and regulatory subunits of RNA-dependent RNA polymerase (RNAP). To this end, we describe here the identification of numerous, previously unidentified sRNAs and their incorporation into a new standardized cataloging and annotation system. The identification and annotation procedures are based on a number of RNAseq experiments performed in three different S. aureus backgrounds (MRSA252, NCTC 8325, and USA300). We then apply RNAseq to evaluate the expression patterns of these elements when grown in human serum, thus probing for possible connections between sRNAs and S. aureus pathogenicity. In addition, we characterize the role of two small RNAP subunits, δ and ω, for S. aureus RNAP function. δ is of particular interest, as it is unique to Gram-positive bacteria; deletion of the subunit results in a loss of transcriptional stringency and decreased expression of numerous virulence determinants. These alterations are accompanied by impaired survival of the δ mutant in whole human blood, increased phagocytosis by human leukocytes, and decreased survival in a murine model septicemia when compared to its parental strain. In contrast, there is no indication of direct and gene-specific transcriptional functions for ω. Rather, we describe a role for ω in the structural integrity of the RNAP complex, where its loss leads to a structural disturbance in the RNAP complex that causes altered affinities for (alternative) σ factors and the δ subunit. Overall, the findings presented here contribute to a better understanding of the intricate regulatory systems that guide the lifestyle of an organism that presents an immense burden to patients and our health care system alike.

Cellular responses to viral infection and non-self tissues depend on presentation of antigenic peptides by polymorphic MHC class I molecules. The regulatory mechanisms controlling MHC class I expression are fundamental to effective immune responses, and in the pig are not fully understood. In this study the cellular responses of SLA class I genes to cytokines were studied by measuring SLA class 1 expression at the cell surface and also by fusing the promoters of the classical genes SLA-1, -2 and -3 and non-classical genes SLA 6 and -7 independently to a luciferase reporter gene. Cell surface expression of SLA class I was measured on Max cells, Shimozuma cells and porcine aortic endothelial cells isolated from inbred pigs of the d/d haplotype and outbred pigs of an unknown haplotype. IFN-alpha and -gamma treatment increased SLA class I expression on d/d PAECs and Max cells but not on outbred PAECs or Shimozuma cells. Analysis of SLA class I promoter activity in Max cells showed constitutive activity of SLA-1, -2, -3, -6, -7 and MIC-2 promoters. In summary, classical SLA promoters were responsive to IFNs and co-expression of the transcription factors IRF-1, NF- KB p65 and CIITA. In contrast to their human counterparts, combined treatment with TNF-alpha and IFN-alpha/-gamma had no synergistic effect on classical SLA class I promoter activity. SLA-1 responded to TNF-alpha and co-expression of the transcription factors IRF-3, -7 and -9. Non-classical promoters were not induced by IFN-alpha or -gamma or CIITA. SLA-7 was responsive to TNF-alpha and co-expression of IRF-1 but not co-expression of NF-kappaB. Interestingly, basal expression of MIC-2 remained unaffected by cytokines or co-expression of transcription factors. These results suggest locus-specific responses of SLA class I genes to cytokines and transcription factors, which can be explained in part by sequence variation in three key SLA class I promoter motifs: ISRE, Enhancer A and SXY. Furthermore, this study has demonstrated that the porcine virus CSFV decreases SLA class I surface expression early during infection and that this effect correlates to decreased constitutive activity of SLA-1, -2 and -7 promoters.

Intramolecular non-covalent interactions between aromatic ligands in chiral Ru(II) and Co(III) complexes have been investigated in this study. Several investigations were carried out and findings given. The results of the study, which demonstrate the significance of non-covalent interactions involving aromatic residues to the determination of the molecular conformation, serve to highlight the suitability of simple chiral metal complexes to act as models for interactions
Doctor of Philosophy (PhD)

For an extension of local fields, a scaffold is shown to be a powerful tool for dealing with the problem of the freeness of fractional ideals over their associated orders (Byott, Childs and Elder: \textit{Scaffolds and Generalized Integral Galois Module Structure}, Ann. Inst. Fourier, 2018). The first class of field extensions admitting scaffolds is \enquote*{near one-dimensional elementary abelian extension}, introduced by Elder (\textit{Galois Scaffolding in One-dimensional Elementary Abelian Extensions}, Proc. Amer. Math. Soc. 2009). However, the scaffolds constructed in Elder's paper arise only from the classical Hopf-Galois structure. Therefore, the study in this thesis aims to investigate scaffolds in non-classical Hopf-Galois structures. Let $L/K$ be a near one-dimensional elementary abelian extension of degree $p^2$ for a prime $p \geq 3.$ We show that, among the $p^2-1$ non-classical Hopf-Galois structures on the extension, there are only $p-1$ of them for which scaffolds may exist, and these exist only under certain restrictive arithmetic condition on the ramification break numbers for the extension. The existence of scaffolds is beneficial for determining the freeness status of fractional ideals of $\mathfrak{O}_L$ over their associated orders. In almost all other cases, there is no fractional ideal which is free over its associated order. As a result, scaffolds fail to exist.

The unifying themes connecting the chapters in this dissertation are the profound and often surprising effects of disorder in classical and quantum systems and the tremendous insight gained from a classical perspective, even in quantum systems. In particular, we investigate disorder in the form of weak, spatially correlated random potentials, i.e. far from the Anderson Localization regime. We present a new scar-like phenomenon in quantum wells. With the introduction of local impurities to the oscillator, the eigenstates localize onto classical periodic orbits of the unperturbed system. Compared to traditional scars in chaotic billiards, these scars are both more common and stronger. Though the unperturbed system has circular symmetry, the random perturbation selects a small number of orientations which are shared by many scarred states -- dozens or even hundreds -- over a range of energies. We show, via degenerate perturbation theory, that the cause of the new scars is the combination of an underlying classical resonance of the unperturbed system and a perturbation induced coupling that is strongly local in action space. Next we examine the same type of local perturbation applied to an open system: branched flow. Caustics in the manifold of trajectories have been implicated in the formation of strong branches. We show that caustic formation is intimately tied to compression of manifolds of trajectories in phase space, which has important implications for the position space density. We introduce the "Kick and Drift" model, a generalization of the standard map. The model is a good approximation to the full two dimensional dynamics of a wave propagating over a weak random potential, but it provides a simpler framework for studying branched flow. Next we develop a classical model for electrons executing cyclotron motion in a graphene flake and implement it numerically. We derive classical equations of motion for electrons moving through the graphene flake with a position dependent effective mass due to fluctuations in the background carrier density. I apply these methods to an experiment performed by the Westervelt group. They imaged the flow of electrons in a graphene flake by measuring the transresistance as they rastered a charged scanning probe microscope tip over the surface. My simulations show that the regions with the greatest change in transresistance do always coincide with the regions with the highest current density. Furthermore I show that the experimental results can qualitatively reproduced by treating the system classically. Finally, we extend Heller's thawed Gaussian approximation from second order in the classical action to third order, in order to capture curvature in phase space. Such phase space dynamics are ubiquitous in systems with weak random potentials, such as those discussed above. We derive a closed form solution, but find that more work needs to be done to make it numerically tractable and competitive with other methods. A semiclassical method capturing phase space curvature could provide insight into the behavior of scars away from the hbar goes to zero limit.
Physics

Thesis (Ph. D.)--University of California, San Diego, 2009.
Title from first page of PDF file (viewed October 22, 2009). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 155-163).

Intramolecular non-covalent interactions between aromatic ligands in chiral Ru(II) and Co(III) complexes have been investigated in this study. Several investigations were carried out and findings given. The results of the study, which demonstrate the significance of non-covalent interactions involving aromatic residues to the determination of the molecular conformation, serve to highlight the suitability of simple chiral metal complexes to act as models for interactions

Thesis (Ph.D.) -- University of Western Sydney, 2003.
"A thesis submitted as a requirement for admission to the degree of Doctor of Philosophy" Includes bibliographical references (leaves vi, 194-200).

The strong association of the human leukocyte antigen HLA-B27 (B27), with spondyloarthropathies (SpA), was discovered more than four decades ago, yet the role B27 plays in disease pathogenesis remains unclear. It has been demonstrated that HLA-B27 can form non-classical FHC forms, including B27 FHC homodimers (B272) and misfolded FHCs. Two leading theories of SpA pathogenesis proposed that both cell surface NC-B27 (the B27 homodimer theory) and intracellular (the B27 misfolding and UPR theory) can drive immune responses in SpA. Several studies demonstrated that cell surface NC-B27 binds to immune receptors and suggested that these interactions can activate Th17 immunity. My DPhil project focuses on the investigation of the cell surface expression of NC-B27 molecules in cells and tissues obtained from AS patients and B27 TG2 rats. I used both existing reagents and a novel HD6 antibody, generated against B272, to examine the expression of HLA-B27 by flow cytometry, confocal microscopy and immunoprecipitation. This thesis provides evidence that the expression of HD6- and HC10-reactive molecules in AS patients is rather restricted to specific cell types (e.g. osteoclasts) and possibly particular environmental factors and tissue types (e.g. synovial fluid and joint tissue). My data using B27 TG2 rats demonstrated that resident joint cells express HD6- and HC10-reactive molecules before the onset of clinical manifestations. Furthermore, I showed increased expression of NC-B27 on antigen presenting cells (APCs), and CD161+ and CD8+ cell populations in blood and secondary lymphoid organs. Based on these findings I hypothesized that cell surface expression of NC-B27 may not only be crucial for activation of Th17-driven immune responses, but may also shift the balance between immune tolerance and activation. Importantly, the expression of potentially pathogenic HD6-reactive molecules is restricted to specific cell and tissue types hence HD6 antibody may be a potential future therapeutic agent in SpA.

Aquesta tesis parteix d'una pregunta aparentment ingènua: Què passa si es separen dos sistemes físics que estaven en contacte? Un dels descobriments més rellevants del segle passat és que els sistemes que obeeixen les lleis de la mecànica quàntica, en comptes de les lleis clàssiques, romanen intrínsecament connectats fins i tot quan estan separats físicament. Aquest fenomen és conegut com entrellaçament o entanglement. Aquí, ens preguntem quelcom més profund: pertany l'entrellaçament exclusivament als sistemes quàntics o és comú a totes les teories no clàssiques? I, donat el cas, com es pot comparar l'entrellaçament quàntic amb l'entrella çament que pertany a d'altres teories? La primera part de la tesis tracta amb aquestes qüestions considerant la teoria quàntica com a part d'un grup més ampli de teories físiques anomenat general probabilistic theories (GPTs). El Capítol 1 repassa les motivacions que hi ha darrera el formalisme GPT, contextualitzant el Capítol 2, on plantegem les preguntes mencionades en conjectures formals adjuntant-ne la nostre contribució cap a una solució completa. Al Capítol 3, considerem l'entrellaçament a nivell de mesures i no d'estats, la qual cosa ens porta cap a la investigació d'una de les seves principals implicacions, data hiding. En aquest marc, determinem la màxima efi ciència de el data hiding que un sistema quàntic pot exhibir i també el màxim valor entre tots els GPTs, trobant que els primers escalen amb l'arrel quadrada dels darrers. En la segona part d'aquest manuscrit estudiem alguns problemes relacionats amb l'entrellaçament quàntic. Al Capítol 4, discutim la seva resistència al soroll blanc, modelitzat amb canals que actuen tant local com globalment. Aquests canals depenen d'un nombre limitat de paràmetres, això fa que siguem capaços de respondre totes les preguntes bàsiques relacionades amb les propietats de transformació de l'entrellaçament. El Capítol 5 presenta la nostre visió sobre l'entrellaçament gaussià, amb especial focus en el rol del anomenat `positive partial transposition cri- terion' en aquest context. Extensament, fent servir tècniques d'anàlisis de matrius com ara Schur complements i matrix means, presentem demostracions de resultats clàssics generalitzant-los i resolent algun dels problemes oberts existents en la matèria. La tercera part de la tesis es basa en formes més generals de correlacions no clàssiques en sistemes bipartits i de variable contínua. Al Capítol 6 investiguem el Gaussian steering i problemes relacionats en la seva quantificació, així com presentem un esquema general que permeti consistentment classificar correlacions de sistemes bipartits gaussians en `clàssiques' i `quàntiques'. Finalment, el Capítol 7 explora alguns dels problemes relacionats amb strong subadditivity en desigualtats de matrius que juga un paper clau en el nostre anàlisis de correlacions en estats gaussians bipartits. Entre d'altres coses, la teoria que desenvolupem ens serveix per concloure que una Rényi-2 versió gaussiana del difús squashed entanglement coincideix amb el corresponent entrellaçament de formació quan s'avalua en estats gaussians.
Esta tesis versa sobre una cuestión aparentemente naíf: ¿qué ocurre cuando se separan dos sistemas físicos que estaban juntos previamente? Uno de los mayores descubrimientos del siglo pasado es que los sistemas que obedecen leyes mecano-cuánticas, en lugar de clásicas, permanecen ligados inextricablemente incluso tras haber sido separados físicamente, un fenómeno conocido como entrelazamiento. Aquí nos preguntamos algo más profundo si cabe: ¿es el entrelazamiento una característica exclusiva de los sistemas cuánticos o es común a todas las teorías no-clásicas? Y, si es este el caso, ¿cuán fuerte es el entrelazamiento mecano-cuántico comparado con aquel exhibido por otras teorías? La primera parte de esta tesis trata estas cuestiones considerando la teoría cuántica como parte de un conjunto más amplio de teorías físicas, colectivamente llamadas teorías probabilísticas generales (TPG). En el Capítulo 2 revisamos la sólida motivación que subyace al formalismo TPG, preparando el terreno para el Capítulo 2, donde traducimos las anteriores cuestiones a conjeturas precisas, y donde presentamos nuestro progreso hacia una solución completa. En el Capítulo 3 consideramos el entrelazamiento a nivel de medidas en vez de estados, lo cual conduce a la investigación de una de sus implicaciones principales, la ocultación de información. En este contexto, determinamos el máximo poder de ocultación de información que puede exhibir un sistema mecano-cuántico, así como el mayor valor entre todas las TPG, hallando que el primero crece como la raíz cuadrada del segundo. En la segunda parte de este manuscrito exploramos algunos de los problemas relacionados con el entrelazamiento cuántico. En el Capítulo 4 discutimos su resistencia al ruido blanco modelado por canales que actúan bien local o bien globalmente. Debido al número limitado de parámetros de los que dependen estos canales, somos capaces de responder todas las preguntas básicas que conciernen a diversas propiedades de la transformación del entrelazamiento. En el siguiente Capítulo 5 presentamos nuestra perspectiva sobre el tema del entrelazamiento gaussiano, con un énfasis particular sobre el papel del célebre \criterio de la transposición parcial positiva" en este contexto. Empleando extensivamente herramientas del análisis matricial como los complementos de Schur y las medias matriciales, presentamos pruebas unificadas de resultados clásicos, extendiéndolos y cerrando algunos de los problemas abiertos en el campo. La tercera parte de esta tesis se ocupa de formas más generales de correlaciones no-clásicas en sistemas bipartitos de variable continua. En el Capítulo 6 estudiamos el \steering" gaussiano y problemas relacionados con su cuantificaci ón, y dise~namos un esquema general que permite clasificar consistentemente correlaciones de estados gaussianos bipartitos en \clásicas" y \cuánticas". Finalmente, en el Capítulo 7 exploramos algunos problemas vinculados a una desigualdad matricial de \subaditividad fuerte" que desempe~na un papel crucial en nuestro análisis de las correlaciones en los estados gaussianos bipartitos. Entre otras cosas, la teoría que desarrollamos nos permite concluir que una versión Rényi-2 gaussiana del escurridizo squashed entanglement coincide en estados gaussianos con el correspondiente entrelazamiento de formación
This thesis is concerned with a seemingly naive question: what happens when you separate two physical systems that were previously together? One of the greatest discovery of the last century is that systems that obey quantum me- chanical instead of classical laws remain inextricably linked even after they are physically separated, a phenomenon known as entanglement. This leads im- mediately to another, deep question: is entanglement an exclusive feature of quantum systems, or is it common to all non-classical theories? And if this is the case, how strong is quantum mechanical entanglement as compared to that exhibited by other theories? The first part of the thesis deals with these questions by considering quan- tum theory as part of a wider landscape of physical theories, collectively called general probabilistic theories (GPTs). Chapter 1 reviews the compelling motiva- tions behind the GPT formalism, preparing the ground for Chapter 2, where we translate the above questions into precise conjectures, and present our progress toward a full solution. In Chapter 3 we consider entanglement at the level of measurements instead of states, which leads us to the investigation of one of its main implications, data hiding. In this context, we determine the maximal data hiding strength that a quantum mechanical system can exhibit, and also the maximum value among all GPTs, finding that the former scales as the square root of the latter. In the second part of this manuscript we explore some problems connected with quantum entanglement. In Chapter 4 we discuss its resistance to white noise, as modelled by channels acting either locally or globally. Due to the limited number of parameters on which these channels depend, we are able to answer all the basic questions concerning various entanglement transformation properties. The following Chapter 5 presents our view on the topic of Gaussian entanglement, with particular emphasis on the role of the celebrated `positive partial transposition criterion' in this context. Extensively employing matrix analysis tools such as Schur complements and matrix means, we present unified proofs of classic results, further extending them and closing some open problems in the field along the way. The third part of this thesis concerns more general forms of non-classical correlations in bipartite continuous variable systems. In Chapter 6 we look into Gaussian steering and problems related to its quantification, moreover devising a general scheme that allows to consistently classify correlations of bipartite Gaussian states into `classical' and `quantum' ones. Finally, Chapter 7 explores some problems connected with a `strong subadditivity' matrix inequality that plays a crucial role in our analysis of correlations in bipartite Gaussian states. Among other things, the theory we develop allows us to conclude that a Rényi-2 Gaussian version of the elusive squashed entanglement coincides with the corre- sponding entanglement of formation when evaluated on Gaussian states.

This thesis intends to familiarize the reader with the concepts of photon statistics and correlations in quantum optics. Developing light sources that emit quantum states is central for the realization of quantum technologies. One important step in characterizing these sources is the measurement of field fluctuations and correlations, by coincidence measurements. The expectation value of a coincidence measurement, a simultaneous measurement of two intensities (or, more general, four fields), is represented by the fourth-order correlation function. The value of the correlation function, at zero delay between the detection of two photons, reveals important properties of the state to which they belonged, for example the fluctuations of the photon number. Since predictability is important for many applications, light sources emitting single photons are also characterized by the indistinguishability of consecutively emitted photons, or of two photons from separate emitters. In paper I we investigate blinking behaviour in quantum emitters, and its effect on the interference pattern and photon statistics with photons from two separate emitters. Blinking refers to an emitters transition into a non-emitting state, and subsequent transition back to an emitting state. We show that blinking can not be treated as linear loss, when measuring the fourth-order correlation function for two emitters in a Hong-Ou-Mandel setup. In general, a measurement of the fourth-order correlation function is robust to loss, which makes it a very practical tool. However, the relation between recorded coincidence counts and the correlation function is only direct in the limit of zero detection efficiency, and depends on the detection system. In paper II, we show that by adding a variable attenuation in the beam path, we can trace back to the ''true'' value of the correlation function at zero quantum efficiency. This method improves accuracy in correlation measurements by decreasing a systematic error at the expense of an increased statistical error, which is easier to handle, extending the use of coincidence methods to classical and non-classical multi-photon states.

QC 20180517

Non-classical logics, or variants of non-classical logics, have rapidly been developed together with the progress of computer science since the 20th century. Typically, we have found that many variants of non-classical logics are represented as ordered algebraic structures, more precisely as lattice expansions. From this point of view, we can think about the study of ordered algebraic structures, like lattice expansions or more generally poset expansions, as a universal approach to non-classical logics. Towards a general study of non-classical logics, in this dissertation, we discuss canonicity and bi-approximation in non-classical logics, especially in lattice expansions and poset expansions. Canonicity provides us with a connection between logical calculi and space-based semantics, e.g. relational semantics, possible world semantics or topological semantics. Note that these results are traditionally considered over bounded distributive lattice-based logics, because they are based on Stone representation. Today, thanks to the recent generalisation of canonical extensions, we can talk about the canonicity over poset expansions. During our investigation of canonicity over poset expansions, we will find the notion of bi-approximation, and apply it to non-classical logics, especially with resource sensitive logics.

One of the main goals of the theory of open quantum systems is to devise methods which help preserve the quantum properties of a system interacting with its environment. One possible pathway to achieve this goal is to use non-Markovian reservoirs, characterized by information backflows and revivals of certain quantum properties. These reservoirs usually require advanced engineering techniques, which may turn their implementation impractical. In this dissertation we propose an alternative technique: the injection of a classical colored noise, which induces the desired quantum non-Markovianity. In order to do that, we investigate the dynamics of a quantum system interacting with its surrounding environment and under the injection of a classical stochastic colored noise. A time-local master equation for the system is derived by using the stochastic wave function formalism and functional calculus. Afterwards, the non-Markovianity of the evolution is detected by using the Andersson, Cresser, Hall and Li measure, which is based on the decay rates of the master equation in canonical Lindblad-like form. Finally, we evaluate the measure for three different colored noises and study the interplay between environment and noise pump necessary to induce quantum non-Markovianity, as well as the energy balance of the system.
Um dos objetivos principais da teoria de sistemas quânticos abertos é desenvolver métodos que ajudem a preservar as propriedades quânticas de um sistema interagindo com o ambiente. Um possível caminho para alcançar essa meta é usar reservatórios não-Markovianos, caracterizados por refluxos de informação e renascimento de certas propriedades quânticas. Esses reservatóris geralmente requerem o uso de técnicas avançadas de engenharia, o que pode tornar sua implementação impraticável. Nessa dissertação nós propomos uma técnica alternativa: a injeção de um ruído colorido clássico, o qual induz a desejada não-Markovianidade quântica. De modo a fazer isso, nós investigamos a dinâmica de um sistema quântico interagindo com o ambiente e sob a injeção de um ruído colorido clássico estocástico. Uma equação mestra local no tempo é derivada usando-se do formalismo da função de onda estocástica e de técnicas de cálculo funcional. Após isso, a não-Markovianidade da evolução é detectada através da medida de Andersson, Cresser, Hall e Li, a qual é baseada nos coeficientes da equação mestra na forma de Lindblad-like canônica. Finalmente, nós calculamos a medida para três diferentes ruídos coloridos e estudamos a relação entre o ambiente e o bombeio estocástico necessária para induzir não-Markovianidade quântica, assim como o balanço de energia do sistema.

This thesis develops techniques and ideas on proof search. Proof search is used with one of two meanings. Proof search can be thought of either as the search for a yes/no answer to a query (theorem proving), or as the search for all proofs of a formula (proof enumeration). This thesis is an investigation into issues in proof search in both these senses for some non-classical logics. Gentzen systems are well suited for use in proof search in both senses. The rules of Gentzen sequent calculi are such that implementations can be directed by the top level syntax of sequents, unlike other logical calculi such as natural deduction. All the calculi for proof search in this thesis are Gentzen sequent calculi. In Chapter 2, permutation of inference rules for Intuitionistic Linear Logic is studied. A focusing calculus, ILLF, in the style of Andreoli ([And92]) is developed. This calculus allows only one proof in each equivalence class of proofs equivalent up to permutations of inferences. The issue here is both theorem proving and proof enumeration. For certain logics, normal natural deductions provide a proof-theoretic semantics. Proof enumeration is then the enumeration of all these deductions. Herbelin's cut- free LJT ([Her95], here called MJ) is a Gentzen system for intuitionistic logic allowing derivations that correspond in a 1-1 way to the normal natural deductions of intuitionistic logic. This calculus is therefore well suited to proof enumeration. Such calculi are called 'permutation-free' calculi. In Chapter 3, MJ is extended to a calculus for an intuitionistic modal logic (due to Curry) called Lax Logic. We call this calculus PFLAX. The proof theory of MJ is extended to PFLAX. Chapter 4 presents work on theorem proving for propositional logics using a history mechanism for loop-checking. This mechanism is a refinement of one developed by Heuerding et al ([HSZ96]). It is applied to two calculi for intuitionistic logic and also to two modal logics; Lax Logic and intuitionistic S4. The calculi for intuitionistic logic are compared both theoretically and experimentally with other decision procedures for the logic. Chapter 5 is a short investigation of embedding intuitionistic logic in Intuitionistic Linear Logic. A new embedding of intuitionistic logic in Intuitionistic Linear Logic is given. For the hereditary Harrop fragment of intuitionistic logic, this embedding induces the calculus MJ for intuitionistic logic. In Chapter 6 a 'permutation-free' calculus is given for Intuitionistic Linear Logic. Again, its proof-theoretic properties are investigated. The calculus is proved to be sound and complete with respect to a proof-theoretic semantics and (weak) cut- elimination is proved. Logic programming can be thought of as proof enumeration in constructive logics. All the proof enumeration calculi in this thesis have been developed with logic programming in mind. We discuss at the appropriate points the relationship between the calculi developed here and logic programming. Appendix A contains presentations of the logical calculi used and Appendix B contains the sets of benchmark formulae used in Chapter 4.

This project relates to the non-classical growth of inorganic crystals with interesting morphologies that are highly desirable in industry. All crystals were synthesized via hydrothermal or solvothermal methods and their growth was studied by stopping each reaction at a range of different times, extracting the particles and analysing them using a variety of characterisation techniques. The main techniques used were scanning electron microscopy and transmission electron microscopy but other techniques, such as powder X-ray diffraction and thermal gravimetric analysis, were also employed. Decorated ZnO microstadiums were studied where ZnO nanocones coat the inner and outer columnar walls of ZnO microstadiums. It was revealed that the polymer in the synthetic solution enhanced the aggregation of nanocrystallites of precursor ions on the microstadium surfaces, which then underwent recrystallization, forming ZnO nanocones. The presence of organic agents was also found to be crucial in the non-classical growth mechanisms of CaCO₃ and RHO-ZIF crystals as the presence of charged groups on the organic molecules led to the aggregation of precursor molecules/ions, preventing classical growth. The disordered aggregates underwent surface recrystallization, forming ‘core-shell' structures where a thin layer of single crystal encased a disordered core. Over time the crystallisation extended from the surface inwards, towards the core, until true single crystals were formed. Organic molecules were also shown to play a role in the non-classical growth of 8-branched Cu₂O structures. In this case, however, studies of the electronic configuration of the main terminating facets of Cu₂O crystals revealed another key factor in their non-classical growth. Terminating hydroxyl groups on the Cu₂O surfaces could have different charges depending on the number of Cu⁺ ions they were coordinated to. The terminating {111} faces were the only ones to be coated with negatively charged hydroxyl groups, which explained the rapid growth on these surfaces as they were able to attract the positively charged metal/polymer precursor clusters. This new phenomenon was also found to be the main driving force in the rapid growth of branches in snowflake-like Fe₂O₃ crystals despite no organic agent being used. In this case, the {11-20} faces of the seed crystals had positively charged hydroxyl groups that were able to rapidly attract the negatively charged [Fe(CN) ₆]³⁻ ions in the aqueous solution.

This dissertation examines the application of the Liouville operator to problems in classical mechanics. An approximation scheme or methodology is sought that would allow the calculation of the position and momentum of an object at a specified later time, given the initial values of the object's position and momentum at some specified earlier time. The approximation scheme utilizes matrix techniques to represent the Liouville operator. An approximation scheme using the Liouville operator is formulated and applied to several simple one-dimensional physical problems, whose solution is obtainable in terms of known analytic functions. The scheme is shown to be extendable relative to cross products and powers of the variables involved. The approximation scheme is applied to a more complicated one-dimensional problem, a quartic perturbed simple harmonic oscillator, whose solution is not capable of being expressed in terms of simple analytic functions. Data produced by the application of the approximation scheme to the perturbed quartic harmonic oscillator is analyzed statistically and graphically. The scheme is reapplied to the solution of the same problem with the incorporation of a drag term, and the results analyzed. The scheme is then applied to a simple physical pendulum having a functionalized potential in order to ascertain the limits of the approximation technique. The approximation scheme is next applied to a two-dimensional non-perturbed Kepler problem. The data produced is analyzed statistically and graphically. Conclusions are drawn and suggestions are made in order to continue the research in several of the areas presented.
Ph. D.

New materials can be fabricated using small scaled building blocks as a repetition unit. Nanoparticles with their unique size-tuneable properties from quantum confinement can especially be utilised to form two- and three-dimensional ordered assemblies to introduce them into what would normally be considered to be incompatible matrices. Furthermore, new collective properties that derive from the ordered arrangement of the building blocks, are accomplished. Additionally, different materials can be combined by mixing different building blocks during self-assembly, so that size ranges and material combinations that are difficult to achieve by other means can be formed. The arrangement of small particles into highly ordered arrangements can be realised via self-assembly. To achieve such assemblies, highly monodisperse nanoparticular building blocks with a size distribution below 5 % have to be synthesised. The production and variation in the size of both lead chalcogenide and noble metal nanoparticles is presented in this work. Moreover, the syntheses of multicomponential nanoparticles (PbSe/PbS and Au/PbS) are investigated. Non-classical crystallisation methodologies with their varyious self-assembly mechanisms are used for the formation of highly symmetrical mesocrystals and supracrystals. Analogous to classical crystallisation methods and their formation processes the interparticle interactions, attractive as well as repulsive, determine the resulting crystalline structure. Variation of the environmental parameters consequently leads to structural variation due to the changing interparticle interactions. In contrast to classical crystallisation the length scale of the interparticle forces stays constant as the size dimension of the self-assembled building unit is changed. Two different non-classical crystallisation pathways are investigated in this work. One pathway focuses on the slow destabilisation of nanoparticles in organic media by the addition of a non-solvent. In this approach optimisation of parameters for the formation of highly symmetrical three-dimensional mesostructures are studied. Furthermore, to shine some light onto the mechanism of self-assembly, the intrinsic arrangement of the building units in a mesocrystal and the steps of non-solvent addition are analysed. The mechanistic investigations explain the differences observed in mesocrystal formation between metal and semiconductor nanoparticles. The lower homogeneity of the building units of the metal nanoparticles leads to smaller and less defined superstructures in comparison to semiconductor building blocks. Another pathway of non-classical crystallisation is the usage of electrostatic interactions as the driving force for self-assembly and supracrystal formation. Therefore, the building blocks are transferred into aqueous media and stabilised with oppositely charged ligands. The well-know procedure for metal nanoparticles was adapted for semiconductor materials. The lower stability of these nanoparticles in aqueous solution induces an agglomeration of the semiconductor nanoparticles without including oppositely charged metal nanoparticles. The destabilisation effect can be increased by the addition of equally charged metal nanoparticles in a salting out type process. In comparison to the slow formation of mesocrystals achieved via destabilisation in an organic media (up to 4 weeks), the salting out procedure takes place within two hours, but the faster agglomeration causes a less well defined assembly of the building units in the mesocrystals. Moreover, the arrangement of semiconductor nanoparticles with organic molecules such as polymers and proteins was investigated in order to use the nanoparticles as a light harvesting component. In combination with the directly bound polymer the charge carrier may be directly transferred to the conductive thiophene-based polymer, so that infrared light can be transformed into an electrical signal for use in further applications such as solar cells. The advantage of the nanoparticle-protein system is the self-assembly across a liquid-liquid interface and additionally a Förster resonance energy transfer can occur at this phase boundary. Hence, it is possible to transfer highly energetic photons directly to biological samples without destroying the biological material.

In Reaction-Diffusion systems, some parameters can influence the behavior of other parameters in that system. Thus reaction diffusion equations are often used to model the behavior of biological phenomena. The Fitzhugh Nagumo partial differential equation is a reaction diffusion equation that arises both in population genetics and in modeling the transmission of action potentials in the nervous system. In this paper we are interested in finding solutions to this equation. Using Lie groups in particular, we would like to find symmetries of the Fitzhugh Nagumo equation that reduce this non-linear PDE to an Ordinary Differential Equation. In order to accomplish this task, the non-classical method is utilized to find the infinitesimal generator and the invariant surface condition for the subgroup where the solutions for the desired PDE exist. Using the infinitesimal generator and the invariant surface condition, we reduce the PDE to a mildly nonlinear ordinary differential equation that could be explored numerically or perhaps solved in closed form.

For 200 years, Fourier’s law has been used to describe heat transfer with excellent results. However, as technology advances, more and more situations arise where heat conduction is not well described by the classical equations. Examples are applications with extremely short time scales such as ultra fast laser heating, or very small length scales such as the heat conduction through nanowires or nanostructures in general. In this thesis we investigate alternative models which aim to correctly describe the non-classical effects that appear in extreme situations and which Fourier’s law fails to describe. A popular approach is the Guyer-Krumhansl equation and the framework of phonon hydrodynamics. This formalism is particularly appealing from a mathematical point of view since it is analogous to the Navier-Stokes equations of fluid mechanics, and from a physical point of view, since it is able to describe the physics in a simple and elegant way. In the first part of the thesis we use phonon hydrodynamics to predict the size-dependent thermal conductivity observed experimentally in nanostructures such as nanowires or thin films. In particular, we show that the Guyer-Krumhansl equation is suitable to capture the dependence of the thermal conductivity on the size of the physical system under consider- ation. During the modelling process we use the analogy with fluids to incorporate a slip boundary condition with a slip coefficient that depends on the ratio of the phonon mean free path to the characteristic size of the system. With only one fitting parameter we are able to accurately reproduce experimental observations corresponding to nanowires and nanorods of different sizes. The second part of the thesis consists of studying the effect of the non-classical fea- tures on melting and solidification processes. We consider different extensions and in- corporate them into the mathematical description of a solidification process in a simple, one-dimensional geometry. In chapter 5 we employ an effective Fourier law which replaces the original thermal conductivity by a size-dependent expression that accounts for non-local effects. In chapter 6 we use the Maxwell-Cattaneo and the Guyer-Krumhansl equations to formulate the Maxwell-Cattaneo-Stefan and the Guyer-Krumhansl-Stefan problems respec- tively. After performing a detailed asymptotic analysis we are able to reduce both models to a system of two ordinary differential equations and obtain excellent agreement with the cor- responding numerical solutions. In situations near Fourier resonance, which is a particular case where non-classical effects in the Guyer-Krumhansl model cancel each other out, the solidification kinetics are very similar to those described by the classical model. However, in this case we see that non-classical effects are still observable in the evolution of the heat flux through the solid, which suggests that this is a quantity which is more convenient to determine the presence of these effects in phase change processes.
La llei de Fourier ha estat una peça clau per a descriure la conducció de calor des de que fou proposada fa gairabé 200 anys. No obstant, a mesura que avança la tecnologia ens hi trobem més sovint amb situacions on les equacions clàssiques perden la seva validesa. En aquesta tesi investiguem alguns models alternatius que tenen com a objectiu descriure la conducció de calor en situacions on la llei de Fourier no és aplicable. Un model que s'ha aconseguit establir com un extensió vàlida de la llei de Fourier és l'equació de Guyer i Krumhansl i el marc de la hidrodinàmica de fonons derivat d'aquesta. Es tracta d'un model particularment interessant, ja que les equacions són anàlogues a les equacions per a fluids dins de la hidrodinàmica clàssica. A la primera part de la tesi considerem aquesta equació per a descriure la conducció de calor estàtica per nanofibres de seccions transversals circulars i rectangulars. En particular, calculem una conductivitat tèrmica efectiva i trobem que és possible reproduïr els resultats experimentals amb un sol paràmetre d'adjust. En el cas de nanofibres cilíndriques, no és necessari cap paràmetre d'adjust si es consideren unes certes condicions de vora per al flux. Una conseqüència d'haver de considerar extensions per a la llei de Fourier és que s'ha d'estudiar l'efecte que tenen aquests canvis en la descripció de processos de canvi de fase. En la segona part de la tesi investiguem els efectes que tenen diversos models sobre la solidificació d'un líquid unidimensional. Al capítol 5 estudiem el cas en el que considerem la conductivitat tèrmica com a una funció de la mida del sòlid i que incorpora característiques que són importants quan el tamany del sòlid és comparable a les longituds característiques dels fonons, mentres que al capítol 6 considerem l'equació de Guyer i Krumhansl dels capítols anteriors. En ambdós casos, un anàlisi asimptòtic ens permet reduïr la complexitat del problema i proposar models reduïts formats per un parell de'equacions diferencials ordinàries.

My Ph.D. thesis constitutes an investigation into the ways in which non-verbal communication (NVC) is represented and relayed by ancient authors through the use of the written word. This written expression of NVC can be represented in conjunction with oral communication, or independently of it, offering intentionally chosen insight into particular perspectives, concepts or situations. The reasons why a specific author, or authors, chose to include certain non-verbal details are considered, as is the cultural, symbolic, and literary significance of each example. The thesis approaches the subject from historical, anthropological, sociological and philosophical perspectives, while retaining an appreciation of the chronological and methodological limitations of studying the behaviour of a society which cannot be directly experienced. My thesis is intended to fill a gap in the historical scholarship of classical Athens as, with a few notable exceptions, the study of NVC remains virtually ignored by ancient historians and classicists. Indeed, most of the research in this area belongs to the discipline of art history and does not include a thorough consideration of the subject through the use of literary and historical sources. My research of NVC includes the study of gesture and body language, as well as investigations into kinesics, manipulable elements of appearance, autonomic nervous system responses, haptics, posture, gait, and mobility. Within these areas of inquiry there exist sub-divisions that must also be taken into consideration, e.g., gender, age, socio-economic status, and race. Furthermore, the symbolism and meaning of any element of NVC do not remain static, and the changes and alterations occurring within the means of communication of the society under investigation are critical to any attempt at understanding the role of NVC in that community. The point of departure for my research is the Attic orators. However, the scope of my work is by no means limited to oratory. Descriptions of NVC are used throughout Greek prose and verse, allowing a web of comparable and conflicting usage to be unravelled. Of particular interest to my work is the influence of early physiognomies and physiognomical thought on the textual usage of the body. In order to establish continuity or change in the attitudes and understanding of NVC in antiquity, the texts I consider are not restricted to the classical period, but spread into adjacent centuries. For methodological reasons, I have divided this dissertation according to body part or function, and have chosen particular aspects of NVC for detailed analysis, both on a practical and on a theoretical level. While each body movement represents a certain emotion or symbolises a particular response or message, bodily traits and actions need also be considered within the wider context of Greek thought. Bodily movement and expression are evaluated in relation to basic Greek concepts such as the psyche, the body, schema, beauty, civic ideals and values, etc. My thesis deals with NVC both as an expression of the ideal and as a possible reflection of reality, taking into consideration its role both as a means to fantasise and as a tool of criticism.