Stretchable Electronics is an emerging class of electronics that allow electronics to be bent, conform, ex and stretch while still retaining its full functionality. Other than bending, existing and conforming, adding stretchability to electronic systems can open up a new frontier for a myriad of applications. Especially in the medical sector, these stretchable devices can increase the scope of monitoring and ease and comfort of the patient. All kinds of wearable devices can be based on these technologies to augment our daily lives. With the kind of state of art technology available to the common man today, the bar has already been set for the performance of such devices. Hence, its imperative that these stretchable devices perform at this level and should be capable of adapting to the market to serve the mass requirement. Hence, it becomes inevitable to use metal interconnects to provide very low resistance and easy adhesion to commercial electronic components. Another aspect of such devices is an adhesion ability with which we can attach it to various kinds of surfaces. In this thesis, we propose a new multi-layered PDMS structure approach to bring stretchability in the device. For all kinds of adhesion requirements, various ratios of PDMS: Cross-linker have been used. These different ratios of PDMS: Cross-linker changes the mechanical and adhesive properties of the cured PDMS. Hence, the same material can be used as the stretchable substrate as well as to serve various adhesion requirements. A soft adhesion allows us to attach it to the human body/other surfaces. The adhesion can be tailored to be quite conformal and strong, yet its removal is quite gentle to the skin. A higher curing ratio makes the PDMS very sticky and soft. Aluminum/Copper foils can be directly stuck upon it and tracks can be then etched out to get a printed circuit. Since this adhesive layer is quite soft, it acts as a cushion and reduces the amount of stress transferred to the metal interconnects. Hence, stretchable circuits with metal interconnects can be realized. The electronic components can be then attached upon it via normal soldering techniques/using conductive ink. Various devices that can be built with the proposed techniques have been coined the term CAS (Conformal Active Sheets) to allow easy reference to such kind of devices. Since the substrate is soft, physical handling of such devices becomes an issue as one tries to transfer the circuit pattern. Hence, direct etching of the metal foil was explored via high pulsed current discharge technique. A CNC machine was also designed to try various ways of direct etching of the metal foil in an accurate and repeatable fashion.

The reduction of noise generated by new and existing engineering products is of increasing importance commercially, socially and environmentally. Commercially, the noise emission of vehicles, such as cars and aircraft, may often be considered a selling point and the effects of noise pollution on human health and the environment has led to legislation restricting the noise emissions of many engineering products. Noise prediction schemes are important tools to help us understand and develop a means of controlling noise. Acoustic problems present numerous challenges to traditional CFD-type numerical methods rendering all but the most trivial problems unsuitable. Difficulties relate to the length scale discrepancies which arise due to the relatively tiny pressure and density fluctuations of an acoustic wave propagating over large distancesto the point of interest; the result being large computational domains to capture wave behaviour accurately between source and observer. Noise prediction may be performed using a hybrid Computational Aero-Acoustics (CAA) scheme, an approach to noise prediction which alleviates many issues associated with exclusively numerical or analytical approaches. Hybrid schemes often rely on knowledge of a Green’s function, representing the scattering of the geometry, to propagate source fluctuations to the far-field. Presently, these functions only exist in analytical form for relatively simple geometries. This research develops principles for the robust calculation of Green’s functions for general situations. In order to achieve this, three techniques to computeGreen’s functions for the Helmholtz equation within an extended class of 2D geometries are developed, evaluated and compared. Where appropriate, their extension to 3D is described. Guidance is provided on the selection of a suitable numerical method in practice given knowledge of the geometry of interest. Through inclusion of the numerical methods for the construction of Green’s functions presented here, the applicability of existing hybrid schemes will be significantly extended. Thus, it is expected that noise predictions may be performed on a more general range of geometries while exploiting the computational efficiency of hybrid prediction schemes.

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Monocentric lenses provide compact, broadband, high resolution, wide-field imaging. However, they produce a curved image surface and have found limited use. The use of an appropriately machined fiber bundle to relay the curved image plane onto a flat focal plane array (FPA) has recently emerged as a potential solution. Unfortunately the spatial sampling that is intrinsic to the fiber bundle relay can have a negative effect on image resolution, and vignetting has been identified as another potential shortcoming of this solution. This thesis describes a metamaterial lens yielding a high-performance image relay from a curved surface to a flat focal plane. Using quasi-conformal transformation optics, a Maxwell's fish-eye lens is transformed into a concave-plano shape. A design with a narrower range of constitutive parameters is deemed more likely to be manufacturable. Therefore, the way in which the particular shape of the concave-plano reimager influences the range of needed constitutive parameters is explored. Finally, image quality metrics, such as spot size and light efficiency, are quantified.

Thermodynamical formalism is a relatively recent area of pure mathematics owing a lot to some classical notions of thermodynamics. On this thesis we state and prove some of the main results in the area of thermodynamical formalism. The first chapter is an introduction to ergodic theory. Some of the main theorems are proved and there is also a quite thorough study of the topology that arises in Borel probability measure spaces. In the second chapter we introduce the notions of topological pressure and measure theoretic entropy and we state and prove two very important theorems, Shannon-McMillan-Breiman theorem and the Variational Principle. Distance expanding maps and their connection with the calculation of topological pressure cover the third chapter. The fourth chapter introduces Gibbs states and the very important Perron-Frobenius Operator. The fifth chapter establishes the connection between pressure and geometry. Topological pressure is used in the calculation of Hausdorff dimensions. Finally the sixth chapter introduces the notion of conformal measures.

Cette thèse a pour but de résoudre certains problèmes de connexion et de décrire diverses propriétés asymptotiques des fonctions de Painlevé V et I. Dans le cas de l’équation de Painlevé V, nous approchons ces problèmes en développant une nouvelle approche basée sur la théorie conforme des champs bidimensionelle. Nous proposons de calculer les blocs conformes irréguliers de première et seconde espèce par confluence des blocs conformes réguliers de Virasoro. Une conséquence de cette construction est la solution du problème de connexion de l’équation de Painlevé V entre 0 et +i∞. Les formules pour les normalisations relatives (constantes de connexion) de la fonction tau de Painlevé V entre 0, +∞, et +i∞ sont également proposées. Enfin, le développement asymptotique complet de la fonction tau à courte distance pour des données de monodromie génériques est prouvé. Ce résultat est obtenu en construisant une représentation de la fonction tau en termes d’un déterminant de Fredholm. Dans le cas de l’équation de Painlevé I, nous présentons les constantes de connexion relatant les asymptotiques de la fonction tau sur les cinq raies canoniques à l’infini. Ce résultat est obtenu en construisant une extension de la forme différentielle de Jimbo-Miwa-Ueno à l’espace des données de monodromie. Ces constantes de connexion sont exprimées en termes de dilogarithmes de coordonnées de type cluster dans l’espace des données de Stokes. / The aim of this thesis is to solve several connection problems and describe asymptotic properties of Painlevé V and I functions. In the case of Painlevé V equation, we approach these problems by developing a new toolbox based on two dimensional conformal field theory. We propose to compute irregular conformal blocks of the first and second kind by confluence of regular Virasoro conformal blocks. One consequence of this construction is the solution of the connection problem for Painlevé V equation between 0 and +i∞. Formulas for the relative normalizations (connection constants) of Painlevé V tau function between 0, +∞, and +i∞ are also proposed. Finally, the full asymptotic expansion of the tau function at short distances for generic monodromy data is proved. This result is obtained by constructing a Fredholm determinant representation for the tau function. In the case of Painlevé I equation, we present connection constants relating asymptotics of the tau function on the five canonical rays at infinity. This result is obtained by extending the definition of the Jimbo-Miwa-Ueno differential to the space of monodromy data. These connection constants are expressed in terms of dilogarithms of cluster type coordinates on the space of Stokes data.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21567号 / 理博第4474号 / 新制||理||1642(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 高柳 匡, 教授 青木 慎也, 教授 田中 貴浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22233号 / 理博第4547号 / 新制||理||1653(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 河合 俊哉, 教授 大槻 知忠, 教授 入谷 寛 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Background: In drug discovery morphological profiles can be used to identify and establish a drug's biological activity or mechanism of action. Quantitative structure-activity relationship (QSAR) is an approach that uses the chemical structures to predict properties e.g., biological activity. Support Vector Machine (SVM) is a machine learning algorithm that can be used for classification. Confidence measures as conformal predictions can be implemented on top of machine learning algorithms. There are several methods that can be applied to improve a model’s predictive performance. Aim: The aim in this project is to evaluate if ligand-based modelling can be improved by combining features from chemical structures, target predictions and morphological profiles. Method: The project was divided into three experiments. In experiment 1 five bioassay datasets were used. In experiment 2 and 3 a cell painting dataset was used that contained morphological profiles from three different classes of kinase inhibitors, and the classes were used as endpoints. Support vector machine, liblinear models were built in all three experiments. A significant level of 0.2 was set to calculate the efficiency. The mean observed fuzziness and efficiency were used as measurements to evaluate the model performance. Results: Similar trends were observed for all datasets in experiment 1. Signatures+CDK13+TP which is the most complex model obtained the lowest mean observed fuzziness in four out of five times. With a confidence level of 0.8, TP+Signatures obtained the highest efficiency. Signatures+Morphological Profiles+TP obtained the lowest mean observed fuzziness in experiment 2 and 3. Signatures obtained the highest correct single label predictions with a confidence of 80%. Discussion: Less correct single label predictions were observed for the active class in comparison to the inactive class. This could have been due to them being harder to predict. The morphological profiles did not contribute with an improvement to the models predictive performance compared to Signatures. This could be due to the lack of information obtained from the dataset. Conclusion: A combination of features from chemical structures and target predictions improved ligand-based modelling compared to models only built on one of the features. The combination of features from chemical structures and morphological profiles did not improve the ligand-based models, compared to the model only built on chemical structures. By adding features from target predictions to a model built with features from chemical structures and morphological profiles a decrease in mean observed fuzziness was obtained.

This diploma thesis deals with the influence of the surface texturing of non-conformal surfaces at the friction coefficient. In the work were made adjustment of experimental apparatus for measuring friction in the contact between ball and flat disk. Friction coefficient was calculated by the size of the torque on the ball, which was measured by the torque sensor. For recording and processing signal from the sensor was designed software that makes it possible to measure the coefficient of friction for selected conditions (loading of contact, speed of rubbing surfaces and rolling-sliding conditions). Experiments were carried out with smooth and textured ball, glass, and steel disc at different speeds and rolling-sliding conditions. To determine the effect of the influence of the surface texturing at the friction coefficient the size of the coefficient of friction of smooth and textured ball was compared. It was found that the microtexture of the friction coefficient has little effect.