Inspired by biological membrane shaping in the cell through means of curvature-inducing proteins, we investigate the interplay between membrane curvature and the distribution and movement of shape-inducing objects which are free to move as a consequence of the underlying shape. We initially study the self-assembly of a filament, taken as a proxy for the cross-section of a biomembrane, which is primarily driven by the chemical kinetics of attaching proteins and find that, under certain mechanical stiffness regimes of the attaching proteins, pattern formation occurs. Regions of high and low protein concentration form before spatially uniform filament shapes are obtained by means of protein adhesion and movement governed by diffusion and local curvature-seeking. However, noting that the curvature-mediated protein movement on membranes has been biologically observed to be long-range, we next study the self-assembly of embedded inclusions on a membrane as a result of the underlying geometry. We first derive an interaction law for the shape-mediated interaction of inclusions which break symmetry and find that there is a finite equilibrium distance to which the inclusions will aggregate. We derive corresponding equations of motion which describe this curvature-mediated aggregation mechanism and, using this framework, we investigate some of the properties of these self-assembled configurations, including their energy, stability, and their collective elastic behavior. Lastly, we consider the interaction energies of embedded inclusions on a periodic domain and determine that this mechanism may explain computational results of how proteins form rings to promote tubulation on cylindrical membranes.

No description available.

In this thesis a number of issues related to oceanographic problems have been dealt with on the basis of applying asymptotic methods.  The first study focused on the tidal generation of internal waves, a process which is quantifed by the conversion rates. These have traditionally been calculated by using the WKB approximation. However, the systematic imprecision of this theory for the lowest modes as well as turbulence at the seabed level affect the results. To handle these anomalies we introduced another asymptotic technique, homogenization theory, which led to signifcant improvements, especially for the lowest modes.  The second study dealt with the dynamical aspects of a nonlinear oscillator which can be interpreted as a variant of the classical two-box models used in oceanography. The system is constituted by two connected vessels containing a fluid characterised by a nonlinear equation of state and a large volume differences between the vessels is prescribed. It is recognised that the system, when performing relaxation oscillations, exhibits almost-discontinuous jumps between the two branches of the slow manifold of the problem. The lowest-order analysis yielded reasonable correspondence with the numerical results.  The third study is an extension of the lowest-order approximation of the relaxation oscillations undertaken in the previous paper. A Mandelstam condition is imposed on the system by assuming that the total heat content of the system is conserved during the discontinuous jumps.  In the fourth study an asymptotic analysis is carried out to examine the oscillatory behaviour of the thermal oscillator. It is found that the analytically determined corrections to the zeroth-order analysis yield overall satisfying results even for comparatively large values of the vessel-volume ratio. / At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.

In this thesis, analytical analysis and design techniques for wireless communications with diversity are studied. The impact of impairments such as correlated fading is analyzed using statistical models. Countermeasures designed to overcome, or even exploit, such effects are proposed and examined. In particular two applications are considered, satellite broadcast to vehicular terminals and communication using transmitters and receivers equipped with multiple antennas. Mobile satellite broadcast systems offer the possibility of high data rate services with reliability and ubiquitous coverage. The design of system architectures providing such services requires complex trade-offs involving technical, economical, and regulatory aspects. A satisfactory availability can be ensured using space, terrestrial, and time diversity techniques. The amount of applied diversity affects the spectral efficiency and system performance. Also, dedicated satellite and terrestrial networks represent significant investments and regulatory limitations may further complicate system design. The work presented in this thesis provides insights to the technical aspects of the trade-offs above. This is done by deriving an efficient method for estimating what resources in terms of spectrum and delay are required for a broadcast service to reach a satisfactory number of end users using a well designed system. The results are based on statistical models of the mobile satellite channel for which efficient analytical design and error rate estimation methods are derived. We also provide insight to the achievable spectral efficiency using different transmitter and receiver configurations. Multiple-element antenna communication is a promising technology for future high speed wireless infrastructures. By adding a spatial dimension, radio resources in terms of transmission power and spectrum can be used more efficiently. Much of the design and analysis work has focused on cases where the transmitter either has access to perfect channel state information or it is blind and the spatial channels are uncorrelated. Herein, systems where the fading of the spatial channels is correlated and/or the transmitter has access to partial channel state information are considered. While maintaining perfect channel knowledge at the transmitter may prove difficult, updating parameters that change on a slower time scale could be realistic. Here we formulate analysis and design techniques based on statistical models of the multichannel propagation. Fundamental properties of the multi-element antenna channel and limitations given by information theory are investigated under an asymptotic assumption on the number of antennas on either side of the system. For example, limiting normal distributions are derived for the squared singular values of the channel matrix and the mutual information. We also propose and examine a practical scheme capable of exploiting partial channel state information. In both applications outlined above, by using statistical models of the channel characteristics in the system design, performance can be improved. The main contribution of this thesis is the development of efficient techniques for estimating the system performance in different scenarios. Such techniques are vital to obtain insights to the impact of different impairments and how countermeasures against these should be designed. / QC 20101019

No description available.

Šiame darbe atliekami stochastinių minimumų asimptotiniai tyrimai. Įrodomos minimumų ribinės teoremos tuo atveju, kai tiesinis normalizavimas neduoda neišsigimusių ribinių skirstinių, tokiu atveju taikau netiesinį minimumų normalizavimą. Konkretaus skirstinio atveju randamos netiesinės normalizavimo funkcijos, kurių pagalba yra gaunami minimumų klasikiniai ribiniai skirstiniai. Įrodoma Perkėlimo teorema netiesiniam normalizavimui. Darbo tikslai: • ištirti netiesinio normalizavimo reikalingumą; • išanalizuoti netiesinio normalizavimo galimybes minimumų schemoje. Darbo uždaviniai: • parinkti netiesinio normalizavimo funkciją konkretaus skirstinio atveju; • gauti ribinius klasikinius skirstinius, kai minimumai normalizuojami netiesiškai; • įvertinti konvergavimo greitį ribinėse teoremose; • atlikti aproksimavimo paklaidų kompiuterinę analizę. / This paper is the asymptotic analysis of stochastic minima. Proofs of minima limit theorems are provided for cases, when linear normalization does not give non-degenerate limit distributions. In this cases, non-linear minima normalization is used. For a specific distribution, non-linear normalization functions are calculated, which are then used to get classic limit distributions for minima. Objectives: • Examine the necessity of non-linear normalization; • Analyze the possibilities for non-linear normalization in minimum pattern. Tasks: • Choose non-linear normalization function for a specific distribution; • Get classic limit distributions, where minima are normalized non-linearly; • Investigate the rate of convergence within the limit theorems; • Perform computer-based analysis of approximation errors.

This thesis is concerned with the mathematical modelling of elastic-plastic deformation in regimes of stress far exceeding the yield stress. Such scenarios are typically encountered in violent impact testing, where millimetre-thick samples of metal are subjected to pressures on the order of the bulk modulus of the material. We begin with an overview of violent impact testing, with particular attention paid to a specific class of experiments known as isentropic compression experiments (ICEs), which will provide motivation for the mathematical modelling and analysis in subsequent chapters. In chapter 2, by appealing to sound notions from rational mechanics and thermodynamics, we construct a mathematical model which aims to encapsulate the essential phenomena involved in violent elastic-plastic deformation. This is followed in chapter 3 with a numerical analysis of the mathematical model in uniaxial strain, which is the geometry relevant ICEs. In chapters 4 and 5, we corroborate the observations made in chapter 3 via a systematic mathematical analysis. In particular, our focus will be on the elastic and plastic waves that can propagate through finite metal samples during isentropic compression. Finally, in chapter 6, we explore the applicability of our model to other geometries, specifically the radially axisymmetric expansion of a circular cavity embedded in an infinite elastic-plastic medium. We conclude with a summary of our findings and suggest some avenues for future investigation.

In screen-printed silicon-crystalline solar cells, the contact resistance of a thin interfacial glass layer between the silicon and the silver electrode plays a limiting role for electron transport. The motivation of this project is to gain increased understanding of the transport mechanisms of the electrons across this layer, which can be exploited to provide higher performance crystalline silicon solar cells. Our methodology throughout is to formulate and analyse mathematical models for the electron transport, based on the drift diffusion equations. In the first chapter we outline the problem and provide a summary of relevant theory. In Chapter 2 we formulate a one-dimensional model for electron transport across the glass layer, that we solve both numerically and by employing asymptotic techniques. Chapter 3 extends the model presented in Chapter 2 to two dimensions. To solve the two-dimensional model numerically we devise and validate a new spectral method. The short circuiting of current through thinner regions of the glass layer enables us to find limiting asymptotic expressions for the average current density for two different canonical glass layer profiles. In Chapter 4 we include quantum mechanical effects into the one-dimensional model outlined in Chapter 2 and find that they have a negligible effect on the contact resistance of the glass layer. We model the boundary effects present at the silicon emitter-glass interface in Chapter 5. Finally, in Chapter 6 we summarise our key results, suggest possible future work, and outline the implications of our work to crystalline silicon solar cell manufacturers.

Cette thèse porte sur la propagation des ondes acoustiques dans des milieux périodiques.Ces milieux ont des propriétés remarquables car le spectre associée à l’opérateur d’ondesdans ces milieux a une structure de bandes : il existe des plages de fréquences danslesquelles les ondes monochromatiques ne se propagent pas. Plus intéressant encore, enintroduisant des défauts linéiques dans ce type de milieux, on peut créer des modes guidésà l’intérieur de ces bandes de fréquences interdites. Dans ce manuscrit nous montrons qu’ilest possible de créer de tels modes guidés dans le cas de milieux périodiques particuliersde type quadrillage : plus précisément, le domaine périodique considéré est constitué duplan R2 privé d’un ensemble infini d’obstacles rectangulaires régulièrement espacés (d’unedistance ") dans deux directions orthogonales du plan, que l’on perturbe localement endiminuant la distance entre deux colonnes d’obstacles. Les résultats sont ensuite étendusau cas 3D.Ce travail comporte un aspect théorique et un aspect numérique. Du point de vue théoriquel’analyse repose sur le fait que, comme " est petit, le spectre de l’opérateur associé ànotre problème est "proche" du spectre d’un problème posé sur le graphe obtenu commela limite géométrique du domaine quand " tend vers 0. Or, pour le graphe limite, il estpossible de calculer explicitement le spectre. Ensuite, en utilisant des méthodes d’analyseasymptotique on étudie le spectre de l’opérateur non-limite. On illustre les résultats théoriquespar des résultats numériques obtenus à l’aide d’une méthode numérique spécialementdédiée aux milieux périodiques : cette dernière est basée sur la réduction du problèmede valeurs propres initial (linéaire) posé dans un domaine non-borné à un problème nonlinéaireposé dans un domaine borné (en utilisant l’opérateur de Dirichlet-to-Neumannexact). / The present work deals with propagation of acoustic waves in periodic media. Thesemedia have particularly interesting properties since the spectrum associated with theunderlying wave operator in such media has a band-gap structure: there exist intervals offrequences for which monochromatic waves do not propagate. Moreover, by introducinglinear defects in this kind of media, one can create guided modes inside the bands offorbidden frequences. In this work we show that it is possible to create such guidedmodes in the case of particular periodic media of grid type: more precisely, the periodicdomain in question is R2 minus an infinite set of rectangular obstacles periodically spacedin two orthogonal directions (the distance between two neighbour obstacles being "),which is locally perturbed by diminishing the distance between two columns of obstacles.The results are extended to the 3D case.This work has a theoretical and a numerical aspect. From the theoretical point of view theanalysis is based on the fact that, " being small, the spectrum of the operator associatedwith our problem is "close" to the spectrum of a problem posed on a graph which is ageometric limit of the domain as " tends to 0. However, for the limit graph the spectrumcan be computed explicitly. Then, we study the spectrum of the non-limit operatorusing asymptotic analysis. Theoretical results are illustrated by numerical computationsobtained with a numerical method developed for study of periodic media: this method isbased on the reduction of the initial (linear) eigenvalue problem posed in an unboundeddomain to a non-linear problem posed in a bounded domain (using the exact Dirichletto-Neumann operator).

In this dissertation, the performance of cooperative cognitive systems with spectrum sharing is investigated. A low-complexity and high performance node selection strategy is proposed for two different of cooperative cognitive systems models. In the first model, the secondary network is composed by one source node that communicates with one among L destinations through a direct link and also assisted by one among N AF or DF relays nodes. The selected secondary destination employs a selection combining technique for choosing the best link (direct or dual-hop link) from the secondary source. Considering an underlay spectrum sharing approach, the secondary communication is performed taking into account an interference constraint, where the overall transmit power is limited by the interference at the primary receiver as well as by the maximum transmission power available at the respective nodes. An asymptotic analysis is carried out, revealing that the diversity order of the considered system is not affected by the interference, and equals to L + N. In the second model, by its turn, the secondary network is composed by one source, N AF or DF relays, and one destination. However, it is assumed the presence of M primary receivers. A relay selection strategy is proposed with the aim of maximing the end-to-end signal-to-noise ratio and, at the same time, to satisfy the interference constraints imposed by these primary receivers. After the relay selection procedure is performed, the secondary destination chooses the best path (direct link or relaying link) by employing a selection combining scheme. An asymptotic analysis is carried out, revealing that the system diversity order equals to N + 1, and showing that it is not affected neither by the number of primary receivers nor by the interference threshold. A close-form expression and an approximation for the outage probability is derived for the DF and AF protocols, respectively. / Nesta dissertaÃÃo, o desempenho de sistemas cooperativos cognitivos com compartilhamento espectral à investigado. Uma estratÃgia de seleÃÃo de nÃs de baixa complexidade e alto desempenho à proposta para dois modelos distintos de redes cooperativas cognitivas. No primeiro modelo, a rede secundÃria à composta por um nà fonte que comunica-se com um dentre L nÃs destinos atravÃs de um link direto e atravÃs de um dentre N nÃs relays decodifica-e-encaminha (DF) ou amplifica-e-encaminha (AF). O nà destino secundÃrio selecionado emprega uma tÃcnica de combinaÃÃo por seleÃÃo para selecionar o melhor link (direto ou auxiliar) a partir da fonte secundÃria. Considerando um ambiente com compartilhamento espectral, tem-se que a comunicaÃÃo secundÃria à realizada levando em consideraÃÃo uma restriÃÃo de interferÃncia, na qual a potÃncia de transmissÃo à governada pela interferÃncia no receptor primÃrio bem como pela mÃxima potÃncia de transmissÃo dos respectivos nÃs secundÃrios. Uma anÃlise assintÃtica à realizada, revelando que a ordem de diversidade do sistema nÃo à afetada pela interferÃncia, sendo igual a L + N. Jà no segundo modelo, a rede secundÃria à composta por uma fonte, N relays DF ou AF e um nà destino, no entanto assume-se a presenÃa de M receptores primÃrios. A seleÃÃo do relay deve satisfazer as restriÃÃes de interferÃncia impostas por estes Ãltimos. ApÃs a seleÃÃo de relay ser realizada, o nà destino seleciona o melhor caminho (link direto ou link via relay) proveniente da fonte utilizando um combinador por seleÃÃo. Uma anÃlise assintÃtica à realizada, revelando que a ordem de diversidade do esquema proposto iguala a N + 1, o que mostra que a mesma nÃo à afetada nem pelo nÃmero de receptores primÃrios nem pelo limiar de interferÃncia. Uma expressÃo em forma fechada para a probabilidade de outage à obtida para ambos protocolos cooperativos. SimulaÃÃes Monte Carlo sÃo apresentadas com o intuito de validar as anÃlises propostas.