Academic literature on the topic '51°'

I/D 51 -- GENERAL COUNCIL, November 1995 -- SPIRITANS AND COMMUNICATION -- ARE SPIRITANS COMMUNICATORS? -- (pg. 1) -- MASS MEDIA, A DANGER OR AN ANSWER? -- (pg. 3) -- PERENNIAL QUESTIONS THAT CHALLENGE US -- (pg. 4) -- MEDIA, A CHALLENGE FOR EVERYONE? -- (pg. 6) -- CONCLUSION -- (pg. 8)

The future of particle physics in the next 30 years must include detailed study of neutrinos. The first proof of physics beyond the Standard Model of particle physics is evident in results from recent neutrino experiments which imply that neutrinos have mass and flavour mixing. The Neutrino Factory is the leading contender to measure precisely the neutrino mixing parameters to probe beyond the Standard Model physics. Significantly, one must look to measure the mixing angle Θ₁₃ and investigate the possibility of leptonic CP violation. If found this may provide a key insight into the origins of the matter/anti-matter asymmetry seen in the universe, through the mechanism of leptogenesis. The Neutrino Factory will be a large international multi-billion dollar experiment combining novel new accelerator and long-baseline detector technology. Arguably the most important and costly features of this facility are the proton driver and cooling channel. This thesis will present simulation work focused on determining the optimal proton driver energy to maximise pion production and also simulation of the transport of this pion flux through some candidate transport lattices. Bench-marking of pion cross-sections calculated by MARS and GEANT4 codes to measured data from the HARP experiment is also presented. The cooling channel aims to reduce the phase-space volume of the decayed muon beam to a level that can be efficiently injected into the accelerator system. The Muon Ionisation Cooling Experiment (MICE) hosted by the Rutherford Appleton laboratory, UK is a proof-of-principle experiment aimed at measuring ionisation cooling. The experiment will run parasitically to the ISIS accelerator and will produce muons from pion decay. The MICE beamline provides muon beams of variable emittance and momentum to the MICE experiment to enable measurement of cooling over a wide range of beam conditions. Simulation work in the design of this beamline is presented in this thesis as are results from an experiment to estimate the flux from the target into the beamline acceptance

Access to family-friendly working time arrangements is unequally spread both within and between workplaces, leaving many working parents with difficulties in combining employment with family responsibilities. The British and German governments have started to address this problem, but have done so in different ways. Focusing on time allocation in the work/family interface and its implications for gender and employment relations, this thesis explores the differences between the British and German government strategies to improve access to family-friendly working time arrangements for working parents, and how variation can be explained. As the flexibility requirements of employers and employees often diverge and can be in conflict, the thesis further investigates to what extent the German and British policy strategies were designed to empower working parents to access the time flexibility they need. It applies an empowerment perspective to the analysis of policy choice and design and draws on the policy making literature to analyse cross-national variation. Between 1997 and 2005, the incoming centre-left New Labour and ‘Red-Green’ governments both introduced information campaigns and employment rights to improve access. The lack of economic incentives for the provision and take-up of family-friendly working time arrangements reduced the overall empowering potential of the British and German strategies. Although similar at the level of policy choice, employment rights and information campaigns varied at the level of policy design with different implications for access. The thesis concludes that family-friendly working time policy did not achieve a significant redistribution of control over working time to employees in either of the two countries. This can be in part explained by a strong employer lobby and opportunities to influence policy choice and design, but also by the ‘competitive advantage’ of childcare services over family-friendly working time policy, directing government resources to more ‘employer-friendly’ reconciliation policies.

The aim of this thesis is to examine the Clean Development Mechanism (CDM) as a new instrument for technology transfer to developing countries, especially Bangladesh, in order to analyse its potential and develop policies and strategies for its successful implementation. The main research question the thesis addresses is whether the Clean Development Mechanism can assist the sustainable development of developing countries, such as Bangladesh. Under the 1997 Kyoto Protocol, the Clean Development Mechanism allows developed countries to invest in abatement opportunities in developing countries and receive credit for the resulting emissions reductions, thus becoming a tool for technology transfer. In the past, developing countries have been eager to participate in technology transfer but this has often come at a cost and not in the most beneficial way. The spirit of the CDM is to support sustainable development and encourage mutually beneficial transfer of appropriate technologies. The CDM is a form of market tool in which valuable goods and services are to be bought and sold. A number of technical, regulatory, project finance and administrative functions must be performed for this tool to operate. Many of these functions may be most effectively undertaken by private markets or existing international institutions. However, developing countries face problems during international technology transfer, that are still apparent under the CDM; for example: lack of proper knowledge, inadequate bargaining power, insufficient skilled persons and capable human resources, not enough adaptive capabilities, limited number of sophisticated physical facilities, fear about the effective control over national assets, uncertainty about the effects of foreign investment on the exploitation of national resources, etc. On the other hand, the CDM has the potential to fund 'technological leapfrogging' that would enable developing countries to bypass inefficient choices, such as coal technology, made by industrialised countries. Poverty alleviation and development problems have been the main concern of poor countries among an obvious shortage of good will on the part of governments in industrialised countries to contribute towards these aims. New mechanisms that can stimulate investment from government as well as the private sector are needed to combat these shortcomings. Does the CDM have the potential to contribute to these broader goals? This research explores how the Clean Development Mechanism can potentially play such a role and how suitable it is within the broader picture of poverty and underdevelopment in the case of Bangladesh. This thesis argues that the CDM, which came into force early in 2005, has the potential to become a useful tool in coping with climate change and benefit the entire global population. However, the majority of developing countries will have to balance national necessities, such as poverty eradication, food security and education, with encouraging CDM projects. The only way the CDM can contribute to sustainable development in these parts of the world (including Bangladesh) is if the mechanism embraces simultaneously social, economic and environmental responsibility and avoids becoming yet another tool to make the economically rich more richer.

This thesis focuses on the long time behaviour of solutions to Fisher-KPP reaction-diffusion equations involving fractional diffusion. This type of equation arises, for example, in spatial propagation or spreading of biological species (rats, insects,...). In population dynamics, the quantity under study stands for the density of the population. It is well-known that, under some specific assumptions, the solution tends to a stable state of the evolution problem, as time goes to infinity. In other words, the population invades the medium, which corresponds to the survival of the species, and we want to understand at which speed this invasion takes place. To answer this question, we set up a new method to study the speed of propagation when fractional diffusion is at stake and apply it on three different problems. Part I of the thesis is devoted to an analysis of the asymptotic location of the level sets of the solution to two different problems : Fisher-KPP models in periodic media and cooperative systems, both including fractional diffusion. On the first model, we prove that, under some assumptions on the periodic medium, the solution spreads exponentially fast in time and we find the precise exponent that appears in this exponential speed of propagation. We also carry out numerical simulations to investigate the dependence of the speed of propagation on the initial condition. On the second model, we prove that the speed of propagation is once again exponential in time, with an exponent depending on the smallest index of the fractional Laplacians at stake and on the reaction term. Part II of the thesis deals with a two dimensional environment, where reproduction of Fisher-KPP type and usual diffusion occur, except on a line of the plane, on which fractional diffusion takes place. The plane is referred to as 'the field' and the line to 'the road', as a reference to the biological situations we have in mind. Indeed, it has long been known that fast diffusion on roads can have a driving effect on the spread of epidemics. We prove that the speed of propagation is exponential in time on the road, whereas it depends linearly on time in the field. Contrary to the precise asymptotics obtained in Part I, for this model, we are not able to give a sharp location of the level sets on the road and in the field. The expansion shape of the level sets in the field is investigated through numerical simulations.
Esta tesis se centra en el comportamiento en tiempos grandes de las soluciones de la ecuación de Fisher- KPP de reacción-difusión con difusión fraccionaria. Este tipo de ecuación surge, por ejemplo, en la propagación espacial o en la propagación de especies biológicas (ratas, insectos,...). En la dinámica de poblaciones, la cantidad que se estudia representa la densidad de la población. Es conocido que, bajo algunas hipótesis específicas, la solución tiende a un estado estable del problema de evolución, cuando el tiempo tiende a infinito. En otras palabras, la población invade el medio, lo que corresponde a la supervivencia de la especie, y nosotros queremos entender con qué velocidad se lleva a cabo esta invasión. Para responder a esta pregunta, hemos creado un nuevo método para estudiar la velocidad de propagación cuando se consideran difusiones fraccionarias, además hemos aplicado este método en tres problemas diferentes. La Parte I de la tesis está dedicada al análisis de la ubicación asintótica de los conjuntos de nivel de la solución de dos problemas diferentes: modelos de Fisher- KPP en medios periódicos y sistemas cooperativos, ambos consideran difusión fraccionaria. En el primer modelo, se prueba que, bajo ciertas hipótesis sobre el medio periódico, la solución se propaga exponencialmente rápido en el tiempo, además encontramos el exponente exacto que aparece en esta velocidad de propagación exponencial. También llevamos a cabo simulaciones numéricas para investigar la dependencia de la velocidad de propagación con la condición inicial. En el segundo modelo, se prueba que la velocidad de propagación es nuevamente exponencial en el tiempo, con un exponente que depende del índice más pequeño de los Laplacianos fraccionarios y también del término de reacción. La Parte II de la tesis ocurre en un entorno de dos dimensiones, donde se reproduce un tipo ecuación de Fisher- KPP con difusión estándar, excepto en una línea del plano, en el que la difusión fraccionada aparece. El plano será llamado "campo" y la línea "camino", como una referencia a las situaciones biológicas que tenemos en mente. De hecho, desde hace tiempo se sabe que la difusión rápida en los caminos puede causar un efecto en la propagación de epidemias. Probamos que la velocidad de propagación es exponencial en el tiempo en el camino, mientras que depende linealmente del tiempo en el campo. Contrariamente a los precisos exponentes obtenidos en la Parte I, para este modelo, no fuimos capaces de dar una localización exacta de los conjuntos de nivel en la carretera y en el campo. La forma de propagación de los conjuntos de nivel en el campo se investiga a través de simulaciones numéricas

The goal of this thesis is to show global instability or Arnold's diffusion in the elliptic restricted three body problem (ERTBP) by proving the existence of pseudo-trajectories diffusing along the phase space for certain ranges of the eccentricity of the primaries (e), the angular momentum of the comet (G) and the parameter of mass (µ). More precisely, the results presented in his thesis, are valid for G big enough, eG bounded and µ small enough. The thesis is divided in two chapters and two appendices. The chapter one, contains all the main results. After introducing the ERTBP, we use McGehee coordinates to define the infinity manifold, which turn to be a three dimensional invariant manifold in the extended phase space which behaves topologically as a Normally Hyperbolic Invariant Manifold (NHIM), although it is of parabolic type. This means that the rate of approach and departure from it along its invariant manifolds is polynomial in time, instead of exponential-like as happens in a standard NHIM. On the other hand, the inner dynamics is trivial, since it is formed by a two-parameter family of 2p-periodic orbits in the 5D extended phase space which correspond to constant solutions in the 4D phase space. As a consequence, the stable and unstable manifold of the infinity manifold are union of the stable and unstable manifolds of its periodic orbits, and as long as these manifolds intersect along transversal heteroclinic orbits, the scattering map can be defined, as De la Llave, Seara and Delshams did. Unfortunately, since the inner dynamics of the infinity manifold is so simple, the classical mechanisms of diffusion, consisting of combining the inner and outer dynamics, do not work here. Instead, as a novelty, we will be able to find two different scattering maps which will be combined in a suitable way to provide orbits whose angular momentum increases. The asymptotic formula of the scattering map relies entirely in the computation of the so called Menikov potential as defined in the works of Delshams, Gutiérrez and Seara. The first derivative of the Melnikov potential gives the first order approximation of the distance between the stable and unstable invariant manifolds of the infinity manifold whenever the parameter of mass is exponentially small. Given this setting, a series of lemmas and propositions will lead to a formula of the dominant terms of this Melnikov potential. The key idea is to compute its Fourier coefficients which will be exponentially small when the angular momentum is large and an explicit formula will be not possible, therefore and effective computation will be necessary. To do so the product eG will play a key role which lead to theorems 1.5 and 1.6, the former gives an asymptotic formula for the Melnikov potential whenever eG is samll, and the latter whenever eG is finite. Both of them requires µ to be exponentially small with respect to G, and G to be big enough. These theorems naturally produce asymptotic formulas for the scattering maps in both cases and are the base for theorems 1.15 and 1.16 which formulate the existence of pseudo-trajectories in the ERTBP. In chapter two, we provide the details and the proofs of the results concerning the asymptotic formulas, given in chapter one, for the Melnikov potential and the scattering maps, including effective bounds of every error function involved. The appendices have the more technical results needed to complete in a rigorous way every proof, but because of its nature, can be relegated to the end, to make easier to follow up the main proofs.
El objetivo de esta tesis es mostrar inestabilidad global o difusión de Arnold en el problema restringido de tres cuerpos elíptico (PTCRE) mostrando la existencia de pseudo-trayectorias difusivas en el espacio fase para ciertos rangos de la excentricidad (e), el momento angular del cometa (G) y el parámetro de masa (µ). Mas precisamente, los resultados presentados, son válidos para G suficientemente grande, eG acotado y µ suficientemente pequeño. La tesis está dividida en dos capítulos y dos apéndices. El capítulo 1, contiene todos los resultados principales. Después de introducir el PTCRE, usamos coordenadas de McGehee para definir la variedad de infinito, que será de dimensión tres en el espacio fase extendido y que topológicamente se comporta como una variedad invariante normalmente hiperbólica (NHIM), aunque es de tipo parabólico. Esto significa que la tasa de acercamiento y alejamiento de ella a lo largo de sus variedades invariantes es polinomial, en lugar de exponencial como sucede en una NHIM estándar. Por otra parte, la dinámica interior es trivial ya que está formada por una familia de orbitas con 2 parámetros y de período 2p en el espacio extendido 5D que corresponden a soluciones constantes en el espacio reducido 4D. Como consecuencia, las variedades estables e inestables de la variedad de infinito son la unión de las variedades estables e inestables de sus orbitas periódicas y siempre que estas variedades se intersequen sobre orbitas heteroclínicas transversales, el scattering map puede ser definido como hicieron De la Llave, Seara y Delshams . Desafortunadamente, ya que la dinámica interior de la variedad de infinito es muy simple, el mecanismo de difusión clásico, que consiste en combinar la dinámica interior con la exterior, no funciona aquí. En su lugar, como una novedad, seremos capaces de encontrar dos scattering maps diferentes que serán combinados de manera adecuada para producir orbitas cuyo momento angular crezca. La fórmula asintótica del scattering map recae enteramente en el cálculo del llamado potencial de Melnikov, como es definido en los trabajos de Delshams, Gutiérrez y Seara. La primer derivada del potencial de Melnikov da la aproximación a primer orden de la distancia entre las variedades estable e inestable de la variedad de infinito cuando el parámetro de masa es exponencialmente pequeño. Con este planteamiento, una serie de lemas y proposiciones conducirán a la fórmula de los términos dominantes del potencial de Melnikov. La idea clave es calcular sus coeficientes de Fourier, que serán exponencialmente pequeños cuando el momento angular es grande y una fórmula explícita no será posible, así que un cálculo efectivo será necesario. Para hacerlo, el producto eG jugará un papel clave que conducirá a los teoremas 1.5 y 1.6, el primero da una fórmula asintótica del potencial de Melnikov cuando eG es pequeño y el segundo cuando eG es finito. Ambos requieren que µ sea exponencialmente pequeño con respecto a G, y G suficientemente grande. Estos teoremas naturalmente producirán las fórmulas asintóticas de los scattering maps para ambos casos y son la base de los teoremas 1.15 y 1.16, que formulan la existencia de pseudo-trayectorias en el PTCRE. En el capítulo 2, damos los detalles y las pruebas de los resultados concernientes a las formulas asintóticas, dadas en el capítulo 1, para el potencial de Melnikov y los scattering maps, incluyendo las cotas efectivas de cada error involucrado. Los apéndices tienen los resultados mas técnicos que son necesarios para completar de forma rigurosa cada prueba, pero que por su naturaleza, pueden ser relegados al final para hacer seguir las pruebas con mas facilidad.

The main topic of the thesis is the study of Elliptic PDEs. It is divided into three parts: (I) integro-differential equations, (II) stable solutions to reaction-diffusion problems, and (III) weighted isoperimetric and Sobolev inequalities. Integro-differential equations arise naturally in the study of stochastic processes with jumps, and are used in Finance, Physics, or Ecology. The most canonical example of integro-differential operator is the fractional Laplacian (the infinitesimal generator of the radially symmetric stable process). In the first Part of the thesis we find and prove the Pohozaev identity for such operator. We also obtain boundary regularity results for general integro-differential operators, as explained next. In the classical case of the Laplacian, the Pohozaev identity applies to any solution of linear or semilinear problems in bounded domains, and is a very important tool in the study of elliptic PDEs. Before our work, a Pohozaev identity for the fractional Laplacian was not known. It was not even known which form should it have, if any. In this thesis we find and establish such identity. Quite surprisingly, it involves a local boundary term, even though the operator is nonlocal. The proof of the identity requires fine boundary regularity properties of solutions, that we also establish here. Our boundary regularity results apply to fully nonlinear integro-differential equations, but they improve the best known ones even for linear ones. Our work in Part II concerns the regularity of local minimizers to some elliptic equations, a classical problem in the Calculus of Variations. More precisely, we study the regularity of stable solutions to reaction-diffusion problems in bounded domains. It is a long standing open problem to prove that all stable solutions are bounded, and thus regular, in dimensions n<10. In dimensions n>=10 there are examples of singular stable solutions. The question is still open in dimensions 4El tema principal de la tesi és l'estudi d'EDPs el·líptiques. La tesi està dividida en tres parts: (I) equacions integro-diferencials, (II) solucions estables de problemes de reacció-difusió, i (III) desigualtats isoperimètriques i de Sobolev amb pesos. Les equacions integro-differencials apareixen de manera natural en l'estudi de processos estocàstics amb salts (processos de Lévy), i s'utilitzen per modelitzar problemes en Finances, Física, o Ecologia. L'exemple més canònic d'operador integro-diferencial és el Laplacià fraccionari (el generador infinitesimal d'un procés estable i radialment simètric). A la Part I de la tesi trobem i demostrem la identitat de Pohozaev per aquest operador. També obtenim resultats de regularitat a la vora per operadors integro-diferencials més generals, tal com expliquem a continuació. En el cas clàssic del Laplacià, la identitat de Pohozaev s'aplica a qualsevol solució de problemes lineals o semilineals en dominis acotats, i és una eina molt important en l'estudi d'EDPs el·líptiques. Abans del nostre treball, no es coneixia cap identitat de Pohozaev pel Laplacià fraccionari. Ni tan sols es sabia quina forma hauria de tenir, en cas que existís. En aquesta tesi trobem i demostrem aquesta identitat. Sorprenentment, la identitat involucra un terma de vora local, tot i que l'operador és no-local. La demostració de la identitat requereix conèixer el comportament precís de les solucions a la vora, cosa que també obtenim aquí. Els nostres resultats de regularitat a la vora s'apliquen a equacions integro-diferencials completament no-lineals, però milloren els resultats anteriors fins i tot per a equacions lineals. A la Part II estudiem la regularitat dels minimitzants locals d'algunes equacions el·líptiques, un problema clàssic del Càlcul de Variacions. En concret, estudiem la regularitat de les solucions estables a problemes de reacció-difusió en dominis acotats. És un problema obert des de fa molts anys demostrar que totes les solucions estables són acotades (i per tant regulars) en dimensions n<10. En dimensions n>=10 hi ha exemples de solucions estables singulars. La questió encara està oberta en dimensions 4