Tuning Synchronization through mobility and limited vision

Màster Oficial en Física Avançada, , Facultat de Física, Universitat de Barcelona, Curs: 2016, Tutors: Oleguer Sagarra, Luce Prignano i Albert Díaz-Guilera.In this work we analyse the emergence of synchronization in a population of mobile Integrate-and-Fire oscillators with limited vision. By proposing novel interaction rules among oscillators we bridge phenomenology detected in a variety of previous models. In particular, we explore the effect that the effective asymmetry of interactions have on the non monotonic behaviour observed in the synchronization time of the population as a function of their velocities. We recover non linear features with the same origin as [1] but considering only geometrical interactions, and we study the scaling properties of the model as well as predict the values of the parameters where the different dynamical regimes take place

Influence of topology in the mobility enhancement of pulse-coupled oscillator synchronization

In this work we revisit the nonmonotonic behavior (NMB) of synchronization time with velocity reported for systems of mobile pulse-coupled oscillators (PCOs). We devise a control parameter that allows us to predict in which range of velocities NMB may occur, also uncovering the conditions allowing us to establish the emergence of NMB based on specific features of the connectivity rule. Specifically, our results show that if the connectivity rule is such that the interaction patterns are sparse and, more importantly, include a large fraction of nonreciprocal interactions, then the system will display NMB. We furthermore provide a microscopic explanation relating the presence of such features of the connectivity patterns to the existence of local clusters unable to synchronize, termed frustrated clusters, for which we also give a precise definition in terms of simple graph concepts. We conclude that, if the probability of finding a frustrated cluster in a system of moving PCOs is high enough, NMB occurs in a predictable range of velocities

A General and Predictive Understanding of Thermal Transport from 1D- and 2D-Confined Nanostructures : Theory and Experiment

Altres ajuts: Acord transformatiu CRUE-CSICHeat management is crucial in the design of nanoscale devices as the operating temperature determines their efficiency and lifetime. Past experimental and theoretical works exploring nanoscale heat transport in semiconductors addressed known deviations from Fourier's law modeling by including effective parameters, such as a size-dependent thermal conductivity. However, recent experiments have qualitatively shown behavior that cannot be modeled in this way. Here, we combine advanced experiment and theory to show that the cooling of 1D- and 2D-confined nanoscale hot spots on silicon can be described using a general hydrodynamic heat transport model, contrary to previous understanding of heat flow in bulk silicon. We use a comprehensive set of extreme ultraviolet scatterometry measurements of nondiffusive transport from transiently heated nanolines and nanodots to validate and generalize our ab initio model, that does not need any geometry-dependent fitting parameters. This allows us to uncover the existence of two distinct time scales and heat transport mechanisms: an interface resistance regime that dominates on short time scales and a hydrodynamic-like phonon transport regime that dominates on longer time scales. Moreover, our model can predict the full thermomechanical response on nanometer length scales and picosecond time scales for arbitrary geometries, providing an advanced practical tool for thermal management of nanoscale technologies. Furthermore, we derive analytical expressions for the transport time scales, valid for a subset of geometries, supplying a route for optimizing heat dissipation

Generalized Hydrodynamic Heat Transport in Semiconductors

La tesis presenta una descripció unificadora d'una varietat d'experiments de transport tèrmic a la micro i nano escala en semiconductors com el silici o el germani. S'utilitza un model de transport de calor hidrodinàmic per predir la resposta no difusiva de sistemes complexes en situacions de rellevància tecnològica, com el procés de refredament d'un component electrònic alliberant calor cap a un substrat semiconductor. El model no utilitza paràmetres d'ajust en funció de la geometria, sinó que utilitza paràmetres calculats des de primers principis. Els efectes de mida petita o alta freqüència es capturen a través de condicions de contorn específiques i, per tant, el model és una eina útil pel disseny de dispositiu micro electrònics. Degut a que la descripció hidrodinàmics pel silici no és el mètode convencional, en aquesta tesis es posa especial èmfasis en determinar l'aplicabilitat del model en múltiples experiments de manera unificadora. Com a resultat, s'identifiquen fenòmens no difusius com la propagació del segon so en camps tèrmics fluctuants en germani o múltiples temps de relaxació en l'evolució tèrmica d'escalfadors nano estructurats en silici. A més, la descripció hidrodinàmica es compara amb altres models moderns per descriure els mateixos experiments, i es proporciona un resum de les eines teòriques necessàries (la termodinàmica de no equilibri i la teoria cinètica). Utilitzant les evidències experimentals que s'aporten, es conclou que el model hidrodinàmic té capacitat predictiva de la resposta tèrmica de materials com el silici a la nano escala dins d'un cert rang d'aplicabilitat.Ésta tesis presenta una descripción unificadora de una variedad de experimentos de transporte térmico a la micro y nano escala en semiconductores como el silicio o el germanio. Se utilitza un modelo de transporte de calor hidrodinámico para predecir la respuesta no difusiva de sistemas complejos en situacions de relevancia tecnológica, como el proceso de enfriamento de un componente electrónico liberando calor hacia un sustrato semiconductor. El modelo no utilitza parámetros de ajuste en función de la geometría, sinó que utiliza parámetros calculados des de primeros principios. Los efectos de tamaño reducido o alta frecuencia se capturan a través de condiciones de contorno específicas y, por tanto, el modelo es una herramienta útil para el diseño de dispositivos micro electrónicos. Dado que la descripción hidrodinámica para el silicio no es el método convencional, en ésta tesis se presta especial atención a determinar la aplicabilidad del modelo en múltiples experimentos de forma unificadora. Como resultado, se identifican fenómenos no difusivos como la propagación de segundo sonido en campos térmicos fluctuantes en germanio, o múltiples tiempos de relajación en la evolución térmica de calentadores nano estructurados en silicio. Además, la descripción hidrodinámica se compara con otros modelos modernos para describir los mismos experimentos, y se proporciona un resumen de las herramientas teóricas necesarias (la termodinámica de no equilibrio y la teoria cinética). Utilizando las evidencias experimentales que se aportan, se concluye que el modelo hidrodinámico tiene capacidad predictiva de la respuesta térmica de materiales como el silicio a la nano escala dentro de un cierto rango de aplicabilidad.This thesis presents a unifying description of a variety of experiments on micro- and nano-scale heat transport in semiconductors like silicon or germanium. A hydrodynamic-like heat transport model is used to predict the non-diffusive thermal response of complex systems in technologically relevant situations, like the process of energy release from nanostructured heat sources towards a semiconductor substrate. The model does not use geometry-dependent or fitted parameters, but use intrinsic material properties that can be calculated from first principles. Small-size and high-frequency effects are captured through the use of specific boundary conditions, thus resulting in a practical tool for complex microelectronic device design. Since hydrodynamic modeling is not the state-of-the-art approach to describe standard semiconductors like silicon, special care is devoted to quantitatively determine the applicability of the model, and multiple experiments using different techniques are considered and studied in a unifying way. As a result, previously unreported non-Fourier phenomena in materials like silicon or germanium is identified and demonstrated (e.g. second sound in rapidly varying thermal fields or multiple decay times characterizing the evolution of nano-structured heaters). Furthermore, the hydrodynamic description is compared with alternative modern frameworks describing size and frequency effects in semiconductor heat transport, and a summarized overview of the theoretical background, namely non-equilibrium thermodynamics and kinetic theory, is presented. In light of the extensive experimental evidence provided, this thesis demonstrate the predictive capability of hydrodynamic-like thermal transport modeling in semiconductors within a certain range of applicability that is well beyond the diffusive regime

Més enllà de la geometria euclidiana: l'espai hiperbòlic

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2015, Director: Vicenç Navarro AznarEuclides, around 300 B.C., wrote The Elements, famous work where he brilliantly reflected his conception of plane geometry based on a list of definitions of geometric terms, five logical notions and the following five postulates: 1. A straight line may be drawn joining any two points. 2. A finite straight line may be extended indefinitely in a straight line. 3. A circle may be drawn with any center and any radius. 4. All right angles are equal. 5. If a straight line intersects two straight lines in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. The first four postulates clearly have an axiomatic nature, since they are easy to conceive and reflect our intuitive understanding of space around us. However, the fifth postulate seems to be not enough self-evident to be accepted without a proof. In fact, for over two thousand years it was believed that the fifth postulate could be derived from the other four. Carl Friedrich Gauss, in the nineteenth century, was the first to demonstrate that indeed the fifth postulate is independent of the others, and he also made a transcendental discovery: the fifth postulate restricts geometry to a flat universe, without curvature, and by modifying it one obtain new consistent geometries that describe other possible universes with other curvatures, which are called the non-euclidian geometries. Unfortunately, Gauss never published this results. Years later, noneuclidian geometries were rediscovered independently by Nikolai Lobachevsky and J ́anos Bolyai. The historical papers, where these ideas were published for the first time, can be consulted: On the principles of geometry, Lobachevsky (1829) and The absolute science of space, Bolyai (1832). Moreover, the modern geometric tools developed by Behrnard Riemann and Gauss himself among others, make use of the differential analysis in order to describe the space in a less axiomatic and more universal way, so that the different possible geometries have emerged naturally and perfectly classified and have became useful to develop physical theories with profound implications as the Theory of General Relativity of Einstein. The main goal of this work is to show how modern geometry, the Riemannian, has allowed to classify the different spaces in terms of their curvatures and to establish dualities between them. This development is carried out in the first chapter, where we demonstrate the fundamental results that solve the problem. As we shall see, by imposing that the curvature is constant, we reach to three possible spaces: the euclidian one (non curved), the spherical one (positively curved) and the hyperbolic one (negatively curved). The first two cases are briefly described in the first chapter.Additionally, we show how the isometries of the space can be used to identify the manifolds that contains. The most surprising result that we obtain, without any doubt, is the existence of the hyperbolic space, which is totally consistent by itself and presents clear dualities with the other two. Furthermore, it reflects the space-time geometry according to the Theory of General Relativity. Hence, it is the right one to capture the metrical properties of the Universe. However, the hyperbolic space can not be intuitively conceived and has an elusive nature. This is the motivation of the second part of the work that is contained in the second and third chapters. The aim is to familiarize the reader with this space for an arbitrary dimension through different models that reduce the level of abstraction that it presents. Therefore, the different models are presented in a constructive way in the second chapter by using the tools of the Riemannian geometry. In the third chapter, the different isometric transformations of the hyperbolic space are shown, allowing the study of its invariances and its manifolds. In order to present a self-contained text, we include an appendix where all the essential ideas of Riemannian geometry that we use in the work are developed. This extra chapter also contains some appreciations that motivate the objectives of the work. Several sources of information have been used with the intention of optimizing the amount of formalism and results presented. In order to facilitate the deepening of the contents by the reader, at the beginning of each chapter we indicate the different sources that can be followed in parallel with the text

Influence of topology in the mobility enhancement of pulse-coupled oscillator synchronization

In this work we revisit the nonmonotonic behavior (NMB) of synchronization time with velocity reported for systems of mobile pulse-coupled oscillators (PCOs). We devise a control parameter that allows us to predict in which range of velocities NMB may occur, also uncovering the conditions allowing us to establish the emergence of NMB based on specific features of the connectivity rule. Specifically, our results show that if the connectivity rule is such that the interaction patterns are sparse and, more importantly, include a large fraction of nonreciprocal interactions, then the system will display NMB. We furthermore provide a microscopic explanation relating the presence of such features of the connectivity patterns to the existence of local clusters unable to synchronize, termed frustrated clusters, for which we also give a precise definition in terms of simple graph concepts. We conclude that, if the probability of finding a frustrated cluster in a system of moving PCOs is high enough, NMB occurs in a predictable range of velocities