Ao longo da história, diversas foram as tentativas da ciência em sistematizar o conhecimento sobre as cidades. Um conjunto de recentes descobertas empíricas deu início a uma nova ciência urbana, fundamentada nos sistemas complexos( BATTY , 2013). Uma das raízes empíricos dessa ciência está nas análises de escalamento entre diversas variáveis urbanas com a população das cidades. Como hipótese fundamental, propõe-se que por mais diferentes que sejam, parece existir um padrão muito claro de escalamento entre a população dos centros urbanos com variáveis de produção socioeconômica (superlinear) e variáveis infraestruturais (sublinear). Um modelo de campo médio proposto por Bettencourt( BETTENCOURT , 2013) parece apresentar uma prossível explicação para a origem dessas leis de escala nas interações sociais. Essa hipótese ainda carece, entretanto, de maiores comprovações empíricas e de maiores explorações do modelo proposto. O presente trabalho apresenta os resultados de uma exploração das leis de escala entre as cidades brasileiras e uma tradução do modelo de Bettencourt em uma estrutura de modelagem por agentes. Os padrões de escalamento das cidades brasileiras parecem seguir aqueles encontrados em outras cidades do mundo com certa robustez. Escalamentos de variáveis de arrecadação e de despesas foram estudados e as cidades brasileiras parecem otimizá-los a medida que crescem. O modelo se mostrou coerente com os fatos observados empiricamente e indicou que cidades muito desiguais tendem a ter menores produções socioeconômicas e que áreas de interações maiores e custos de transporte menores tendem a produzir mais interações socioeconômicas / Throughout history science has tried in many ways to sistematyze the knowledge about cities. Recent empirical discoveries started a new urban science, based on complex systems and data science( BATTY , 2013). One of the empirical foundation of this science is the scaling laws of diferent urban variables in relation to the urban population size. As a main hypothesis, it is sugested that as diferent as cities may be, there seems to be an evident scaling pattern between population size and socioeconomic production (superlinear) and infrastrufture variables (sublinear). A mean field model proposed by Bettencourt( BETTENCOURT , 2013) appears to present a plausible explanation for the origin of scaling laws in social interactions. However, this hypothesis still lacks more concluding empirical proof and further study of the model itself. This paper presents the results of an exploration of the scaling laws among Brazilian cities and a translation of Bettencourts model in a ABM framework. The scaling patterns of Brazilian cities appear to follow those found in other cities in the world with a certain robustness. Tax revenues and costs scaling were studied and Brazilian cities seem to optimize them as they grow. The model proved to be consistent with the facts observed empirically and indicated that very unequal city tend to have lower socioeconomic productions and greater areas of interactions and lower transportation costs tends to imply greater socioeconomic productions

Ao longo da história, diversas foram as tentativas da ciência em sistematizar o conhecimento sobre as cidades. Um conjunto de recentes descobertas empíricas deu início a uma nova ciência urbana, fundamentada nos sistemas complexos( BATTY , 2013). Uma das raízes empíricos dessa ciência está nas análises de escalamento entre diversas variáveis urbanas com a população das cidades. Como hipótese fundamental, propõe-se que por mais diferentes que sejam, parece existir um padrão muito claro de escalamento entre a população dos centros urbanos com variáveis de produção socioeconômica (superlinear) e variáveis infraestruturais (sublinear). Um modelo de campo médio proposto por Bettencourt( BETTENCOURT , 2013) parece apresentar uma prossível explicação para a origem dessas leis de escala nas interações sociais. Essa hipótese ainda carece, entretanto, de maiores comprovações empíricas e de maiores explorações do modelo proposto. O presente trabalho apresenta os resultados de uma exploração das leis de escala entre as cidades brasileiras e uma tradução do modelo de Bettencourt em uma estrutura de modelagem por agentes. Os padrões de escalamento das cidades brasileiras parecem seguir aqueles encontrados em outras cidades do mundo com certa robustez. Escalamentos de variáveis de arrecadação e de despesas foram estudados e as cidades brasileiras parecem otimizá-los a medida que crescem. O modelo se mostrou coerente com os fatos observados empiricamente e indicou que cidades muito desiguais tendem a ter menores produções socioeconômicas e que áreas de interações maiores e custos de transporte menores tendem a produzir mais interações socioeconômicas / Throughout history science has tried in many ways to sistematyze the knowledge about cities. Recent empirical discoveries started a new urban science, based on complex systems and data science( BATTY , 2013). One of the empirical foundation of this science is the scaling laws of diferent urban variables in relation to the urban population size. As a main hypothesis, it is sugested that as diferent as cities may be, there seems to be an evident scaling pattern between population size and socioeconomic production (superlinear) and infrastrufture variables (sublinear). A mean field model proposed by Bettencourt( BETTENCOURT , 2013) appears to present a plausible explanation for the origin of scaling laws in social interactions. However, this hypothesis still lacks more concluding empirical proof and further study of the model itself. This paper presents the results of an exploration of the scaling laws among Brazilian cities and a translation of Bettencourts model in a ABM framework. The scaling patterns of Brazilian cities appear to follow those found in other cities in the world with a certain robustness. Tax revenues and costs scaling were studied and Brazilian cities seem to optimize them as they grow. The model proved to be consistent with the facts observed empirically and indicated that very unequal city tend to have lower socioeconomic productions and greater areas of interactions and lower transportation costs tends to imply greater socioeconomic productions

Any rere any milions d'hectàrees són destruïdes pels incendis forestals, no només a Europa sinó arreu del món, tan sols cal recordar els dramàtics episodis viscuts a Califòrnia i Austràlia recentment. A banda de l'evident impacte mediambiental que això provoca -emissió de gasos d'efecte hivernacle, pèrdua de biodiversitat, acceleració de l'erosió del sòl, etc.- els incendis són també un problema social de primer ordre, que posa en perill a les persones i els seus béns. Davant d'aquesta situació, en les darreres dècades s'ha impulsat fortament la recerca en l'àmbit dels incendis forestals. Tanmateix, l'estudi dels incendis forestals és certament complex per les condicions i l'entorn on aquests es desenvolupen, a banda també del gran nombre de fenòmens -físics, químics i socials- que interaccionen al llarg de diferents escales espacials i temporals, per a donar lloc a l'inici i propagació del foc. És per això que bona part de la recerca sobre el comportament dels incendis forestals ha tingut lloc bàsicament al laboratori, tot i que qüestions com ara com traslladar aquests resultats experimentals als incendis reals, o bé fins a quin punt aquest tipus d'experimentació és útil o què és el que realment es pot extrapolar i què no, no han tingut encara cap resposta clara.L'objectiu d'aquesta tesi ha estat doncs el de contribuir a l'estudi del canvi d'escala en l'experimentació en incendis forestals pel què fa al comportament del foc, mitjançant les tècniques de l'anàlisi dimensional i de semblança. En primer lloc s'ha realitzat una extensa revisió bibliogràfica centrada bàsicament en aquells treballs que havien aplicat d'alguna manera o altra l'anàlisi dimensional i de semblança a l'estudi dels incendis i en particular dels incendis forestals. S'ha vist que no es possible realitzar un escalatge complet d'aquest fenomen i que el més utilitzat ha estat l'escalatge de Froude. A més s'ha detectat que mai abans s'ha aplicat aquest tipus d'anàlisi als models que s'utilitzen normalment avui dia en l'experimentació de laboratori. A continuació s'ha fet doncs una anàlisi exhaustiva de totes les variables que determinen el comportament d'un incendi forestal en els diferents escenaris experimentals (de laboratori i de camp). A partir d'aquestes variables s'ha realitzat una anàlisi dimensional per a estudiar la propagació d'un front de flames -tan bàsic com en condicions de vent i pendent- així com una anàlisi de semblança que ha permès obtenir les lleis d'escala per a les diferents variables que caracteritzen la propagació d'un incendi forestal. S'ha dissenyat i executat un programa experimental al laboratori amb l'objectiu de validar si es complien les lleis d'escala trobades i de determinar-ne el rang de validesa i les possibles causes en cas que no es complissin.Els resultats obtinguts han mostrat que per a fronts de flama bàsics propagant-se sense vent ni pendent, totes les variables analitzades segueixen les lleis d'escala derivades de l'estudi teòric, en el rang de longituds de front de flama abraçat que va dels 25 cm als 3 m. Nogensmenys cal remarcar que paràmetres com la humitat i el tipus de combustible o les característiques de la instal·lació experimental utilitzada poden alterar enormement els resultats si no es controlen adequadament. En el cas dels fronts de flama propagant pendent amunt, els resultats han mostrat que les lleis d'escala de la geometria de flama es compleixen per a tot el rang de pendents estudiat que va de 0 fins a 30°, mentre que en el cas de la llei d'escala de la velocitat de propagació deixa de complir-se per a pendents de 30°. Finalment, en el cas dels fronts de flama propagant en condicions de vent, els resultats han mostrat que per a velocitats del vent superiors a aproximadament 2,5 m/s les lleis d'escala tant de la velocitat de propagació com de la geometria de flama deixen de complir-se.Al final d'aquest treball s'apunten les causes que poden conduir a l'incompliment de les lleis d'escala així com als factors que poden restar validesa als experiments efectuats a escala de laboratori, quan es vol extrapolar els resultats a escales més grans o fins i tot a incendis reals. / Year after year millions of hectares are destroyed by wildland fires, not only in Europe but all over the world; just remember the dramatic episodes recently occurred in California or Australia. Besides the evident environmental impact caused by these fires -emission of greenhouse gases, biodiversity loss, soil erosion, etc- wildland fires represent also a social problem of primary order that threatens human life and their assets.Because of this situation, during the last decades research on wildland fires has been greatly boosted. Nevertheless, the study of forest fires is really complex due to the conditions and the environment in which they develop and to the number of phenomena -physical, chemical and social- that interact all along the different spatial and temporal scales that give rise to the start and development of a fire. That is partly the reason because the study of wildland fire behaviour has mainly been developed in laboratories, but questions like how these experimental results can be translated to real fires?, or is really this kind of experimentation useful?, or what can be extrapolated? These questions have not yet received a clear answer.The goal of this work was to improve the knowledge on the effect of changing the scale in the experimental study of forest fire behaviour, by means of dimensional and similarity analysis. First an extended bibliographic review has been done, centred on those works that had applied in one or another way the dimensional and similarity analysis to the study of fires and more specifically to forest fires. It was observed that it is not possible to undergo a complete scaling of a forest fire and that the most used partial scaling technique was the Froude scaling. Moreover it was detected that this kind of analysis was never before applied to the laboratory models used currently to obtain experimental data on wildland fires. Thus, an exhaustive analysis of all the variables affecting forest fire behaviour has been carried out for the diverse experimental scenario (in the lab and field). From these variables, a complete dimensional analysis has been developed in order to study the spread of a flames front -both in basic conditions and with slop or wind- and a subsequent similarity analysis has provided the scaling laws governing all the variables under study. A complete experimental program has been designed and developed in the laboratory with the aim of validating the scaling laws previously found and to establish the possible causes of any failure of the laws. The results obtained show that in the case of a basic flame front, spreading under no wind and no slope conditions, all the variables analysed followed the scaling laws obtained during the theoretical study for flames front lengths ranging from 25 cm to 3 m. For the tests under slop conditions, the results indicate that the scaling laws corresponding to the flame geometry are verified for all the slopes tested which range from 0 to 30°, while in the case of the rate of spread scaling law is no longer verified for the 30° slope. Finally, in the case of flame fronts spreading under wind conditions, the results show that for wind speed values greater than 2,5 m/s neither of the scaling laws corresponding to the flame geometry and the rate of spread, are verified. It has also been observed that parameters such as moisture content, the type of fuel or the specific design of the experimental device used can have a big influence on the results obtained if they are not adequately controlled.At the end of this work, the main causes leading to the failure of the scaling laws are pointed out together with the factors that can make the laboratory experiments less reliable when trying to extrapolate the results to larger scales or even to real fires.

Fundamental aspects of turbulence and turbulent mixing are investigated using direct numerical simulations (DNS) of stationary isotropic turbulence, with Taylor-scale Reynolds numbers ranging from 8 to 650 and Schmidt numbers from 1/8 to 1024. The primary emphasis is on important scaling issues that arise in the study of intermittency, mixing and turbulence under solid-body rotation. Simulations up to 2048^3 in size have been performed using large resource allocations on Terascale computers at leading supercomputing centers. Substantial efforts in algorithmic development have also been undertaken and resulted in a new code based on a two-dimensional domain decomposition which allows the use of very large number of processors.Benchmark tests indicate very good parallel performance for resolutions up to 4096^3 on up to 32768 processors. Investigation of intermittency through the statistics of dissipation and enstrophy in a series of simulations at the same Reynolds number but different resolution indicate that accurate results in high-order moments require a higher degree of fine-scale resolution than commonly practiced. At the highest Reynolds number in our simulations (400 and 650) dissipation and enstrophy exhibit extreme fluctuations of O(1000) the mean which have not been studied in the literature before and suggest a universal scaling of small scales. Simulations at Reynolds number of 650 on 2048^3 grids with scalars at Sc=1/8 and 1 have allowed us to obtain the clearest evidence of attainment of inertial-convective scaling in the scalar spectrum in numerical simulations to date whereas results at high Sc support k^{-1} viscous-convective scaling. Intermittency for scalars as measured by the tail of the PDF of scalar dissipation and moments of scalar gradient fluctuations is found to saturate at high Sc. Persistent departures from isotropy are observed as the Reynolds number increases. However, results suggest a return to isotropy at high Schmidt numbers, a tendency that appears to be stronger at high Reynolds numbers. The effects of the Coriolis force on turbulence under solid-body rotation are investigated using simulations on enlarged solution domains which reduce the effects of periodic boundary conditions.

The theory describing the scaling properties of quantum field theory is introduced. The symmetry principles behind scale and conformal transformations are reviewed together with the renormalisation group. A method for improving perturbative calculations of physical quantities in the infra-red limit is developed using general analyticity properties valid for all unitary quantum field theories. The infra-red limit of a physical quantity is shown to equal the limiting value of the Borel transform in a complex scale parameter, where the order of the Borel transform is related to the domain of analyticity. It is shown how this general result can be used to improve perturbative calculations in the infra-red limit. First, the infra-red central charge of a perturbed conformal field theory is considered, and for the unitary minimal models perturbed by ɸ(1,3) the developed approximation is shown to be very close to the exact results by improving only a one loop perturbation. The other example is the infra-red limit of the critical exponents of x(^4) theory in three dimensions, where our approximation is within the limits of other approximations. The exact renormalisation group equation is studied for a theory with exponential interactions and a background charge. It is shown how to incorporate the background charge, and using the operator product expansion together with the equivalence between the quantum group restricted sine-Gordon model and the unitary minimal models perturbed by ɸ(1,3), the equation obtained is argued to describe the flow between unitary minimal models. Finally, a semi-classical approximation of the low energy limit of a bosonic membrane is studied where the action is taken to be the world-volume together with an Einstein-Hilbert term. A solution to the linearized equations of motion is determined describing a membrane oscillating around a flat torus.

Les décollements turbulents massifs sont des phénomènes communs qui peuvent causer des pertes et de nuisances aérodynamiques importantes dans les écoulements industriels, par exemple à l’arrière d’une aile d’avion. Ce travail contribue à leur compréhension par l’analyse phénoménologique d’un décollement turbulent, représentatif d’un grand nombre d’écoulements réels. Le premier objectif est d’identifier les lois d’échelle des décollements turbulents, notamment en rapport avec les caractéristiques de l’écoulement à l’amont de la rampe. Un deuxième objectif est l’analyse, à grande et à petite échelle, des mécanismes de transport de fluide qui pilotent le fonctionnement des décollements. A cet effet, une approche originale est proposée, basée sur une description expérimentale et analytique de la couche cisaillée décollée et des interfaces turbulentes qui la délimitent. Nos résultats suggèrent que les lois d’échelle du décollement varient de façon complexe selon l’interaction de la couche limite à l’amont, de la couche cisaillée et de l’écoulement potentiel extérieur. La taille du décollement est liée à l’intensité de l’entraînement turbulent de masse dans la couche cisaillée, qui à son tour dépend de la turbulence dans la couche limite, bien à l’amont du point de décollement. Cette dépendance pourrait s’appliquer à toute la gamme d’échelles turbulentes responsables du transport de masse. Ces observations montrent clairement le rôle de la couche cisaillée dans le fonctionnement des décollements massifs et suggèrent la faisabilité de stratégies de contrôle nouvelles, de type retro-action ou prédictif, basée sur l’entrainement turbulent. / Massive turbulent separations are common phenomena that can cause sizeable aerodynamical losses and detrimental effects in industrial flows, for example on airplane wings. This work contributes to their understanding with a phenomenological analysis of a canonical turbulent separation, representative of a large number of real flows. The first objective is to identify the scaling laws of turbulent separations, in particular with respect to their dependencies on the characteristics of the flow upstream of the ramp. A second objective is the analysis, both at large and small scale, of the transfert mechanisms that drive the functioning of separated flows. To this end, a new approach is proposed, centered on the experimental and analytical description of the separated shear layer and of the turbulent interfaces that bound it. Our results suggest that the scaling laws of the separated flow vary in a complex way, in function of the interaction of the incoming boundary layer, the separated shear layer and the free-stream. The size of the separation is related to the intensity of turbulent mass entrainment within the shear layer, which in turn depends on the turbulence in the incoming boundary layer, well upstream of the separation point. This dependency might apply over the entire range of turbulent length scales that are responsible for mass transfer. These observations clearly show the role of the shear layer in the functioning of massive separation. They also suggest the feasibility of new control strategies, both of feedback and feed-forward type, based on turbulent entrainment.

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Made available in DSpace on 2015-03-26T13:35:13Z (GMT). No. of bitstreams: 1 texto completo.pdf: 1486986 bytes, checksum: a086a712989295bff60986e7d0bcdd7e (MD5) Previous issue date: 2010-02-25 / Fundação de Amparo a Pesquisa do Estado de Minas Gerais / Cadmium telluride films grown on glass substrates covered by fluorine doped tin oxide (TCO) were studied by generic dynamical scaling theory proposed by L ópez et al. [Phys. Rev. Lett. 84, 2199 (2000)]. The samples were grown by Ferreira et al. [Appl. Phys. Lett. 88, 244102 (2006)] using hot wall epitaxy and the interface scaling properties were investigated in this work using the power spectrum, height-height correlation function, and interface width. The theory adopted has six scaling exponents, but only four of them are independent. However, in order to classify which growth regime the system follows one should analyze three of these exponents, namely, α, αloc and αs which are related to the global, local, and power spectrum fluctuations, respectively. The results show that the studied system exhibit anomalous scaling behavior characterized by global roughness exponent di fferent from the local one. Actually, in agreement with the adopted theory we have found a growth regime ruled by faceted interfaces, characterized by αloc = 1 and α ≠ αs > 1. This prediction of the anomalous scaling theory was corroborated by atomic force microscopy of the samples. We conjecture that non-local effects, caused by the initial disorder imposed by the amorphous substrate, rule the anomalous scaling. / Filmes de telureto de cádmio crescidos sobre substratos de vidro recobertos com oxido de estanho dopado com flúor (TCO) foram estudados usando a teoria de escala dinâmica proposta por Lopez et al. [Phys. Rev. Lett. 84, 2199 (2000)]. As amostras foram crescidas por Ferreira et al. [Appl. Phys. Lett. 88, 244102 (2006)] usando a técnica de epitaxia por paredes quentes e as propriedades de escala da interface foram investigadas neste trabalho através do espectro de potência, da função de correlação de alturas e da espessura da interface. A teoria usada possui seis expoentes de escala, sendo quatro independentes. Entretanto, para classificar qual regime de crescimento o sistema obedece deve-se analisar três desses expoentes, a saber, α, αloc e αs relacionados com as flutuações globais, locais e do espectro de potência da interface, respectivamente. Os resultados mostram que o sistema estudado apresenta comportamento de escala anômalo caracterizado pelo expoente de rugosidade global diferente da rugosidade local. Mais precisamente, em acordo com a teoria usada, encontramos um regime de crescimento com interfaces facetadas caracterizadas por α loc = 1 e α ≠ α s > 1. Essa previsão da teoria de escala anômala foi corroborada através de microscopia de força atômica das amostras. Conjecturamos que efeitos não-locais originados pela desordem inicial imposta pelo substrato amorfo são os fatores que originam o comportamento de escala anômalo.

L'invariance d'échelle repose sur l'intuition que les dynamiques temporelles ne sont pas gouvernées par une (ou quelques) échelle(s) caratéristique(s). Cette propriété est massivement utilisée dans la modélisation et l'analyse de données univariées issues d'applications réelles. Son utilisation pratique se heurte pourtant à deux difficultés dans les applications modernes : les propriétés d'invariance d'échelle ne sont plus nécessairement homogènes en temps ou espace ; le caractère multivarié des données rend fortement non linéaires et non convexes les fonctionnelles à minimiser pour l'estimation des paramètres d'invariance d'échelle. La première originalité de ce travail est d'envisager l'étude de l'invariance d'échelle inhomogène comme un problème conjoint de détection/segmentation et estimation et d'en proposer une formulation par minimisation de fonctionnelles vectorielles, construites autour de pénalisation par variation totale, afin d'estimer à la fois les frontières délimitant les changements et les propriétés d'invariance d'échelle de chaque région. La construction d'un algorithme de débruitage par variation totale vectorielle à la volée est proposée. La seconde originalité réside dans la conception d'une procédure de minimisation de fonctionnelle non convexe type « branch and bound » pour l'identification complète de l'extension bivariée, du mouvement brownien fractionnaire, considéré comme référence pour la modélisation de l'invariance d'échelle univariée. Cette procédure est mise en œuvre en pratique sur des données de trafic Internet dans le contexte de la détection d'anomalies. Dans un troisième temps, nous proposons des contributions spécifiques au débruitage par variation totale : modèle poissonnien d'attache aux données en relation avec un problème de détection d'états pour la fluorescence intermittente ; sélection automatique du paramètre de régularisation. / Scale invariance relies on the intuition that temporal dynamics are not driven by one (or a few) characteristic scale(s). This property is massively used in the modeling and analysis of univariate data stemming from real-world applications. However, its use in practice encounters two difficulties when dealing with modern applications: scaling properties are not necessarily homogenous in time or space ; the multivariate nature of data leads to the minimization of highly non-linear and non-convex functionals in order to estimate the scaling parameters.The first originality of this work is to investigate the study of non-homogenous scale invariance as a joint problem of detection/segmentation and estimation, and to propose its formulation by the minimization of vectorial functionals constructed around a total variation penalization, in order to estimate both the boundaries delimiting the changes and the scaling properties within each region.The second originality lies in the design of a branch and bound minimization procedure of non-convex functional for the full identification of the bivariate extension of fractional Brownian motion, considered as the reference for modeling univariate scale invariance. Such procedure is applied in practice on Internet traffic data in the context of anomaly detection.Thirdly, we propose some contributions specific to total variation denoising: Poisson data-fidelity model related to a state detection problem in intermittent fluorescence ; automatic selection of the regularization parameter.

L'énigme de la transition vitreuse réside en grande partie dans le fait que lorsqu'un matériau entre dans l'état dit surfondu, sa dynamique ralentit de façon spectaculaire, donnant l'impression d'une transition vers un état solide, sans que pour autant on ne parvienne à constater de transition thermodynamique par les expériences usuelles.Autrement dit, on ne parvient pas à expliquer le ralentissement spectaculaire de la dynamique par la croissance d'une longueur mesurable expérimentalement.Ceci conduit à la prolifération de théories souvent contradictoires quant à l'origine de la dynamique vitreuse.Durant la dernière décennie une piste prometteuse de mise en évidence d'une telle longueur a été proposée : il s'agit de la mesure des réponses diélectriques non linéaires d'ordre 3 du matériau ainsi que de leur évolution en température. En effet, les réponses non linéaires reflètent les effets collectifs caractéristiques de l'ordre amorphe, qui ne se traduisent que dans les fonctions de corrélations d'ordre élevé.Durant cette thèse nous avons construit sur ces bases expérimentales et théoriques, une expérience de mesure des réponses non linéaires d'ordre 5. En exploitant ces résultats sur la réponse diélectrique d'ordre 5 et des résultats précédents sur la réponse d'ordre 3, nous sommes parvenus, en collaboration avec une équipe d'expérimentateurs et de théoriciens, à fournir des indices forts de l'existence d'un point critique thermodynamique dans le Glycérol et le Propylène Carbonate. Ceci constitue une avancée significative dans la compréhension des matériaux vitreux.En particulier, cette découverte permet de poser des contraintes fortes sur les théories existantes et contribue à clore certains débats théoriques ayant eu cours sur plusieurs décennies. / The puzzle of the glass transition mainly resides in the fact that a supercooled liquid undergoes when cooled down, a spectacular dynamics slow down, while no evidence of any kind of thermodynamic transition has been measured through usual means.The absence of any known growth of a length scale that could explain the glassy dynamics leads to a wide range of competing models and theories trying to explain the origins of this dynamics.In the last decade, a promising lead has been put forward, that could allow the community to experimentally access such a growing length scale, through third order non-linear dielectric response measurements, and more in particular this response's temperature dependence. Indeed, non-linear response measurements reflect the collective effects that characterize the amorphous order and translate into high order correlation functions.During this PhD, we have built upon this experimental and theoretical background to design a fifth order non-linear dielectric response measurement experiment. In collaboration with a team of experimentalists and theoreticians, we have used these results in conjunction with third order response measurement results to make a very strong case advocating the existence of a thermodynamic critical point in Glycerol and Propylene Carbonate. This is a very significant advance in the understanding of the behaviour of glassy materials.This ground breaking discovery puts very strong constraints on existing theories and will contribute to end some decades-long theoretical debates within the glassy community.