Estudamos nessa dissertação um modelo para um gás em contato com dois banhos de partículas a potenciais químicos distintos. Isso foi feito através de um modelo de gás na rede (modelo de Ising) em que esta é dividida em duas sub-redes R1 e R2 e a evolução temporal se dá através da competição de duas dinâmicas markovianas: uma (dinâmica A) realiza o fluxo de partículas de uma sub-rede a outra, simulando o contato com um banho térmico à temperatura T , enquanto a outra (dinâmica B) tira ou põe partículas nas sub-redes, simulando o contato com banhos de partículas a potenciais químicos mu1 e mu2 e temperatura T . Estudamos, através de aproximações de campo médio dinâmico e de simulações de Monte Carlo, o diagrama de fases e as propriedades críticas do modelo, obtendo comportamento crítico similar ao do modelo de Ising de equilíbrio, exceto em uma pequena região do diagrama de fases em que detectam-se fases reentrantes. Calculamos também a produção de entropia do modelo. O estudo do comportamento crítico dessa grandeza deu origem a um novo expoente crítico zeta relacionado à divergência da derivada da produção de entropia com relação à temperatura. Obtivemos zeta=0 (divergência logaritimica). Verificamos, por fim, utilizando nesse caso aproximações de campo médio, o limite de validade de dois teoremas da termodinâmica de não equilíbrio: o teorema da mínima produção de entropia e o critério universal de evolução. Com relação ao primeiro teorema, determinamos em que limites podemos considerar a dinâmica do modelo como uma dinâmica que descreve um sistema próximo a uma situação de equilíbrio termodinâmico. Com relação ao critério universal de evolução, encontramos situações para as quais o teorema aparentemente não é satisfeito. Acreditamos que esse fato se deva a um elemento de instabilidade trazido indevidamente pela aproximação (de campo médio) utilizada. A investigação dessa questão foi postergada para um próximo trabalho. / We studied a model of a gas in contact with two baths of particles. We used a model of a gas in a lattice (Ising model) in which the net is divided in two: the sub-net R1 and the sub-net R2. The system evolves in time according to the competition between two dynamics: one (dynamic A) that realizes the flow of particles from one sub-net to the other, simulating the contact with a heat bath at temperature T while the other one (dynamic B ) removes or put particles in the sub-nets, simulating the contact with particle baths at chemical potentials mu1 and mu2 and temperature T. We studied, using mean-field approximations and Monte Carlo simulations, the phase diagram and the critical properties of the model, getting similar critical behavior to the Ising model in equilibrium, except in a small region of the phase diagram in which there are reentrant phases. We also calculated the entropy production of the model. The study of its critical behavior results in the definition of a new critical exponent zeta related to the divergence of the derivative of the entropy production with respect to the temperature. We obtained zeta =0 (logarithmic divergence). We verified, finally, using in this case mean-field approximations, the limit of validity of two theorems from nonequilibrium thermodynamics: the minimum entropy production theorem and the universal evolution criteria. Regarding the first theorem, we determined in what limits we can consider the model\' s dynamics as ``close\'\' to equilibrium. Regarding the universal evolution criteria, we found situations in which the theorem is apparently violated. We believe that this violation must be consequence of an improper instability element brought by the approximation (of mean-field) used. The investigation of this question was delayed to a next work.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-09-12T14:11:57Z No. of bitstreams: 1 andrerodriguesdesouza.pdf: 1851529 bytes, checksum: c9b62f26af4296734a019aad8efb36dd (MD5) / Approved for entry into archive by Diamantino Mayra (mayra.diamantino@ufjf.edu.br) on 2016-09-13T12:57:07Z (GMT) No. of bitstreams: 1 andrerodriguesdesouza.pdf: 1851529 bytes, checksum: c9b62f26af4296734a019aad8efb36dd (MD5) / Made available in DSpace on 2016-09-13T12:57:07Z (GMT). No. of bitstreams: 1 andrerodriguesdesouza.pdf: 1851529 bytes, checksum: c9b62f26af4296734a019aad8efb36dd (MD5) Previous issue date: 2011-02-17 / FAPEMIG - Fundação de Amparo à Pesquisa do Estado de Minas Gerais / Em sociedade simples como vespas do gênero Polistes, rainhas podem regular a atividade de operárias. Contudo, investigações recentes demonstraram que esse não é o único padrão para o gênero. Existem espécies onde a atividade das operárias não depende da rainha. Essas descobertas motivam estudos com outras espécies para encontrar sistemas intermediários, que podem auxiliar no entendimento da evolução da organização social em vespas sociais. Neste estudo é demonstrado que rainhas de P. versicolor não monopolizam a regulação da atividade colonial e a estimulação física das operárias ao forrageio. Além disso, membros da colônia utilizam a agressão como mecanismo de estímulo ao forrageio. Esses resultados sugerem que a regulação da atividade de operárias em P. versicolor está mais próxima de um sistema descentralizado, auto-organizado e independente da rainha. / Regulation of worker activity in the social wasp Polistes versicolor : In simple societies like Polistes wasps, queens can regulate worker activity. However, recent investigations have shown that this is not the only pattern for this genus. There are some species in which some aspects of worker activity is not queen dependent. These findings motivate studies with other species to find intermediate systems, which may aid in understanding the evolution of work organization in social wasps. Firstly, it was demonstrated that queens of P. versicolor don`t monopolize colony activity initiation and don’t stimulate worker foraging. In addition, colony members use aggression as a mechanism of foraging stimulation. These results suggest that regulation of worker activity seems to be close to a decentralized, self-organized, queen independent system.

Abstract The aim of this thesis is to devise novel cooperative paradigms that allow small base stations (SBSs) to perform joint optimizations in the field of interference and spectral resource management, in an automated, self-organizing way. Fostering cooperation requires a careful negotiation process and incurs additional operational costs that can ultimately limit the scalability of such an approach. Hence, we design cooperative models around the self-organizing functions of small cell networks, through which each SBS dynamically adapts its own cooperative strategy to the current network status. In the first part of the thesis, we study the co-tier interference in the downlink of an underlay small cell tier. Showing that mutual interference is a limiting factor, we propose a cooperative scheme based on the concept of interference alignment. Thereby, the SBSs autonomously devise their cooperative strategy, select partner small base stations and suppress the mutual interference via alignment. In the second part, we extend the above problem by considering additional constraints posed by non-cooperative macro cell users sharing the spectrum with the SBSs. Due to the dimension of such a problem, we show that interference alignment solutions do not often exist, hence, we propose a distributed solution based on the concept of interference draining for solving the interfering signals in the space-frequency domain. Finally, we focus on inter-tier cooperation and propose an adaptive hybrid access policy based on spectrum leasing, which jointly enhances the SBSs' transmission capacity and the macro cell users' QoS . In the studied scenarios, we highlight how SBSs' individual performance is network-dependent, due to the shared nature of the spectrum and the network infrastructure. For addressing such issues, we use novel concepts from coalitional games in partition form in which the strategic decisions are optimized by accounting for external effects, such as interference or dynamic spectrum allocation. Based on the properties of optimality of coalitional games in partition form, the proposed cooperative solutions show two key features. First, by leveraging on decentralized strategic decisions, complex interference management techniques, such as interference alignment or draining, can be implemented in practical, scalable way. Second, although notable cooperative solutions exists for certain problem dimensions, the proposed algorithms are shown to be effective for a wide range of network sizes, by achieving significant data rate enhancement and low overhead. / Tiivistelmä Työssä käsitellään merkittäviä häiriön ja radioresurssien hallintaongelmia ja ehdotetaan käytännöllisiä yhteistoiminnallisuusmalleja, jotka tuottavat merkittäviä suorituskykyparannuksia, ja samaan aikaan ottavat huomioon yhteistyön kustannukset ja strategisten päätösten vaikutuksen piensolujen keskinäiseen suorituskykyyn. Työn ensimmäisessa osassa tutkitaan makro- ja piensoluverkon välistä häiriötä laskevalla siirtosuunnalla. Koska keskinäishäiriö osoittautuu merkittäväksi rajoittavaksi tekijäksi, ehdotetaan yhteistyömenetelmää, joka perustuu ns. häiriön laskostamiseen. Tällaisessa menetelmässä pientukiasemat päättävät itsenäisesti yhteistyöstrategiansa ja valitsevat ne tukiasemat, joiden kanssa tehdään yhteistyötä ja vaimennetaan keskinäishäiriötä laskostamalla. Työn toisessa osassa edellämainittua ongelmaa laajennataan ottamalla huomioon rajoitteet, jotka aiheutuvat samoja taajuusresursseja jakavista, mutta piensolutukiasemien kanssa yhteistyötä tekemättömistä makrosoluista. Ongelman laajuudesta havaitaan, että yleensä häiriön laskostusratkaisua ei löydy tällaisessa ongelmassa. Niinpä ehdotetaan hajautettua häiriön kohdennukseen perustuvaa ratkaisua, jossa häiriösignaalit lomitellaan tila-taajuustasossa. Työn viimeisessä osassa keskitytään eri tyyppisten tukiasemasolujen kesken käytävään yhteistyöhön ja ehdotetaan mukautuvaa taajuusspektrin vuokraamiseen perustuvaa hybridi-käyttöoikeusmenetelmää, joka parantaa piensolujen kapasiteettia ja makrosolukäyttäjien palvelun laatua. Kaikissa tutkituissa menetelmissä korostetaan kuinka yksittäisen pientukiaseman suorituskyky on verkosta riippuvainen johtuen jaetusta taajuuskaistasta ja verkkoinfrastuktuurista. Näissä skenaarioissa käytetään uusia ositukseen perustuvia ns. liittoumapelikonsepteja. Tämän tyyppisissä peleissä strategiset päätökset on optimoitu ottamalla huomioon ulkoiset tekijät kuten häiriö ja dynaaminen taajuuden allokointi. Ositukseen perustuvien liitoumapelien optimaalisuus- ja stabiilisuusominaisuuksien pohjalta ehdotetaan hajautettuja algoritmeja tutkittuihin ongelmiin. Ehdotetut yhteistoiminnalliset ratkaisut osoittavat kaksi avaintekijää. Ensinnäkin käyttämällä hajautettuja strategisia päätöksiä kompleksiset häiriönhallintatekniikat, kuten häiriön lomittelu ja kohdennus, voidaan toteuttaa käytännöllisesti siten, että hyöty-kustannussuhde on tasapainossa. Toiseksi, vaikka merkittäviä yhteistyöratkaisuja on olemassa tietyn dimensioisiin ongelmiin, ehdotetut algoritmit ovat osoittautuneet tehokkaiksi hyvin erikokoisissa verkoissa. Samalla on saavutettu merkittäviä datanopeusparannuksia ja hyvä skaalautuvuus.

Abstract This thesis aims to evaluate networking aspects of autonomous packets access systems when dynamically and adaptively performing resource and network management. In this context, Quality of Service (QoS)-aware solutions for resource sharing and control (e.g., channel access, load control, interference management and routing techniques among others) in large-scale wireless networks are envisaged. We propose and investigate distributed coordination mechanisms for controlling the co-channel interference generated in multi-tier coexistence scenarios consisting of macrocells underlaid with short-range small cells. The rationale behind employing such mechanism is to opportunistically reuse resources without compromising ongoing transmissions on the overlaid macrocells, while still guaranteeing QoS in both tiers. To mitigate the resulting co-channel interference, the underlaid tiers of small cells use distributed mechanism that relies on minimal signaling exchange, e.g., the Time Division Duplexing (TDD)-underlay approach which is based on regular busy tones. Herein, stochastic geometry is used to model network deployments, while higherorder statistics through the cumulants concept is utilized to characterize the probability distribution of the aggregate interference at the tagged receiver. To conduct our studies, we consider a shadowed fading channel model incorporating log-normal shadowing and Nakagami-m fading. In addition, various network algorithms, such as power control and frequency (re)allocation, are included in the analytical framework. To evaluate the performance of the proposed solutions, we also derive closed-form expressions for the outage probability and average spectral efficiency with respect to the receiver of interest under various channel conditions and network configurations. Results show that the analytical framework matches well with numerical results obtained from Monte Carlo simulations, and that the coordination mechanisms substantially improve the performance of overlaid macrocell networks, while also benefiting small cells. In contrast to the uncoordinated Frequency Division Duplexing mode, the coordinated TDD-underlay solution shows a reduction in the outage probability, while the average spectral efficiency increases at high loads. Although more elaborated interference control techniques such as, downlink bitmap and distributed antennas systems become needed, when the density of uncoordinated small cells in the underlaid tier gets high. / Tiivistelmä Tämä väitöskirja pyrkii arvioimaan autonomisia pakettikytkentäisiä järjestelmiä verkon näkökulmasta, kun resurssien ja verkon hallinta tapahtuu dynaamisesti ja adaptiivisesti. Tässä yhteydessä suunnitellaan QoS-tietoisia ratkaisuja resurssien jakamiseen ja hallintaan (esim. kanavan allokointi, kuorman hallinta, häiriön käsittely ja reititystekniikat) suuren skaalan langattomiin verkkoihin. Ehdotamme ja tutkimme hajautettuja koordinointimekanismeja monikanavien häiriöiden hallintaan monitasoisissa skenaarioissa, jotka koostuvat lyhyen kantaman soluista makrosoluissa. Peruste näille mekanismeille on resurssien opportunistinen uudelleenkäyttö tinkimättä käynnissä olevista lähetyksistä suuremmissa makrosoluissa, samalla kun QoS taataan molemman tason lähetyksissä. Pienentääkseen aiheutuvaa monikanavahäiriöitä, alemman tason pienet solut käyttävät hajautettua mekanismia, kuten esimerkiksi säännöllisiin varattu-ääniin perustuvaa Time Division Duplexing (TDD) - mekanismia, vähällä signaalien vaihdon määrällä. Stokastista geometriaa käytetään mallintamaan verkkoja, kun taas korkeamman tason tilastollista laskentaa kumulanttimenetelmän käsitteen kautta käytetään kuvaamaan kokonaishäiriön todennäköisyysjakaumaa merkityssä vastaanottimessa. Käsittelemme varjostuvaa ja häipyvää kanavamallia sisältäen log-normaalin varjostumisen ja Nakagamim häipymisen. Lisäksi sisällytämme analyyttiseen työhön monenlaisia verkkoalgoritmeja tehohallintaan ja taajuuden (uudelleen)allokointiin. Ehdotettujen ratkaisujen tehokkuuden arvioimiseksi johdamme myös suljetut muodot katkosten todennäköisyyksille ja keskimääräiselle spektrin käytön tehokkuudelle halutun vastaanottimen suhteen monissa kanavatiloissa ja verkon kokoonpanoissa. Tulokset osoittavat, että analyyttisen työn tulokset vastaavat hyvin Monte Carlo - simulaatioilla saatujen numeeristen tulosten kanssa ja että koordinointimekanismit parantavat makrosoluverkkojen tehokkuutta merkittävästi, samalla kun myös pienet solut hyötyvät. Toisin kuin koordinoimaton Frequency Division Duplexing -toimintatila, koordinoitu TDD-toimintatila pienentää katkosten todennäköisyyttä samalla kun keskimääräinen spektrin käytön tehokkuus kasvaa suurella kuormalla. Toisaalta kehittyneemät häiriönhallintatekniikat, kuten alalinkki bittikartta sekä hajautetut antennijärjestelmät, tulevat tarpeelliseksi, kun pienten koordinoimattomattomien solujen tiheys kasvaa alemmalla tasolla.

This dissertation aim is to investigate the application of higher-ordered feedback architectures, as a control system for an autonomous robot, on delayed response task problems in the area of evolutionary robotics. For the two architectures of interest a theoretical and practical experiment study is conducted to elaborate how these architectures cope with the road-sign problem, and extended versions of the same. In the theoretical study conducted in this dissertation focus is on the features of the architectures, how they behave and act in different kinds of road-sign problem environments in earlier work. Based on this study two problem environments are chosen for practical experiments. The two experiments that are tested are the three-way and multiple stimuli road-sign problems. Both architectures seams to be cope with the three-way road-sign problem. Although, both architectures are shown to have difficulties solving the multiple stimuli road-sign problem with the current experimental setting used. This work leads to two insights in the way these architectures cope with and behave in the three-way road-sign problem environment and delayed response tasks. The robot seams to learn to explicitly relate its actions to the different stimuli settings that it is exposed to. Firstly, both architectures forms higher abstracted representations of the inputs from the environment. These representations are used to guide the robots actions in the environment in those situations were the raw input not was enough to do the correct actions. Secondly, it seams to be enough to have two internal representations of stimuli setting and offloading some stimuli settings, relying on the raw input from the environment, to solve the three-way road-sign problem. The dissertation works as an overview for new researchers on the area and also as take-off for the direction to which further investigations should be conducted of using higher-ordered feedback architectures.

Den klassiska approachen till navigering innefattar att agenten håller en intern representativ modell av omgivningen. Denna approach har emellertid många nackdelar, speciellt för dynamiska miljöer. En modernare approach är att förlita sig på den faktiska omgivningen istället för en modell av denna. Detta arbete presenterar en undersökning av navigeringsproblemet och hur väl det löses av agenter vars kontrollmekanismer utgörs artificiella neurala nätverk. Tillförlitligheten hos de två neurala arkitekturerna Extended sequential cascaded network och Self-organized recurrent network bestäms genom experiment. Det visas i experimenten att Extended sequential cascaded network är den mest tillförlitliga arkitekturen av de två när navigeringsproblemet skall angripas. Det visas även att Extended sequential cascaded network tränar fram ett helt reaktivt beteende i samtliga experiment. Slutsatsen som kan dras av detta är att svåra problem inte alltid kräver avancerade arkitekturer för att lösastillfredsställande.

In swarm robotics, the control of a group of robots is often fully distributed and does not rely on any leader. In this thesis, we are interested in understanding how to design collective decision making processes in such groups. Our approach consists in taking inspiration from nature, and especially from self organization in social insects, in order to produce effective collective behaviors in robot swarms. We have devised four robotics experiments that allow us to study multiple facets of collective decision making. The problems on which we focus include cooperative transport of objects, robot localization, resource selection, and resource discrimination. <p><p>We study how information is transferred inside the groups, how collective decisions arise, and through which particular interactions. Important properties of the groups such as scalability, robustness, and adaptivity are also investigated. We show that collective decisions in robot swarms can effectively arise thanks to simple mechanisms of imitation and amplification. We experimentally demonstrate their implementation with direct or indirect information transfer, and with robots that can distinguish the available options partially or not at all. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

The topic of this thesis is procrastination. Procrastination is "the illogical, but deliberate delaying of planned action, which is accompanied by a commitment to alternative activities." (Sliviaková 2010, p. 3). Occasional procrastination however mostly harmless is only a small step from procrastination chronic. Chronic procrastination already points at undesirable situation, the malfunction of a healthy lifestyle and self-control. That view is the starting point for the research work of the problem, which investigates the symptoms of procrastination among primary and secondary school pupils. Procrastination is usually being considered in relation to adults' behaviour. The question asked is whether it is relevant to consider procrastination also in relation to children at primary school. In the theoretical part, we therefore first gathered and compiled the available data about the topic from various Czech and foreign sources, mainly to define with necessary precision the object of the study (procrastination) and learned the wider context of the issue (time management, self- management). The survey is based on interviews with six parents and thirty pupils from 1st to 5th grade. The method of research used with pupils was author a story that allowed them to identify themselves with a certain type of...

[pt] Motivado pela riqueza de fenômenos produzidos pelos seres vivos, este trabalho busca estudar a formação de padrões espaciais de populações biológicas. De um ponto de vista mesoscópico, definimos os processos básicos que podem ocorrer na dinâmica, construindo uma equação diferencial parcial para a evolução da distribuição da população. Essa equação incorpora duas generalizações de um modelo pre-existente para a dinâmica de um espécie, que leva em conta interações de longo alcance (não locais). A primeira generalização consiste em considerar que a difusão é não linear, isto é, é afetada pela densidade local de tal modo que o coeficiente de difusão segue uma lei de potência. Por outro lado, visto a alta complexidade envolvida na natureza dos parâmetros do modelo, introduzimos como segunda generalização parâmetros que flutuam no tempo. Idealizamos estas flutuações como um ruído descorrelacionado temporalmente e que obedece uma distribuição gaussiana (ruído branco). Para estudar o modelo resultante, utilizamos uma abordagem analítica e numérica. As ferramentas analíticas se baseiam na linearização da equação de evolução e portanto são aproximadas. Todavia, complementadas com resultados numéricos, conseguimos extrair conclusões relevantes. A não localidade das interações induz a formação de padrões. O alcance dessas interações é o que determina o modo dominante presente nos padrões. Assim, para valores dos parâmetros acima de um limiar crítico, emergem padrões. Analiticamente, mostramos que, mesmo abaixo desse limiar, as flutuações nos parâmetros podem induzir a aparição de ordem espacial. Os efeitos da difusão não-linear são captados superficialmente pela análise linear. Numericamente, mostraremos que sua presença modifica a forma dos padrões. Observamos, especialmente, a existência de uma transição quando alternamos entre o caso em que a difusão é facilitada por altas densidades e o caso oposto. Para o primeiro caso, verificamos que os padrões se tornam fragmentados, ou seja, a população é agora composta de sub-grupos desconectados. / [en] Motivated by the richness of phenomena produced by living beings, this work aims to study the formation of spatial patterns in biological populations. From the mesoscopic point of view, we define the basic processes that may occur in the dynamics, building a partial differential equation for the evolution of the population distribution. This equation incorporates two generalizations of a pre-existing model for the dynamics of one species, which takes into account long-range (nonlocal) interactions. The first generalization is to consider that diffusion is nonlinear, i.e., it is affected by the local density such that the diffusion coeficient follows a power law. On the other hand, because of the high complexity involved in the nature of model parameters, we introduced as a second generalization time-fluctuating parameters. We idealize these fluctuations as Gaussian temporally uncorrelated (white) noises. To study the resulting model, we use an analytical and numerical approach. Analytical tools are based on the linearization of the evolution equation and are therefore approximate. However, as evidenced by numerical results, we draw important conclusions. The nonlocal feature of the interaction is the main mechanism which induces pattern formation. We show that the extent of these interactions is what characterizes the dominant mode. Thus, for parameter values above a critical threshold patterns emerge. Analytically, we also show that even below this threshold, fluctuations in the parameters can induce the appearance of spatial order. The effects of nonlinear diffusion are only superficially captured by the linear analysis. Numerically, we show that their presence modifies the patterns shape. We mainly observed the existence of a qualitative difference between the cases when diffusion is facilitated or not by high densities. In the first case, we note that the patterns become fragmented, that is, population becomes composed of disconnected clusters.

Barrières de transport (TB) sont un élément clé dans le contrôle de transport turbulent et atteindre la haute performance des ‘plasmas brûlants’. Les études théoriques abordent l’autorégulation de la turbulence comme une explication possible pour la formation de TB, mais une compréhension complète de ces dynamiques complexes est toujours manquante. Dans ce contexte, nous abordons l’auto-organisation dans le transport turbulent dans les plasmas de fusion dans le but de présenter une nouvelle compréhension de la dynamique des TB. Les outils numériques que nous utilisons des simulations de portée de la turbulence gyrocinétique plus complexe à simple turbulence des fluides 2D et prédateur-proie comme modèles.Deux principales caractéristiques de l'auto-organisation, les avalanches et les flux zonal (ZF), semblent contrôler transport à grande échelle. Dans la région de SOL (Scrape Off layer), événements avalancheux intermittents ne permettent pas séparation d'échelle dans le temps ou l'espace entre champs moyens et les modalités de fluctuation. Dans le bord (edge), la génération des doubles couches de cisaillement dans les profils de vitesse réduit le transport turbulent. Un modèle turbulent 2D pour la génération de ‘piedestal’, qui est non spécifique des plasmas de tokamak, a été mis au point, le piedestal étant localisée à l'interface entre les régions a différent amortissement d'écoulement zonal: edge et SOL. Les événements de relaxation quasi-périodiques sont étudiés réduisent le modèle à trois couplage des modes pour identifier l'interaction entre les streamers et les ZF et le rôle du Reynolds stress dans la génération et la saturation du TBs / Transport barriers (TB) are a key element in controlling turbulent transport and achieving high performance burning plasmas. Theoretical studies are addressing the turbulence self-regulation as a possible explanation for transport barrier formation but a complete understanding of such complex dynamics is still missing. In this context, we address self-organized turbulent transport in fusion plasmas with the aim of presenting a novel understanding of transport barriers dynamics. The numerical tools we use span simulations from the most complex gyrokinetic turbulence to simpler 2D fluid turbulence and predator-prey like models.Two features of self-organizations, avalanches and zonal flows (ZFs), appear to control large scale transport. In the SOL (Scrape Off Layer) , intermittent avalanche events do not allow for time or space scale separation between mean fields and fluctuation terms. In the edge, the generation of long living double shear layers in the profiles of the velocity reduces radial turbulent transport. Such radially distributed barriers govern profile corrugations. A 2D turbulent model for pedestal generation, which is not specific of Tokamak plasmas, has been developed, the pedestal being localized at the interface between regions with different zonal flow damping: the edge region, where zonal flows are weakly damped by collisions, and the SOL region characterized by zonal flow damping due to boundary conditions. Quasi-periodic relaxation events are studied reducing the model to three modes coupling to identify the interplay between streamers and ZFs and the role of Reynolds stress in the generation and saturation of TBs.