Die heutige und zukünftige Entwicklung beim Entwurf von Axialverdichtern für die Anwendung in Flugzeugtriebwerken ist immer stärker davon geprägt, ein möglichst großes Druckverhältnis mit möglichst wenigen Stufen zu erzeugen. Ziel ist es, möglichst viel Leistung mit möglichst geringem Gewicht umzusetzen, um die Effizienz der Maschine weiter zu verbessern. Um dies zu erreichen, muss eine Erhöhung der Stufendruckverhältnisse und damit eine Erhöhung der Stufenbelastung in Kauf genommen werden. Die höhere Belastung hat jedoch einen Anstieg der Verluste aufgrund der stärker werdenden Sekundärströmungen zur Folge, und wirkt sich zunächst negativ auf die Stabilität und den Wirkungsgrad der Maschine aus. Diese negativen Effekte können nur durch eine Weiterentwicklung der Schaufelgeometrie kompensiert werden. Hierbei stoßen die derzeit benutzten Entwurfsmethoden jedoch an ihre Grenzen. Aus diesem Grund wurde ein neues Verfahren für den dreidimensionalen Entwurf von Rotoren in Axialverdichtern entwickelt. In dieser Arbeit wird dessen Entwicklung präsentiert. Das Verfahren umfasst die systematische Anwendung von Pfeilung und V-Stellung, sowie die dreidimensionale inverse Berechnung der radialen Skelettlinienverteilung. Um damit eine Verbesserung des Rotorwirkungsgrades zu erreichen, müssen vor allem die kritischen wand- bzw. spaltnahen Bereiche optimal an die Strömungsumgebung angepasst werden. Die vorliegende Arbeit beschreibt ausführlich die theoretischen Grundlagen der Rotorströmung und des Rotorentwurfs. Basierend darauf werden für die Umsetzung eines vollständigen dreidimensionalen Schaufelentwurfs zwei Panelverfahren zur Berechnung der dreidimensionalen jedoch reibungslosen Strömung, zur Lösung der Nachrechen- bzw. der Entwurfsaufgabe, entwickelt. Die Panelverfahren werden angewandt, um eine Methodik für den effektiven Einsatz von Pfeilung, V-Stellung und inverser Skelettlinienberechnung für den dreidimensionalen Rotorentwurf festzulegen. Die gewonnenen Erkenntnisse werden anschließend für den Entwurf eines hochbelasteten Rotors in einem einstufigen Niedergeschwindigkeitsverdichter nach dieser neuen Entwurfsmethodik genutzt. Anhand von Ergebnissen aus Rechnungen und Messungen für diesen Rotor wird die Wirksamkeit des Verfahrens demonstriert. / The recent and future design of axial compressors for aero engines is strongly affected by the aim to generate a high pressure ratio with less stages to increase power and reduce weight to achieve an improved efficiency. This can only be achieved when the stage pressure ratio is raised which leads to increased stage loading. But the higher stage loading results in higher losses caused by stronger secondary flows. This has a negative effect on compressor stability and efficiency. To counteract the negative effects enhanced blade geometries are necessary. With the recently used design methods this is hardly to achieve. For that reason a new method for the three-dimensional design of rotors and stators in axial compressors has been developed. This report summarizes that work. The method accounts for the systematic application of sweep and dihedral as well as the three-dimensional inverse calculation of the camber-line distributions along blade height. To achieve improved efficiency the regions close to the end-walls and the tip and hub gap have to be adapted to the flow environment. The recent report described in detail the theoretical background of the compressor blade flow and compressor blade design. Based on that, two inviscid panel methods for the fully three-dimensional design of compressor blades are described. The panel methods are applied to define a methodology for the effective application of sweep, dihedral and inverse camber-line calculation in a three-dimensional blade design process. Afterwards the findings are used to design a highly-loaded single-stage low-speed research compressor rotor. The validity of the presented design method is proven with CFD and test results.

A little over 20 years ago Drinfeld presented the quantum (or Drinfeld) double construction. This construction takes any Hopf algebra and embeds it in a larger quasi-triangular Hopf algebra, which contains an algebraic solution to the constant Yang–Baxter equation. One such class of algebras consists of the Drinfeld doubles of finite groups, which are currently of interest due to their connections with non-Abelian anyons. The smallest non-commutative Drinfeld double of a finite group algebra is the Drinfeld double of D3 , the dihedral group of order six, which was recently used to construct solutions to the Yang–Baxter equation cor- responding to 2-state and 3-state integrable spin chains with periodic boundary conditions. In this thesis we construct R-matrices from the Drinfeld double of dihedral group algebras, D(Dn) and consider their associated integrable systems. The 3-state spin chain from D(D3) is generalised to include open boundaries and it is also shown that there exists a more general R-matrix for this algebra. For general D(Dn) an R-matrix is constructed as a descendant of the zero-field six-vertex model.

A little over 20 years ago Drinfeld presented the quantum (or Drinfeld) double construction. This construction takes any Hopf algebra and embeds it in a larger quasi-triangular Hopf algebra, which contains an algebraic solution to the constant Yang–Baxter equation. One such class of algebras consists of the Drinfeld doubles of finite groups, which are currently of interest due to their connections with non-Abelian anyons. The smallest non-commutative Drinfeld double of a finite group algebra is the Drinfeld double of D3 , the dihedral group of order six, which was recently used to construct solutions to the Yang–Baxter equation cor- responding to 2-state and 3-state integrable spin chains with periodic boundary conditions. In this thesis we construct R-matrices from the Drinfeld double of dihedral group algebras, D(Dn) and consider their associated integrable systems. The 3-state spin chain from D(D3) is generalised to include open boundaries and it is also shown that there exists a more general R-matrix for this algebra. For general D(Dn) an R-matrix is constructed as a descendant of the zero-field six-vertex model.

Made available in DSpace on 2015-05-15T11:46:00Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 564673 bytes, checksum: caec7ef95e0e9b70eb60b56bfa2f6547 (MD5) Previous issue date: 2011-08-03 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this paper we study finite Abelian groups, where state and prove the fundamental theorem of finitely generated abelian groups, as well as determine a characterization of automorphisms of a p-group, moreover, we exhibit an algorithm that determines the count of the number of automorphisms of p-groups. Finally, we show the automorphisms of the non-Abelian dihedral group. / Neste trabalho estudamos Grupos Abelianos finitos, onde enunciamos e provamos o Teorema fundamental dos grupos abelianos finitamente gerados, bem como determinamos uma caracterização dos automorfismos de um p-grupo, além disso, exibimos um algoritmo que determina a contagem do número de automorfismos desses p-grupos. Por fim, mostramos os automorfismos do grupo não-Abeliano Diedral .

Desde o início da década de 2010, o aumento do preço do combustível de aviação e a pressão da sociedade para redução da emissão de gases nocivos ao meio ambiente, junto com a necessidade de redução de ruído durante as fases de decolagem e pouso, levaram as companhias aéreas a buscar aeronaves mais eficientes. Para suprir essa demanda, os fabricantes de aviões comerciais solucionaram esse problema através do uso de motores de maior desempenho, que apresentam maior diâmetro que motores de gerações passadas. Desse modo, foi necessário projetar asas com maior diedro na região da raiz, possibilitando a instalação desses novos motores, e diedro menor após a seção do motor, adotando assim a solução de asa em gaivota. O presente trabalho visa analisar o impacto de diferentes tipos de asas em gaivota nos coeficientes aerodinâmicos de uma aeronave de configuração comercial típica. Para tanto, foi realizada uma revisão bibliográfica dos estudos envolvendo asas em gaivota. Numa primeira fase foi feito um estudo analítico das características aerodinâmicas de alguns modelos de aeronaves com asa em gaivota, e em uma segunda fase, foram empregadas ferramentas computacionais para analisar seus comportamentos aerodinâmicos. Posteriormente, em uma terceira fase, esses modelos foram ensaiados no túnel de vento do LAE (Laboratório de Aerodinâmica da EESC/USP), e os resultados das três fases foram comparados. / Since the beginning of the 2010s, the increasing price of aviation fuel and the pressure of society to reduce the emission of harmful gases into the environment, coupled with the need of noise reduction during the takeoff and landing, induce carrier companies to look for more efficient airplanes. To furnish this demand, the airplane manufacturers solved the problem using high performance engines, which present a larger diameter than the engines from previous generations. Thereby, it was necessary to project wing with higher dihedral on the root portion, enabling the installation of these new engines, and a lower dihedral after the engine section, thus adopting a gull wing solution. This research project aims at analyzing the impact of different types of gull wing on the aerodynamic coefficients of a typical commercial configuration airplane. For this purpose, a bibliographic review about the studies related to gull wings was performed. In a first phase, an analytical analysis of the aerodynamic characteristics of some airplane model with gull wings was done, and in a second phase, computational programs was used to study their aerodynamic behavior. Later, in a third phase, these models were tested in the wind tunnel of LAE (Laboratory of Aerodynamics of EESC/USP), and the results from the three phases were compared.

In this thesis, we will explore the structure of Terwilliger algebras over several different types of finite groups. We will begin by discussing what a Schur ring is, as well as providing many different results and examples of them. Following our discussion on Schur rings, we will move onto discussing association schemes as well as their properties. In particular, we will show every Schur ring gives rise to an association scheme. We will then define a Terwilliger algebra for any finite set, as well as discuss basic properties that hold for all Terwilliger algebras. After specializing to the case of Terwilliger algebras resulting from the orbits of a group, we will explore bounds of the dimension of such a Terwilliger algebra. We will also discuss the Wedderburn decomposition of a Terwilliger algebra resulting from the conjugacy classes of a group for any finite abelian group and any dihedral group.

<p> The nitrogen and hydrogen-deuterium isotope effects have been measured for the base-promoted elimination reactions of cis-and trans-2-phenylcyclopentyltrimethylammonium ions and cis-and trans-2-phenylcyclohexyltrimethylammonium ions. The observations have been interpr eted as indicative of a concerted E2 mechanism for both trans and cis elimination processes. In the cis eliminations, however, proton transfer to base is far advanced at the transition state resulting in a much higher degree of carbanionic character ass ociated with the transition state than for the trans eliminations. </p> <p> The kinetic isotope effect results for these cyclic systems establish that the two bond-rupture processes complement each other; the greater the extent of proton transfer to base at the transition state, the smaller is the extent of C-N bond weakening. These observations are interpreted in terms of the coupling of the motion which extends the lengths of the H-C and C-N bonds at the transition state and the approach to coplanarity of the bonds involved in the elimination process. </p> / Thesis / Doctor of Philosophy (PhD)

Ces dernières années, un intérêt croissant est porté aux réflecteurs rétro-directifs aplatis dans le but de remplacer le réflecteur diédrique conventionnel, trop encombrant pour de nombreuses applications. Dans un premier temps, cette thèse étudie deux techniques différentes permettant de réduire l’épaisseur d’un réflecteur diédrique. L’Optique de transformation modifie la constitution matérielle de son volume intérieur alors que la modulation d’impédance de surface introduit une distribution d’impédance à sa surface. On examine également la possibilité de combiner ces deux techniques pour tirer le meilleur parti de chacune d’elle. La deuxième partie de cette thèse étudie l’origine des réflexions parasites pour les panneaux utilisant la modulation d’impédance de surface et propose de nouvelles règles de conception pour atténuer leurs niveaux. Finalement, une mise en oeuvre pratique est proposée pour une modulation d'impédance de surface généralisée qui utilise des impédances complexes et surpasse les performances de la modulation d’impédance classique. / In recent years, increasing interest incompact reflectors with retrodirective response is perceived since the conventional dihedral reflector is too bulky to be integrated within most applications. First, this thesis investigates two different techniques that might lead to lower profiles of the dihedral reflector. It explores the use of Transformation Optics that modifies the filling volume of such a device and Surface Impedance Modulation that introduces an impedance distribution over its surface. It also inspects the possibility of combining those two techniques to take benefit of their complementary advantages. The second part of this thesis investigates the source of parasitic lobes for surface impedance modulated panels and proposes new design rules to mitigate their levels. Finally, it also proposes a practical implementation for a specific setting of the generalized surface impedance modulation that makes use of complex impedances and outperforms a panel implementing the classical modulation.

Made available in DSpace on 2015-03-13T17:08:28Z (GMT). No. of bitstreams: 1 CamilaA_DISSERT_1-52.pdf: 4763596 bytes, checksum: 04aa5b36a81ca3019e267dac640c6e31 (MD5) Previous issue date: 2010-02-25 / The Araripe Basin is located over Precambrian terrains of the Borborema Province, being part of Northeast Brazil inner basins. Its origin is related to the fragmentation of the Gondwana supercontinent and consequently opening of South Atlantic during early Cretaceous. The basin has a sedimentary infill encompassing four distinct evolution stages, comprising Paleozoic syneclisis, pre-rift, rift and post-rift. The target of this study comprises the post-rift section of the basin focusing deformational styles which affect evaporates from Ipubi Member of the Santana Formation, which is composed by gypsum and anidrite layers interbedded with shales. These units occur widespread across the basin. In the central part of the basin, near Nova Olinda-Santana do Cariri, evaporites are affected by an essentialy brittle deformation tipified by fibrous gypsum filled fractures, cutting massive layers of gypsum and anidrite. Veins with variable orientations and dips are observed in the region distributed over three main populations: i) a dominant NWSE with shallow to moderate NE dipping population, consisting of gypsum filled veins in which fibers are normal to vein walls; i) NE-SW veins with moderate SE dips containing subhorizontal growth fibers; and iii) N-S veins with shallow E-W dips with fibers oblique to vein walls. In the west portion of the basin, near Trindade-Ipubi-Araripina towns, evaporate layers are dominantly constituted by gypsum/anidrite finely stratified, showing a minor density of veins. These layers are affected by a unique style of deformation, more ductile, typified by gentle to open horizontal normal folding with several tens of meters length and with double plunging NW-SE or NE-SW hinges, configuring domic features. In detail, gypsum/anidrite laminae are affected by metre to decimeter scale close to tight folding, usually kinked, with broken hinges, locally turning into box folds. Veins show NE-SW main directions with shallow NE dips, growth fibers are parallel to vein walls, constituting slickenfibers. This region is marked by faults that affect Araripina Formation with NW-SE, NE-SW and E-W directions. The main structural styles and general orientations of structures which affected the post-rift section of Araripe Basin yielded important kinematic information analysis which led us to infer a E-W to NE-SW extension direction to the northeastern part of the Basin, whereas in the southeastern part, extension occurred in N-S direction. Thus, it was possible to determine a regional kinematic setting, through this analysis, characterizing a NE-SW to ENE-WSW system for the post-rift section, which is compatible with the tension settings for the Sout American Plate since Albian. Local variations at the fluid pressure linked (or not) to sedimentary overload variation define local tension settings. This way, at the northeastern portion of the basin, the post-rift deformation was governed by a setting which ? 1 is sub-horizontal trending NE-SW and, ? 3 is sub-vertical, emphasizing a reverse fault situation. At the southwestern portion however there was characterized a strike slip fault setting, featuring ? 1 trending ENEWSW and ?3 trending NNW-SSE / A Bacia do Araripe est? inserida sobre os terrenos pr?-cambrianos da Prov?ncia Borborema, fazendo parte das bacias interiores do Nordeste do Brasil. Sua origem est? relacionada ? fragmenta??o do supercontinente Gondwana e consequente abertura do Atl?ntico Sul durante o Cret?ceo Inferior. Possuindo um preenchimento sedimentar que abrange quatro est?gios distintos de sua evolu??o, compreendendo as tectonossequ?ncias de Sin?clise Paleoz?ica, Pr?- Rifte, Rifte e P?s-Rifte. O objeto de estudo deste trabalho, compreende a se??o p?srifte da bacia, focando os estilos deformacionais que afetam os evaporitos do Membro Ipubi da Forma??o Santana, constitu?da por camadas de gipsita e anidrita intercaladas com folhelho, de ocorr?ncia abrangente em toda a Bacia do Araripe Na parte Norte da bacia, nas proximidades de Nova Olinda-Santana do Cariri os evaporitos s?o afetados por uma deforma??o essencialmente fr?gil, tipificada por fraturas preenchidas por gipsita fibrosa, recortando camadas de gipsita e anidrita geralmente maci?as. Na regi?o s?o observados veios com orienta??es e mergulhos bastante variados, distribuindo-se segundo tr?s popula??es principais: (i) uma com dire??o dominante NW-SE, com mergulhos suaves a moderados essencialmente para NE, geralmente preenchidos por gipsita cujas fibras disp?em-se ortogonalmente ?s paredes dos veios; (ii) veios NE-SW com mergulhos moderados para SE, contendo fibras de crescimento suborizontais; e (iii) veios N-S, com mergulhos suaves para E-W, cujas as fibras encontram-se obliquas ?s paredes desses veios. Na regi?o oeste da bacia, nas proximidades de Trindade-Ipubi-Araripina a camadas de evaporitos s?o dominantemente constitu?das por gipsita/anidrita finamente estratificada, apresentando uma densidade menor de veios. Essas camadas s?o afetadas por uma deforma??o peculiar, de car?ter mais d?ctil , tipificada por dobras horizontais, de perfil suave a aberto, com comprimento de onda de v?rias dezenas de metros, n?o raro apresentando charneiras com duplo caimento, com orienta??es NWSE ou NE-SW, constituindo fei??es d?micas. Em detalhe, as l?minas de gipsita/anidrita tamb?m s?o afetadas por dobras de escala m?trica a decim?trica, em geral de perfil fechado a apertado, muitas vezes apresentando estilo em kink (n?o ? raro nestes casos ocorrer ruptura da charneira), localmente constituindo dobras em caixa. Os veios (ocorrendo de forma mais rara) apresentam dire??es principais NE-SW, com mergulhos suaves para SE, as fibras de crescimento disp?em-se paralelamente ?s paredes dos veios, funcionando como slickenfibers. Est? regi?o ? marcada pelas falhas que afetam as rochas da Forma??o Araripina apresentando dire??es NW-SE, NE-SW e E-W. De posse das an?lises dos estilos e da orienta??o geral das estruturas que afetam a se??o p?s-rifte na Bacia do Araripe, atrav?s do m?todo dos diedros retos, foram obtidas informa??o importante quanto ? an?lise cinem?tica da deforma??o, possibilitando assim, definir os sentidos de transporte tect?nico predominantes e a infer?ncia do estado de paleotens?es que governou a instala??o das estruturas tect?nicas presentes. Sendo assim, foi poss?vel definir um regime cinem?tico regional, a partir desta an?lise, caracterizado a se??o p?s-rifte por um sistema de compress?o NE-SW a ENEWSW, regime este condizente com o que vem atuando na Placa Sul-Americana desde, pelo menos, o Albiano. Varia??es locais da press?o de fluidos somadas (ou n?o) a varia??es da sobrecarga sedimentar definem regimes cinem?ticos particulares. Assim, na por??o nordeste da bacia, a deforma??o p?s-rifte foi governada por um regime em que ?1 ? suborizontal e apresenta dire??o NE-SW, e ?3 ? subvertical, denotando um regime de falha inversa . J? na por??o sudoeste da Bacia do Araripe foi caracterizado um regime de falha transcorrente , apresentando ?1 na dire??o ENE-WSW e ?3 orientado segundo NNW-SSE

Comprendre la dynamique locale des protéines dans leur état natif (structure repliée etfonctionnelle) est essentiel pour comprendre leur dynamique globale et leur fonction biologique. Aucours de cette thèse, nous avons étudié la dynamique locale de plusieurs petites protéines enmesurant les fluctuations de sondes locales le long de la séquence d’acide aminé de ces protéines.Nous avons essayé de comprendre la dynamique de ces sondes locales, comment celles-ci serelaxaient entre leurs différentes conformations, comment leurs fluctuations étaient corrélées lesunes aux autres et comment peuvent-elles être reliées à la fonction biologique des protéines.Dans les trois premiers chapitres, nous introduisons les concepts du mouvement Browniende rotation libre, de la spectroscopie par Résonance Magnétique Nucléaire (RMN) et de ladynamique moléculaire (DM). Dans les chapitres 4 et 5, nous avons étudié la dynamique desliaisons amides de la chaine principale (backbone) des protéines sur leurs paysages d’énergie libre.Dans le chapitre 4, nous avons démontré que les fluctuations des liaisons amide dubackbone de la protéine VA3 sont décrites par une diffusion rotationnelle anormale plutôt que parune diffusion rotationnelle libre généralement utilisée pour interpréter les données RMN enrelaxation de spins et en couplage résiduel dipolaire. [...] Dans le chapitre 5, nous avons démontré la diffusion rotationnelle anormale de ces liaisons jusqu’à une échelle de temps de 100 ns en utilisant dix simulations de DM de 1 μs de la protéineUbiquitine. Nous avons aussi étudié la convergence des paramètres RMN extraits des trajectoiresde DM en fonction de leur durée. [...] Dans le chapitre 6, nous avons réalisé une l’étude de la corrélation entre les mouvements du backbone et des chaines latérales des protéines. [...] Dans la première partie du dernier chapitre de cette thèse, nous avons étudié l’évolution de la corrélation dynamique entre les chaines latérales et la chaine principale d’une protéine durant des évènements de dépliement/repliement. Pour cette étude préliminaire, nous avons utilisé unesimulation de DM d’un « ultra-fast folder » nommé Trp-cage réalisée à 380K. Nous avons confirméles résultats précédemment trouvés pour les protéines dans leur état natif. Nous avons observél’augmentation de la corrélation entre les séries temporelles yn(t) and δn(t) pendant un évènementde dépliement caractérisé par la sortie du tryptophane de sa cage. Un paramètre stérique s aégalement été défini afin de quantifier les intéractions des chaines latérales avec leurenvironnement. Dans une seconde partie de ce dernier chapitre, nous présentons une étudepréliminaire du dépliement d’un « downhill folder » nommé gpW sous contrainte d’une force. Pourcaractériser le dépliement de la protéine gpW, nous avons calculé les chemical shifts des atomes Cª et Hⁿ du backbone le long de sa séquence en fonction d’une coordonnée réactionnelle choisie comme étant la distance entre les Cª de résidus C- et N- terminaux. Nous avons démontré qu’il était difficile de discerner un comportement particulier à partir des tous les chemical shifts en fonction de la distance. Cependant, en moyennant la valeur des chemical shifts en sur tous lesrésidus de la protéine nous trouvons que l’évolution de cette valeur moyenne en fonction de ladistance permettait de décrire les évènements du dépliement de la protéine en fonction de lacoordonnée de réaction durant la simulation de DM / Understand the local dynamics of proteins in their native state, i.e. in their folded functionalstructure, is a prerequisite to understand their global dynamics and their biological function. In thepresent thesis, we investigated the local dynamics of several small proteins by recording thefluctuations of local probes along the amino-acid sequence of those proteins. We tried tounderstand the dynamics of the local probe, i.e. how they relax between their differentconformations, how their fluctuations are correlated to each other, how their fluctuations arerelated to the function of the proteins. In the first three chapters, we introduced the concepts of the free rotational Brownian motion, of the Nuclear Magnetic Resonance spectroscopy and of the Molecular Dynamics (MD)simulations. In chapters 4 and 5, we studied the dynamics of the backbone amide bonds of theproteins on their free-energy landscape. In chapter 4, we demonstrated that the fluctuations of the backbone amide bonds of the protein VA3 are described by a rotational anomalous diffusion rather than by a free rotationaldiffusion, as often assumed in the interpretation of the raw NMR-measured data (Spin relaxation(SR) data and Residual Dipolar Coupling (RDC) data. [...] In chapter 5, we demonstrated the anomalous diffusion of backbone amide bonds up to 100 ns by using ten MD trajectories of 1 μs of duration for the protein ubiquitin. We also studied the convergence of the NMR-derived parameters extracted from the MD trajectories in function of their duration. [...] In chapter 6, we addressed the question of the correlation between the motions of the side chains and main chain of a protein. [...] In the first part of the final chapter of the present thesis, we investigated the evolution of the correlation between the side-chain and the main-chain motions of a protein during unfolding/folding events. In this preliminary work, we used a single MD simulation of the ultrafast folder Trp-cage performed at 380 K. We confirmed the results found for proteins in theirnative state. We observed an increase of the correlation between the two time series yn(t) and δn(t) during an unfolding event characterized, here, by the exit of the TRP residue of its “cage”.A steric parameter s was also defined in order to quantify interactions of the amino-acid side chainwith its environment. In a second part of the last chapter, we present a preliminary study of theunfolding of the downhill folder gpW under a mechanical force. To characterized the unfolding ofgpW, we computed the chemical shift of the Cª and of the Hⁿ atoms along the amino-acidsequence of the protein in function of a reaction coordinate: the distance, rCªCª , between the Cª atoms of the N and C terminal residues. We demonstrated that it is hard to distinguish a typical behavior of all the chemical shift of all the residues along the amino-acid sequence in function of the distance rCªCª . However, by averaging the chemical shift over all the residues of the protein we found that the evolution of the average value of the chemical shift described the unfolding eventsof the protein during the MD simulations