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Modelagem de esforços de VIV em risers em catenária / Modeling of VIV forces in a catenary riserTsukada, Raphael Issamu, 1983- 24 August 2018 (has links)
Orientador: Celso Kazuyuki Morooka / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica e Instituto de Geociências / Made available in DSpace on 2018-08-24T00:38:15Z (GMT). No. of bitstreams: 1
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Previous issue date: 2013 / Resumo: Durante os últimos anos, as Vibrações Induzidas por Vórtices (VIV) foram intensamente estudadas a partir de experimentos com cilindros retos instalados verticalmente ou horizontalmente, que diferem significativamente das tubulações curvas em forma de catenária, encontradas nos risers em catenária. Desta forma, as VIVs para esta configuração de riser ainda são pouco compreendidas. Nesse sentido, neste trabalho é proposto um procedimento para o cálculo das VIVs em riser em catenária no domínio do tempo, utilizando as hipóteses do princípio da independência, que considera que apenas a componente normal da velocidade de correnteza em relação ao eixo do riser é significativa para as VIVs. Uma abordagem semi-empírica é adotada para calcular as forças transversais das VIVs, com base em coeficientes hidrodinâmicos encontrados a partir de experimentos com cilindros rígidos oscilando transversalmente ao escoamento. A frequência das forças de VIV é calculada através da mudança da frequência natural do riser devido à variação da massa adicional com a velocidade reduzida. Uma vez que respostas multi-modais podem ocorrer, um procedimento com base nas observações experimentais de células de desprendimento de vórtices e regiões de power-in são adotadas para determinar os modos de vibração excitados pelas VIVs. Dois experimentos com modelos flexíveis foram analisados. A partir do primeiro experimento verificou-se a validade das considerações do princípio da independência para tubos flexíveis. Já o segundo experimento teve a finalidade de entender o comportamento dinâmico de risers em catenária devido às VIVs, que demonstrou grande influência do comportamento das traveling waves na resposta da estrutura às VIVs. Por fim, o procedimento de cálculo das VIVs foi comparado com resultados experimentais para diferentes configurações e apresentou uma boa concordância. / Abstract: During the last years, the Vortex Induced Vibrations (VIV) were intensively studied from experiments with straight cylinders installed vertically or horizontally, which differ significantly from curved cylinders in catenary shape, found in catenary risers. Thus, for this riser configuration, VIVs are still poorly understood. Accordingly, this thesis proposes a procedure for the calculation of VIVs in catenary riser in the time domain, using the assumptions of the principle of independence, under which only the normal component of the flow velocity relative to the riser axis is significant to VIV. A semiempirical approach is adopted to calculate the transverse forces of VIV based on hydrodynamic coefficients found from experiments with rigid cylinders oscillating transversely to the flow. The frequency of the VIV forces is calculated by changing the natural frequency of the riser due to the variation of added mass in relation to the reduced velocity. Since multi-modal responses can occur, a procedure based on experimental observations of vortex shedding cells and power-in regions are adopted to determine the vibration modes excited by VIV. Two experiments with flexible models were analyzed. From the first experiment, the validity of the considerations of the principle of independence for flexible pipes is verified. The second experiment aimed to understand the dynamic behavior of catenary risers due to VIV, which showed a great influence of traveling wave's behavior in the response of the structure to VIV. Finally, the procedure of calculating VIV was compared with experimental results for different configurations and showed good agreement. / Doutorado / Explotação / Doutor em Ciências e Engenharia de Petróleo
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Análise da dinâmica dos movimentos de um riser híbrido auto-sustentável (RHAS) / Analysis of the dynamic motion of a self-standing hybrid riserShiguemoto, Denis Antonio 21 August 2018 (has links)
Orientadores: Celso Kazuyuki Morooka, Eugênio Libório Feitoza Fortaleza / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica e Instituto de Geociências / Made available in DSpace on 2018-08-21T00:36:50Z (GMT). No. of bitstreams: 1
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Previous issue date: 2012 / Resumo: Descobertas recentes de petróleo em laminas d'água cada vez mais profundas tem motivado o desenvolvimento de novas configurações de sistemas de produção de petróleo. Neste contexto, o Riser Hibrido Auto Sustentável (RHAS) surge como uma alternativa para produção de petróleo em águas ultraprofundas...Observação: O resumo, na íntegra, poderá ser visualizado no texto completo da tese digital / Abstract: Recent discoveries of petroleum in water depths deeper and deeper have motivated the development of new configurations of petroleum production systems. In this context, the Self Standing Hybrid Riser (SSHR) is an alternative to petroleum production in ultra deep waters...Note: The complete abstract is available with the full electronic document / Mestrado / Explotação / Mestre em Ciências e Engenharia de Petróleo
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An isothermal experimental study of the unsteady fluid mechanics of gas turbine fuel injector flowfieldsMidgley, Kristofer January 2005 (has links)
Low-emissions combustor design is crucially important to gas turbine engine manufacturers. Unfortunately, many designs are susceptible to unsteady oscillations that can result in structural fatigue and increased noise. Computational approaches that resolve flow unsteadiness, for example Large Eddy Simulation (LES), are being explored as one avenue to help understand such phenomena. However, in order to quantifY the accuracy of LES predictions, benchmark validation data in suitably chosen test cases are required. Comprehensive experimental data covering both time-averaged and timeresolved features are currently scarce. It was the aim of this thesis, therefore, to provide such data .in a configuration representing the near-field of a typical gas turbine fuel injector. It was decided to focus on the fuel injector since many unsteady events are believed to originate because of the transient interactions between the fuel injector flow and the main combustor flow. A radial fed two-stream fuel injector, based on a preexisting industrial gas-turbine Turbomeca design was used, since this geometry was known to be susceptible to unsteadiness. The fuel injector was investigated under isothermal conditions to place emphasis on the fluid mechanical behaviour of the fuel injector, including detailed capture of any unsteady phenomena present. Light Sheet Imaging (LSI) systems were used as the primary experimental technique to provide high quality spatially and temporally resolved instantaneous velocity and scalar field information in 2D planes (using ParticieImage Velocimetry (PIV) and Planar LaserInduced Fluorescence (PUF) techniques). Several methods were employed to extract information quantifYing the flow unsteadiness and improve visualisation of timedependent large-scale turbulent structures. Proper Orthogonal Decomposition (POD) analysis enabled clear identification of the dominant modes of energy containing structures. The results indicated that periodic high-energy containing vortex structures occurred in the swirl stream shear layer, emerging from the fuel injector. These formed a two-strong two-weak rotating vortex pattern which propagated down the main duct flow path. The formation of these vortices was found to be a function of the swirl number and originated due to an interaction between the forward moving swirl flow and the furthest upstream penetration point ofthe recirculation zone present in the main duct flow. Dependent on the magnitude of the swirl number (influencing the swirl stream cone angle) and the geometry of the fuel injector, the vortex formation point was sometimes found inside the fuel injector itself. If the vortices originated inside the fuel injector they appeared much more coherent in space and time and of higher energy. A second unsteady high energy containing phenomenon was also identified, namely a Precessing Vortex Core (PVC), which was damped out if the fuel injector contained a central jet. The dynamics of the PVC interacted with the dynamics of the swirl stream shear layer vortices to reduce there strength. Transient scalar measurements indicated that there was a clear connection between the unsteady vortex pattern and the rate of mixing, resulting in bursts of high heat release and is therefore identified as one source of combustor oscillations. Future fuel injector designs need to pay close attention to these unsteady features in selecting swirl number and internal geometry parameters.
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Analyse physique d'écoulements décollés fortement tridimensionnels par expérimentation. Structuration spatio-temporelle et sensibilité à une turbulence amont / Experimental and physical analysis of detached and massively three-dimensional flows. Spatio-temporal structuring and sensitivity to upstream turbulenceAffejee, Faisal 24 September 2015 (has links)
Ce travail a pour objectif l’étude du tourbillon conique engendré à partir d’une maquette générique représentant un montant de baie de véhicule automobile. Cette structure tourbillonnaire est responsable de fortes fluctuations sur les vitres latérales et génère du bruit dans l’habitacle. Ces véhicules étant soumis à des vents turbulents, la sensibilité de la dynamique de cette structure tourbillonnaire à une turbulence amont a été étudiée, en plaçant une grille à l’entrée de la veine d’essais de la soufflerie.Les propriétés spatiales et temporelles des champs de vitesse et de pression pariétale ont été étudiées en associant simultanément la mesure de la vitesse par Stéréo-PIV haute fréquence à la mesure de pression pariétale fluctuante par capteurs déportés. Nous avons montré qu’un niveau modéré de turbulence amont (intensité : 6%) se traduit par une modification très importante de la dynamique du tourbillon et de la pression pariétale fluctuante associée. Notre conjecture est qu’en l’absence de turbulence externe, la contribution principale au Cp’ est liée à l’empreinte du coeur tourbillonnaire et du décollement secondaire induit. Au contraire, en présence de turbulence amont, la forte augmentation du Cp’ semble associée à une réponse globale de la structure tourbillonnaire.L’étude de la dynamique spatio-temporelle à partir des corrélations pression-vitesse a permis de mettre en évidence le couplage fort existant entre la dynamique de la nappe cisaillée et celle du coeur de la structure tourbillonnaire. Il existe ainsi une modulation de la fréquence de battement de la structure pilotée par la géométrie de la maquette et par les caractéristiques de la turbulence amont (intensité et échelle intégrale). / This work aims to study conical vortices generated from a generic model representing the A-pillar of an automotive vehicle. This vortex structure is responsible of strong fluctuations on the side window and generates noise in the cabin. As these vehicles are subjected to the turbulent wind, the sensitivity of vortex structure dynamics to an upstream turbulence was studied by adding a grid at the test section entrance of the wind tunnel.The spatial and temporal properties of the velocity fields and the wall pressure were studied by simultaneously combining High Speed Stereo-PIV and wall fluctuating pressure measurements with distant sensors. It is shown that a moderate level of upstream turbulence (6% of intensity) results in a very significant change of the vortex dynamics and the associated wall fluctuating pressure. Our assumption is that in the absence of external turbulence, the main Cp’ contributionis linked to the footprint of the vortex core and of the induced secondary separation. On the contrary, in the presence of upstream turbulence, the strong increase of Cp’ seems to be associated with a global response of the vortex structure. The study of the spatio-temporal dynamics withpressure-velocity correlations allowed highlighting the strong coupling between the dynamics ofthe shear layer and of the core of the vortex structure. Thus, there is a modulation of the flapping frequency of the vortex controlled by the geometry of the model and by the characteristics ofthe upstream turbulence (intensity and integral length scale).
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Etude expérimentale paramétrique des propriétés et transitions de l'écoulement intra-cavitaire en cavité ouverte et contrôle de l'écoulement / Experimental parametric study of properties and transitions of the flow inside an open cavity and control of the flowDouay, Christelle 04 June 2014 (has links)
Ce travail porte sur la caractérisation de la dynamique intra-cavitaire en cavité ouverte, dont il existe peu d'études expérimentales, ainsi que sur le contrôle de cet écoulement. Nous avons réalisé une étude paramétrique des régimes primaire et secondaire de l'écoulement dans lesquels des structures de type Taylor-Görtler apparaissent. Nous avons identifié les seuils de bifurcation et montré leur nature systématiquement supercritique. Nous avons également montré que différentes familles de modes propagatifs ou stationnaires pouvaient être sélectionnées en fonction de la géométrie de la cavité. Cela a confirmé des prédictions réalisées dans des analyses de stabilité linéaire de l'écoulement de base. Nous avons montré que le régime secondaire résulte de la superposition d'ondes propagatives gauche et droite. Une tentative d'identification des coefficients des équations complexes couplées de Ginzburg-Landau décrivant cette dynamique a été conduite mais la sensibilité des coefficients à de multiples paramètres n'a pas permis d'obtenir des coefficients physiquement acceptables. Un forçage des oscillations de la couche cisaillée a été entrepris à l'aide d'un actionneur plasma froid à décharge à barrière diélectrique placé en amont de la cavité. L'analyse de la réponse de l'écoulement à un forçage périodique d'amplitude variable a permis d'identifier des plages d'accrochage en fréquence. Enfin, nous avons réalisé un contrôle en boucle fermée des oscillations de la couche cisaillée à l'aide d'une loi de contrôle à retard proposée par Pyragas dans le cadre des systèmes dynamiques chaotiques. / This work is devoted to the characterization of the dynamic inside an open cavity flow, for which few experimental studies exist. A control of the flow has been also investigated. We have performed a parametric study of the first and second regime of the flow for which Taylor-Görtler vortices type appear. Bifurcation thresholds have been identified and their systematic supercritical nature has been highlighted. We have also showed that different family of propagating or stationary modes can be selected depending on the geometry of the cavity. This has confirmed predictions obtained by linear stability analysis of the base flow in the literature. We have showed that the second regime results from the superposition of left and right propagating waves. We attended to identify coefficients of the complex coupled Ginzburg-Landau equations that describe the dynamics but the values of the coefficients are sensitive to multiple parameters. A control of oscillations of the shear layer has been achieved by the mean of a plasma actuator with dielectric barrier discharge located upstream of the cavity. Locked regimes have been identified by the analysis of the flow response to a periodic perturbation with different amplitude. Finally, we have performed a closed loop control of the oscillations of the shear layer using a delay feedback control law proposed by Pyragas in the context of chaotic dynamical systems.
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Morphologie et évolution des tourbillons de Rossby bidimensionnels dans les disques protoplanétaires / Structure and evolution of 2D Rossby vortices in protoplanetary disksSurville, Clément 11 December 2013 (has links)
Le rôle des tourbillons anticycloniques dans l'évolution des disques protoplanétaires et, en particulier, dans les mécanismes de formation des planétésimaux, est au coeur des défis actuels de l'astrophysique moderne. C'est pourquoi une étude approfondie de leur structure et de leur dynamique est primordiale.Grâce à un outil numérique spécifiquement développé pour l'étude des disques, nous avons revisité l'Instabilité en Ondes de Rossby dans le régime non linéaire, et découvert l'existence d'une cascade des modes de perturbation qui permet de mieux comprendre la formation des tourbillons par cette instabilité.Leur structure à été décrite par un modèle gaussien innovant, remarquablement en accord avec les résultats numériques. Grâce à un échantillon de près de 300 tourbillons, nous avons borné le domaine des dimensions radiales, azimutales et de la vorticité. Deux familles de tourbillons possibles ont été distinguées : (i) les tourbillons incompressibles, stables et quasi-stationnaires; (ii) les tourbillons compressibles, très mobiles et associés à l'émission d'ondes de densité. Leur persistance sur plus de 1000 rotations confirme l'observabilité de tous ces tourbillons. Enfin, nous avons caractérisé leur migration vers l'étoile en fonction de leur géométrie, du gradient de pression et de l'échelle de hauteur du disque. Pour la première fois, une expression analytique permet d'estimer le taux de migration en fonction de ces paramètres; l'échelle de temps pour tomber sur étoile peut aller de 10^6 à 100 rotations. Suivant un modèle de viscosité alpha, la perte de moment cinétique pourrait être suffisante pour maintenir un taux d'accrétion significatif dans la zone morte. / The role of anticyclonic vortices in the protoplanetary disk evolution and in how do planetesimals form are among the most important chalenges of the modern astrophysics. That is why an exhaustive study of the structure and the evolution of these vortices is necessary.Thanks to a numerical code specificly designed for the study of these disks, we have revisited the Rossby Wave Instability in the nonlinear regime, and have discovered that a cascade of the perturbation modes can explain the formation of the vortices created by this instability.We have described the structure of these Rossby vortices with a new gaussian vortex model, which accurately fits the numerical results. A sample of 300 different vortices led us to define the bondaries of the radial and azimuthal extent as well as the vorticity of the vortices. We have distinguished two main families : (i) the incompressible family, which is stable and quasi stationnary ; (ii) the compressible family, moving and exciting density waves. We found them surviving more than 1000 orbits, a clear confirmation of their observability.Finaly, we have caracterized the inward migration of the vortices as a fonction of their shape, their vorticity, but also of the pressure gradient and the scale height of the disk. For the first time, we exhibit a equation relating the migration rate to these parameters. The time scale of the migration ranges from 10^6 to just 100 rotations of the disk. Extremely steep pressure gradients are needed to reverse the migration to an outward regime. Following the alpha viscosity approch, the loss of kinetic momentum due to this migration would be sufficient to sustain the accretion in the dead zone.
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[pt] ESCOAMENTO SECUNDÁRIO EM UM ANULAR PARCIALMENTE OBSTRUÍDO COM ROTAÇÃO DO CILINDRO INTERNO / [en] SECONDARY FLOW IN PARTIALLY-OBSTRUCTED ANNULAR SPACE WITH INNER CYLINDER ROTATION25 April 2005 (has links)
[pt] O escoamento em um espaço anular parcialmente obstruído é
estudado
para uma geometria entre cilindros concêntricos. A
obstrução parcial é uma
primeira aproximação de um escoamento em um espaço anular
com um leito de
cascalhos sedimentado que ocorre no processo de perfuração
de poços para
produção de óleo e gás, particularmente no caso de poços
inclinados e
horizontais. A presença de uma placa de obstrução parcial
promove a assimetria
no escoamento de tal modo que interfere na formação do
regime de vórtices de
Taylor. O campo de velocidade para esses escoamentos foi
obtido via solução
numérica e experimental. Nas simulações numéricas, as
equações de
conservação de massa e quantidade de movimento linear foram
resolvidas para
um escoamento de fluido newtoniano e não newtoniano pela
técnica de volumes
finitos. Os resultados experimentais foram obtidos a partir
de campos
instantâneos e médios de velocidade em planos meridionais
do espaço anular
usando a técnica de velocimetria por imagens de partículas
(PIV). As medições
focalizaram a obtenção do número de Reynolds rotacional
crítico e a obtenção
do perfil de velocidade axial passando pelo olho do
vórtice. Os resultados
mostram que o número de Reynolds crítico é diretamente
afetado pelo grau de
obstrução do espaço anular, assim como a largura dos
vórtices de Taylor. O
resultado dos perfis de velocidade axial calculados
concorda bem com os
resultados obtidos experimentalmente. A transição para o
regime de vórtices de
Taylor também é bem prevista pelo método numérico. Os
resultados numéricos
para a largura dos vórtices de Taylor não apresentam boa
concordância,
dependendo das condições de contorno estipuladas. A
presença da placa de
obstrução parcial promove uma recirculação circunferencial
no escoamento que
interage com o escoamento de vórtices de Taylor formando um
escoamento
complexo a partir de níveis de obstrução moderados. / [en] The flow inside a horizontal annulus due to the inner
cylinder rotation is
studied. The bottom of the annular space is partially
blocked by a plate parallel to
the axis of rotation, thereby destroying the
circumferential symmetry of the
annular space geometry. This flow configuration is found in
the drilling process of
horizontal petroleum wells, where a bed of cuttings is
deposited at the bottom
part of the annulus. The velocity field for this flow was
obtained both numerically
and experimentally. In the numerical work, the equations
which govern the threedimensional,
laminar flow of Newtonian and non-Newtonian liquids were
solved
via a finite-volume technique. In the experimental
research, the instantaneous
and time-averaged flow fields over two-dimensional
meridional sections of the
annular space were measured employing the particle image
velocimetry (PIV)
technique, both for Newtonian and power-law liquids.
Attention was focused on
the determination of the onset of secondary flow in the
form of distorted Taylor
vortices. The results showed that the critical rotational
Reynolds number is
directly influenced by the degree of obstruction of the
flow. The influence of the
obstruction is more perceptible in Newtonian than non-
Newtonian liquids. The
larger is the obstruction, the larger is the critical
Taylor number. The height of the
obstruction also controls the width of the vortices. The
calculated steady state
axial velocity profiles agreed well with the corresponding
measurements.
Transition values of the rotational Reynolds number are
also well predicted by the
computations. However, the measured and predicted values
for the vortex size
do not agree as well. Transverse flow maps revealed a
complex interaction
between the Taylor vortices and the zones of recirculating
flow, for moderate to
high degrees of flow obstruction.
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Vektorová Kerrova magnetometrie / Vectorial Kerr magnetometryFlajšman, Lukáš January 2015 (has links)
Increased complexity of novel magnetic materials in the last decade has placed high demands on the manufacturing process as well as on the characterization. One of the possibilities for characterization of magnetic samples is to exploit the magneto-optical effects. The presented work uses the magneto-optical Kerr effect as a major characterization technique to probe the magnetic properties of samples. We have developed a mathematical model describing the effect of the magnetization on the polarized light and present an apparatus capable of measuring the response given by the light-matter interaction. The experimental results show the performance of the apparatus on the various magnetic systems including meta-stable iron layers, Stoner-Wohlfarth particles and magnetic vortices. The scanning vectorial Kerr magnetometer allowed us to probe the vector of magnetization with diffraction limited resolution below 500 nm.
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Phenomenological theory of chiral states in magnets with Dzyaloshinskii-Moriya interactionsButenko, Ganna 20 March 2013 (has links)
This thesis presents the theoretical studies of chiral magnetic structures, which exist or are affected by antisymmetric Dzyaloshinskii-Moriya interactions. The theoretical approach is based on the phenomenological model of ferromagnetic materials lacking inversion symmetry. Equilibrium magnetic states are described as static structures in the micromagnetic low temperature limit with a fixed magnitude of the magnetization. The studies are focused on two cases: (i) magnetization structures that are affected by chiral exchange so that a particular chirality of these structures is selected, and (ii) novel solitonic states that are called chiral Skyrmions and only exist because of the chiral exchange.
Vortex states in magnetic nanodisks provide the simplest example of a handed magnetization structure, where effects of the chiral couplings may become noticeable. A chiral exchange here favours one chirality of such a vortex state over the other. This effect can stem from surface-induced or other defect-related chiral Dzyaloshinskii-Moriya exchange. The different chiral versions of the vortex states are shown to display strong dependencies on the materials properties of such nanodisks. Within a micromagnetic model for these effects, numerical calculations of the shape, size, and stability of the vortices in equilibrium as functions of magnetic field and the material and geometrical parameters provide a general analysis of the influence of the broken mirror symmetry caused by the surface/interfaces or structural defect on their properties. The Dzyaloshinskii-Moriya interactions impose differences in the energies and sizes of vortices with different chirality: these couplings can considerably increase sizes of vortices with one sense of rotation and suppress vortices with opposite sense of rotation. Torsions related to lattice defects can cause similar to the surface-induced chiral couplings. A general phenomenological magneto-elastic formulation for this torsional chirality selection is given. It is applied to calculate similar effects on vortex states in magnetic disks with a screw dislocation at their center.
In systems with strong chiral exchange the magnetic equilibrium states themselves become chiral twisted structures. The most interesting structures in this context are the two-dimensional solitonic states that are now known as chiral Skyrmions. The properties and stability of multiply twisted states composed of these particle-like units are the subject of the second part of this thesis. These states compete with the well known onedimensionally modulated helical states in non-centrosymmetric magnetic systems. Studies of modulated states in cubic helimagnets have shown, that in absence of additional effects, the only thermodynamically stable state is a cone helix. Uniaxial distortions, that can be caused by uniaxial stresses in the bulk samples or arise due to surface effects in thin films, suppress the helical states and stabilize Skyrmion lattices in a broad range of thermodynamical parameters. Using the phenomenological theory for modulated and localized states in chiral magnets, the equilibrium parameters of the Skyrmion and helical states have been derived as functions of applied magnetic field and induced uniaxial anisotropy. These results show that due to a combined effect of induced uniaxial anisotropy and an applied magnetic field, Skyrmion lattices can be formed as thermodynamically stable states.
The theoretical results provide a comprehensive description of the evolution of modulated states in an applied magnetic field depending on type of anisotropy. The cases of a uniaxial anisotropy of easy axis and easy plane type with fields applied along its axis are investigated in detail. Existence of Skyrmion-lattice states in the easy axis case as thermodynamic field-induced phase is demonstrated. The results explain recent observation of Skyrmion lattices by magnetic Lorentz microscopy in thin foils of cubic chiral magnets. In systems with easy plane type of anisotropy, Skyrmion states do not form thermodynamic phases in applied fields along the axis. However, distorted Skyrmion phases can exist in fields applied perpendicularly to the axis. In this configuration of anisotropy axis and fields, both the helical states and the Skyrmions display elliptical distortions. The investigated micromagnetic model maps out the basic helical and Skyrmionic states expected to exist in cubic and nearly cubic chiral magnets.
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Universality of Kolmogorov's Cascade Picture in Inverse Energy Cascade Range of Two-dimensional turbulence / 2次元乱流のエネルギー逆カスケード領域における、コルモゴロフのカスケード描像の普遍性についてMizuta, Atsushi 23 May 2014 (has links)
京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18446号 / 理博第4006号 / 新制||理||1578(附属図書館) / 31324 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 藤 定義, 教授 佐々 真一, 教授 早川 尚男 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM
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