Relevant bibliographies by topics / Lagrangian surfaces

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Lagrangian surfaces'

Author: Grafiati
Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Lagrangian surfaces"

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Zhao, Yaomin, Yue Yang, and Shiyi Chen. "Evolution of material surfaces in the temporal transition in channel flow." Journal of Fluid Mechanics 793 (March 23, 2016): 840–76. http://dx.doi.org/10.1017/jfm.2016.152.

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We report a Lagrangian study on the evolution of material surfaces in the Klebanoff-type temporal transitional channel flow. Based on the Eulerian velocity field from the direct numerical simulation, a backward-particle-tracking method is applied to solve the transport equation of the Lagrangian scalar field, and then the isosurfaces of the Lagrangian field can be extracted as material surfaces in the evolution. Three critical issues for Lagrangian investigations on the evolution of coherent structures using material surfaces are addressed. First, the initial scalar field is uniquely determined based on the proposed criteria, so that the initial material surfaces can be approximated as vortex surfaces, and remain invariant in the initial laminar state. Second, the evolution of typical material surfaces initially from different wall distances is presented, and then the influential material surface with the maximum deformation is identified. Large vorticity variations with the maximum curvature growth of vortex lines are also observed on this surface. Moreover, crucial events in the transition can be characterized in a Lagrangian approach by conditional statistics on the material surfaces. Finally, the influential material surface, which is initially a vortex surface, is demonstrated as a surrogate of the vortex surface before significant topological changes of vortical structures. Therefore, this material surface can be used to elucidate the continuous temporal evolution of vortical structures in transitional wall-bounded flows in a Lagrangian perspective. The evolution of the influential material surface is divided into three stages: the formation of a triangular bulge from an initially disturbed streamwise–spanwise sheet, rolling up of the vortex sheet near the bulge ridges with the vorticity intensification and the generation and evolution of signature hairpin-like structures with self-induced dynamics of vortex filaments.
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PAVLOTSKY, I. P., and M. STRIANESE. "SOME PECULIAR PROPERTIES OF THE DARWIN’S LAGRANGIAN." International Journal of Modern Physics B 09, no. 23 (October 20, 1995): 3069–83. http://dx.doi.org/10.1142/s0217979295001166.

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In the post-Galilean approximation the Lagrangians are singular on a submanifold of the phase space. It is a local singularity, which differs from the ones considered by Dirac. The dynamical properties are essentially peculiar on the studied singular surfaces. In the preceding publications,1,2,3 two models of singular relativistic Lagrangians and the rectilinear motion of two electrons, determined by Darwin’s Lagrangian, were examined. In the present paper we study the peculiar dynamical properties of the two-dimensional Darwin’s Lagrangian. In particular, it is shown that the minimal distance between two electrons (the so called “radius of electron”) appears in the two-dimensional motion as well as in one-dimensional case. Some new peculiar properties are discovered.
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Carriazo, Alfonso, Verónica Martín-Molina, and Luc Vrancken. "Null pseudo-isotropic Lagrangian surfaces." Colloquium Mathematicum 150, no. 1 (2017): 87–101. http://dx.doi.org/10.4064/cm7107s-12-2016.

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Kossowski, Marek. "Prescribing invariants of Lagrangian surfaces." Topology 31, no. 2 (April 1992): 337–47. http://dx.doi.org/10.1016/0040-9383(92)90026-e.

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Kawasaki, Morimichi. "Superheavy Lagrangian immersions in surfaces." Journal of Symplectic Geometry 17, no. 1 (2019): 239–49. http://dx.doi.org/10.4310/jsg.2019.v17.n1.a5.

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Hind, Richard. "Lagrangian unknottedness in Stein surfaces." Asian Journal of Mathematics 16, no. 1 (2012): 1–36. http://dx.doi.org/10.4310/ajm.2012.v16.n1.a1.

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YANG, YUE, and D. I. PULLIN. "On Lagrangian and vortex-surface fields for flows with Taylor–Green and Kida–Pelz initial conditions." Journal of Fluid Mechanics 661 (October 1, 2010): 446–81. http://dx.doi.org/10.1017/s0022112010003125.

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For a strictly inviscid barotropic flow with conservative body forces, the Helmholtz vorticity theorem shows that material or Lagrangian surfaces which are vortex surfaces at time t = 0 remain so for t > 0. In this study, a systematic methodology is developed for constructing smooth scalar fields φ(x, y, z, t = 0) for Taylor–Green and Kida–Pelz velocity fields, which, at t = 0, satisfy ω·∇φ = 0. We refer to such fields as vortex-surface fields. Then, for some constant C, iso-surfaces φ = C define vortex surfaces. It is shown that, given the vorticity, our definition of a vortex-surface field admits non-uniqueness, and this is presently resolved numerically using an optimization approach. Additionally, relations between vortex-surface fields and the classical Clebsch representation are discussed for flows with zero helicity. Equations describing the evolution of vortex-surface fields are then obtained for both inviscid and viscous incompressible flows. Both uniqueness and the distinction separating the evolution of vortex-surface fields and Lagrangian fields are discussed. By tracking φ as a Lagrangian field in slightly viscous flows, we show that the well-defined evolution of Lagrangian surfaces that are initially vortex surfaces can be a good approximation to vortex surfaces at later times prior to vortex reconnection. In the evolution of such Lagrangian fields, we observe that initially blob-like vortex surfaces are progressively stretched to sheet-like shapes so that neighbouring portions approach each other, with subsequent rolling up of structures near the interface, which reveals more information on dynamics than the iso-surfaces of vorticity magnitude. The non-local geometry in the evolution is quantified by two differential geometry properties. Rolled-up local shapes are found in the Lagrangian structures that were initially vortex surfaces close to the time of vortex reconnection. It is hypothesized that this is related to the formation of the very high vorticity regions.
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Bektaş, Burcu, Marilena Moruz, Joeri Van der Veken, and Luc Vrancken. "Lagrangian submanifolds of the nearly Kähler 𝕊3 × 𝕊3 from minimal surfaces in 𝕊3." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 03 (December 27, 2018): 655–89. http://dx.doi.org/10.1017/prm.2018.43.

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AbstractWe study non-totally geodesic Lagrangian submanifolds of the nearly Kähler 𝕊3 × 𝕊3 for which the projection on the first component is nowhere of maximal rank. We show that this property can be expressed in terms of the so-called angle functions and that such Lagrangian submanifolds are closely related to minimal surfaces in 𝕊3. Indeed, starting from an arbitrary minimal surface, we can construct locally a large family of such Lagrangian immersions, including one exceptional example. We also show that locally all such Lagrangian submanifolds can be obtained in this way.
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Craizer, Marcos. "Equiaffine characterization of Lagrangian surfaces in ℝ4." International Journal of Mathematics 26, no. 09 (August 2015): 1550074. http://dx.doi.org/10.1142/s0129167x15500743.

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For non-degenerate surfaces in ℝ4, a distinguished transversal bundle called affine normal plane bundle was proposed in [K. Nomizu and L. Vrancken, A new equiaffine theory for surfaces in ℝ4, Internat. J. Math. 4(1) (1993) 127–165]. Lagrangian surfaces have remarkable properties with respect to this normal bundle, like for example, the normal bundle being Lagrangian. In this paper, we characterize those surfaces which are Lagrangian with respect to some parallel symplectic form in ℝ4.
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HASHIMOTO, YOSHITAKE, and KIYOSHI OHBA. "CUTTING AND PASTING OF RIEMANN SURFACES WITH ABELIAN DIFFERENTIALS I." International Journal of Mathematics 10, no. 05 (August 1999): 587–617. http://dx.doi.org/10.1142/s0129167x99000239.

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We introduce a method of constructing once punctured Riemann surfaces by cutting the complex plane along "line segments" and pasting by "parallel transformations". The advantage of this construction is to give a good visualization of the deformation of complex structures of Riemann surfaces. In fact, given a positive integer g, there appears a family of once punctured Riemann surfaces of genus g which is complete and effectively parametrized at any point. Our construction naturally gives each of the resulting surfaces what we call a Lagrangian lattice Λ, a certain subgroup of the first homology. Furthermore Λ and the puncture determine an Abelian differential ωΛ of the second kind on the Riemann surface. Using Λ and ωΛ we consider the Kodaira–Spencer maps and some extension of the family to obtain any once punctured Riemann surface with a Lagrangian lattice. In particular we describe the moduli space of once punctured elliptic curves with Lagrangian lattices.
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Dissertations / Theses on the topic "Lagrangian surfaces"

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Zhang, Liuyang [Verfasser], Wolfgang [Akademischer Betreuer] Soergel, Ernst [Akademischer Betreuer] Kuwert, and Guofang [Akademischer Betreuer] Wang. "On the gap phenomena of the Willmore and Lagrangian surfaces." Freiburg : Universität, 2021. http://d-nb.info/1233966200/34.

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BASTIANELLI, FRANCESCO. "The geometry of second symmetric product of curves." Doctoral thesis, Università degli Studi di Pavia, 2009. http://hdl.handle.net/10281/21080.

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We deal with several problems on the surfaces obtained as second symmetric products of smooth projective curves. In particular, we treat both some attempts at extending the notion of gonality for curves and some classical problems, as the study of the ample cone in the Néron-Severi group. Moreover, we develop a family of examples of Lagrangian surfaces having particular topological properties.
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Moruz, Marilena. "Étude des sous-variétés dans les variétés kählériennes, presque kählériennes et les variétés produit." Thesis, Valenciennes, 2017. http://www.theses.fr/2017VALE0003/document.

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Cette thèse est constituée de quatre chapitres. Le premier contient les notions de base qui permettent d'aborder les divers thèmes qui y sont étudiés. Le second est consacré à l'étude des sous-variétés lagrangiennes d'une variété presque kählérienne. J'y présente les résultats obtenus en collaboration avec Burcu Bektas, Joeri Van der Veken et Luc Vrancken. Dans le troisième, je m'intéresse à un problème de géométrie différentielle affine et je donne une classification des hypersphères affines qui sont isotropiques. Ce résultat a été obtenu en collaboration avec Luc Vrancken. Et enfin dans le dernier chapitre, je présente quelques résultats sur les surfaces de translation et les surfaces homothétiques, objet d'un travail en commun avec Rafael López
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Malic, Goran. "Grothendieck's dessins d'enfants and the combinatorics of Coxeter groups." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/grothendiecks-dessins-denfants-and-the-combinatorics-of-coxeter-groups(dd51878a-7b63-4bd2-9d27-74f10350d44e).html.

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In this thesis we study the properties of Lagrangian matroids of dessins d'enfants (also known as maps on orientable surfaces) and their behaviour under the action of the absolute Galois group Gal(Q). We show that while the Lagrangian matroid of a dessin itself is not invariant under this action, some of its properties, namely its width and parity, are. We also study the partial duals of a dessin and their Lagrangian matroids and show that certain partial duals can always be defined over their field of moduli. We prove some results on the representations of Lagrangian matroids as well. A relationship between dessins, their partial duals and tropical curves arising from monodromy groups of dessins is observed.
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Ferraz, Marcus Vinicíus de Souza. "Interação fluido-estrutura no contato lubrificado entre asperezas e plano rígido via elementos finitos." Universidade Federal de Juiz de Fora (UFJF), 2018. https://repositorio.ufjf.br/jspui/handle/ufjf/6693.

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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
O conhecimento da topografia das superfícies e uma compreensão da interação entre elas é essencial para qualquer estudo que envolva os fenômenos de atrito, desgaste e lubrificação. O estudo da relação entre o atrito e os parâmetros de rugosidade é um problema difícil e de interesse tanto industrial como acadêmico e trabalhos experimentais e teóricos têm mostrado que uma película de fluido entre duas superfícies rugosas em movimento relativo impede o contato sólido - sólido e pode proporcionar atrito muito baixo e desgaste desprezível. A modelagem matemática utilizada neste trabalho é baseada em modelos clássicos, tais como a equação de Reynolds para a descrição dos fenômenos hidrodinâmicos e as formulações de Hertz (1896) e Greenwood e Williamson (1966) para a modelagem do contato das asperezas entre as superfícies rugosas. Para tratar a complexidade das interações entre o fluido e os pares sólidos contactados, a descrição Lagrangiana-Euleriana Arbitrária é apresentada nesta pesquisa. Através do Método dos Elementos Finitos um modelo tridimensional é gerado no Abaqus ®, a fim de identificar as pressões de contato, as tensões tangenciais e normais resultantes e os coeficientes de atrito decorrrentes do deslizamento entre uma superfície texturizada e lubrificada e um plano rígido (em analogia aos modelos de contato clássicos), cujos perfis de rugosidade são construídos a partir de informações da rugosidade média quadrática de superfícies dentárias. São avaliados também a sensibilidade de alguns parâmetros do lubrificante na determinação do coeficiente de atrito e são propostos modelos com condições de contorno distintas. Entretanto, para a verificação destes últimos busca-se reproduzir qualitativamente o resultado encontrado por Lorentz (2013) na investigação numérica de sistemas tribológicos no regime misto de lubrificação. A metodologia aqui proposta emerge como uma alternativa eficaz no campo da Tribologia, na predição do coeficiente de atrito e outras variáveis pertinentes a um fenômeno ainda pouco compreendido. Realiza-se uma análise de sensibilidade dos parâmetros de modelagem, a fim de identificar como os mesmos afetam consideravelmente o comportamento mecânico na interface de contato.
The knowledge of the topography of surfaces and an understanding of the interaction between them is essential for any study involving the phenomena of friction, wear and lubrication. The study of the relationship between friction and roughness parameters is a difficult problem of both industrial and academic interest and experimental and theoretical works have shown that a fluid film between two rough surfaces in relative motion prevents solid - solid contact and can provide very low friction and negligible wear. The mathematical modeling used in this paper is based on classical models, such as the Reynolds equation for the description of the hydrodynamic phenomena and the formulations of Hertz (1896) and Greenwood e Williamson (1966) of the contact between the asperities of rough surfaces. To address the complexity of the interactions between the fluid and the contacted solid pairs, the Lagrangian-Eulerian Arbitrary description is presented in this research. Through the Finite Element Method, a three-dimensional model is generated in Abaqus ®R to identify contact pressures, resulting tangential and normal stresses, and friction coefficients resulting from sliding between a textured and lubricated surface and a rigid plane (in analogy to classic contact models), whose roughness profiles are constructed from information on the quadratic roughness of dental surfaces. The sensitivity of some lubricant parameters in the determination of the coefficient of friction is also evaluated and models with different boundary conditions are proposed. However, for the vefrification of the latter, it is sought to qualitatively reproduce the result found by Lorentz (2013) in the numerical investigation of tribological systems without mixed lubrication regime. A methodology proposed here emerges as an effective alternative in the field of Tribology, in the prediction of the coefficient of friction and other relevant variables to a phenomenon still little understood. A sensitivity analysis of the modeling parameters is performed, in order to identify how they considerably affect the mechanical behavior at the contact interface.
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Silverberg, Jon P. "On Lagrangian meshless methods in free-surface flows." Thesis, (1.7 MB), 2005. http://edocs.nps.edu/AR/topic/theses/2005/Jan/05Jan_Silverberg.pdf.

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Thesis (Master of Engineering in Ocean Engineering)--University of California at Berkeley, 2004.
"January 2005." Description based on title screen as viewed on May 25, 2010. DTIC Descriptor(s): Fluid Dynamics, Lagrangian Functions, Equations Of Motion, Acceleration, Formulations, Grids, Continuum Mechanics, Gaussian Quadrature, Derivatives (Mathematics), Compact Disks, Boundary Value Problems, Polynomials, Interpolation, Pressure, Operators (Mathematics). DTIC Identifier(s): Multimedia (CD-Rom), Moving Grids, Meshless Discretization, Lifs (Lagrange Implicit Fraction Step), Lagrangian Dynamics, Meshless Operators, Mlip (Multidimensional Lagrange Interpolating Polynomials), Flux Boundary Conditions, Radial Basis Functions Includes bibliographical references (58-59).
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Battista, Thomas Andrew. "Lagrangian Mechanics Modeling of Free Surface-Affected Marine Craft." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/82928.

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Although ships have been used for thousands of years, modeling the dynamics of marine craft has historically been restricted by the complex nature of the hydrodynamics. The principal challenge is that the vehicle motion is coupled to the ambient fluid motion, effectively requiring one to solve an infinite dimensional set of equations to predict the hydrodynamic forces and moments acting on a marine vehicle. Additional challenges arise in parametric modeling, where one approximates the fluid behavior using reduced-order ordinary differential equations. Parametric models are typically required for model-based state estimation and feedback control design, while also supporting other applications including vehicle design and submarine operator training. In this dissertation, Lagrangian mechanics is used to derive nonlinear, parametric motion models for marine craft operating in the presence of a free surface. In Lagrangian mechanics, one constructs the equations of motion for a dynamic system using a system Lagrangian, a scalar energy-like function canonically defined as the system kinetic energy minus the system potential energies. The Lagrangian functions are identified under ideal flow assumptions and are used to derive two sets of equations. The first set of equations neglects hydrodynamic forces due to exogenous fluid motions and may be interpreted as a nonlinear calm water maneuvering model. The second set of equations incorporates effects due to exogenous fluid motion, and may be interpreted as a nonlinear, unified maneuvering and seakeeping model. Having identified the state- and time-dependent model parameters, one may use these models to rapidly simulate surface-affected marine craft maneuvers, enabling model-based control design and state estimation algorithms.
Ph. D.
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Lê, Thanh-Tâm. "Surfaces lagrangiennes dans les surfaces projectives complexes." Paris 7, 2002. http://www.theses.fr/2002PA077104.

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Mazzini, Ana Paula. "Um método de Lagrangianos aumentados e sua aplicação em otimização de malhas." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-29032012-141547/.

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Métodos de Lagrangianos aumentados são muito utilizados para resolver problemas de minimização de funções sujeitas a restrições gerais. Em particular, estudamos um método de Lagrangianos aumentados que utiliza a função PHR, implementado em ALGENCAN, e observamos seu comportamento quando o aplicamos na resolução de um problema encontrado na área de Computação Gráfica. O problema estudado é um problema encontrado na geração de malhas de superfícies, na etapa de pós-processamento, para o qual propomos uma técnica de otimização visando a melhoria dos elementos da malha. Quando se trata de geração de malhas de superfícies em \'R POT. 3\', parametrizações de malhas triângulares que representam superfícies são usadas em muitas aplicações de processamento de malhas para vários fins. Muitas vezes é necessário preservar a métrica da superfície e, assim, minimizar a deformação do ângulo e da área. A técnica que propomos de otimização visa melhorar as distorções de ângulos e áreas impostas por uma parametrização. Para verificar o comportamento da técnica proposta, implementamo-na em C++ e utilizamos algumas malhas de modelos clássicos da literatura para realizar os experimentos numéricos. Os resultados obtidos foram promissores
Augmented Lagrangian methods are frequently used to solve minimization problems subject to general constraints. In particular, we study an augmented Lagrangian method that uses the PHR function, implemented in ALGENCAN, and observe its behavior when applied to solve a problem found in the field of Computer Graphics. The problem we will study and solve is found in the post-processing stage of the surface mesh generation, for which we propose an optimization technique to improve the mesh elements. When it comes to meshing surfaces in \'R POT..3\', triangular meshes parametrizations are widely used in applications of mesh processing. It is often necessary to preserve the surface metric and, thus, minimize the angle and area deformation. The optimization technique we propose aims to improve the distortions imposed by a parametrization onto angles and areas. To assert the efectiveness of the proposed technique, we implemented it in C++ language and used some classic mesh models from the literature to performe numerical experiments. The results were promising
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Doukouré, Moussa. "Variabilité des flux turbulents de surface au sein du bassin versant d'Ara au Bénin." Thesis, Grenoble, 2011. http://www.theses.fr/2011GRENU014/document.

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La circulation atmosphérique en Afrique de l'Ouest est caractérisée par des vents de sud-ouest (mousson) pendant la saison humide et par des vents de nord-est (harmattan) pendant la saison sèche. Cette alternance des saisons est due aux variations de pression liée à l'état des surfaces (rugosité, albédo, végétation) en réaction au forçage solaire. Ces mêmes états de surface génèrent une variabilité de flux turbulents de surface et des circulations secondaires qui rendent complexes les analyses des mesures effectuées sur place en vue de documenter les interactions surface-atmosphère. La modélisation fine échelle (LES) couramment utilisée dans l'étude de la couche limite atmosphérique est requise pour pouvoir palier à ces difficultés en raison de sa capacité à prendre en compte les flux turbulents en 3D et sur topographie complexe. Notre site d'étude est le bassin versant d'ARA située au Nord du Bénin dans un contexte Soudanien avec des propriétés de surface variables. Une analyse climatique est effectuée sur la base des observations de radiosondage, de radar UHF et de stations au sol afin d'extraire des données composites représentatives des saisons sèche et humide. Ces données composites ont servi par la suite à forcer le modèle Méso-NH dans sa version LES. Pour pouvoir caractériser les échelles de longueur des flux turbulents de surface relatives aux saisons sèche et humide, les données standard de forçage de surface de Méso-NH que sont le relief GTOPO30 (1km de résolution) et la végétation ECOCLIMAP (1km de résolution) ont été respectivement remplacer par le SRTM (90m de résolution) et les données de SPOT/HRV (20m de résolution) reéchantillonné à 90m de résolution. A l'aide d'outils statistiques comme la variographie 2D et le suivi Lagrangien, il ressort que la variabilité spatiale de la chaleur sensible H est gouvernée par le couple vent-relief tandis que celle de la chaleur latente E est difficile à mettre en lien sur végétation hétérogène (SPOT/HRV) en saison sèche. En saison humide, la variabilité spatiale du champ H dépend du vent tandis que celle du champ E dépend de la végétation. Cette étude révèle dans tous les cas que les échelles caractéristiques de ces deux champs diffèrent dans les mêmes conditions de forçage de surface et atmosphérique
West Africa atmosphere circulation is characterized by south-westerly wind (monsoon regime) during the wet season and north-easterly wind (harmattan regime) during the dry season. This alternation of wind regime is due to surface pressure variability linked to surface heterogeneities. Surface heterogeneities generate surface flux variability, secondary circulation and make complex analysis when trying to document surface-atmosphere feedbacks. LES modelling usually used for boundary-layer studies due to its potential to take into account 3D turbulence over complex topography, is used here to overcome these difficulties. Our site of interest is located in north of Benin characterized by Soudanian climate and heterogeneous surface properties. Climate analysis are first performed with radiosoundings, UHF radar, and EC station data in order to extract composite profile representing dry and wet season.. These composite profiles are then used to force atmosphere part of the Méso-NH LES model. To characterize turbulent fluxes length scales relative to dry and wet season, standard surface forcing data with Méso-NH like GTOPO30 orography (1km ) and ECOCLIMAP vegetation (1km) are respectively replaced by SRTM (90m) and SPOT/HRV vegetation data (20m) resampled to 90m. Along with statistical tools like 2D variography and Lagrangian, we notice that during dry season on heterogeneous vegetation, sensible heat flux H is more driven by wind and orography while we not able to discuss the latent heat flux E case. During wet season with the same surface forcing, it appears that H is driven by wind while E is more dependent to vegetation variability. Our study concludes in all case that H and E are not characterized by the same length scale
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Books on the topic "Lagrangian surfaces"

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Canada. Dept. of Fisheries and Oceans. Surface Circulation in Dixon Entrance Results From Lagrangian and Eulerian Measurements. S.l: s.n, 1986.

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Ibragimov, Zair. Topics in several complex variables: First USA-Uzbekistan Conference on Analysis and Mathematical Physics, May 20-23, 2014, California State University, Fullerton, California. Providence, Rhode Island: American Mathematical Society, 2016.

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Mann, Peter. Constrained Lagrangian Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0008.

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This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations using Lagrange multipliers; these can be used to reduce the number of coordinates until a linearly independent minimal set is obtained that describes a constraint surface within configuration space, so that Lagrange equations can be set up and solved. Motion is understood to be confined to a constraint submanifold. The variational formulation of non-holonomic constraints is then discussed to derive the vakonomic formulation. These erroneous equations are then compared to the central Lagrange equation, and the precise nature of the variations used in each formulation is investigated. The vakonomic equations are then presented in their Suslov form (Suslov–vakonomic form) in an attempt to reconcile the two approaches. In addition, the structure of biological membranes is framed as a constrained optimisation problem.
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Mann, Peter. Symmetries & Lagrangian-Hamilton-Jacobi Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0011.

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This chapter discusses conservation laws in Lagrangian mechanics and shows that certain conservation laws are just particular examples of a more fundamental theory called ‘Noether’s theorem’, after Amalie ‘Emmy’ Noether, who first discovered it in 1918. The chapter starts off by discussing Noether’s theorem and symmetry transformations in Lagrangian mechanics in detail. It then moves on to gauge theory and surface terms in the action before isotropic symmetries. continuous symmetry, conserved quantities, conjugate momentum, cyclic coordinates, Hessian condition and discrete symmetries are discussed. The chapter also covers Lie algebra, spontaneous symmetry breaking, reduction theorems, non-dynamical symmetries and Ostrogradsky momentum. The final section of the chapter details Carathéodory–Hamilton–Jacobi theory in the Lagrangian setting, to derive the Hamilton–Jacobi equation on the tangent bundle!
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Mann, Peter. Liouville’s Theorem & Classical Statistical Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0020.

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This chapter returns to the discussion of constrained Hamiltonian dynamics, now in the canonical setting, including topics such as regular Lagrangians, constraint surfaces, Hessian conditions and the constrained action principle. The standard approach to Hamiltonian mechanics is to treat all the variables as being independent; in the constrained case, a constraint function links the variables so they are no longer independent. In this chapter, the Dirac–Bergmann theory for singular Lagrangians is developed, using an action-based approach. The chapter then investigates consistency conditions and Dirac’s different types of constraints (i.e. first-class constraints, second-class constraints, primary constraints and secondary constraints) before deriving the Dirac bracket from simple arguments. The Jackiw–Fadeev constraint formulation is then discussed before the chapter closes with the Güler formulation for a constrained Hamilton–Jacobi theory.
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Zeitlin, Vladimir. Rotating Shallow-Water Models with Moist Convection. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0015.

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It is shown how the standard RSW can be ’augmented’ to include phase transitions of water. This chapter explains how to incorporate extra (convective) vertical fluxes in the model. By using Lagrangian conservation of equivalent potential temperature condensation of the water vapour, which is otherwise a passive tracer, is included in the model and linked to convective fluxes. Simple relaxational parameterisation of condensation permits the closure of the system, and surface evaporation can be easily included. Physical and mathematical properties of thus obtained model are explained, and illustrated on the example of wave scattering on the moisture front. The model is applied to ’moist’ baroclinic instability of jets and vortices. Condensation is shown to produce a transient increase of the growth rate. Special attention is paid to the moist instabilities of hurricane-like vortices, which are shown to enhance intensification of the hurricane, increase gravity wave emission, and generate convection-coupled waves.
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Book chapters on the topic "Lagrangian surfaces"

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Matsushita, Daisuke. "On Deformations of Lagrangian Fibrations." In K3 Surfaces and Their Moduli, 237–43. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29959-4_9.

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Daniel, Patrik, Matej Medl’a, Karol Mikula, and Mariana Remešíková. "Reconstruction of Surfaces from Point Clouds Using a Lagrangian Surface Evolution Model." In Lecture Notes in Computer Science, 589–600. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-18461-6_47.

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Dorfmeister, Josef F., and Hui Ma. "A New Look at Equivariant Minimal Lagrangian Surfaces in $${\mathbb {C}} P^2$$ C P 2." In Springer Proceedings in Mathematics & Statistics, 97–125. Tokyo: Springer Japan, 2016. http://dx.doi.org/10.1007/978-4-431-56021-0_5.

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Mielke, Alexander. "Capillarity surface waves." In Hamiltonian and Lagrangian Flows on Center Manifolds, 103–8. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0097553.

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Wilson, J. D., T. K. Flesch, and B. P. Crenna. "Estimating Surface-Air Gas Fluxes by Inverse Dispersion Using a Backward Lagrangian Stochastic Trajectory Model." In Lagrangian Modeling of the Atmosphere, 149–62. Washington, D. C.: American Geophysical Union, 2013. http://dx.doi.org/10.1029/2012gm001269.

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Zirwes, Thorsten, Feichi Zhang, Jordan A. Denev, Peter Habisreuther, Henning Bockhorn, and Dimosthenis Trimis. "Implementation of Lagrangian Surface Tracking for High Performance Computing." In High Performance Computing in Science and Engineering '20, 223–36. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80602-6_15.

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Guerrini, Federica. "Data-Informed Models for the Coupled Dispersal of Microplastics and Related Pollutants Applied to the Mediterranean Sea." In Special Topics in Information Technology, 3–14. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-15374-7_1.

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AbstractMicroplastic pollution is a ubiquitous environmental threat, in particular to the oceans. In the marine environment, microplastics are not just passively transported by sea currents, but often get contaminated with organic pollutants during the journey. The uptake of chemicals onto microplastics can worsen the adverse effects of microplastics to marine organisms; however, investigation on this urgent phenomenon is hampered by the impossibility of monitoring and tracking such small plastic fragments during their motion at sea. This work aims at addressing the need for an effective modelling of the advection–diffusion processes jointly involving microplastics and the pollutants they carry to further our understanding of their spatiotemporal patterns and ecological impacts, focusing on the Mediterranean Sea. Here we present the conceptual design, methodological settings, and modelling results of a novel, data-informed 2D Lagrangian–Eulerian modelling framework that simultaneously describes (i) the Lagrangian dispersal of microplastic on the sea surface, (ii) the Eulerian advection–diffusion of selected organic contaminants, and (iii) the gradient-driven chemical exchanges between microplastic particles and chemical pollutants in the marine environment in a simple, yet comprehensive way. Crucial to the realism of our model is exploiting the wide variety and abundance of data linked with drivers of Mediterranean marine pollution by microplastics and chemicals, ranging from national censuses to satellite data of surface water runoff and GPS ship tracking, other than the use of oceanographic reanalyses to inform microplastics’ motion at sea. The results of our method applied to a multi-year simulation contribute to a first basin-wide assessment of the role of microplastics as a vehicle of other pollutants of concern in the marine environment. The framework proposed here is intended as a flexible tool to help advance knowledge towards a comprehensive description of the multifaceted threat of marine plastic pollution and an informed support to targeted mitigation policies.
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Tosaka, N., R. Sugino, and H. Kawabata. "Boundary Element-Lagrangian Solution Method for Nonlinear Free Surface Problems." In Boundary Element Methods in Engineering, 131–39. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-84238-2_18.

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Huntley, Helga S., B. L. Lipphardt, and A. D. Kirwan. "Surface Drift Predictions of the Deepwater Horizon Spill: The Lagrangian Perspective." In Monitoring and Modeling the Deepwater Horizon Oil Spill: A Record-Breaking Enterprise, 179–95. Washington, D. C.: American Geophysical Union, 2011. http://dx.doi.org/10.1029/2011gm001097.

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Koschdon, Karl, and Michael Schäfer. "A Lagrangian-Eulerian Finite-Volume Method for Simulating Free Surface Flows of Granular Avalanches." In Dynamic Response of Granular and Porous Materials under Large and Catastrophic Deformations, 83–108. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-36565-5_3.

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Conference papers on the topic "Lagrangian surfaces"

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EJIRI, N. "COMPLEX SUBMANIFOLDS AND LAGRANGIAN SUBMANIFOLDS ASSOCIATE WITH MINIMAL SURFACES IN TORI." In Proceedings of the 8th International Workshop on Complex Structures and Vector Fields. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812709806_0009.

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Kasper, Robert, Johann Turnow, and Nikolai Kornev. "Multiphase Eulerian-Lagrangian LES of particulate fouling on structured heat transfer surfaces." In THMT-18. Turbulence Heat and Mass Transfer 9 Proceedings of the Ninth International Symposium On Turbulence Heat and Mass Transfer. Connecticut: Begellhouse, 2018. http://dx.doi.org/10.1615/thmt-18.780.

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Pearson, Stewart, and Sean V. Hum. "Using Augmented Lagrangian Methods to Design Electromagnetic Surfaces with Far Field Constraints." In 2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting. IEEE, 2020. http://dx.doi.org/10.1109/ieeeconf35879.2020.9329978.

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Triphahn, Christopher W., and Eric Loth. "Impact Efficiency Preditions On Icing Surfaces Using the Lagrangian Parcel Volume Method." In 5th AIAA Atmospheric and Space Environments Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2013. http://dx.doi.org/10.2514/6.2013-2545.

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Bou-Zeid, Elie, Charles Meneveau, and Marc B. Parlange. "Applications of the Lagrangian Dynamic Model in LES of Turbulent Flow Over Surfaces With Heterogeneous Roughness Distributions." In ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/ht-fed2004-56127.

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We study turbulent flow over surfaces with varying roughness scales, using large eddy simulation (LES). The goal is to use LES results to formulate effective boundary conditions in terms of effective roughness height and blending height, to be used for RANS. The LES are implemented with the dynamic Smagorinsky model based on the Germano identity. However, as is well-known, when this identity is applied locally, it yields a coefficient with unphysically strong fluctuations and averaging is needed for better realism and numerical stability. The traditional approach consists of averaging over homogeneous directions, for example horizontal planes in channel flow. This requirement for homogeneous directions in the flow field and the concomitant inability to handle complex geometries renders the use of this model questionable in studying the effect of surface heterogeneity. Instead, a new version of the Lagrangian dynamic subgrid-scale (SGS) model [1] is implemented. A systematic set of simulations of flow over patches of differing roughness is performed, covering a wide range of patch length scales and surface roughness values. The simulated mean velocity profiles are analyzed to identify the height of the blending layer and used to measure the effective roughness length. Extending ideas introduced by Miyake [2] and Claussen [3], we have proposed a simple expression for effective surface roughness and blending height knowing local surface patch roughness values and their lengths [4]. Results of the model agreed well with the LES results when the heterogeneous surface consisted of patches of equal sizes. The model is tested here for surfaces with patches of different sizes.
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Yang, Pinghai, Kang Li, and Xiaoping Qian. "Topologically Enhanced Slicing of MLS Surfaces." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-29125.

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Growing use of massive scan data in various engineering applications has necessitated research on point-set surfaces. A point-set surface is a continuous surface defined directly with a set of discrete points. This paper presents a new approach that extends our earlier work on slicing point-set surfaces into planar contours for rapid prototyping usage. This extended approach can decompose a point-set surface into slices with guaranteed topology. Such topological guarantee stems from the use of Morse theory based topological analysis of the slicing operation. The Morse function for slicing is a height function restricted to the point-set surface, an implicitly defined moving least-squares (MLS) surface. We introduce a Lagrangian multiplier formulation for critical point identification from the restricted surface. Integral lines are constructed to form Morse-Smale complex and the enhanced Reeb graph. This graph is then used to provide seed points for forming slicing contours, with the guarantee that the sliced model has the same topology as the input point-set surface. The extension of this approach to degenerate functions on point-set surface is also discussed.
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Fedele, R. "An effective strategy to transform second-gradient equilibrium equations from the Eulerian to the Lagrangian configuration." In AIMETA 2022. Materials Research Forum LLC, 2023. http://dx.doi.org/10.21741/9781644902431-101.

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Abstract. In this communication the problem of transforming the equilibrium equations from the Eulerian to the Lagrangian form is discussed with reference to materials governed by second-gradient energy densities. In particular, novel theoretical achievements are outlined, which represent intermediate steps to attain the purpose: the transformation of edge vectors and of complementary orthogonal projectors over the boundary surface; a novel formula based on the divergence theorem for curved surfaces with boundary, relating material and spatial expressions; a remarkable relationship between Lagrangian and Eulerian (hyper-)stress tensors of different orders.
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Benson, David J., and Shigenobu Okazawa. "Eulerian-Lagrangian Coupling in Finite Element Calculations With Applications to Machining." In ASME/JSME 2004 Pressure Vessels and Piping Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/pvp2004-2860.

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Multi-material Eulerian finite element methods are attractive for problems in solid mechanics where new free surfaces are created, e.g., the formation of chips in machining. One weakness associated with the Eulerian finite element formulation, however, is the interaction of materials at the contact interface. The standard mixture theories effectively bond the materials together, and prohibit the relative slip between the materials that is crucial for an accurate machining simulation. In this paper, we compare the results of a machining calculation performed using an Eulerian formulation with a contact mixture theory and a coupled Eulerian-Lagrangian calculation, where the workpiece is Eulerian, and the tool is Lagrangian.
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Cherubini, S., M. D. de Tullio, P. De Palma, and G. Pascazio. "Optimal Perturbations in Boundary Layer Flows Over Rough Surfaces." In ASME 2012 Fluids Engineering Division Summer Meeting collocated with the ASME 2012 Heat Transfer Summer Conference and the ASME 2012 10th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/fedsm2012-72219.

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This work provides a three-dimensional energy optimization analysis, looking for perturbations inducing the largest energy growth at a finite time in a boundary-layer flow in the presence of roughness elements. Amplification mechanisms are described which by-pass the asymptotical growth of Tollmien–Schlichting waves. The immersed boundary technique has been coupled with a Lagrangian optimization in a three-dimensional framework. Two types of roughness elements have been studied, characterized by a different height. The results show that even very small roughness elements, inducing only a weak deformation of the base flow, can strongly localize the optimal disturbance. Moreover, the highest value of the energy gain is obtained for a varicose perturbation, pointing out the importance of varicose instabilities for such a flow and a different behavior with respect to the secondary instability theory of boundary layer streaks.
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Walls, Kenneth C., and David L. Littlefield. "Validation of an Improved Contact Method for Multi-Material Eulerian Hydrocodes in Three-Dimensions." In 2019 15th Hypervelocity Impact Symposium. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/hvis2019-060.

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Abstract Realistic and accurate modeling of contact for problems involving large deformations and severe distortions presents a host of computational challenges. Due to their natural description of surfaces, Lagrangian finite element methods are traditionally used for problems involving sliding contact. However, problems such as those involving ballistic penetrations, blast-structure interactions, and vehicular crash dynamics, can result in elements developing large aspect ratios, twisting, or even inverting. For this reason, Eulerian, and by extension Arbitrary Lagrangian-Eulerian (ALE), methods have become popular. However, additional complexities arise when these methods permit multiple materials to occupy a single finite element.
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Reports on the topic "Lagrangian surfaces"

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Shen, Lian, and Robert A. Dalrymple. Hybrid Eulerian and Lagrangian Simulation of Steep and Breaking Waves and Surface Fluxes in High Winds. Fort Belvoir, VA: Defense Technical Information Center, September 2010. http://dx.doi.org/10.21236/ada542504.

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Kokjohn, Sage. Development and Validation of a Lagrangian Soot Model Considering Detailed Gas Phase Kinetics and Surface Chemistry. Office of Scientific and Technical Information (OSTI), December 2019. http://dx.doi.org/10.2172/1580657.

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Shen, Lian, and Robert A. Dalrymple. Hybrid Eulerian and Lagrangian Simulation of Steep and Breaking Waves and Surface Fluxes in High Winds. Fort Belvoir, VA: Defense Technical Information Center, September 2012. http://dx.doi.org/10.21236/ada590591.

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Shen, Lian, and Robert A. Dalrymple. Hybrid Eulerian and Lagrangian Simulation of Steep and Breaking Waves and Surface Fluxes in High Winds. Fort Belvoir, VA: Defense Technical Information Center, September 2011. http://dx.doi.org/10.21236/ada557102.

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Musculus, Mark P. July 2018 Progress Report for Sandia National Laboratories on DE-EE0007300 Development and Validation of a Lagrangian Soot Model Considering Detailed Gas Phase Kinetics and Surface Chemistry. Office of Scientific and Technical Information (OSTI), July 2018. http://dx.doi.org/10.2172/1463071.

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