Academic literature on the topic 'Eulerian perturbation theory'
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Journal articles on the topic "Eulerian perturbation theory"
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Almeida, Juan P. Beltrán, Josué Motoa-Manzano, Jorge Noreña, Thiago S. Pereira, and César A. Valenzuela-Toledo. "Structure formation in an anisotropic universe: Eulerian perturbation theory." Journal of Cosmology and Astroparticle Physics 2022, no. 02 (February 1, 2022): 018. http://dx.doi.org/10.1088/1475-7516/2022/02/018.
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Abstract We present an effective Eulerian description, in the non-relativistic regime, of the growth of cosmological perturbations around a homogeneous but anisotropic Bianchi I spacetime background. We assume a small deviation from isotropy, sourced at late times for example by dark energy anisotropic stress. We thus derive an analytic solution for the linear dark matter density contrast, and use it in a formal perturbative approach which allows us to derive a second order (non-linear) solution. As an application of the procedure followed here we derive analytic expressions for the power spectrum and the bispectrum of the dark matter density contrast. The power spectrum receives a quadrupolar correction as expected, and the bispectrum receives several angle-dependent corrections. Quite generally, we find that the contribution of a late-time phase of anisotropic expansion to the growth of structure peaks at a finite redshift between CMB decoupling and today, tough the exact redshift value is model-dependent.
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Aviles, Alejandro, Arka Banerjee, Gustavo Niz, and Zachary Slepian. "Clustering in massive neutrino cosmologies via Eulerian Perturbation Theory." Journal of Cosmology and Astroparticle Physics 2021, no. 11 (November 1, 2021): 028. http://dx.doi.org/10.1088/1475-7516/2021/11/028.
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Abstract We introduce an Eulerian Perturbation Theory to study the clustering of tracers for cosmologies in the presence of massive neutrinos. Our approach is based on mapping recently-obtained Lagrangian Perturbation Theory results to the Eulerian framework. We add Effective Field Theory counterterms, IR-resummations and a biasing scheme to compute the one-loop redshift-space power spectrum. To assess our predictions, we compare the power spectrum multipoles against synthetic halo catalogues from the QUIJOTE simulations, finding excellent agreement on scales k ≲ 0.25 h Mpc-1. One can obtain the same fitting accuracy using higher wave-numbers, but then the theory fails to give a correct estimation of the linear bias parameter. We further discuss the implications for the tree-level bispectrum. Finally, calculating loop corrections is computationally costly, hence we derive an accurate approximation wherein we retain only the main features of the kernels, as produced by changes to the growth rate. As a result, we show how FFTLog methods can be used to further accelerate the loop computations with these reduced kernels.
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Kozlikin, Elena, Robert Lilow, Felix Fabis, and Matthias Bartelmann. "A first comparison of Kinetic Field Theory with Eulerian Standard Perturbation Theory." Journal of Cosmology and Astroparticle Physics 2021, no. 06 (June 1, 2021): 035. http://dx.doi.org/10.1088/1475-7516/2021/06/035.
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NANDY, MALAY K., and JAYANTA K. BHATTACHARJEE. "MODE-COUPLING THEORY, DYNAMIC SCALING, AND TWO-DIMENSIONAL TURBULENCE." International Journal of Modern Physics B 09, no. 09 (April 20, 1995): 1081–97. http://dx.doi.org/10.1142/s0217979295000446.
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A self-consistent mode-coupling scheme, along with dynamic scaling ideas, is used to obtain a renormalized perturbation theory in the Eulerian framework from Wyld’s perturbation theory of the forced Navier-Stokes equation. For the force-correlation behaving as k−(d−4+y), the Kolmogorov and Kraichnan-Batchelor scaling spectra of two-dimensional turbulence for the inverse energy cascade, [Formula: see text] and the direct entropy cascade, [Formula: see text], are obtained for y=4 and y=6 respectively, including the logarithmic correction for the latter. Unlike the usual Eulerian formulations (e.g. the direct-interaction approximation), the theory is finite in the energy regime, while it becomes marginal in the enstrophy regime, leading to the logarithmic correction. Calculations yield C=6.447 and C′=1.923 at one-loop order, which are in exact agreement with those of field-theoretic renormalization group calculations [P. Olla, Phys. Rev. Lett. 67, 2465 (1991)]. However, a self-consistent treatment of the logarithmic scalings in E(k) and the inverse response-time yields a different value: C′=2.201. The theory is free of any external parameter; the choice of y(=4 or 6) is dictated by the condition of conserved transfer of energy or enstrophy.
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Roth, Nina, and Cristiano Porciani. "Testing standard perturbation theory and the Eulerian local biasing scheme against N-body simulations." Monthly Notices of the Royal Astronomical Society 415, no. 1 (May 13, 2011): 829–44. http://dx.doi.org/10.1111/j.1365-2966.2011.18768.x.
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Roycroft, R., J. P. Sauppe, and P. A. Bradley. "Double cylinder target design for study of hydrodynamic instabilities in multi-shell ICF." Physics of Plasmas 29, no. 3 (March 2022): 032704. http://dx.doi.org/10.1063/5.0083190.
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Cylindrical implosions are used to study hydrodynamic instability growth for inertial confinement fusion (ICF) applications, as the cylindrical geometry allows for easier diagnostic access while retaining convergence effects. In this work, we use the established cylindrical implosion platform [Palaniyappan et al., Phys. Plasmas 27, 042708 (2020)] to inform the double shell ICF campaign [Montgomery et al., Phys. Plasmas 25, 092706 (2018)]. We present a design for a double cylindrical target as an analogue to the double shell ICF capsule in order to study hydrodynamic instability growth on the high-Z inner shell. Our design work is done with two-dimensional (2D) Eulerian radiation-hydrodynamics simulations, considering the axial uniformity of the implosion and feasibility of measuring the instability growth of pre-seeded single mode sinusoidal perturbations. We discuss in depth the design for a target to be directly driven at the OMEGA laser facility [Boehly et al., Opt. Commun. 133, 495 (1997)]. We evaluate the design for axial implosion symmetry and visibility of instability growth using synthetic radiographs constructed from the simulations, as the instability growth on the inner cylinder is experimentally measured using x-ray radiography of the implosion. We find that the seeded perturbation growth on the inner cylinder should be visible in an experiment, even with axial implosion asymmetry and preheat. We compare our 2D simulations with linear theory predictions for perturbation growth and show that a cylinder with lower azimuthal mode number (mode-20) perturbations compares more favorably with linear theory, while a cylinder with higher azimuthal mode number (mode-40) perturbations at the same starting amplitude saturates and is over-predicted by linear theory.
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Arico', Giovanni, Raul Angulo, and Matteo Zennaro. "Accelerating Large-Scale-Structure data analyses by emulating Boltzmann solvers and Lagrangian Perturbation Theory." Open Research Europe 1 (June 15, 2022): 152. http://dx.doi.org/10.12688/openreseurope.14310.2.
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The linear matter power spectrum is an essential ingredient in all theoretical models for interpreting large-scale-structure observables. Although Boltzmann codes such as CLASS or CAMB are very efficient at computing the linear spectrum, the analysis of data usually requires 104-106 evaluations, which means this task can be the most computationally expensive aspect of data analysis. Here, we address this problem by building a neural network emulator that provides the linear theory (total and cold) matter power spectrum in about one millisecond with ≈0.2%(0.5%) accuracy over redshifts z ≤ 3 (z ≤ 9), and scales10-4 ≤ k [h Mpc-1] < 50. We train this emulator with more than 200,000 measurements, spanning a broad cosmological parameter space that includes massive neutrinos and dynamical dark energy. We show that the parameter range and accuracy of our emulator is enough to get unbiased cosmological constraints in the analysis of a Euclid-like weak lensing survey. Complementing this emulator, we train 15 other emulators for the cross-spectra of various linear fields in Eulerian space, as predicted by 2nd-order Lagrangian Perturbation theory, which can be used to accelerate perturbative bias descriptions of galaxy clustering. Our emulators are specially designed to be used in combination with emulators for the nonlinear matter power spectrum and for baryonic effects, all of which are publicly available at http://www.dipc.org/bacco.
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Arico', Giovanni, Raul Angulo, and Matteo Zennaro. "Accelerating Large-Scale-Structure data analyses by emulating Boltzmann solvers and Lagrangian Perturbation Theory." Open Research Europe 1 (December 16, 2021): 152. http://dx.doi.org/10.12688/openreseurope.14310.1.
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The linear matter power spectrum is an essential ingredient in all theoretical models for interpreting large-scale-structure observables. Although Boltzmann codes such as CLASS or CAMB are very efficient at computing the linear spectrum, the analysis of data usually requires 104-106 evaluations, which means this task can be the most computationally expensive aspect of data analysis. Here, we address this problem by building a neural network emulator that provides the linear theory (total and cold) matter power spectrum in about one millisecond with ≈0.2%(0.5%) accuracy over redshifts z ≤ 3 (z ≤ 9), and scales10-4 ≤ k [h Mpc-1] < 50. We train this emulator with more than 200,000 measurements, spanning a broad cosmological parameter space that includes massive neutrinos and dynamical dark energy. We show that the parameter range and accuracy of our emulator is enough to get unbiased cosmological constraints in the analysis of a Euclid-like weak lensing survey. Complementing this emulator, we train 15 other emulators for the cross-spectra of various linear fields in Eulerian space, as predicted by 2nd-order Lagrangian Perturbation theory, which can be used to accelerate perturbative bias descriptions of galaxy clustering. Our emulators are specially designed to be used in combination with emulators for the nonlinear matter power spectrum and for baryonic effects, all of which are publicly available at http://www.dipc.org/bacco.
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Larsson, Jonas. "A new Hamiltonian formulation for fluids and plasmas. Part 1. The perfect fluid." Journal of Plasma Physics 55, no. 2 (April 1996): 235–59. http://dx.doi.org/10.1017/s002237780001881x.
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A new formulation of the Hamiltonian structure underlying the perfect fluid equations is presented. Besides time, a parameter c is also used. Correspondingly, there are two interdependent systems of equations expressing time evolution and e evolution respectively. The accessibility equations define the e dynamics and give the variation in the usual Eulerian fluid variables as determined by the generating functions. The time evolutions of both the Eulerian fluid variables and the generating functions are obtained from an action principle. The consistency of the e and the time dynamics is crucial for this formulation, i.e. the accessibility equations must be propagated in time by the Euler–Lagrange equations. The reason for introducing this new formulation is its power in certain applications where the existing Hamiltonian alternatives seem less convenient to use. In particular, it is a promising tool for Hamiltonian perturbation theory. We consider the small-amplitude expansion, and find, very simply and naturally, the Hermitian structure of the linearized ideal fluid equations as well as coupling coefficients for resonant three-wave interaction exhibiting the Manley–Rowe relations.
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ZHAO, MING, and MOHAMED S. GHIDAOUI. "TRANSIENT DYNAMICS OF STREAK AND LONGITUDINAL VORTICES IN SHEAR FLOW WITH WAVE." International Journal of Modern Physics: Conference Series 19 (January 2012): 139–53. http://dx.doi.org/10.1142/s2010194512008689.
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Langmuir circulations are alternating right and left helical vortices in the ocean having horizontal axes parallel to the wind. They are manifested by floating material on the ocean surface as streaks. The laboratory wind driven shear flow demonstrate streak feature with/without wave condition. When the wave is present the explanation of results with Craik-Leibovich instability mechanism, originally proposed for weak current shear in ocean, is not appropriate for some problem as in the laboratory the current shear is strong. The existing normal mode analysis based on the generalized Lagrangian mean formulation for wave with strong shear is not able to capture the fully dynamics of streak and longitudinal vortices. We extend Craik-Leibovich theory to strong shear in Eulerian framework but focusing on the fully perturbation evolution dynamics. Transient dynamics of perturbation is studied with an initial value problem. In this approach the effect of shear and wave and its interaction are made clear. The transient growth in the time period without wave is significant and is crucial to the initial preferred wave number observed in the experiments. The optimal longitudinal vortex form perturbation is searched and the preferred spanwise wave number predicted is well consistent with experimental data of wind shear and wave.
Dissertations / Theses on the topic "Eulerian perturbation theory"
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Taffoni, Giuliano. "Formation and Evolution of Dark Matter Haloes in Hierarchical Models for Structure Formation." Doctoral thesis, SISSA, 2002. http://hdl.handle.net/20.500.11767/4286.
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The layout of this thesis is the following. In Chapter 2, I introduce some basic elements of modem cosmology and devote special attention to recent observational constraints on cosmological parameters. I also review the theory of gravitational instability, paying particular attention to the theory of collapse of the initial density perturbations. Chapter 3 deals with the issue of hierarchical clustering. I present a Monte Carlo code to generate catalogues of haloes based on the EPS formalism, and then compare its results with numerical simulations. In Chapters 4, 5, and 6 PINOCCHIO code is presented and tested. First, I describe the analytical backbones of this algorithm and then test the code against numerical simulations in order to verify its ability of estimating the statistical properties of the hierarchical clustering of haloes. I will show that PINOCCHIO can also reproduce the numerical experiments to an object-by-object level. In the last two Chapters, I study the evolution of satellites in DM haloes. Chapter 7 derives a simple formula for the decaying time of rigid satellites orbiting in Navarro Frank & White haloes, while Chapter 8 studies the fate of mass loosing satellites which sink in the main DM halo. Conclusions are presented in the last sections of the chapters containing
original results (namely, Chapter 3,4,5,6,7,8) and summarized in Chapter 9.
Conference papers on the topic "Eulerian perturbation theory"
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Fouques, Sébastien, and Csaba Pákozdi. "A Numerical Investigation of Steep Irregular Wave Properties With a Mixed-Eulerian Lagrangian HOS Method." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18216.
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Abstract The design of structures at sea requires knowledge on how large and steep waves can be. Although extreme waves are very rare, their consequences in terms of structural loads, such as wave impact or ringing, are critical. However, modelling the physical properties of steep waves along with their probability of occurrence in given sea states has remained a challenge. On the one hand, standard linear and weakly nonlinear wave theories are computationally efficient, but since they assume that the steepness parameter is small, they are unable to capture extreme waves. On the other hand, recent simulation methods based on CFD or fully nonlinear potential solvers are able to capture the physics of steep waves up to the onset on breaking, but their large computational cost makes it difficult to investigate rare events. Between these two extremes, the High-Order Spectral (HOS) method, which solves surface equations, is both efficient and able to capture highly nonlinear effects. It may then represent a good compromise for long simulations of steep waves. Unfortunately, it is based on a perturbation expansion where the small parameter is the wave steepness, and consequently, simulations tend to become unstable when steep wave events occur. In this work, we investigate the properties of irregular waves simulated with a modified HOS method, in which the sea surface is described with a Lagrangian representation, i.e. by computing the position and the velocity potential of individual surface particles. By doing so, nonlinear properties of the surface elevation are simply captured by the modulation of the horizontal and vertical particle motion. The same steep wave is then described more linearly with a Lagrangian representation, which reduces the instabilities of the HOS method. The paper focuses on bi-chromatic waves and irregular waves simulated from a JONSWAP spectrum. We compare simulations performed with the standard HOS and the modified Lagrangian methods for various HOS-orders.
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El Bouzidi, Salim, Marwan Hassan, Lais L. Fernandes, and Atef Mohany. "Numerical Characterization of the Area Perturbation and Timelag for a Vibrating Tube Subjected to Cross-Flow." In ASME 2014 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/pvp2014-28452.
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Fluidelastic instability can have disastrous effects on the integrity of steam generators. Over the last five decades there has been a great deal of research done in an attempt to understand this phenomenon. These efforts have resulted in several theoretical models and design guidelines. The semi-analytical model of fluidelastic instability initially developed by Lever and Weaver is based on a single tube in a channel flow. The mechanism responsible for instability was found to be one of flow redistribution. While previous studies have been able to characterize the pressure and velocity within a tube bundle, the behaviour of the area of the channel has not yet been fully investigated. The current study aims to characterize the area of the channel surrounding the tube. Reynolds Averaged Navier Stokes (RANS) equations are cast in an Arbitrary Lagrangian Eulerian (ALE) form and are used to compute the flow conditions in a rigid tube bundle due to a single flexible tube vibrating in the transverse direction. The properties of the velocity field are used to determine the channel boundaries. Properties of the channel area such as area perturbation, mean area, and area phase are investigated for various reduced flow velocities. Dynamic simulations are conducted to determine the impact on the stability threshold for transverse fluid force cases using a mass damping parameter range of 10–200.
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Rollin, Bertrand, Frederick Ouellet, Bradford Durant, Rahul Babu Koneru, and S. Balachandar. "Shock-Induced Multiphase Instability in a High Volume Fraction Finite-Thickness Particle Layer." In ASME 2021 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/fedsm2021-65446.
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Abstract We study the interaction of a planar air shock with a perturbed, monodispersed, particle curtain using point-particle simulations. In this Eulerian-Lagrangian approach, equations of motion are solved to track the position, momentum, and energy of the computational particles while the carrier fluid flow is computed in the Eulerian frame of reference. In contrast with many Shock-Driven Multiphase Instability (SDMI) studies, we investigate a configuration with an initially high particle volume fraction, which produces a strongly two-way coupled flow in the early moments following the shock-solid phase interaction. In the present study, the curtain is about 4 mm in thickness and has a peak volume fraction of about 26%. It is composed of spherical particles of d = 115μm in diameter and a density of 2500 kg.m−3, thus replicating glass particles commonly used in multiphase shock tube experiments or multiphase explosive experiments. We characterize both the evolution of the perturbed particle curtain and the gas initially trapped inside the particle curtain in our planar three-dimensional numerical shock tube. Control parameters such as the shock strength, the particle curtain perturbation wavelength and particle volume fraction peak-to-trough amplitude are varied to quantify their influence on the evolution of the particle cloud and the initially trapped gas. We also analyze the vortical motion in the flow field. Our results indicate that the shock strength is the primary contributor to the cloud particle width. Also, a classic Richtmyer-Meshkov instability mixes the gas initially trapped in the particle curtain and the surrounding gas. Finally, we observe that the particle cloud contribute to the formation of longitudinal vortices in the downstream flow.