Academic literature on the topic 'Methods: n-body simulations'
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Journal articles on the topic "Methods: n-body simulations"
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Aarseth, Sverre J. "N-body codes." Proceedings of the International Astronomical Union 2, no. 14 (August 2006): 428–29. http://dx.doi.org/10.1017/s1743921307011210.
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AbstractWe review some advances relating to direct N-body codes. In particular, there has been significant progress in dealing with large-N systems containing a few dominant members. The simulation of massive black holes also requires treatment of relativistic effects for strongly bound two-body orbits. Although somewhat costly, the addition of post-Newtonian terms is still straightforward when used in connection with regularization methods. Several versions of multiple regularization are especially well suited to studying black hole problems. We also report on a new stability criterion for the general three-body problem which will provide a robust test in systems where hierarchies are a troublesome feature, as in the case of star cluster simulations with primordial binaries.
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Hernandez, David M., Sam Hadden, and Junichiro Makino. "Are long-term N-body simulations reliable?" Monthly Notices of the Royal Astronomical Society 493, no. 2 (February 19, 2020): 1913–25. http://dx.doi.org/10.1093/mnras/staa388.
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ABSTRACT N-body integrations are used to model a wide range of astrophysical dynamics, but they suffer from errors which make their orbits diverge exponentially in time from the correct orbits. Over long time-scales, their reliability needs to be established. We address this reliability by running a three-body planetary system over about 200 e-folding times. Using nearby initial conditions, we can construct statistics of the long-term phase-space structure and compare to rough estimates of resonant widths of the system. We compared statistics for a wide range of numerical methods, including a Runge–Kutta method, Wisdom–Holman method, symplectic corrector methods, and a method by Laskar and Robutel. ‘Improving’ an integrator did not increase the phase-space accuracy, but simply increasing the number of initial conditions did. In fact, the statistics of a higher order symplectic corrector method were inconsistent with the other methods in one test.
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Murtagh, F. D. "Hierarchical trees in N-body simulations: Relations with cluster analysis methods." Computer Physics Communications 52, no. 1 (December 1988): 15–18. http://dx.doi.org/10.1016/0010-4655(88)90166-x.
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Mukherjee, Diptajyoti, Qirong Zhu, Hy Trac, and Carl L. Rodriguez. "Fast Multipole Methods for N-body Simulations of Collisional Star Systems." Astrophysical Journal 916, no. 1 (July 1, 2021): 9. http://dx.doi.org/10.3847/1538-4357/ac03b2.
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Bowers, Kevin J., Ron O. Dror, and David E. Shaw. "Zonal methods for the parallel execution of range-limited N-body simulations." Journal of Computational Physics 221, no. 1 (January 2007): 303–29. http://dx.doi.org/10.1016/j.jcp.2006.06.014.
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Wang, Long, Rainer Spurzem, Sverre Aarseth, Keigo Nitadori, Peter Berczik, M. B. N. Kouwenhoven, and Thorsten Naab. "Acceleration of hybrid MPI parallel NBODY6++ for large N-body globular cluster simulations." Proceedings of the International Astronomical Union 10, S312 (August 2014): 260–61. http://dx.doi.org/10.1017/s174392131500798x.
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AbstractPrevious research on globular clusters (GCs) dynamics is mostly based on semi-analytic, Fokker-Planck, Monte-Carlo methods and on direct N-body (NB) simulations. These works have great advantages but also limits since GCs are massive and compact and close encounters and binaries play very important roles in their dynamics. The former three methods make approximations and assumptions, while expensive computing time and number of stars limit the latter method. The current largest direct NB simulation has ~ 500k stars (Heggie 2014). Here, we accelerate the direct NB code NBODY6++ (which extends NBODY6 to supercomputers by using MPI) with new parallel computing technologies (GPU, OpenMP + SSE/AVX). Our aim is to handle large N (up to 106) direct NB simulations to obtain better understanding of the dynamical evolution of GCs.
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Geller, Aaron M., Jarrod R. Hurley, and Robert D. Mathieu. "The progeny of stellar dynamics and stellar evolution within an N-body model of NGC 188." Proceedings of the International Astronomical Union 5, S266 (August 2009): 258–63. http://dx.doi.org/10.1017/s1743921309991128.
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AbstractWe present a direct N-body simulation modeling the evolution of the old (7 Gyr) open cluster NGC 188. This is the first N-body open cluster simulation whose initial binary population is directly defined by observations of a specific open cluster: M35 (150 Myr). We compare the simulated color–magnitude diagram at 7 Gyr to that of NGC 188, and discuss the blue stragglers produced in the simulation. We compare the solar-type main-sequence binary period and eccentricity distributions of the simulation to detailed observations of similar binaries in NGC 188. These results demonstrate the importance of detailed observations in guiding N-body open cluster simulations. Finally, we discuss the implications of a few discrepancies between the NGC 188 model and observations and suggest a few methods for bringing N-body open cluster simulations into better agreement with observations.
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Korkidis, Giorgos, Vasiliki Pavlidou, Konstantinos Tassis, Evangelia Ntormousi, Theodore N. Tomaras, and Konstantinos Kovlakas. "Turnaround radius of galaxy clusters in N-body simulations." Astronomy & Astrophysics 639 (July 2020): A122. http://dx.doi.org/10.1051/0004-6361/201937337.
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Aims. We use N-body simulations to examine whether a characteristic turnaround radius, as predicted from the spherical collapse model in a ΛCDM Universe, can be meaningfully identified for galaxy clusters in the presence of full three-dimensional effects. Methods. We use The Dark Sky Simulations and Illustris-TNG dark-matter-only cosmological runs to calculate radial velocity profiles around collapsed structures, extending out to many times the virial radius R200. There, the turnaround radius can be unambiguously identified as the largest nonexpanding scale around a center of gravity. Results. We find that: (a) a single turnaround scale can meaningfully describe strongly nonspherical structures. (b) For halos of masses M200 > 1013 M⊙, the turnaround radius Rta scales with the enclosed mass Mta as Mta1/3, as predicted by the spherical collapse model. (c) The deviation of Rta in simulated halos from the spherical collapse model prediction is relatively insensitive to halo asphericity. Rather, it is sensitive to the tidal forces due to massive neighbors when these are present. (d) Halos exhibit a characteristic average density within the turnaround scale. This characteristic density is dependent on cosmology and redshift. For the present cosmic epoch and for concordance cosmological parameters (Ωm ∼ 0.3; ΩΛ ∼ 0.7) turnaround structures exhibit a density contrast with the matter density of the background Universe of δ ∼ 11. Thus, Rta is equivalent to R11 – in a way that is analogous to defining the “virial” radius as R200 – with the advantage that R11 is shown in this work to correspond to a kinematically relevant scale in N-body simulations.
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Modi, Chirag, Shi-Fan Chen, and Martin White. "Simulations and symmetries." Monthly Notices of the Royal Astronomical Society 492, no. 4 (January 28, 2020): 5754–63. http://dx.doi.org/10.1093/mnras/staa251.
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ABSTRACT We investigate the range of applicability of a model for the real-space power spectrum based on N-body dynamics and a (quadratic) Lagrangian bias expansion. This combination uses the highly accurate particle displacements that can be efficiently achieved by modern N-body methods with a symmetries-based bias expansion which describes the clustering of any tracer on large scales. We show that at low redshifts, and for moderately biased tracers, the substitution of N-body-determined dynamics improves over an equivalent model using perturbation theory by more than a factor of two in scale, while at high redshifts and for highly biased tracers the gains are more modest. This hybrid approach lends itself well to emulation. By removing the need to identify haloes and subhaloes, and by not requiring any galaxy-formation-related parameters to be included, the emulation task is significantly simplified at the cost of modelling a more limited range in scale.
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Heggie, Douglas C. "The Gravitational Million-Body Problem." Symposium - International Astronomical Union 208 (2003): 81–92. http://dx.doi.org/10.1017/s0074180900207043.
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We review what has been learned recently using N-body simulations about the evolution of globular clusters. While simulations of star clusters have become more realistic, and now include the evolution of single and binary stars, the prospect of reaching large enough N is still a distant one. Nevertheless more restricted kinds of simulations have recently brought valuable progress for certain problems of current observational interest, including the origin and structure of tidal tails of globular clusters. In addition, such simulations have forced us to rethink some basic aspects of stellar dynamics, including, in particular, the process of escape. Finally we turn to faster, approximate methods for studying star cluster dynamics, where the role of N-body simulations is one of calibration.
Dissertations / Theses on the topic "Methods: n-body simulations"
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Garrison, Lehman H., Daniel J. Eisenstein, Douglas Ferrer, Marc V. Metchnik, and Philip A. Pinto. "Improving initial conditions for cosmological N -body simulations." OXFORD UNIV PRESS, 2016. http://hdl.handle.net/10150/621729.
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In cosmological N-body simulations, the representation of dark matter as discrete 'macroparticles' suppresses the growth of structure, such that simulations no longer reproduce linear theory on small scales near k(Nyquist). Marcos et al. demonstrate that this is due to sparse sampling of modes near k(Nyquist) and that the often-assumed continuum growing modes are not proper growing modes of the particle system. We develop initial conditions (ICs) that respect the particle linear theory growing modes and then rescale the mode amplitudes to account for growth suppression. These ICs also allow us to take advantage of our very accurate N-body code ABACUS to implement second-order Lagrangian perturbation theory (2LPT) in configuration space. The combination of 2LPT and rescaling improves the accuracy of the late-time power spectra, halo mass functions, and halo clustering. In particular, we achieve 1 per cent accuracy in the power spectrum down to k(Nyquist), versus k(Nyquist)/4 without rescaling or k(Nyquist)/13 without 2LPT, relative to an oversampled reference simulation. We anticipate that our 2LPT will be useful for large simulations where fast Fourier transforms are expensive and that rescaling will be useful for suites of medium-resolution simulations used in cosmic emulators and galaxy survey mock catalogues. Code to generate ICs is available at https://github.com/lgarrison/zeldovich-PLT.
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Arico, Giovanni. "Testing the methods to reconstruct and model the Baryonic Acoustic Oscillations of different tracers using N-body simulations." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13167/.
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The accelerated expansion of the Universe and the nature of the Dark Energy are still open questions in cosmology. One of the most powerful ways to investigate these issues is to map the large-scale structure of the Universe, to constrain its expansion history and growth of structures.
In particular, baryon acoustic oscillations (BAO) occurred at recombination make a peak in the correlation function of galaxies at the characteristic scale of the sound horizon (a sufficiently large scale to “protect” the signal from strong non-linearities), or alternatively a series of oscillations in the power spectrum. Since the sound horizon can be estimated with a great precision from the position of the first peak in the angular power spectrum of the Cosmic Microwave Background (which has the same physical origin of BAO, oscillations of the baryons-photons plasma), the BAO peak in the correlation function can be used as a standard ruler, providing paramount cosmological information.
The aim of this thesis is to systematically test and possibly improve the state-of- the-art statistical methods to model the BAO peak, taking into account the non-linear evolution of matter overdensities, redshift-space distortions and the bias of cosmic tracers. To do that, we analyse mock samples of galaxies, quasars and galaxy clusters extracted from one of the largest available cosmological hydrodynamical simulations. We extract cosmological constraints from the BAO peak through different statistical tools in the redshift range 0.2 < z < 2.
Although the BAO peak is at large scales, non-linear growth and galaxy peculiar velocities make the BAO signal smoothed and broader with respect to linear predictions, especially at low redshifts. A possible method to overcome these issues is the so-called reconstruction of the density field: one of the primary goals of this work is to implement a reconstruction method, to check its performances as a function of sample selections and redshift.
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Bucklein, Brian K. "In Search of Empty Places: Voids in the Distribution of Galaxies." BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2138.
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We investigate several techniques to identify voids in the galaxy distribution of matter in the universe. We utilize galaxy number counts as a function of apparent magnitude and Wolf plots to search a two- or three-dimensional data set in a pencil-beam fashion to locate voids within the field of view. The technique is able to distinguish between voids that represent simply a decrease in density as well as those that show a build up of galaxies on the front or back side of the void. This method turns out to be primarily useable only at relatively short range (out to about 200 Mpc). Beyond this distance, the characteristics indicating a void become increasingly difficult to separate from the statistical background noise. We apply the technique to a very simplified model as well as to the Millennium Run dark matter simulation. We then compare results with those obtained on the Sloan Digital Sky Survey. We also created the Watershed Void Examiner (WaVE) which treats densities in a fashion similar to elevation on a topographical map, and then we allow the "terrain" to flood. The flooded low-lying regions are identified as voids, which are allowed to grow and merge as the level of flooding becomes higher (the overdensity threshold increases). Void statistics can be calculated for each void. We also determine that within the Millennium Run semi-analytic galaxy catalog, the walls that separate the voids are permeable at a scale of 4 Mpc. For each resolution that we tested, there existed a characteristic density at which the walls could be penetrated, allowing a single void to grow to dominate the volume. With WaVE, we are able to get comparable results to those previously published, but often with fewer choices of parameters that could bias the results. We are also able to determine the the density at which the number of voids peaks for different resolutions as well as the expected number of void galaxies. The number of void galaxies is amazingly consistent at an overdensity of −0.600 at all resolutions, indicating that this could be a good choice for comparing models.
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Xufen, Wu. "Numerical modeling of modified Newtonian dynamics in galaxies : testing the external field effects." Thesis, University of St Andrews, 2010. http://hdl.handle.net/10023/1706.
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Galaxies are natural laboratories for testing fundamental physics on the nature of the dark matter. MOdified Newtonian Dynamics (MOND) has been tested for over 20 years on small and large scales. While there are several versions of how MOND extrapolates to the large scales, and these versions are not yet fully successful, the original Bekenstein-Milgrom version of MOND is fully predictive and works very well on galaxy scales. However, little work has been done to explore this theory beyond fitting the rotation curves and Tully-Fisher relation of isolated disc galaxies. So far little is known of MONDian elliptical galaxies accelerating in any galaxy cluster. A defining feature of MOND is that internal dynamics of the galaxy depends on the overall acceleration of the galaxy. The existence of cuspy triaxial equilibria for elliptical galaxies is the minimal requirement to MOND. With the PhD project here, I constructed and then further studied the evolution and stability of gravitationally bound systems resembling like cuspy elliptical galaxies, both in isolation and when embedded in a uniform external field. I also studied the escape speeds from spiral galaxies, in particular by comparing the potentials of the Milky Way Galaxy in the Cold Dark Matter (CDM) and MOND frameworks.
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Alzahrani, Abdulrahman. "Contractivity-Preserving Explicit 2-Step, 6-Stage, 6-Derivative Hermite-Birkhoff–Obrechkoff Ode Solver of Order 13." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/32564.
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In this thesis, we construct a new optimal contractivity-preserving (CP) explicit, 2-step, 6-stage, 6-derivative, Hermite--Birkhoff--Obrechkoff method of order 13, denoted by HBO(13) with nonnegative coefficients, for solving nonstiff first-order initial value problems y'=f(t,y), y(t_0)=y_0. This new method is the combination of a CP 2-step, 6-derivative, Hermite--Obrechkoff of order 9, denoted by HO(9), and a 6-stage Runge-Kutta method of order 5, denoted by RK(6,5). The new HBO(13) method has order 13.
We compare this new method, programmed in Matlab, to Adams-Bashforth-Moulton method of order 13 in PECE mode, denoted by ABM(13), by testing them on several frequently used test problems, and show that HBO(13) is more efficient with respect to the CPU time, the global error at the endpoint of integration and the relative energy error. We show that the new HBO(13) method has a larger scaled interval of absolute stability than ABM(13) in PECE mode.
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Etcheverry, Arnaud. "Simulation de la dynamique des dislocations à très grande échelle." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0263/document.
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Le travail réalisé durant cette thèse vise à offrir à un code de simulation en dynamique des dislocations les composantes essentielles pour permettre le passage à l’échelle sur les calculateurs modernes. Nous abordons plusieurs aspects de la simulation numérique avec tout d’abord des considérations algorithmiques. Pour permettre de réaliser des simulations efficaces en terme de complexité algorithmique pour des grandes simulations, nous explorons les contraintes des différentes étapes de la simulation en offrant une analyse et des améliorations aux algorithmes. Ensuite, une considération particulière est apportée aux structures de données. En prenant en compte les nouveaux algorithmes, nous proposons une structure de données pour bénéficier d’accès performants à travers la hiérarchie mémoire. Cette structure est modulaire pour faire face à deux types d’algorithmes, avec d’un côté la gestion du maillage nécessitant une gestion dynamique de la mémoire et de l’autre les phases de calcul intensifs avec des accès rapides. Pour cela cette structure modulaire est complétée par un octree pour gérer la décomposition de domaine et aussi les algorithmes hiérarchiques comme le calcul du champ de contrainte et la détection des collisions. Enfin nous présentons les aspects parallèles du code. Pour cela nous introduisons une approche hybride, avec un parallélisme à grain fin à base de threads, et un parallélisme à gros grain de type MPI nécessitant une décomposition de domaine et un équilibrage de charge.Finalement, ces contributions sont testées pour valider les apports pour la simulation numérique. Deux cas d’étude sont présentés pour observer et analyser le comportement des différentes briques de la simulation. Tout d’abord une simulation extrêmement dynamique, composée de sources de Frank-Read dans un cristal de zirconium est utilisée, avant de présenter quelques résultats sur une simulation cible contenant une forte densité de défauts d’irradiationThis research work focuses on bringing performances in 3D dislocation dynamics simulation, to run efficiently on modern computers. First of all, we introduce some algorithmic technics, to reduce the complexity in order to target large scale simulations. Second of all, we focus on data structure to take into account both memory hierachie and algorithmic data access. On one side we build this adaptive data structure to handle dynamism of data and on the other side we use an Octree to combine hierachie decompostion and data locality in order to face intensive arithmetics with force field computation and collision detection. Finnaly, we introduce some parallel aspects of our simulation. We propose a classical hybrid parallelism, with task based openMP threads and domain decomposition technics for MPI
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Vraštil, Michal. "Studium temné energie a modifikované gravitace a jejich vliv na kosmologické parametry vesmíru." Doctoral thesis, 2020. http://www.nusl.cz/ntk/nusl-437550.
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Title: Study of dark energy and modified gravity and their influence on the cosmological parameters of the universe Author: Michal Vraštil Institute: Institute of Physics of the Czech Academy of Sciences Supervisor: RNDr. Michael Prouza, Ph.D., Institute of Physics of the Czech Academy of Sciences Abstract: Discovery of the accelerated expansion of the Universe poses a major theoretical puzzle. Although the assumption of a non-zero cosmological constant provides a minimal extension of general relativity that is consistent with observational data, many theories of modified gravity have been suggested as possible alternatives due to serious problems connected with the cosmological constant. Numerical predictions of structure formation for these models in the fully non-linear regime are very expensive and it is difficult, if not impossible, to explore such a huge space of models and parameters using high-resolution N-body simulations. Even in the mildly nonlinear regime, perturbative methods can become extremely complex. We explore whether simplified dynamical approximations, applicable for a certain set of cosmological probes, can be used to investigate models of modified gravity with acceptable accuracy in the latter instance. For the case of chameleon gravity, we found that it is screened away on scales...
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Pavlík, Václav. "Modelování Velké mlhoviny v Orionu." Master's thesis, 2014. http://www.nusl.cz/ntk/nusl-336596.
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Title: Modelling the Orion Nebula Cluster Author: Václav Pavlík Department: Astronomical Institute of the Charles University Supervisor: doc. RNDr. Ladislav Šubr, Ph.D. (Astronomical Institute of the Charles University) Abstract: Young star clusters are widely discussed from the point of view of their evolution and structure. In this work we focused our attention on studying a typical representative of these objects - the Orion Nebula Cluster (ONC, M 42) - based on the observational data, including their confrontation with N- body models from Šubr et al. (2012). These numerical models were inspired by the recently proposed evolutionary scenario, according to which the star clusters begin their evolution from very dense initial conditions. From the analysis of the X-ray sources we revealed that the ONC is likely to be rotationally symmetric in the inner area (� 0.7 pc). Further analysis including also optical and IR observational data led us to the conclusion that the ONC is elongated from the North-East to the South-West on large scales (up to 2 pc). We also compared radial profiles of different mass groups of stars and we discovered a possibly inverse mass segregation between stars with masses in the interval (1 ; 5) M⊙ and the stars less massive than 0.5 M⊙ in the range from 0.5 pc to 1.5 pc. This...
Book chapters on the topic "Methods: n-body simulations"
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Amor, M., F. Argüello, J. López, O. Plata, and E. L. Zapata. "A Data Parallel Formulation of the Barnes-Hut Method for N-Body Simulations." In Applied Parallel Computing. New Paradigms for HPC in Industry and Academia, 342–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-70734-4_40.
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"Predictor–corrector methods." In Gravitational N-Body Simulations, 18–31. Cambridge University Press, 2003. http://dx.doi.org/10.1017/cbo9780511535246.003.
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AARSETH, SVERRE J. "Direct Methods for N-Body Simulations." In Multiple Time Scales, 377–418. Elsevier, 1985. http://dx.doi.org/10.1016/b978-0-12-123420-1.50017-3.
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Yokota, Rio, and Lorena A. Barba. "Treecode and Fast Multipole Method for N-Body Simulation with CUDA." In GPU Computing Gems Emerald Edition, 113–32. Elsevier, 2011. http://dx.doi.org/10.1016/b978-0-12-384988-5.00009-7.
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El-Bakry, Hazem, and Nikos Mastorakis. "A Modified High Speed Hopfield Neural Model for Perfect Calculation of Magnetic Resonance Spectroscopy." In Biocomputation and Biomedical Informatics, 158–77. IGI Global, 2010. http://dx.doi.org/10.4018/978-1-60566-768-3.ch010.
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In this chapter, an automatic determination algorithm for nuclear magnetic resonance (NMR) spectra of the metabolites in the living body by magnetic resonance spectroscopy (MRS) without human intervention or complicated calculations is presented. In such method, the problem of NMR spectrum determination is transformed into the determination of the parameters of a mathematical model of the NMR signal. To calculate these parameters efficiently, a new model called modified Hopfield neural network is designed. The main achievement of this chapter over the work in literature (Morita, N. and Konishi, O., 2004) is that the speed of the modified Hopfield neural network is accelerated. This is done by applying cross correlation in the frequency domain between the input values and the input weights. The modified Hopfield neural network can accomplish complex dignals perfectly with out any additinal computation steps. This is a valuable advantage as NMR signals are complex-valued. In addition, a technique called “modified sequential extension of section (MSES)” that takes into account the damping rate of the NMR signal is developed to be faster than that presented in (Morita, N. and Konishi, O., 2004). Simulation results show that the calculation precision of the spectrum improves when MSES is used along with the neural network. Furthermore, MSES is found to reduce the local minimum problem in Hopfield neural networks. Moreover, the performance of the proposed method is evaluated and there is no effect on the performance of calculations when using the modified Hopfield neural networks.
Conference papers on the topic "Methods: n-body simulations"
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Naghib Lahouti, Arash, Lakshmana Sampat Doddipatla, Horia Hangan, and Kamran Siddiqui. "Experimental and Numerical Study of the Three Dimensional Instabilities in the Wake of a Blunt Trailing Edge Profiled Body." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30536.
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The wake of nominally two dimensional bluff bodies is dominated by von Ka´rma´n vortices, which are accompanied by three dimensional instabilities beyond a threshold Reynolds number. These three dimensional instabilities initiate as dislocations in the von Ka´rma´n vortices near the trailing edge, which evolve into pairs of counter-rotating vortices further downstream. The wavelength of the three dimensional instabilities depends on profile geometry and Reynolds number. In the present study, the three dimensional wake instabilities for a blunt trailing edge profiled body, composed of an elliptical leading edge and a rectangular trailing edge, have been studied in Reynolds numbers ranging from 500 to 1200, based on the thickness of the body. Numerical simulations, Laser Induced Fluorescence (LIF) flow visualization, and Particle Image Velocimetry (PIV) methods have been used to identify the instabilities. Proper Orthogonal Decomposition (POD) has been used to analyze the velocity field data measured using PIV. The results confirm the existence of three dimensional instabilities with an average wavelength of 2.0 to 2.5 times thickness of the body, in the near wake. The findings are in agreements with the values reported previously for different Reynolds numbers, and extend the range of Reynolds numbers in which the three dimensional instabilities are characterized.
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Grama, Ananth Y., Vipin Kumar, and Ahmed Sameh. "Scalable parallel formulations of the barnes-hut method for n-body simulations." In the 1994 ACM/IEEE conference. New York, New York, USA: ACM Press, 1994. http://dx.doi.org/10.1145/602770.602846.
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Anderson, Kurt S. "Improved “Order-N” Performance Algorithm for the Simulation of Constrained Multi-Rigid-Body Dynamic Systems." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21334.
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Abstract This paper presents an algorithm for the efficient numerical analysis and simulation of modest to heavily constrained multi-rigid-body dynamic systems. The algorithm can accommodate the spatial motion of general multi-rigid-body systems containing arbitrarily many closed loops in O(n + m) operations overall for systems containing n generalized coordinates, and m independent algebraic constraints. The presented approach does not suffer from the performance (speed) penalty encountered by most other of the so-called “O(n)” state-space formulations, when dealing with constraints which tend to actually show O(n + m + nm + nm2 + m3) performance. Additionally, these latter formulations may require additional constraint violation stablization procedures (e.g. Baumgarte’s method, coordinate partitioning, etc.) which can contribute significant additional computation. The presented method suffers less from this difficulty because the loop closure constraints at both the velocity and acceleration level are directly embedded within the formulation. Due to these characteristics, the presented algorithm should offer superior computing performance relative to other methods in situations involving both large n and m.
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Anderson, Kurt S., and Michael J. A. Sadowski. "An Efficient Method for Contact/Impact Problems in Multibody Systems: Topologies With Many Loops." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48340.
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This paper presents an algorithm for the efficient numerical analysis and simulation of contact/impact problems in modest to heavily constrained multi-rigid-body dynamic systems. The algorithm can accommodate the spatial motion of general multirigid-body systems containing arbitrarily many closed loops in O(n+m) operations overall for systems containing n generalized coordinates, and m independent algebraic constraints. The presented method uses a generalized momentum balance approach to determine the velocity jumps which take place across impacts in such constrained multibody dynamic systems. The presented method does not suffer from the performance (speed) penalty encountered by most other momentum balance methods given its O(n + m) cost, and exact direct embedded consideration of the all constraints. Due to these characteristics, the presented algorithm offers superior computing performance relative to other methods in situations involving both large n and m.
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Duan, Shanzhong, and Andrew Ries. "An Efficient O(N) Algorithm for Computer Simulation of Rigid Body Molecular Dynamics." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-42032.
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Molecular dynamics is effective for a nano-scale phenomenon analysis. There are two major computational costs associated with computer simulation of atomistic molecular dynamics. They are calculation of the interaction forces and formation/solution of equations of motion. In this paper, an O(N) (order N) procedure is presented for calculation of the interaction forces and formation/solution of equations of motion. For computational costs associated with potentials or interaction forces, an internal coordinate method is used. Use of the internal coordinate method makes application of multi-rigid body molecular dynamics to an atomistic molecular system become possible. The algorithm based on the method makes the calculation considerably more practical for large-scale problems encountered in molecular dynamics such as conformation dynamics of polymers. For computational costs associated with formation/solution of equations of motion, Kane method and the internal coordinate method are used for recursive formation and solution of equations of motion of an atomistic molecular system. However, in computer simulation of atomistic molecular dynamics, the inclusion of lightly excited all degrees of freedom of an atom, such as inter-atomic oscillations and rotation about double bonds with high frequencies, introduces limitations to the simulation. The high frequencies of these degrees of freedom force the use of very small integration step sizes, which severely limit the time scales for the atomic molecular simulation over long periods of time. To improve this, holonomic constraints such as strictly constant bond lengths and bond angles are introduced to freeze these high frequency degrees of freedom since they have insignificant effect on long time scale processes in conformational dynamics. In this way, the procedure developed in multibody dynamics can be utilized to achieve higher computing efficiency and an O(N) computational performance can be realized for formation/solution of equations of motion.
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Sadowski, Michael J., and Kurt S. Anderson. "Recursive Coordinate Reduction: An Addendum." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85566.
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This paper presents an addendum to the Recursive Coordinate Reduction (RCR) algorithm for the efficient numerical analysis and simulation of modest to heavily constrained multi-rigid-body dynamic systems. The RCR algorithm can accommodate the spatial motion of broad categories of multi-rigid-body systems containing arbitrarily many closed loops in O(n + m) operations overall for systems containing n generalized coordinates, and m independent algebraic constraints. The presented approach does not suffer from the performance (speed) penalty encountered by most other of the so-called “(n)” state-space formulations, and does not require additional constraint violation stabilization procedures (e.g. Baumgartes method, coordinate partitioning, etc.). Due to these characteristics, the presented algorithm should offer superior computing performance relative to other methods in many situations involving both large n and m. This paper will specifically address an unpublished recursive step in the handling of “floating” loop base bodies, as well as present an extension to “spur” topologies.
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Anderson, Kurt S., and Michael J. A. Sadowski. "An Efficient Method for Contact/Impact Problems in Multibody Systems: Tree Topologies." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48339.
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This paper presents an algorithm for the efficient numerical analysis and simulation of contact/impact problems in tree topology multi-rigid-body dynamic systems. The algorithm can accommodate the jumps in structure which occur in the equations of motion of general multi-rigid-body tree systems due to a contact/impact event between bodies, or due to the locking of joints. The presented method uses a generalized momentum balance approach to determine the velocity jumps which take place across impacts in such multibody dynamic systems, and where necessary explicitly determines impact impulsive loads (both working and non-working). The presented method does not suffer from the performance (speed) penalty encountered by most other momentum balance methods given its O(n) overall cost, and exact direct embedded consideration of the all constraints. Due to these characteristics, the presented algorithm offers superior computing performance relative to other methods in situations involving both large n and potentially many unilateral constraints.
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Sadowski, Michael J., and Kurt S. Anderson. "An Efficient Method for a Category of Contact/Impact Problems in Multibody Systems: Tree Topologies." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85563.
Full textAbstract:
This paper presents an algorithm for the efficient numerical analysis and simulation of a category of contact/impact problems in multi-rigid-body dynamic systems with tree topologies. The algorithm can accommodate the jumps in structure which occur in the equations of motion of general multi-rigid-body systems due to a contact/impact event between bodies, or due to the locking of joints as long as the resulting system is a tree topology. The presented method uses a generalized momentum balance approach to determine the velocity jumps which take place across impacts in such multibody dynamic systems where event constraint forces are of the “non-working” category. The presented method does not suffer from the performance (speed) penalty encountered by most other momentum balance methods given its O(n) overall cost, and exact direct embedded consideration of all the constraints. Due to these characteristics, the presented algorithm offers superior computing performance relative to other methods in situations involving both large n and potentially many unilateral constraints.
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Maxey, M. R., S. Dong, D. Liu, and J. Xu. "Simulation of Particulate Flows With the Force-Coupling Method (Keynote Paper)." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45713.
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One of the challenges in the numerical simulation of a system of particles in a fluid flow is to balance the need for an accurate representation of the flow around individual particles with the feasibility of simulating the fully-coupled dynamics of large numbers of particles. Over the past few years, several techniques have been developed for the direct numerical simulation of dispersed two-phase flows. Examples include the ALE-FEM formulation described by Hu et al. [1] and the DLM method of Patankar et al. [2]. The former uses a finite element mesh that conforms to the shape and position of each particle and evolves dynamically as the particles move, while the latter employs a fixed mesh and constraints are imposed in the volume of fluid occupied by the particle to reproduce a corresponding rigid body motion. In both the aim is to fully resolve the flow dynamics for each particle and there is a corresponding demand for high resolution of the flow. A typical approach used for gas-solid flows has been the point-force method that combines a Lagrangian tracking of individual particles with an Eulerian formulation for force feedback on the fluid flow. The latter approach has worked well for very small particles in systems of negligible void fraction but significant mass loading. The resolution level is very low and often the particles are smaller than the spacing between grid points. Its success comes from the averaging effect of large numbers of small particles and the fact that the influence of an individual particle is weak. The approach though is inaccurate for liquid-solid or bubbly flows when the individual particles are of finite size and the void fractions may easily be larger than 1%. In tracking the individual particles an equation of motion is formulated that relates the particle acceleration to the fluid forces acting on the particle, and these forces such as drag and lift are parameterized in terms of the local fluid velocity, velocity gradients and history of the fluid motion. Once flow modification is included however, it is harder to specify the local flow. The parameterizations also become more complex as effects of finite Reynolds number or wall boundaries are included. As a numerical procedure, the force-coupling method (FCM) does not require the same level of resolution as the DLM or ALE-FEM schemes and avoids the limitations of the point-force method. It gives a self-consistent scheme for simulating the dynamics of a system of small particle using a fixed numerical mesh and resolves the flow except close to the surface of each particle. Distributed, finite force-multipoles are used to represent the particles, and FCM is able to predict quite well the motion of isolated particles in shear flows and the interaction between moving particles. The method also provides insights into how the two-phase flow may be described theoretically and modeled. The idea of the force-coupling method was first introduced by Maxey et al. [3]. The basic elements of the method are given by Maxey & Patel [4] and Lomholt & Maxey [5]. In the basic version of the method, fluid is assumed to fill the whole flow domain, including the volume occupied by the particles. The presence of each particle is represented by a finite force monopole that generates a body force distribution f(x,t) on the fluid, which transmits the resultant force of the particles on the flow to the fluid. The velocity field u(x,t) is incompressible and satisfies ∇·u=0(1)ρDuDt=−∇p+μ∇2u+f(x,t),(2) where μ is the fluid viscosity and p is the pressure. The body force due to the presence of NP bubbles is f(x,t)=∑n=1NpF(n)Δ(x−Y(n)(t)),(3)Y(n)(t) is the position of the nth spherical particle and F(n)(t) is the force this exerts on the fluid. The force monopole for each particle is determined by the function Δ(x), which is specified as a Gaussian envelope Δ(x)=(2πσ2)−3/2exp(−x2/2σ2)(4) and the length scale σ is set in terms of the particle radius a as a/σ = π. The velocity of each particle V(n)(t) is found by forming a local average of the fluid velocity over the region occupied by the particle as V(n)(t)=∫u(x,t)Δ(x−Y(n)(t))d3x.(5) If mP and mF denote the mass of a particle and the mass of displaced fluid, the force of the particle acting on the fluid is F(n)=(mP−mF)(g−dV(n)dt).(6) This force is the sum of the net external force due to buoyancy of the particle and the excess inertia of the particle over the corresponding volume of displaced fluid. In addition a short-range, conservative force barrier is imposed to represent collisions between particles and prevent overlap. A similar barrier force is imposed, normal to the wall, to represent collisions between a particle and a rigid wall. With this scheme the body forces induce a fluid motion equivalent to that of the particles. The dynamics of the particles and the fluid are considered as one system where fluid drag on the particles, added-mass effects and lift forces are internal to the system. The method does not resolve flow details near to the surface of a particle, and indeed the no-slip condition is not satisfied on surface. At distances of about half a particle radius from the surface the flow though is fairly well represented. While there is no explicit boundary condition on the particle surface, the condition (5) ensures that the bubble and the surrounding fluid move together. The method has been applied to a variety of flow problems. Lomholt et al. [6] compared experimental results for the buoyant rise of particles in a vertical channel filled with liquid with results from corresponding simulations with FCM. The particle Reynolds numbers were in the range of 0 to 5 and the results agreed well. The wake-capture and the drafting, kissing and tumbling of pairs of particles, or of a group of three particles were found to match. Comparisons have made too with full direct numerical simulations performed with a spectral element code [7]. Liu et al. [8] examined the motion of particles in a channel at both low and finite Reynolds numbers, up to Re = 10. There was in general good agreement between the FCM results and the DNS for the particle motion, and the flow details were consistent away from the particle surface. There has been extensive work in the past on the sedimentation of particles in a homogeneous suspension, mainly for conditions of Stokes flow. Climent & Maxey [9] have verified that the FCM scheme reproduces many of the standard features found for Stokes suspensions. The results for finite Reynolds numbers illustrate how the structure of the suspension changes as fluid inertia is introduced, in particular limiting the growth in velocity fluctuation levels with system size. Further work has been done by Dance [10] on sedimenting suspensions in bounded containers. Recently we have been studying the dynamics of drag reduction by injecting micro-bubbles into a turbulent channel flow. This has been proven through experiments over the past 30 years to be an effective means for drag reduction but the details of the mechanisms involved have not been determined. Numerical simulations by Xu et al. [11] have shown clear evidence of drag reduction for a range of bubble sizes. A key feature is the need to maintain a concentration of bubbles in the near-wall region. In the talk, the method will be described and example results given. Specific issues relevant to gas-solid flows will be discussed.
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Xu, Yu, and Yulin Wu. "Parallel Simulation of the Turbulent Flow Through a Pump-Turbine Runner." In ASME 2002 Joint U.S.-European Fluids Engineering Division Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/fedsm2002-31197.
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In this paper, authors use the parallel calculation methods to solve the incompressible turbulent flow through a pump-turbine runner. The calculation aims at probing the road using parallel calculation methods to simulate complex flow field. The simulation is conducted based on the N-S equations, by using the k-ε model. SIMPLEC algorithm [1] is adopted in the numerical procedure with body-fitted coordination [2] and staggering grid system. The calculation is carried out on the THTF “Explore 108” Cluster Computer, where Solaris8.0 plays the roles of operating system and MPI1.2 as message-passing interface. The results of parallel simulation agree well with those of serial simulation, which shows that the parallel algorithms are feasible and useful to numerical simulation.