scholarly journals Accurate initial conditions for cosmological N-body simulations: minimizing truncation and discreteness errors

2020 ◽  
Vol 500 (1) ◽  
pp. 663-683
Author(s):  
Michaël Michaux ◽  
Oliver Hahn ◽  
Cornelius Rampf ◽  
Raul E Angulo
Keyword(s):  
Perturbation Theory ◽  
Displacement Field ◽  
Large Scale ◽  
Initial Conditions ◽  
Initial Condition ◽  
Summary Statistics ◽  
Fluid Limit ◽  
Third Order ◽  
Truncation Errors ◽  
The Continuum

ABSTRACT Inaccuracies in the initial conditions for cosmological N-body simulations could easily be the largest source of systematic error in predicting the non-linear large-scale structure. From the theory side, initial conditions are usually provided by using low-order truncations of the displacement field from Lagrangian perturbation theory, with the first- and second-order approximations being the most common ones. Here, we investigate the improvement brought by using initial conditions based on third-order Lagrangian perturbation theory (3LPT). We show that with 3LPT, truncation errors are vastly suppressed, thereby opening the portal to initializing simulations accurately as late as z = 12 (for the resolution we consider). We analyse the competing effects of perturbative truncation and particle discreteness on various summary statistics. Discreteness errors are essentially decaying modes and thus get strongly amplified for earlier initialization times. We show that late starting times with 3LPT provide the most accurate configuration, which we find to coincide with the continuum fluid limit within 1 per cent for the power- and bispectrum at z = 0 up to the particle Nyquist wavenumber of our simulations (k ∼ 3h Mpc−1). In conclusion, to suppress non-fluid artefacts, we recommend initializing simulations as late as possible with 3LPT. We make our 3LPT initial condition generator publicly available.

scholarly journals Higher-order Lagrangian perturbative theory for the Cosmic Web

2014 ◽  
Vol 11 (S308) ◽  
pp. 119-120
Author(s):  
Takayuki Tatekawa ◽  
Shuntaro Mizuno
Keyword(s):  
Perturbation Theory ◽  
Fourth Order ◽  
Initial Conditions ◽  
Higher Order ◽  
Order Perturbation ◽  
Initial Condition ◽  
The Difference ◽  
Fifth Order ◽  
The Universe ◽  
Higher Order Lagrangian

AbstractZel'dovich proposed Lagrangian perturbation theory (LPT) for structure formation in the Universe. After this, higher-order perturbative equations have been derived. Recently fourth-order LPT (4LPT) have been derived by two group. We have shown fifth-order LPT (5LPT) In this conference, we notice fourth- and more higher-order perturbative equations. In fourth-order perturbation, because of the difference in handling of spatial derivative, there are two groups of equations. Then we consider the initial conditions for cosmological N-body simulations. Crocce, Pueblas, and Scoccimarro (2007) noticed that second-order perturbation theory (2LPT) is required for accuracy of several percents. We verify the effect of 3LPT initial condition for the simulations. Finally we discuss the way of further improving approach and future applications of LPTs.

An Analog Method for Real-Time Forecasting of Summer Monsoon Subseasonal Variability

2007 ◽  
Vol 135 (12) ◽  
pp. 4149-4160 ◽  
Author(s):  
Prince K. Xavier ◽  
B. N. Goswami
Keyword(s):  
Real Time ◽  
Summer Monsoon ◽  
Large Scale ◽  
Initial Conditions ◽  
Empirical Orthogonal Functions ◽  
Initial Condition ◽  
Analog Method ◽  
Initial State ◽  
Orthogonal Functions ◽  
Modeling Data

Abstract A physically based empirical real-time forecasting strategy to predict the subseasonal variations of the Indian summer monsoon up to four–five pentads (20–25 days) in advance has been developed. The method is based on the event-to-event similarity in the properties of monsoon intraseasonal oscillations (ISOs). This two-tier analog method is applied to NOAA outgoing longwave radiation (OLR) pentad averaged data that have sufficiently long records of observation and are available in nearly real time. High-frequency modes in the data are eliminated by reconstructing the data using the first 10 empirical orthogonal functions (EOFs), which together explain about 75% of the total variance. In the first level of the method, the spatial analogs of initial condition pattern are identified from the modeling data. The principal components (PCs) of these spatial analogs, whose evolution history of the latest five pentads matches that of the initial condition pattern, are considered the temporal PC analogs. Predictions are generated for each PC as the average evolution of PC analogs for the given lead time. Predicted OLR values are constructed using the EOFs and predicted PCs. OLR data for 1979–99 are used as the modeling data and independent hindcasts are generated for the period 2000–05. The skill of anomaly predictions is rather high over the central and northern Indian region for lead times of four–five pentads. The phases and amplitude of intraseasonal convective spells are predicted well, especially the long midseason break of 2002 that resulted in large-scale drought conditions. Skillful predictions can be made up to five pentads when started from an active initial state, whereas the limit of useful predictions is about two–three pentads when started from break initial conditions. An important feature of this method is that unlike some other empirical methods to forecast monsoon ISOs, it uses minimal time filtering to avoid any possible endpoint effects and hence may be readily used for real-time applications. Moreover, as the modeling data grow with time as a result of the increased number of observations, the number of analogs would also increase and eventually the quality of forecasts would improve.

scholarly journals On the emergence of random initial conditions in fluid limits

2016 ◽  
Vol 53 (4) ◽  
pp. 1193-1205 ◽  
Author(s):  
A. D. Barbour ◽  
P. Chigansky ◽  
F. C. Klebaner
Keyword(s):  
Carrying Capacity ◽  
Classical Result ◽  
Initial Conditions ◽  
Death Process ◽  
Initial Population ◽  
Random Initial Condition ◽  
Initial Condition ◽  
Birth And Death Process ◽  
Fluid Limit ◽  
Random Initial Conditions

Abstract In the paper we present a phenomenon occurring in population processes that start near 0 and have large carrying capacity. By the classical result of Kurtz (1970), such processes, normalized by the carrying capacity, converge on finite intervals to the solutions of ordinary differential equations, also known as the fluid limit. When the initial population is small relative to the carrying capacity, this limit is trivial. Here we show that, viewed at suitably chosen times increasing to ∞, the process converges to the fluid limit, governed by the same dynamics, but with a random initial condition. This random initial condition is related to the martingale limit of an associated linear birth-and-death process.

scholarly journals Transients from initial conditions based on Lagrangian perturbation theory in N-body simulations III: The case of Gadget-2 code

2020 ◽  
Vol 29 (15) ◽  
pp. 2050096
Author(s):  
Takayuki Tatekawa
Keyword(s):  
Perturbation Theory ◽  
Theoretical Prediction ◽  
Initial Conditions ◽  
Higher Order ◽  
Matter Density ◽  
Density Field ◽  
Third Order ◽  
Modern Cosmology ◽  
Different Order ◽  
Higher Order Lagrangian

In modern cosmology, the precision of the theoretical prediction is increasingly required. In cosmological [Formula: see text]-body simulations, the effect of higher-order Lagrangian perturbation on the initial conditions appears in terms of statistical quantities of matter density field. We have considered the effect of third-order Lagrangian perturbation theory (3LPT) on the initial conditions, which can be applied to Gadget-2 code. Then, as statistical quantities, non-Gaussianity of matter density field has been compared between cases of different order perturbations for the initial conditions. Then, we demonstrate the validity of the initial conditions with second-order Lagrangian perturbation theory (2LPT).

Is it a Right Assumption That B and Ge are Distributed Randomly After Growing a Strained HBT-Structure?

2002 ◽  
Vol 716 ◽  
Author(s):  
Victor I. Kol'dyaev
Keyword(s):  
Surface Segregation ◽  
Initial Conditions ◽  
Initial Condition ◽  
Basic Assumptions ◽  
Transient Diffusion ◽  
Segregation Process ◽  
Main Observation

AbstractIt is accepted that surface Ge atoms are considered to be responsible for the surface B segregation process. A set of original experiments is carried out. A main observation from the B and Ge profiles grown at different conditions shows that at certain conditions B is taking initiative and determine the Ge surface segregation process. basic assumptions are suggested to self-consistently explain these original experimental features and what is observed in the literature. These results have a strong implication for modeling the B diffusion in Si1-xGex where the initial conditions should be formulated accounting for the correlation in B and Ge distribution. A new assumption for the initial condition to be “all B atoms are captured by Ge” is regarded as a right one implicating that there is no any transient diffusion representing the B capturing kinetics.

scholarly journals Shell-crossing in a ΛCDM Universe

2020 ◽  
Vol 501 (1) ◽  
pp. L71-L75
Author(s):  
Cornelius Rampf ◽  
Oliver Hahn
Keyword(s):  
Dark Matter ◽  
Perturbation Theory ◽  
Large Scale ◽  
Cold Dark Matter ◽  
Three Dimensional ◽  
Random Initial Data ◽  
Recursion Relations ◽  
Indispensable Tool ◽  
First Time ◽  
Very High

ABSTRACT Perturbation theory is an indispensable tool for studying the cosmic large-scale structure, and establishing its limits is therefore of utmost importance. One crucial limitation of perturbation theory is shell-crossing, which is the instance when cold-dark-matter trajectories intersect for the first time. We investigate Lagrangian perturbation theory (LPT) at very high orders in the vicinity of the first shell-crossing for random initial data in a realistic three-dimensional Universe. For this, we have numerically implemented the all-order recursion relations for the matter trajectories, from which the convergence of the LPT series at shell-crossing is established. Convergence studies performed at large orders reveal the nature of the convergence-limiting singularities. These singularities are not the well-known density singularities at shell-crossing but occur at later times when LPT already ceased to provide physically meaningful results.

scholarly journals Solving nonlinear third-order three-point boundary value problems by boundary shape functions methods

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ji Lin ◽  
Yuhui Zhang ◽  
Chein-Shan Liu
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Initial Conditions ◽  
Boundary Value ◽  
Accurate Solution ◽  
Point Boundary ◽  
Third Order ◽  
Boundary Shape ◽  
Free Function ◽  
New Algorithms

AbstractFor nonlinear third-order three-point boundary value problems (BVPs), we develop two algorithms to find solutions, which automatically satisfy the specified three-point boundary conditions. We construct a boundary shape function (BSF), which is designed to automatically satisfy the boundary conditions and can be employed to develop new algorithms by assigning two different roles of free function in the BSF. In the first algorithm, we let the free functions be complete functions and the BSFs be the new bases of the solution, which not only satisfy the boundary conditions automatically, but also can be used to find solution by a collocation technique. In the second algorithm, we let the BSF be the solution of the BVP and the free function be another new variable, such that we can transform the BVP to a corresponding initial value problem for the new variable, whose initial conditions are given arbitrarily and terminal values are determined by iterations; hence, we can quickly find very accurate solution of nonlinear third-order three-point BVP through a few iterations. Numerical examples confirm the performance of the new algorithms.

scholarly journals The axion-baryon coupling in SU(3) heavy baryon chiral perturbation theory

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Thomas Vonk ◽  
Feng-Kun Guo ◽  
Ulf-G. Meißner
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Heavy Baryon ◽  
Power Counting ◽  
Flavor Symmetry ◽  
Chiral Perturbation ◽  
Third Order ◽  
Stellar Objects ◽  
The Past ◽  
Dense Nuclear Matter

Abstract In the past, the axion-nucleon coupling has been calculated in the framework of SU(2) heavy baryon chiral perturbation theory up to third order in the chiral power counting. Here, we extend these earlier studies to the case of heavy baryon chiral perturbation theory with SU(3) flavor symmetry and derive the axion coupling to the full SU(3) baryon octet, showing that the axion also significantly couples to hyperons. As studies on dense nuclear matter suggest the possible existence of hyperons in stellar objects such as neutron stars, our results should have phenomenological implications related to the so-called axion window.

scholarly journals The anisotropy of the power spectrum in periodic cosmological simulations

2021 ◽  
Vol 503 (4) ◽  
pp. 5638-5645
Author(s):  
Gábor Rácz ◽  
István Szapudi ◽  
István Csabai ◽  
László Dobos
Keyword(s):  
Dark Matter ◽  
Power Spectrum ◽  
Large Scale ◽  
Cold Dark Matter ◽  
Initial Conditions ◽  
Power Spectra ◽  
Cosmological Simulations ◽  
Spherical Collapse ◽  
Lower Amplitude ◽  
Hydrodynamical Simulations

ABSTRACT The classical gravitational force on a torus is anisotropic and always lower than Newton’s 1/r2 law. We demonstrate the effects of periodicity in dark matter only N-body simulations of spherical collapse and standard Lambda cold dark matter (ΛCDM) initial conditions. Periodic boundary conditions cause an overall negative and anisotropic bias in cosmological simulations of cosmic structure formation. The lower amplitude of power spectra of small periodic simulations is a consequence of the missing large-scale modes and the equally important smaller periodic forces. The effect is most significant when the largest mildly non-linear scales are comparable to the linear size of the simulation box, as often is the case for high-resolution hydrodynamical simulations. Spherical collapse morphs into a shape similar to an octahedron. The anisotropic growth distorts the large-scale ΛCDM dark matter structures. We introduce the direction-dependent power spectrum invariant under the octahedral group of the simulation volume and show that the results break spherical symmetry.

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