Lagrangian Acceleration Research Articles

Mock observatory: Two thousand light-cone mock catalogues of luminous red galaxies from the Hyper Suprime-Cam Survey for the cosmological large-scale analysis

ABSTRACT Estimating a reliable covariance matrix for correlation functions of galaxies is a crucial task to obtain accurate cosmological constraints from galaxy surveys. We generate 2000 independent light-cone mock luminous red galaxy (LRGs) catalogues at 0.3 ≤ z ≤ 1.25, designed to cover CAMIRA LRGs observed by the Subaru Hyper Suprime-Cam Subaru Strategic Programme (HSC SSP). We first produce full-sky light-cone halo catalogues using a COmoving Lagrangian Acceleration (COLA) technique, and then trim them to match the footprints of the HSC SSP S20A Wide layers. The mock LRGs are subsequently populated on to the trimmed halo catalogues according to the halo occupation distribution model constrained by the observed CAMIRA LRGs. The stellar mass (M⋆) is assigned to each LRG by the subhalo abundance-matching technique using the observed stellar-mass functions of CAMIRA LRGs. We evaluate photometric redshifts (photo-z) of mock LRGs by incorporating the photo-z scatter, which is derived from the observed M⋆–photo-z-scatter relations of the CAMIRA LRGs. We validate the constructed full-sky halo and light-cone LRG mock catalogues by comparing their angular clustering statistics (i.e. power spectra and correlation functions) with those measured from the halo catalogues of full N-body simulations and the CAMIRA LRG catalogues from the HSC SSP, respectively. We detect clear signatures of baryon acoustic oscillations (BAOs) from our mock LRGs, whose angular scales are well consistent with theoretical predictions. These results demonstrate that our mock LRGs can be used to evaluate covariance matrices at large scales and provide predictions for the BAO detectability and cosmological constraints.

Fast Generation of Mock Galaxy Catalogs with COLA

We investigate the feasibility of using the comoving Lagrangian acceleration (COLA) technique to efficiently generate galaxy mock catalogs that can accurately reproduce the statistical properties of observed galaxies. Our proposed scheme combines the subhalo abundance-matching (SHAM) procedure with COLA simulations, using only three free parameters: the scatter magnitude (σ scat) in SHAM, the initial redshift (z init) of the COLA simulation, and the time stride (da) used by COLA. In this proof-of-concept study, we focus on a subset of BOSS CMASS NGC galaxies within the redshift range z ∈ [0.45, 0.55]. We perform GADGET simulation and low-resolution COLA simulations with various combinations of (z init, da), each using 10243 particles in an 800 h −1 Mpc box. By minimizing the difference between COLA mock and CMASS NGC galaxies for the monopole of the two-point correlation function (2PCF), we obtain the optimal σ scat. We have found that by setting z init = 29 and da = 1/30, we achieve a good agreement between COLA mock and CMASS NGC galaxies within the range of 4–20 h −1 Mpc, with a computational cost lower by 2 orders of magnitude than that of the GADGET N-body code. Moreover, a detailed verification is performed by comparing various statistical properties, such as anisotropic 2PCF, three-point clustering, and power spectrum multipoles, which shows a similar performance of the GADGET mock and COLA mock catalogs with the CMASS NGC galaxies. Furthermore, we assess the robustness of the COLA mock catalogs for different cosmological models, demonstrating consistent results in the resulting 2PCFs. Our findings suggest that COLA simulations are a promising tool for efficiently generating mock catalogs for emulators and machine-learning analyses to explore the large-scale structure of the Universe.

The Role of Particle Inertia and Thermal Inertia in Heat Transfer in a Non-Isothermal Particle-Laden Turbulent Flow

We present an analysis of the effect of particle inertia and thermal inertia on the heat transfer in a turbulent shearless flow, where an inhomogeneous passive temperature field is advected along with inertial point particles by a homogeneous isotropic velocity field. Eulerian–Lagrangian direct numerical simulations are carried out in both one- and two-way coupling regimes and analyzed through single-point statistics. The role of particle inertia and thermal inertia is discussed by introducing a new decomposition of particle second-order moments in terms of correlations involving Lagrangian acceleration and time derivative of particles. We present how particle relaxation times mediate the level of particle velocity–temperature correlation, which gives particle contribution to the overall heat transfer. For each thermal Stokes number, a critical Stokes number is individuated. The effect of particle feedback on the attenuation or enhancement of fluid temperature variance is presented. We show that particle feedback enhances fluid temperature variance for Stokes numbers less than one and damps is for larger than one Stokes number, regardless of the thermal Stokes number, even if this effect is amplified by an increasing thermal inertia.

A universal scaling law for Lagrangian snowflake accelerations in atmospheric turbulence

We use a novel experimental setup to obtain the vertical velocity and acceleration statistics of snowflakes settling in atmospheric surface-layer turbulence, for Taylor microscale Reynolds numbers (Reλ) between 400 and 67 000, Stokes numbers (St) between 0.12 and 3.50, and a broad range of snowflake habits. Despite the complexity of snowflake structures and the non-uniform nature of the turbulence, we find that mean snowflake acceleration distributions can be uniquely determined from the value of St. Ensemble-averaged snowflake root mean square (rms) accelerations scale nearly linearly with St. Normalized by the rms value, the acceleration distribution is nearly exponential, with a scaling factor for the (exponent) of −3/2 that is independent of Reλ and St; kurtosis scales with Reλ, albeit weakly compared to fluid tracers in turbulence; gravitational drift with sweeping is observed for St < 1. Surprisingly, the same exponential distribution describes a pseudo-acceleration calculated from fluctuations of snowflake terminal fall speed in still air. This equivalence suggests an underlying connection between how turbulence determines the trajectories of particles and the microphysics determining the evolution of their shapes and sizes.

Fast production of cosmological emulators in modified gravity: the matter power spectrum

We test the convergence of fast simulations based on the COmoving Lagrangian Acceleration (COLA) method for predictions of the matter power spectrum, specialising our analysis in the redshift range 1 ≤ z ≤ 1.65, relevant to high-redshift spectroscopic galaxy surveys. We then focus on the enhancement of the matter power spectrum in modified gravity (MG), the boost factor, using the Dvali-Gabadadze-Porrati (DGP) theory as a test case but developing a general approach that can be applied to other MG theories. After identifying the minimal simulation requirements for accurate DGP boost factors, we design and produce a COLA simulation suite that we use to train a neural network emulator for the DGP boost factor. Using MG-AREPO simulations as a reference, we estimate the emulator accuracy to be of ∼ 3% up to k = 5 h Mpc-1 at 0 ≤ z ≤ 2. We make the emulator publicly available at: https://github.com/BartolomeoF/nDGPemu.

Saturation and Multifractality of Lagrangian and Eulerian Scaling Exponents in Three-Dimensional Turbulence.

Inertial-range scaling exponents for both Lagrangian and Eulerian structure functions are obtained from direct numerical simulations of isotropic turbulence in triply periodic domains at Taylor-scale Reynolds number up to 1300. We reaffirm that transverse Eulerian scaling exponents saturate at ≈2.1 for moment orders p≥10, significantly differing from the longitudinal exponents (which are predicted to saturate at ≈7.3 for p≥30 from a recent theory). The Lagrangian scaling exponents likewise saturate at ≈2 for p≥8. The saturation of Lagrangian exponents and transverse Eulerian exponents is related by the same multifractal spectrum by utilizing the well-known frozen hypothesis to relate spatial and temporal scales. Furthermore, this spectrum is different from the known spectra for Eulerian longitudinal exponents, suggesting that Lagrangian intermittency is characterized solely by transverse Eulerian intermittency. We discuss possible implications of this outlook when extending multifractal predictions to the dissipation range, especially for Lagrangian acceleration.

Field-level Neural Network Emulator for Cosmological N-body Simulations

We build a field-level emulator for cosmic structure formation that is accurate in the nonlinear regime. Our emulator consists of two convolutional neural networks trained to output the nonlinear displacements and velocities of N-body simulation particles based on their linear inputs. Cosmology dependence is encoded in the form of style parameters at each layer of the neural network, enabling the emulator to effectively interpolate the outcomes of structure formation between different flat Lambda cold dark matter cosmologies over a wide range of background matter densities. The neural network architecture makes the model differentiable by construction, providing a powerful tool for fast field-level inference. We test the accuracy of our method by considering several summary statistics, including the density power spectrum with and without redshift space distortions, the displacement power spectrum, the momentum power spectrum, the density bispectrum, halo abundances, and halo profiles with and without redshift space distortions. We compare these statistics from our emulator with the full N-body results, the COmoving Lagrangian Acceleration (COLA) method, and a fiducial neural network with no cosmological dependence. We find that our emulator gives accurate results down to scales of k ∼ 1 Mpc−1 h, representing a considerable improvement over both COLA and the fiducial neural network. We also demonstrate that our emulator generalizes well to initial conditions containing primordial non-Gaussianity without the need for any additional style parameters or retraining.

Lagrangian acceleration and its Eulerian decompositions in fully developed turbulence

We study the properties of various Eulerian contributions to fluid particle acceleration by using well-resolved direct numerical simulations of isotropic turbulence, with the grid resolution as high as $12288^3$ and the Taylor-scale Reynolds number $R_\lambda$ in the range between 140 and 1300. The variance of convective acceleration, when normalized by Kolmogorov scales, increases linearly with $R_\lambda$, consistent with simple theoretical arguments, but very strongly differing from phenomenological predictions of Kolmogorov's hypothesis as well as Eulerian multifractal models. The scaling of the local acceleration is also linear $R_\lambda$ to the leading order, but more complex in detail. The strong cancellation between the local and convective acceleration -- faithful to the random sweeping hypothesis -- results in the variance of the Lagrangian acceleration increasing only as $R_\lambda^{0.25}$, as recently shown by Buaria \& Sreenivasan [Phys. Rev. Lett. 128, 234502 (2022)]. The acceleration variance is dominated by irrotational pressure gradient contributions, whose variance also follows an $R_\lambda^{0.25}$ scaling; the solenoidal viscous contributions are relatively small and follow a $R_\lambda^{0.13}$, consistent with Eulerian multifractal predictions.

Resolution tests for ΛCDM: A comparison of three cosmological codes

AbstractWe present a series of resolution tests of the Modified Gravity‐Parallel Implementation of the Comoving Lagrangian Acceleration method (MG‐PICOLA) code for the Λ Cold Dark Matter (ΛCDM) model. The tests are a previous step in the analysis of modified gravity models implemented in the code. We measure the non‐linear matter power spectrum of the model and compare it with the prediction obtained with the Boltzmann code CLASS. We also compare the mass power spectrum with results from another N‐body simulation code, Modified Gravity GaLAxy Mocks (MG‐GLAM), to obtain information on the capabilities and performance of MG‐PICOLA for the optimal values of its input parameters.

Some aspects of the pressure field preceding the onset of critical jets in a breaking wave

We consider in this article two-dimensional nonlinear free surface motions in potential theory. There are situations where the onset of critical jet along a free surface can be predicted by analyzing the temporal and spatial variation of the pressure itself and its successive derivatives. In particular, when a local maximum of pressure appears close enough to a free surface where the pressure vanishes, it is expected a great pressure gradient at the free surface and consequently a large Lagrangian acceleration. The present analysis examines this phenomenon. This analysis is facilitated after identifying a line along which the pressure gradient is parallel to one of the eigenvectors of the Hessian matrix of the pressure. In a standard overturning crest, this line connects the tip of the crest to the bottom of the tank in which the flow is simulated. The analysis of its time evolution gives much information into the onset of critical jets. Other types of critical jet can also appear when a region of positive Gaussian curvature of the pressure suddenly grows in the vicinity of the free surface.

Simple lessons from complex learning: what a neural network model learns about cosmic structure formation.

We train a neural network model to predict the full phase space evolution of cosmological N-body simulations. Its success implies that the neural network model is accurately approximating the Green's function expansion that relates the initial conditions of the simulations to its outcome at later times in the deeply nonlinear regime. We test the accuracy of this approximation by assessing its performance on well-understood simple cases that have either known exact solutions or well-understood expansions. These scenarios include spherical configurations, isolated plane waves, and two interacting plane waves: initial conditions that are very different from the Gaussian random fields used for training. We find our model generalizes well to these well-understood scenarios, demonstrating that the networks have inferred general physical principles and learned the nonlinear mode couplings from the complex, random Gaussian training data. These tests also provide a useful diagnostic for finding the model's strengths and weaknesses, and identifying strategies for model improvement. We also test the model on initial conditions that contain only transverse modes, a family of modes that differ not only in their phases but also in their evolution from the longitudinal growing modes used in the training set. When the network encounters these initial conditions that are orthogonal to the training set, the model fails completely. In addition to these simple configurations, we evaluate the model's predictions for the density, displacement, and momentum power spectra with standard initial conditions for N-body simulations. We compare these summary statistics against N-body results and an approximate, fast simulation method called COLA (COmoving Lagrangian Acceleration). Our model achieves percent level accuracy at nonlinear scales of , representing a significant improvement over COLA.

Dynamics of plosive consonants via imaging, computations, and soft electronics

A quantitative understanding of the coupled dynamics of flow and particles in aerosol and droplet transmission associated with speech remains elusive. Here, we summarize an effort that integrates insights into flow-particle dynamics induced by the production plosive sounds during speech with skin-integrated electronic systems for monitoring the production of these sounds. In particular, we uncover diffusive and ballistic regimes separated by a threshold particle size and characterize the Lagrangian acceleration and pair dispersion. Lagrangian dynamics of the particles in the diffusive regime exhibit features of isotropic turbulence. These fundamental findings highlight the value in skin-interfaced wireless sensors for continuously measuring critical speech patterns in clinical settings, work environments, and the home, based on unique neck biomechanics associated with the generation of plosive sounds. We introduce a wireless, soft device that captures these motions to enable detection of plosive sounds in multiple languages through a convolutional neural network approach. This work spans fundamental flow-particle physics to soft electronic technology, with implications in monitoring and studying critical speech patterns associated with aerosol and droplet transmissions relevant to the spread of infectious diseases.

Lagrangian conditional statistics and flow topology in edge plasma turbulence

Lagrangian statistics and particle transport in edge plasma turbulence are investigated using the Hasegawa–Wakatani model and its modified version. The latter shows the emergence of pronounced zonal flows. Different values of the adiabaticity parameter are considered. The main goal is to characterize the role of coherent structures, i.e., vortices and zonal flows, and their impact on the Lagrangian statistics of particles. Computationally intensive long time simulations following ensembles of test particles over hundreds of eddy turnover times are considered in statistically stationary turbulent flows. The flow topology is characterized using the Lagrangian Okubo–Weiss criterion in order to split the flow into topologically different domains. In elliptic and hyperbolic regions, the probability density functions (PDFs) of the residence time have self-similar algebraic decaying tails. However, in the intermediate regions, the PDFs exhibit exponentially decaying tails. Topologically conditioned PDFs of the Lagrangian velocity, and acceleration and density fluctuations are likewise computed. The differences between the classical Hasegawa–Wakatani system and its modified version are assessed, and the role of zonal flows is highlighted. The density flux spectrum, which characterizes the contributions of different length scales, is studied, and its inertial scaling is found to be in agreement with predictions based on dimensional arguments. Analyzing the angular change of particle tracers at different time scales, corresponding to coarse grained curvature, completes the study, and these multiscale geometric statistics quantify the directional properties of the particle motion in different flow regimes.

Clustering in laboratory and numerical turbulent swirling flows

We study the three-dimensional clustering of velocity stagnation points, of nulls of the vorticity and of the Lagrangian acceleration, and of inertial particles in turbulent flows at fixed Reynolds numbers, but under different large-scale flow geometries. To this end, we combine direct numerical simulations of homogeneous and isotropic turbulence and of the Taylor–Green flow, with particle tracking velocimetry in a von Kármán experiment. While flows have different topologies (as nulls cluster differently), particles behave similarly in all cases, indicating that Taylor-scale neutrally buoyant particles cluster as inertial particles.

A generalized weak-scatterer approximation for nonlinear wave–structure interaction in marine hydrodynamics

In this paper, a generalized weak-scatterer (GWS) approximation is proposed for solving nonlinear wave–structure interaction problems. In contrast to the original weak-scatterer (OWS) theory, where the approximated free surface boundary conditions (FSBCs) are Taylor-expanded in the vertical direction from the incident wave surface, we apply Taylor series expansion in an arbitrary direction which, in particular, is tangential to the boundary of the floating structure close to the waterline. This leads to generalized kinematic and dynamic FSBCs for the radiated and scattered waves, along with corresponding expressions of the wave loads. Accordingly, an Arbitrary Lagrangian–Eulerian (ALE) approach is adopted to track the free-surface properties. The new GWS method is more consistent than the OWS model in that the wave markers do not separate from the body surface at the waterline for structures with flare. An Immersed-Boundary Adaptive Harmonic Polynomial Cell (IB-AHPC) method is implemented to solve the corresponding boundary value problems (BVPs) for both the velocity potential and the Lagrangian acceleration potential at each time step. The new formulation introduces additional convective terms in the FSBCs, making them similar to the seakeeping problems for ships with forward speed, and this requires special treatment to avoid instability in the time-domain simulations. Based on a matrix-based eigenvalue stability analysis, we illustrate that stable solutions can be achieved by introducing an upwind-biased scheme to discretize the convective terms in the kinematic FSBC. The proposed model is verified by three wave diffraction problems in regular waves, including a submerged circular cylinder, a rounded-corner rectangular ship section, and a trapezoidal section with a large flare angle.

Enabling matter power spectrum emulation in beyond-ΛCDM cosmologies with COLA

We compare and validate COLA (COmoving Lagrangian Acceleration) simulations against existing emulators in the literature, namely Bacco and Euclid Emulator 2. Our analysis focuses on the non-linear response function, i.e., the ratio between the non-linear dark matter power spectrum in a given cosmology with respect to a pre-defined reference cosmology, which is chosen to be the Euclid Emulator 2 reference cosmology in this paper. We vary three cosmological parameters, the total matter density, the amplitude of the primordial scalar perturbations and the spectral index.By comparing the COLA non-linear response function with those computed from each emulator in the redshift range 0 ≤ z ≤ 3, we find that the COLA method is in excellent agreement with the two emulators for scales up to k ∼ 1 h/Mpc as long as the deviations of the matter power spectrum from the reference cosmology are not too large.We validate the implementation of massive neutrinos in our COLA simulations by varying the sum of neutrino masses to three different values, 0.0 eV, 0.058 eV and 0.15 eV.We show that all three non-linear prescriptions used in this work agree at the 1% level at k ≤ 1 h/Mpc. We then introduce the Effective Field Theory of Dark Energy in our COLA simulations using the N-body gauge method. We consider two different modified gravity models in which the growth of structure is enhanced or suppressed at small scales, and show that the response function with respect to the change of modified gravity parameters depends weakly on cosmological parameters in these models.

Dynamics of towed particles in a turbulent flow

We present an experimental study exploring the dynamics of inertial spheres towed at a constant mean velocity in a turbulent flow. Our work focuses on finite size particles, in the sense that their diameter is significantly larger than the dissipation scale and lies in the range of inertial scales of the background turbulence. Our experimental setup allows to register the Lagrangian velocity and acceleration of particles with different diameters, densities and free-stream velocities. The analysis of towed particles dynamics shows a clear trend of velocity and acceleration fluctuations to be reduced with increasing particle inertia, while acceleration fluctuations are found to be Gaussian, at odds of usual results for finite-size freely advected particles. Besides, the multi-scale spectral dynamics of the particle is shown to be related to that of the background turbulence by a linear second-order band-pass transfer function. We analyse this behaviour at the light of a simple model where the coupling between the particle and the flow is entirely attributed to the drag force, a usual approach for dense point-like particles freely-advected in a turbulent flow, which is known however to fail predicting the transport of freely advected finite-size particles. We show that this drag-dominated model quantitatively predicts the dynamics of finite size towed particles, simply requiring to tune the effective particle response time. This suggests that, contrary to the case of freely advected finite size inertial particles, the towing configuration efficiently emphasises the actual role of the drag force by imposing it as an unambiguous leading term in towed particle/turbulence interactions.

Measurements Of The Energy Dissipation Rate In Homogeneous Turbulence Using Dense 3D Lagrangian Particle Tracking And FlowFit

We present measurements of the full velocity gradient tensor and all volumetric dissipation rate elements based on dense fields of fluid particle trajectories in homogeneous turbulence at Re_λ~270 and ~370 in a Kármán flow between two counter-rotating disks with impellers. Applying the Shake-The-Box (STB) Lagrangian Particle Tracking (LPT) algorithm, we are able to instantaneously track up to 80.000 particles in a volume of 40 x 40 x 15 mm³. The mean interparticle distance is lower than 7 Kolmogorov lengths for the Re_λ ~270 case. A data assimilation scheme (FlowFit) with continuity and Navier-Stokes- constraints is used to interpolate the scattered velocity and acceleration data by a continuous 3D B-Spline representation, enabling to recover (locally) the smallest flow scales. In the presentation, we show Lagrangian velocity and acceleration statistics, as well as the Eulerian counterparts on velocity gradients and pressure fields. We compute the energy dissipation rate directly by making use of quadruples of particle trajectories in close proximity (r < 3η) and compare it to indirect approaches using second-order velocity- and velocityacceleration structure functions in the inertial subrange.

Lagrangian sensors in a stirred tank reactor: Comparing trajectories from 4D-Particle Tracking Velocimetry and Lattice-Boltzmann simulations

In this study, three-dimensional flow measurements by means of 4D-Particle Tracking Velocimetry (4D-PTV) are carried out in a laboratory-scale 3 L stirred tank reactor in order to investigate the flow-following behavior of two different inertial particle types, Polyethylene (PE) particles and alginate beads, at different impeller frequencies. Applied particles mimic Lagrangian sensor particles, which are intended to determine process parameters such as oxygen concentration at their corresponding position inside a bioreactor. Accompanying Lattice-Boltzmann Large Eddy Simulations (LB LES) provide additional information about the fluid flow and the difference in the trajectories between inertial and non-inertial particles. The data acquired from LB LES is validated with the experimental data by means of a Lagrangian and a Eulerian approach. In their tail, the probability distributions show higher Lagrangian velocities and accelerations for 4D-PTV data compared to LB LES data. Time-averaged Eulerian data is utilized to determine particle Reynolds numbers lower than 200. The Stokes number distributions show 10-fold higher values for the alginate beads than for PE particles, however, both particle types do not sufficiently meet the criterion of a flow-following Stokes number of St≤0.01. Generally, time-averaged results from LB LES are in good accordance to the 4D-PTV data. From the LB LES, a theoretical, maximum particle diameter of approx. 20 μm is determined, which meets the criterion of St≤0.01 throughout the reactor. This result implies that with current sensor particle technology it is not possible to meet the flow-following behavior and depict the lifelines of cells during a cultivation process. Therefore, further research is necessary to understand particle trajectories and to translate them into lifelines of cells.

Simulating Lagrangian Subgrid-Scale Dispersion on Neutral Surfaces in the Ocean.

To capture the effects of mesoscale turbulent eddies, coarse‐resolution Eulerian ocean models resort to tracer diffusion parameterizations. Likewise, the effect of eddy dispersion needs to be parameterized when computing Lagrangian pathways using coarse flow fields. Dispersion in Lagrangian simulations is traditionally parameterized by random walks, equivalent to diffusion in Eulerian models. Beyond random walks, there is a hierarchy of stochastic parameterizations, where stochastic perturbations are added to Lagrangian particle velocities, accelerations, or hyper‐accelerations. These parameterizations are referred to as the first, second and third order “Markov models” (Markov‐N), respectively. Most previous studies investigate these parameterizations in two‐dimensional setups, often restricted to the ocean surface. On the other hand, the few studies that investigated Lagrangian dispersion parameterizations in three dimensions, where dispersion is largely restricted to neutrally buoyant surfaces, have focused only on random walk (Markov‐0) dispersion. Here, we present a three‐dimensional isoneutral formulation of the Markov‐1 model. We also implement an anisotropic, shear‐dependent formulation of random walk dispersion, originally formulated as a Eulerian diffusion parameterization. Random walk dispersion and Markov‐1 are compared using an idealized setup as well as more realistic coarse and coarsened (50 km) ocean model output. While random walk dispersion and Markov‐1 produce similar particle distributions over time when using our ocean model output, Markov‐1 yields Lagrangian trajectories that better resemble trajectories from eddy‐resolving simulations. Markov‐1 also yields a smaller spurious dianeutral flux.