Covariant decomposition of the non-linear galaxy number counts and their monopole

We present a fully non-linear and relativistically covariant expression for the observed galaxy density contrast. Building on a null tetrad tailored to the cosmological observer's past light cone, we find a decomposition of the non-linear galaxy over-density into manifestly gauge-invariant quantities, each of which has a clear physical interpretation as a cosmological observable. This ensures that the monopole of the galaxy over-density field (the mean galaxy density as a function of observed redshift) is properly accounted for. We anticipate that this decomposition will be useful for future work on non-linearities in galaxy number counts, for example, deriving the relativistic expression for the galaxy bispectrum. We then specialise our results to conformal Newtonian gauge, with a Hubble parameter either defined globally or measured locally, illustrating the significance of the different contributions to the observed monopole of the galaxy density.

Generalized Transport Equation of The Autocovariance Function of the Density Field and Mass Invariant in Star-forming Clouds

In this Letter, we study the evolution of the autocovariance function of density-field fluctuations in star-forming clouds and thus of the correlation length l c (ρ) of these fluctuations, which can be identified as the average size of the most correlated structures within the cloud. Generalizing the transport equation derived by Chandrasekhar for static, homogeneous turbulence, we show that the mass contained within these structures is an invariant, i.e., that the average mass contained in the most correlated structures remains constant during the evolution of the cloud, whatever dominates the global dynamics (gravity or turbulence). We show that the growing impact of gravity on the turbulent flow yields an increase of the variance of the density fluctuations and thus a drastic decrease of the correlation length. Theoretical relations are successfully compared to numerical simulations. This picture brings a robust support to star formation paradigms where the mass concentration in turbulent star-forming clouds evolves from initially large, weakly correlated filamentary structures to smaller, denser, more correlated ones, and eventually to small, tightly correlated, prestellar cores. We stress that the present results rely on a pure statistical approach of density fluctuations and do not involve any specific condition for the formation of prestellar cores. Interestingly enough, we show that, under average conditions typical of Milky-Way molecular clouds, this invariant average mass is about a solar mass, providing an appealing explanation for the apparent universality of the IMF in such environments.

Gaussianization of peculiar velocities and bulk flow measurement

The line-of-sight peculiar velocities are good indicators of the gravitational fluctuation of the density field. Techniques have been developed to extract cosmological information from the peculiar velocities in order to test cosmological models. These techniques include measuring cosmic flow, measuring two-point correlation and power spectrum of the peculiar velocity fields, and reconstructing the density field using peculiar velocities. However, some measurements from these techniques are biased due to the non-Gaussianity of the estimated peculiar velocities. Therefore, we rely on the 2MTF survey to explore a power transform that can Gaussianize the estimated peculiar velocities. We find a tight linear relation between the transformation parameters and the measurement errors of log-distance ratio. To show an example for the implementation of Gaussianized peculiar velocities in cosmology, we develop a bulk flow estimator and estimate bulk flow from the Gaussianized peculiar velocities. We use 2MTF mocks to test the algorithm, and we find the algorithm yields unbiased measurements. We also find this technique gives smaller measurement errors compared to other techniques. In Galactic coordinates, at the depth of 30 h −1 Mpc, we measure a bulk flow of 332 ± 27 km s−1 in the direction (l,b) = (293° ± 5°, 13° ± 4°). The measurement is consistent with the ΛCDM prediction.

Role of air–sea fluxes and ocean surface density in the production of deep waters in the eastern subpolar gyre of the North Atlantic

Wintertime convection in the North Atlantic Ocean is a key component of the global climate as it produces dense waters at high latitudes that flow equatorward as part of the Atlantic Meridional Overturning Circulation (AMOC). Recent work has highlighted the dominant role of the Irminger and Iceland basins in the production of North Atlantic Deep Water. Dense water formation in these basins is mainly explained by buoyancy forcing that transforms surface waters to the deep waters of the AMOC lower limb. Air–sea fluxes and the ocean surface density field are both key determinants of the buoyancy-driven transformation. We analyze these contributions to the transformation in order to better understand the connection between atmospheric forcing and the densification of surface water. More precisely, we study the impact of air–sea fluxes and the ocean surface density field on the transformation of subpolar mode water (SPMW) in the Iceland Basin, a water mass that “pre-conditions” dense water formation downstream. Analyses using 40 years of observations (1980–2019) reveal that the variance in SPMW transformation is mainly influenced by the variance in density at the ocean surface. This surface density is set by a combination of advection, wind-driven upwelling and surface fluxes. Our study shows that the latter explains ∼ 30 % of the variance in outcrop area as expressed by the surface area between the outcropped SPMW isopycnals. The key role of the surface density in SPMW transformation partly explains the unusually large SPMW transformation in winter 2014–2015 over the Iceland Basin.

Coupling Moving Morphable Voids and Components Based Topology Optimization of Hydrogel Structures Involving Large Deformation

A coupling of moving morphable void and component approach for the topology optimization of hydrogel structures involving recoverable large deformation is proposed in this paper. In this approach, the geometric parameters of moving morphable voids and components are set as design variables to respectively describe the outline and material distribution of hydrogel structures for the first time. To facilitate the numerical simulation of large deformation behavior of hydrogel structures during the optimization process, the design variables are mapped to the density field of the design domain and the density field is then used to interpolate the strain energy density function of the element. Furthermore, the adjoint sensitivity of the optimization formulation is derived and combined with the gradient-based algorithm to solve the topology optimization problem effectively. Finally, two representative numerical examples of the optimization of isotropic hydrogel structures are used to prove the effectiveness of the proposed method, and the optimization design of an anisotropic bionic hydrogel structure is presented to illustrate the applicability of the method. Experimental results are also presented to demonstrate that the explicit topologies obtained from the method can be directly used in the manufacture of hydrogel-based soft devices.

Coupled topology and shape optimization using an embedding domain discretization method

Density-based topology optimization and node-based shape optimization are often used sequentially to generate production-ready designs. In this work, we address the challenge to couple density-based topology optimization and node-based shape optimization into a single optimization problem by using an embedding domain discretization technique. In our approach, a variable shape is explicitly represented by the boundary of an embedded body. Furthermore, the embedding domain in form of a structured mesh allows us to introduce a variable, pseudo-density field. In this way, we attempt to bring the advantages of both topology and shape optimization methods together and to provide an efficient way to design fine-tuned structures without predefined topological features.

Three-dimensional density measurements of a heated jet using laser-speckle tomographic background-oriented schlieren

Three-dimensional density field measurement techniques can be used to understand the complex heat transfer and mixing processes that occur in turbulent flows. Tomographic background-oriented schlieren (BOS) is an optical technique that can be used to measure the instantaneous three-dimensional density field in turbulent flows. Light rays propagating through the flow are deflected from their ambient path due to variations in refractive index related to the spatial density gradients. In BOS, a camera is placed looking through the flow at a reference image, which captures path-integrated information on the refractive index gradients in the form of apparent image displacements Richard and Raffel (2001). The displacements recorded simultaneously from many cameras placed around the flow form the basis of a tomographic reconstruction of the three-dimensional refractive index gradients Goldhahn and Seume (2007), from which the density field is obtained through integration of the gradients and application of the Gladstone-Dale relation.