Related papers: Extracting self-similarity from data
Modeling of fluid flows requires corresponding adequate and effective approaches that would account for multiscale nature of the considered physics. Despite the tremendous growth of computational power in the past decades, modeling of fluid…
The similarities of quantum turbulence with classical hydrodynamics allow quantum fluids to provide essential models of their classical analogue, paving the way for fundamental advances in physics and technology. Recently, experiments on 2D…
We investigate the hydrodynamic recovery of Lattice Boltzmann Method (LBM) by analyzing exact balance relations for energy and enstrophy derived from averaging the equations of motion on sub-volumes of different sizes. In the context of 2D…
Fast and stable fluid simulations are an essential prerequisite for applications ranging from computer-generated imagery to computer-aided design in research and development. However, solving the partial differential equations of…
The discovery of dynamical models from data represents a crucial step in advancing our understanding of physical systems. Library-based sparse regression has emerged as a powerful method for inferring governing equations directly from…
Three-dimensional turbulence is usually studied experimentally by using a spatially localized forcing at large scales (e.g. via rotating blades or oscillating grids), often in a deterministic way. Here, we report an original technique where…
Shell model turbulence is a simplified mathematical framework that captures essential features of incompressible fluid turbulence such as the energy cascade, intermittency and anomalous scaling of the fluid observables. We perform a…
Starting from the microscopic description of a normal fluid in terms of any kind of local interacting many-particle theory we present a well defined step by step procedure to derive the hydrodynamic equations for the macroscopic phenomena.…
When a water drop falls from a faucet, the drop is created with the formation of an axisymmetric constriction region, which thins down to breakup. Such formation of a fluid drop has been extensively studied as a representative of the…
We analyze the statistical properties of three-dimensional ($3d$) turbulence in a rotating fluid. To this end we introduce a generating functional to study the statistical properties of the velocity field $\bf v$. We obtain the master…
We suggest the Hamiltonian approach for fluid mechanics based on the dynamics, formulated in terms of Lagrangian variables. The construction of the canonical variables of the fluid sheds a light of the origin of Clebsh variables, introduced…
This paper develops a smooth model identification and self-learning strategy for dynamic systems taking into account possible parameter variations and uncertainties. We have tried to solve the problem such that the model follows the changes…
Machine learning techniques have been applied to enhance turbulence modeling in recent years. However, the "black box" nature of most machine learning techniques poses significant interpretability challenges in improving turbulence models.…
The algebraic properties of drift-flux two-phase fluids models without gravitational and wall friction forces are studied. More precisely, for the two fluids we consider equation of states of polytropic gases. We perform a classification…
We demonstrate several techniques to encourage practical uses of neural networks for fluid flow estimation. In the present paper, three perspectives which are remaining challenges for applications of machine learning to fluid dynamics are…
Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are…
Machine learning has been successfully applied to grid-based PDE modeling in various scientific applications. However, learned PDE solvers based on Lagrangian particle discretizations, which are the preferred approach to problems with free…
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…
We present a hybrid scheme based on classical density functional theory and machine learning for determining the equilibrium structure and thermodynamics of inhomogeneous fluids. The exact functional map from the density profile to the…
Townsend's attached-eddy hypothesis (AEH) provides a theoretical description of turbulence statistics in the logarithmic region in terms of coherent motions that are self-similar with the wall-normal distance (y). Here, we show the…