arXiv research

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from field measurements, experiments and large-scale simulations at multiple spatiotemporal scales. Machine learning offers a wealth of techniques to extract information from data that could be translated into knowledge about the…

Paper presents a new approach to continuum mechanics using port-Hamiltonian framework.

A new shape space allows optimization of non-smooth shapes in fluid mechanics.

Space-like maximal surfaces and time-like minimal surfaces in Lorentz-Minkowski3-space are both characterized as zero mean curvature surfaces. We are interested in the case where the zero mean curvature surface changes type from space-like to time-like at a given non-degenerate null curve. We consider this phenomenon a…

We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we develop such connections for the case of two spatial dimensions, and demonstrate tha…

Paper applies fluid dynamics to stock market behavior.

New PDEs of mixed type emerge in fluid mechanics and geometry.

Geometric Hydrodynamics tackles open problems in fluid dynamics.

Survey explores cohomology's roles in applied math and sciences.

A machine learning model captures non-Newtonian fluid dynamics from molecular details.

In this paper an approach is proposed to represent a class of dissipative mechanical systems by corresponding infinite-dimensional Hamiltonian systems. This approach is based upon the following structure: for any non-conservative classical mechanical system and arbitrary initial conditions, there exists a conservative …

Calabi's Bernstein-type theorem asserts that a zero mean curvature entire graph in Lorentz-Minkowski space $\boldsymbol L^3$ which admits only space-like points is a space-like plane. Using the fluid mechanical duality between minimal surfaces in Euclidean 3-space $\boldsymbol E^3$ and maximal surfaces in Lorentz-Minko…

A new algebraic method for computing helicity is developed, by discovering a relationship between helicity of fluid mechanics and algebraic polynomial invariants of knot theory. We have constructed a topological invariant $t^{H\left(\mathcal{L}\right)}$ for a link $\mathcal{L}$ of knots, where $H$ is the helicity of a …

Paper develops physics-informed, boundary-constrained Gaussian process for fluid flow field reconstruction.

In this note we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the Borel-Weil contruction of the irreducible unitary representations of SU(2), and looking at the Madelung-Bohm velocity attached to the ensuing spin wave functions. We also show that, in the framework of finite dim…

Rolling Diffusion improves video prediction by progressively corrupting frames based on their temporal position.

We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles used in graph coloring and spectral graph drawing algorithms, examines a measur…

On curved spaces, viscous fluids reach equilibrium quickly.

Existence of a conjugate point in the incompressible Euler flow on a sphere and an ellipsoid is considered. Misiolek (1996) formulated a differential-geometric criterion (we call M-criterion) for the existence of a conjugate point in a fluid flow. In this paper, it is shown that no zonal flow (stationary Euler flow) sa…

Paper tackles uncertainties in reduced-order modeling of complex systems.

We present hidden fluid mechanics (HFM), a physics informed deep learning framework capable of encoding an important class of physical laws governing fluid motions, namely the Navier-Stokes equations. In particular, we seek to leverage the underlying conservation laws (i.e., for mass, momentum, and energy) to infer hid…

We consider the kinematics of specific fluid spacetimes admitting timelike congruences of Ricci Solitons. These fluids includes string cloud, string fluid, perfect fluid, radially symmetric fluid, anisotropic fluid and relativistic magneto-fluid. Results are obtained and important physical aspects are discussed.

Determining whether hypotensive patients in intensive care units (ICUs) should receive fluid bolus therapy (FBT) has been an extremely challenging task for intensive care physicians as the corresponding increase in blood pressure has been hard to predict. Our study utilized regression models and attention-based recurre…

Paper proves a rigidity result for static perfect fluids.

Novel deep learning approach for fast, differentiable fluid simulations.

FLUID-LLM uses LLMs to predict fluid dynamics with improved accuracy.

The study examines perfect fluid spacetimes and their properties.

The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.

In this article, we show how to embed the so-called CH2 equations into the geodesic flow of the Hdiv metric in 2D, which, itself, can be embedded in the incompressible Euler equation of a non compact Riemannian manifold. The method consists in embedding the incompressible Euler equation with a potential term coming fro…

The study examines properties of perfect fluid spacetimes in Einstein's theory.

FunDiff models physical functions using diffusion and autoencoders.

New kernel speeds up graph regression in physics.

Study proves fluid limits of fragmented limit-order markets.

The study identifies unique fluid flow patterns.

This paper presents a novel generative model to synthesize fluid simulations from a set of reduced parameters. A convolutional neural network is trained on a collection of discrete, parameterizable fluid simulation velocity fields. Due to the capability of deep learning architectures to learn representative features of…

Universal model for soft tissue mechanics under shock waves.

New probabilistic constructions for Kähler-Einstein metrics.

Study on static perfect fluid space-time geometry and boundary estimates.

Certain solutions of a sextic sigma-model Lagrangian reminiscent of Skyrme model correspond to perfect fluids with stiff matter equation of state. We analyse from a differential geometric perspective this correspondence extended to general barotropic fluids.

Paper develops a new fluid flow model with energy exchange through boundaries.

The computational cost associated with simulating fluid flows can make it infeasible to run many simulations across multiple flow conditions. Building upon concepts from generative modeling, we introduce a new method for learning neural network models capable of performing efficient parameterized simulations of fluid f…

Survey on matrix hydrodynamics, a 2D fluid model.

Using a simple and well-motivated modification of the stress-energy tensor for a viscous fluid proposed by Lichnerowicz, we prove that Einstein's equations coupled to a relativistic version of the Navier-Stokes equations are well-posed in a suitable Gevrey class if the fluid is incompressible and irrotational. These la…

RotEqNet preserves rotation symmetry in fluid systems using high-order tensors.

Study of $k$-almost Yamabe solitons in perfect fluid spacetimes.

Smartfluidnet accelerates Eulerian fluid simulation with neural networks.

Using numerical simulations of the axisymmetric Navier-Stokes equations with swirl on a no-slip flat boundary, Hsu-Notsu-Yoneda [J. Fluid Mech. 2016] observed the creation of a high-vorticity region on the boundary near the axis of symmetry. In this paper, using a differential geometric approach, we prove that such flo…

Proves well-posedness for hard phase model in general relativity.