A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This paper is a rigorous study of the dual pair structure of the ideal fluid and the dual pair structure for the -dimensional Camassa-Holm (EPDiff) equation, including the proofs of the necessary transitivity results. In the case of the ideal fluid, we show that a careful definition of the momentum maps leads natura…
Paper develops a new fluid flow model with energy exchange through boundaries.
Paper extends port-Hamiltonian model to include internal energy for compressible and incompressible flow.
Investigates fluid flow perturbations using geometric theory.
The paper studies steady motions of fibre-reinforced fluids on curved surfaces.
The paper explores the geometric properties of fluid flows and their symmetries.
We study the Riemannian geometry of 3D axisymmetric ideal fluids. We prove that the exponential map on the group of volume-preserving diffeomorphisms of a -manifold is Fredholm along axisymmetric flows with sufficiently small swirl. Along the way, we define the notions of axisymmetric and swirl-free diffeomorp…
The study identifies conjugate and cut points in ideal fluid motion configurations.
The Lagrangian and Hamiltonian structures for an ideal gauge-charged fluid are determined. Using a Kaluza-Klein point of view, the equations of motion are obtained by Lagrangian and Poisson reductions associated to the automorphism group of a principal bundle. As a consequence of the Lagrangian approach, a Kelvin-Noeth…
This paper provides a precise sense in which the time t map for the Euler equations of an ideal fluid in a region in R^n (or a smooth compact n-manifold with boundary) is a Poisson map relative to the Lie-Poisson bracket associated with the group of volume preserving diffeomorphism group. This is interesting and nontri…
Geometric framework for Newton's equations on diffeomorphism groups.
There is a remarkable and canonical problem in 3D geometry and topology: To understand existing models of 3D fluid motion or to create new ones that may be useful. We discuss from an algebraic viewpoint the PDE called Euler's equation for incompressible frictionless fluid motion. In part I we define a "finite dimension…
We consider solutions to the complex Trkalian equation,~$ \vec{\nabla} \times \vc = \vc ,$ where~$\vc$ is a 3 component vector function with each component in the complex field, and may be expressed in the form~$ \vc = e^{ig} \vec{\nabla} F, $ with~ real and~ complex. We find, there are precisely two classes of s…
The sectional curvature of the volume preserving diffeomorphism group of a Riemannian manifold can give information about the stability of inviscid, incompressible fluid flows on . We demonstrate that the submanifold of the volumorphism group of the solid flat torus generated by axisymmetric fluid flows with swi…
In this mostly pedagogical tutorial article a brief introduction to modern geometrical treatment of fluid dynamics and electrodynamics is provided. The main technical tool is standard theory of differential forms. In fluid dynamics, the approach is based on general theory of integral invariants (due to Poincare and Car…
Toolbox for stochastic Euler equations using Ebin-Marsden theory.
Geometric analysis on diffeomorphism groups for fluid dynamics and information geometry.
We describe first integrals of geostrophic equations, which are similar to the enstrophy invariants of the Euler equation for an ideal incompressible fluid. We explain the geometry behind this similarity, give several equivalent definitions of the Poisson structure on the space of smooth densities on a symplectic manif…
We present a geometric analysis of the incompressible averaged Euler equations for an ideal inviscid fluid. We show that solutions of these equations are geodesics on the volume-preserving diffeomorphism group of a new weak right invariant pseudo metric. We prove that for precompact open subsets of , thi…
The equations of motion of a charged ideal fluid, respectively the superconductivity equation (both in a given magnetic field) are showed to be geodesic equations on a general, respectively central extension of the group of volume preserving diffeomorphisms with right invariant metric. For this, quantization of the mag…
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 …
Study on MHD equilibria on curved spaces without symmetries.
Dirac structures on tangent bundles provide a unified framework for Lagrange--Dirac dynamical systems.
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.
Euler's equations for a two-dimensional system can be written in Hamiltonian form, where the Poisson bracket is the Lie-Poisson bracket associated to the Lie algebra of divergence free vector fields. We show how to derive the Poisson brackets of 2d hydrodynamics of ideal fluids as a reduction from the one associated to…
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.
The study examines properties of perfect fluid spacetimes in Einstein's theory.
This paper constructs an algebra on a 3-torus with specific properties for fluid dynamics.
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…
New algorithms improve vascular flow simulations in aortic aneurysms.
Study on static perfect fluid space-time geometry and boundary estimates.
Given a principal bundle G \rightarrow P \rightarrow B (each being compact, connected and oriented) and a G-invariant metric h^{P} on P which induces a volume form μ^{P}, we consider the group of all unimodular automorphisms SAut(P,μ^{P}):={\varphi\in Diff(P) | \varphi^{*}μ^{P}=μ^{P} and \varphi is G-equivariant} of P …
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.
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 -almost Yamabe solitons in perfect fluid spacetimes.
Smartfluidnet accelerates Eulerian fluid simulation with neural networks.
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…
Geometric Hydrodynamics tackles open problems in fluid dynamics.
Proves well-posedness for hard phase model in general relativity.