Paper presents a brain tumor segmentation method using NGMM and 3D FVF.
problem Automatic brain tumor segmentation from MRIs is challenging.
method Normalized Gaussian Bayesian classifier and 3D Fluid Vector Flow algorithm.
result The method successfully segments brain tumors from MRI images.
Researchers identify surfaces with special fluid flow fields.
problem Understanding fluid flows on curved surfaces.
method Defined and analyzed hydrodynamic Killing vector fields (HKVF) on surfaces.
result Any connected, orientable surface with HKVF is conformally equivalent to one of 14 canonical Riemann surfaces.
LFlows model fluid densities and velocities using invertible maps that satisfy the continuity equation.
problem Modeling fluid densities and velocities continuously in space and time.
method LFlows are based on invertible maps that satisfy the continuity equation, derived from classical theory of Lagrangian flows for smooth vector fields.
result LFlows show higher predictive accuracy in density modeling tasks compared to competing models in 2D and 3D.
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…
Study axisymmetric ideal fluids on 3-manifolds, proving Fredholm properties.
problem Riemannian geometry of axisymmetric ideal fluids.
method Proving Fredholm properties of L2 exponential map for axisymmetric flows. result Axisymmetric diffeomorphisms form a totally geodesic submanifold.
New algorithms improve vascular flow simulations in aortic aneurysms.
problem Limited accuracy of MRI in hemodynamics, patient-specific flow boundary conditions, and CFD's computational demands.
method Physics-Informed Neural Networks (PINNs) and Deep Operator Networks (DeepONets) integrated with 3D Navier-Stokes equations.
result Improved computational efficiency and good agreement with CFD simulations.
Stable long-term predictions for fluid flows using neural networks.
problem Predicting complex dynamics of fluid flows with high temporal stability.
method End-to-end trained neural network architecture combining CNN for spatial compression and LSTM for temporal prediction.
result Novel latent space subdivision (LSS) allows stable and controllable long-term predictions.
A machine learning method predicts rock permeability from 3D images.
problem Efficiently predict permeability of heterogeneous rocks for planetary and robotic applications.
method Machine learning guided 3D properties recognition of rock morphology from 3D micro CT and MRI images.
result The morphology decoder method accurately predicts permeability from 3D images.
Adversarial reinforcement learning optimizes microswimmers' path-planning in turbulent flows.
problem Optimizing microswimmers' paths in turbulent flows for efficient target reach.
method Adversarial-reinforcement learning scheme applied to 2D and 3D turbulent flows.
result Microswimmers can reach targets faster than a naive approach in turbulent flows.
Deep learning predicts fluid flow in porous media, accelerating simulations by orders of magnitude.
problem Accurate simulation of fluid flow in complex porous media requires excessive computational resources.
method Combining deep learning with direct simulation, using Gated U-Net CNNs trained on datasets of 2D and 3D porous media.
result Deep learning predictions can reach over 90% accuracy for permeability estimation and accelerate simulations by orders of magnitude.
Generative model for 3D point clouds using invertible flows.
problem Generating realistic 3D point clouds.
method Invertible flow-based models for point cloud generation with parameter sharing and embedding vectors.
result The model generates high-quality 3D point clouds with good similarity.
We consider 3D flow equations inspired by the renormalization group (RG) equations of string theory with a three dimensional target space. By modifying the flow equations to include a U(1) gauge field, and adding carefully chosen De Turck terms, we are able to extend recent 2D results of Bakas to the case of a 3D Riema…
New method efficiently simulates fluid flows across various conditions.
problem High computational cost in simulating fluid flows.
method Parameter-conditioned sequential generative modeling of neural networks.
result Trained models simulate fluid flows at orders of magnitude faster than traditional methods.
Derives a Hamiltonian model for 3D axially symmetric magnetohydrodynamics.
problem Modeling of 3D axially symmetric magnetohydrodynamics.
method Hamiltonian formulation and matrix discretization.
result First discrete model for 3D magnetohydrodynamics compatible with underlying Lie-Poisson structure.
We present a novel technique for assessing the dynamics of multiphase fluid flow in the oil reservoir. We demonstrate an efficient workflow for handling the 3D reservoir simulation data in a way which is orders of magnitude faster than the conventional routine. The workflow (we call it "Metamodel") is based on a projec…
The paper explores how a geometric flow can turn a black hole into a traversable wormhole.
problem The study investigates how a static, spherically symmetric black hole can be transformed into a traversable wormhole.
method The approach involves analyzing almost η-Ricci-Yamabe solitons and their geometric coupling with the Hawking temperature. result The geometric flow successfully transforms the black hole into a traversable wormhole, opening the throat and preserving the exact cosmological spacetime.
The binormal (or vortex filament) equation provides the localized induction approximation of the 3D incompressible Euler equation. We present explicit solutions of the binormal equation in higher-dimensions that collapse in finite time. The local nature of this phenomenon suggests the appearance of singularity in nearb…
The study identifies unique fluid flow patterns.
problem Understanding incompressible fluid flows with straight streamlines.
method Local differential geometry of line congruences to integrate Euler equations.
result Only specific fluid flows are possible with straight streamlines.
The study examines perfect fluid spacetimes and their properties.
problem Characterizing properties of perfect fluid spacetimes with concircular vector fields.
method Analyzing the conformal curvature tensor, state equation, and solitons in perfect fluid spacetimes.
result Perfect fluid spacetimes with concircular vector fields have specific properties related to the state equation and solitons.
Paper develops a new fluid flow model with energy exchange through boundaries.
problem Modeling ideal fluid flow with energy exchange through boundaries.
method Port-Hamiltonian model based on Stokes-Dirac structures.
result Wide range of fluid dynamical systems can be achieved with this model.
The paper explores the geometric properties of fluid flows and their symmetries.
problem Understanding the geometric properties of fluid flows and their symmetries.
method Analyzing the Euler equation and its relation to geodesic flows on groupoids of multiphase diffeomorphisms.
result Generalized flows, multiphase fluids, and vortex sheets are all geodesics on certain groupoids of multiphase diffeomorphisms.
Paper extends port-Hamiltonian model to include internal energy for compressible and incompressible flow.
problem Modeling fluid flow dynamics with internal energy and constraints.
method Derived port-Hamiltonian model using interconnection maps and added internal energy and constraint forces.
result Model accurately represents both compressible and incompressible fluid flow.
New methods reveal compatible liquid crystal phases in 3D.
problem Understanding compatible director fields in 3D liquid crystals.
method Re-derived compatibility conditions using vector calculus.
result Characterized a wide range of compatible liquid crystal phases.
Investigates fluid flow perturbations using geometric theory.
problem Analyzing linear perturbations in non-equilibrium fluid flows.
method Uses second order variations of the action and Jacobi fields.
result Demonstrates numerical simulations of perturbation dynamics.
Study of k-almost Yamabe solitons in perfect fluid spacetimes.
problem Analyzing k-almost Yamabe solitons in perfect fluid spacetimes. method Examined perfect fluid spacetimes and k-almost Yamabe solitons using Einstein field equations. result Characterized properties of k-almost Yamabe solitons in perfect fluid spacetimes. Characterizes 3D steady Euler flows using homologies.
problem Characterizing 3D steady Euler flows.
method Using commuting zero-flux homologies.
result Steady Euler flows cannot be constructed using plugs.
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~g real and~F complex. We find, there are precisely two classes of s…
Machine learning enhances fluid mechanics by analyzing complex data.
problem Analyzing large volumes of fluid mechanics data.
method Machine learning techniques to extract information from data.
result Machine learning enriches and transforms fluid mechanics research.
In this paper geometrical aspects of perfect fluid spacetime with torse-forming vector field ξare discribed and Ricci soliton in perfect fluid spacetime with torse-forming vector field ξare determined. Conditions for the Ricci soliton to be expanding, steady or shrinking are also given.
Formula for genus of 3D flows based on boundary data.
problem Calculating the genus of flows on 3D integral homology spheres.
method Formula derivation based on Euler characteristic and boundary data.
result Genus is an asymptotic invariant proportional to helicity.
FLUID uses flows to unify filtering and smoothing for complex systems.
problem Bayesian filtering and smoothing for high-dimensional nonlinear systems.
method FLUID encodes observation histories into a fixed summary statistic, using flows for filtering and smoothing.
result FLUID provides accurate approximations of filtering and smoothing distributions.
Identifies most probable flows for Kunita SDEs in fluid dynamics.
problem Modeling stochastic processes with Eulerian noise and deterministic drifts.
method Equipping the domain with a Riemannian metric from the noise, solving the resulting PDEs.
result Most probable flows differ from deterministic flows, especially under noise.
The study identifies conjugate and cut points in ideal fluid motion configurations.
problem Understanding stability and re-convergence of fluid configurations.
method Existence and non-existence of conjugate points in specific fluid configurations, using geometric and physical analysis.
result Existence of conjugate points in Kolmogorov flows and non-existence in Arnold steady states.
Stabilization technique applied to curve shortening flow in 3D space.
problem Stabilizing curve shortening flow in 3D space.
method Applying stabilization technique developed by T. Zelenyak to curve shortening flow in R3. result Derivation of several new monotonicity formulas for curve shortening flow.
The paper studies geometric structures in perfect fluid spacetimes with specific metrics.
problem Analyzing the geometric properties of perfect fluid spacetimes with specific metrics.
method Investigates conditions for conformal Ricci-Yamabe soliton and derives Laplace equations.
result Conditions for expanding, steady, or shrinking conformal Ricci-Yamabe solitons are identified.
Paper proves existence of conjugate points on ellipsoids but not on spheres.
problem Existence of conjugate points in incompressible Euler flows.
method Formulated a differential-geometric criterion (M-criterion) and analyzed flows on spheres and ellipsoids.
result Zonal flows on ellipsoids can satisfy M-criterion, while not on spheres.
Deep learning improves plaque prediction for coronary artery health.
problem Predicting coronary artery plaque health from CT scans.
method 3D RCNN, 2D multi-view ensemble, 2.5D approach.
result Improved prediction accuracy for revascularization decisions.
The paper simplifies proofs and characterizes contact structures in 3D.
problem Contact structures induced by geodesic vector fields in 3D.
method New proofs and characterizations of contact structures.
result Contact structures in 3D are universally tight under certain conditions.
In the present report, by using the Stokes-Helmholtz decomposition theorem the 3-dimensional Navier-Stokes equation (NSE) is uncoupled and transformed into a scalar equation for the velocity potential when the flow field is toroidal. The dynamics of the velocity potential is independent of the vector potential. The red…
Smooth 3D flows from non-smooth starting points.
problem Creating smooth Ricci flows from non-smooth initial conditions.
method Generalized singular Ricci flow applied to 3D complete manifolds.
result Existence of smooth Ricci flows starting from non-smooth initial conditions.
Study Godbillon-Vey invariants in non-Lorentzian spacetimes and fluid dynamics.
problem Characterizing and measuring the local spin of spatial leaves in non-Lorentzian spacetimes.
method Relating intrinsic torsion to Godbillon-Vey class, using geometric structures to model fluid dynamics.
result Godbillon-Vey class represents an obstruction to steady flow of fluid and new conservation laws.
Paper presents a consistent discretization for Hodge decomposition on volumetric meshes.
problem Discretization of Hodge decomposition for vector fields on volumetric meshes.
method Edge-based Nedelec elements and face-based Crouzeix-Raviart elements interplay.
result Stable and efficient method for large-sized models with good performance.
The sectional curvature of the volume preserving diffeomorphism group of a Riemannian manifold M can give information about the stability of inviscid, incompressible fluid flows on M. We demonstrate that the submanifold of the volumorphism group of the solid flat torus generated by axisymmetric fluid flows with swi…
A perfect-fluid space-time of dimension n>3 with 1) irrotational velocity vector field, 2) null divergence of the Weyl tensor, is a generalised Robertson-Walker space-time with Einstein fiber. Condition 1) is verified whenever pressure and energy density are related by an equation of state. The contraction of the Weyl …
Paper finds new criteria for conjugate points in fluid flows.
problem Finding conjugate points in steady 2D Euler flows.
method Develops a new sufficient criterion for conjugate points, applies to any rotational cell, and uses a general construction of steady fluid surfaces.
result Improves on existing criteria and captures all known conjugate points in rotational cells.
Paper develops physics-informed, boundary-constrained Gaussian process for fluid flow field reconstruction.
problem Reconstructing fluid flow fields from limited data.
method Physics-informed, boundary-constrained Gaussian process regression.
result Derives physics-informed kernels for simulating incompressible flows.
New method speeds up GAN training by solving saddle point problem.
problem Slow convergence in training Generative Adversarial Networks (GANs).
method Fluid flow mass transport formulation for strict minimization.
result Quick convergence and meaningful metrics in optimization.
Vortex induced vibrations of bluff bodies occur when the vortex shedding frequency is close to the natural frequency of the structure. Of interest is the prediction of the lift and drag forces on the structure given some limited and scattered information on the velocity field. This is an inverse problem that is not str…