In this paper, we show the existence of real-analytic stationary Navier-Stokes flows with isotropic streamlines in all latitudes in some simply-connected flow region on a rotating round sphere. We also exclude the possibility of having a Poiseuille's flow profile to be one of these stationary Navier-Stokes flows with i…
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48 results for “Stokes flow”
Study reveals how to determine area and curvature from fluid flow resonances.
problem Determining geometric properties from fluid flow data.
method Asymptotic expansion of heat kernel and Steklov spectral invariants.
result Area and total mean curvature can be inferred from Steklov eigenvalues.
Optimization of piecewise smooth shapes under uncertainty using the example of Navier-Stokes flowmath.OC
Optimizes shapes in uncertain Navier-Stokes flow problems.
problem Optimizing shapes with geometric constraints and physical uncertainty.
method Multi-shape calculus and stochastic augmented Lagrangian method.
result Successfully optimized shapes in uncertain Navier-Stokes flow.
This paper clarifies a global structure of Stokes-Dirac structures used for describing interconnected port-Hamiltonian systems defined on manifolds with non-trivial topology under consistent boundary condition.
Direct numerical simulation of Stokes flow through an impermeable, rigid body matrix by finite elements requires meshes fine enough to resolve the pore-size scale and is thus a computationally expensive task. The cost is significantly amplified when randomness in the pore microstructure is present and therefore multipl…
Model uses Navier-Stokes equations to assess liquidity and systemic risk.
problem Traditional models fail to capture real market fluctuations and extreme events.
method Develops and validates a mathematical model based on Navier-Stokes equations, incorporating 13 macroeconomic and financial parameters.
result Model effectively describes liquidity dynamics, systemic risk, and extreme scenarios.
Deep neural network approximates flow averages for rough walls in multiscale simulations.
problem Approximating flow averages in rough-wall Stokes flow simulations.
method Fourier neural operator for local averages, parameterized by local wall geometry.
result Stable and accurate HMM solution with reduced micro problem solving cost.
The Navier-Stokes equations on certain manifolds can perform universal computation.
problem Computational universality in viscous fluids.
method Cosymplectic geometry and harmonic 1-forms.
result Stationary Navier-Stokes solutions exhibit Turing completeness.
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…
A local instability mechanism of the Navier-Stokes flow with swirl on the no-slip flat boundarymath.AP
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…
In this paper, a new algorithm based on differential geometry viewpoint to solve the 3D rotating Navier-Stokes equations with complex Boundary is proposed, which is called Bi-parallel algorithm. For xample, it can be applied to passage flow between two blades in impeller and circulation flow through aircrafts with comp…
Stokes-Dirac structures are infinite-dimensional Dirac structures defined in terms of differential forms on a smooth manifold with boundary. These Dirac structures lay down a geometric framework for the formulation of Hamiltonian systems with a nonzero boundary energy flow. Simplicial triangulation of the underlaying m…
A Dynamics-Informed Gaussian Process Framework for 2D Stochastic Navier-Stokes via Quasi-Gaussianitymath.DS
New framework uses dynamics to justify Gaussian process for turbulent flows.
problem Lack of rigorous justification for Gaussian process priors in turbulent flows.
method Introduces a dynamics-informed Gaussian process framework based on quasi-Gaussianity.
result Provides a principled, long-time dynamical justified GP prior for turbulent flows.
Developed MF-PINNs to solve coupled Stokes-Darcy equations more accurately.
problem Solving coupled Stokes-Darcy equations with varying physical constants.
method Combining VP and SV forms with adjusted weights in MF-PINNs.
result Improved accuracy of streamline and pressure fields in numerical experiments.
Port-Hamiltonian Modeling of Ideal Fluid Flow: Part II. Compressible and Incompressible Flowphysics.flu-dyn
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.
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.
We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The discretization is described in detail and related to finite difference schemes on stagger…
We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the Conformal Ricci Flow Equations because of the role that conformal geometry plays in constraining the scalar curvature. These equ…
Stokes' theorem's boundary maximizes entropy.
problem Characterizing the boundary of a manifold using entropy.
method Maximizing entropy for codimension-1 submanifolds satisfying Stokes' theorem.
result The boundary of a manifold maximizes the entropy functional.
In this paper we introduce and study a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its various properties, prove the global existence of the solution of this flow, discuss its convergence and possible applications, and its relation to the …
Several intrinsic topological ways to encode connections on vector bundles on smooth complex algebraic curves will be described. In particular the notion of {\em Stokes decompositions} will be formalised, as a convenient intermediate category between the Stokes filtrations and the Stokes local systems/wild monodromy re…
Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshesphysics.flu-dyn
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equatio…
Neural Networks improve incompressible flow simulations without complex kernels.
problem Simulating incompressible flows accurately and efficiently.
method Integrates Neural Networks with Random Vortex Dynamics for incompressible Navier-Stokes equations.
result Strictly enforces physical properties like incompressibility and boundary conditions.
Lean 4 formalizes Stokes' theorem for smooth singular cubes.
problem Formalizing Stokes' theorem for singular cubes in arbitrary dimensions.
method Using true differential-form pullback via Frechet derivative, bridging to mathlib4's extDeriv.
result d^2=0 for singular cubical chains, chain-level Stokes extended.
On asymptotically almost periodic solutions to the Navier-Stokes equations on hyperbolic manifoldsmath.AP
Paper studies periodic solutions to Navier-Stokes equations on hyperbolic manifolds.
problem Existence and uniqueness of asymptotically almost periodic solutions to Navier-Stokes equations on hyperbolic manifolds.
method Dispersive and smoothing estimates for the Stokes equation, Massera-type principle, fixed point argument.
result Existence and uniqueness of asymptotically almost periodic mild solutions in spaces.
Study on Navier-Stokes equations on non-compact manifolds, proving existence and decay of solutions.
problem Existence and asymptotic behavior of solutions to Navier-Stokes equations on non-compact manifolds.
method Used -dispersive and smoothing estimates of the Stokes semigroup, fixed point arguments, and Gronwall's inequality.
result Established existence and exponential decay of almost periodic and asymptotically almost periodic mild solutions.
Paper compares five surface Navier-Stokes derivations and finds some are equivalent.
problem Modeling evolving fluidic surfaces using different principles and coordinate systems.
method Systematic comparison of five derivations using tangential and normal components.
result All derivations yield the same tangential surface Navier-Stokes equations.
Novel neural operator predicts complex spatiotemporal dynamics from partial observations.
problem Capturing complex operator dynamics in infinite-dimensional function spaces.
method Integrates Koopman operator theory with deep neural networks to approximate nonlinear operators between Banach spaces.
result BNO achieves robust zero-shot super-resolution in unsteady flow prediction and outperforms conventional methods.
Study submanifolds with boundaries in Heisenberg groups using Stokes' Theorem.
problem Understanding submanifolds with boundaries in Heisenberg groups.
method Introduce and study -regular submanifolds with boundaries, prove Stokes' Theorem for them.
result Prove a version of Stokes' Theorem for submanifolds with boundaries in Heisenberg groups.
We develop an adversarial-reinforcement learning scheme for microswimmers in statistically homogeneous and isotropic turbulent fluid flows, in both two (2D) and three dimensions (3D). We show that this scheme allows microswimmers to find non-trivial paths, which enable them to reach a target on average in less time tha…
Stokes equations help uniquely identify manifold metrics from boundary data.
problem Determining Riemannian metric from boundary Cauchy data.
method Proving uniqueness of metric from Stokes equations Cauchy data.
result Partial derivatives of all orders of the metric on the boundary are uniquely determined.
We compute Stokes matrices and monodromy for the quantum cohomology of projective spaces. We prove that the Stokes' matrix of the quantum cohomology coincides with the Gram matrix in the theory of derived categories of coherent sheaves.
Algorithm describes Fourier transform of Stokes data at infinity.
problem Understanding the Fourier transform of Stokes data at infinity.
method Topological description and algorithmic approach using recent results and language of Stokes local systems.
result Explicit isomorphisms between wild character varieties are induced.
Analyzes tt*-structures from -type Stokes data.
problem Classifying tt*-structures over .
method Isomonodromic deformations with upper unitriangular real Stokes matrices.
result Establishes a direct analytic realization of the classification.
Paper connects Stokes phenomena to quantum groups and Poisson-Lie groups.
problem Analyse Stokes phenomena in Poisson-Lie groups and quantum groups.
method Use Ug-valued Stokes phenomena to construct quantum group U_hg and relate it to Poisson-Lie group G*.
result Show that Ug-valued Stokes phenomena can be obtained as a semiclassical limit of the KZ associator.
Categorifies Stokes coefficients in Chern-Simons theory models.
problem Stokes phenomenon in Chern-Simons theory around flat connections.
method Finite-dimensional model for analytically continued Chern-Simons theory, categorification of Stokes coefficients.
result Stokes coefficients can be promoted to graded vector spaces.
We consider the concept of Stokes-Dirac structures in boundary control theory proposed by van der Schaft and Maschke. We introduce Poisson reduction in this context and show how Stokes-Dirac structures can be derived through symmetry reduction from a canonical Dirac structure on the unreduced phase space. In this way, …
Stokes theorem holds for Lipschitz forms on a smooth manifold.
The paper validates Stokes' theorem for differential subcomplexes in positively graded Lie groups.
problem Validating Stokes' theorem for differential subcomplexes in positively graded Lie groups.
method Introducing geometric conditions and spectral complexes to recover Stokes' theorem on locally smooth intrinsic graphs.
result Stokes' theorem holds for Rumin complex and new spectral complexes on Carnot groups.
The author presents the generalized Stokes theorem for R-linear forms on Lie algebroids (which can be non-local). We apply the Stokes formula on forms to prove that two homotopic homomorphisms of Lie algebroids implies the existence of a chain operator joining their pullback operators.
Study well-posedness of generalized Stokes operator on cylindrical domains.
problem Analyzing the generalized Stokes operator on domains with cylindrical ends.
method Using layer potentials and developing algebra tools for limit and jump relations.
result Well-posedness results for the associated Stokes boundary value problem.
Well-posedness of a generalized Stokes operator on smooth bounded domains via layer-potentialsmath.AP
Proves invertibility of layer potentials for generalized Stokes operators on smooth domains.
problem Invertibility of layer potentials for generalized Stokes operators on smooth domains.
method Developed algebra toolkit to handle layer operators' limit and jump relations; proved Fredholm property and invertibility.
result Proves invertibility of layer potentials for generalized Stokes operators on smooth domains.
For a given bounded domain with smooth boundary, we explicitly calculate the first two coefficients of the asymptotic expansion of the heat trace associated with the Stokes operator as . These coefficients (i.e., heat invariants) provide precise information for the volume of the domain $…
We present type Stokes' theorem for type -chains which extends the fundamental theorem of calculus in higher dimensions.
The paper connects eigenvalue problems for various operators and establishes inequalities and asymptotic formulas for heat traces.
problem Eigenvalue problems and heat trace asymptotics for different operators.
method Establishes connections and inequalities for eigenvalues and heat traces.
result Eigenvalue inequalities and three-term asymptotic formulas for heat traces of various operators.
Study submanifolds with boundary in Heisenberg groups, proving Stokes' Theorem.
problem Understanding submanifolds with boundary in sub-Riemannian Heisenberg groups.
method Introduced examples and proved Stokes' Theorem involving Rumin's differential forms.
result Stokes' Theorem for submanifolds with boundary in Heisenberg groups.
Positive energy representations of affine algebras and Stokes matrices of the affine Toda equationsmath.DG
Constructs positive energy representations from Toda equations Stokes data.
problem Creating positive energy representations of affine algebras.
method Using Stokes data of tt*-Toda equations to construct representations.
result Illustrates construction with examples in conformal field theory.
By proving graph theoretical versions of Green-Stokes, Gauss-Bonnet and Poincare-Hopf, core ideas of undergraduate mathematics can be illustrated in a simple graph theoretical setting. In this pedagogical exposition we present the main proofs on a single page and add illustrations. While discrete Stokes is is old, the …