Study uses neural networks to predict wall quantities in turbulent flows.
problem Predicting wall quantities in turbulent open channel flows.
method Training convolutional neural networks (FCN) and a proposed R-Net architecture to predict wall-shear-stress and wall pressure.
result R-Net architecture performs better and predicts wall quantities with around 10% error.
Neural network predicts turbulence from wall shear stress.
problem Predicting wall-bounded turbulence from wall quantities.
method Fully-convolutional neural network trained on DNS data.
result Improved prediction of turbulence fields and statistics.
Convolutional networks predict turbulence from wall quantities.
problem Predicting turbulence fields from wall-shear-stress components and wall pressure.
method Two CNN models: FCN and FCN-POD, trained on DNS data.
result FCN and FCN-POD models outperform EPOD in predicting turbulence fields.
Neural networks predict flow and elastic stresses in viscoelastic turbulence.
problem Predicting flow and elastic stresses in viscoelastic turbulent flows using limited experimental data.
method Convolutional neural networks trained on wall-normal velocity and pressure data.
result Neural networks accurately predict flow and elastic stresses, especially during low-drag events.
Bayesian Monte-Carlo method assesses uncertainty in shear stress entropy models.
problem Uncertainty in evaluating shear stress entropy models remains an open question.
method Bayesian Monte-Carlo (BMC) uncertainty method to evaluate four entropy models.
result FOCB statistic index determines certainty of entropy models in shear stress estimation.
Study predicts shear stress in compound channels using data mining and machine learning.
problem Predicting shear stress distribution in symmetric compound channels.
method Conducted experiments to measure shear stress. Used data mining and machine learning models (RF, M5P, RC, KStar, AR) to predict.
result Random Forest (RF) model showed highest accuracy with R2=0.9.
Study rigidity in Riemannian manifolds using Pohozoaev and P-function approaches.
problem Rigidity in Serrin's overdetermined problems in Riemannian manifolds.
method Prove a Pohozoaev-type identity, use conformal vector field, and apply P-function approach.
result Show Serrin's type rigidity result in Riemannian manifolds.
Sparse regression models CMs from oscillatory shear data efficiently.
problem Discovering parsimonious constitutive models from oscillatory shear experiments.
method Sparse regression with tensor basis functions, l1 regularization, and greedy two-stage algorithm.
result Inferred CMs extrapolate well beyond training data and flow conditions.
Modeling aortic wall inhomogeneities to predict dissection risks.
problem Predicting localized stress accumulations in the aortic wall due to inhomogeneities.
method Stochastic constitutive model with random field realizations, coupled with a convolutional neural network surrogate.
result The neural network accurately predicts stress distributions and assesses uncertainty in aortic wall stress.
Advances in computational science offer a principled pipeline for predictive modeling of cardiovascular flows and aspire to provide a valuable tool for monitoring, diagnostics and surgical planning. Such models can be nowadays deployed on large patient-specific topologies of systemic arterial networks and return detail…
Geometric Algebra Transformer (GATr) handles various geometric data types efficiently.
problem Lack of a single architecture for diverse geometric data types.
method GATr uses projective geometric algebra, equivariant to E(3), and is a Transformer architecture.
result GATr outperforms non-geometric and equivariant baselines in various geometric tasks.
Paper solves Serrin problem for ring-shaped domains, showing velocity has finitely many maxima.
problem Characterizing rotationally symmetric solutions to a specific PDE on a ring-shaped domain.
method Introduced new arguments in the spirit of comparison geometry to overcome the lack of monotonicity.
result Simplest conditions are not sufficient; rotational symmetry requires finitely many maxima.
HFNO enhances interpretability of turbulent flows through parallel wavenumber bin processing.
problem Opaque inner workings of Fourier Neural Operators (FNOs) hinder physical interpretability.
method Introduces HFNO, a novel FNO-based architecture that processes wavenumber bins in parallel, enhancing interpretability.
result HFNO decomposes turbulent flows across various scales, enabling increased interpretability and multiscale modeling.
Convolutional neural networks (ConvNets) have demonstrated an exceptional capacity to discern visual patterns from digital images and signals. Unfortunately, such powerful ConvNets do not generalize well to arbitrary-shaped manifolds, where data representation does not fit into a tensor-like grid. Hence, many fields of…
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…
Study of circle homeomorphisms with square summable diamond shears.
problem Characterizing circle homeomorphisms with specific summability properties.
method Analysis of homeomorphisms in modular coordinates and comparison to Weil-Petersson class.
result Sharp results comparing new class to Weil-Petersson class and Hölder classes.
Invariants of braids found using shear coordinates in hyperbolic geometry.
problem Finding invariants of braids.
method Using shear coordinates in hyperbolic geometry.
result Developed a method for calculating braids invariants.
Bounding shears in ideal triangulations on hyperbolic surfaces.
problem Bounding shears in ideal triangulations on hyperbolic surfaces.
method Showing an ideal triangulation with bounded shear parameters on hyperbolic surfaces.
result An upper bound on shear parameters depends logarithmically on the surface's topology.
New model reduces bias in cosmic shear measurements.
problem Bias in cosmic shear measurements due to non-well-defined ellipticity.
method Hybrid physical and deep learning Hierarchical Bayesian Model.
result Unbiased estimate of shear on realistic galaxies.
Thurston introduced shear deformations (cataclysms) on geodesic laminations - deformations including left and right displacements along geodesics. For hyperbolic surfaces with cusps, we consider shear deformations on disjoint unions of ideal geodesics. The length of a balanced weighted sum of ideal geodesics is defined…
The paper analyzes thin-shell limits for viscous operators on Riemannian hypersurfaces.
problem Analyzing boundary conditions and thin-shell limits for viscous operators on arbitrary smooth hypersurfaces.
method Decomposing the ambient Bochner Laplacian into intrinsic and radial pieces, proving results for stress-free and Hodge boundary conditions.
result Universal thin-shell limits for viscous operators on arbitrary smooth hypersurfaces, including stress-free and Hodge boundary conditions.
We obtain expressions for the shear and the vorticity tensors of perfect-fluid spacetimes, in terms of the divergence of the Weyl tensor. For such spacetimes, we prove that if the gradient of the energy density is parallel to the velocity, then either the expansion rate is zero, or the vorticity vanishes. This statemen…
Study counts orbits of mapping class group in shearing coordinates.
problem Counting orbits of mapping class group in shearing coordinates.
method Uses shearing coordinates and asymptotics of Teichmüller space.
result Asymptotic behavior of mapping class group orbits in shearing coordinates.
The twist construction is a method to build new interesting examples of geometric structures with torus symmetry from well-known ones. In fact it can be used to construct arbitrary nilmanifolds from tori. In our previous paper, we presented a generalization of the twist, a shear construction of rank one, which allowed …
We parametrize the space Z of Zygmund vector fields on the unit circle in terms of infinitesimal shear functions on the Farey tesselation. Then we express the Hilbert transform and the Fourier coefficients of the Zygmund vector fields in terms of the above parametrization by infinitesimal shear functions. F…
Twisted SL2C local systems on surfaces of finite type appear often in geometry and physics. Most of them arise geometrically as local systems of charts for pleated hyperbolic structures. Bonahon and Thurston's "shear-bend coordinates" parameterize these local systems of charts. On a surface …
Geodesic patterns, shears, and Anosov representations of the modular group.
problem Understanding representations of the modular group into Isom(X).
method Analyzing geodesic patterns, shears, and foliations.
result The Barbot component is homeomorphic to R^2 x [0,∞), with interior and boundary properties.
The twist construction is a geometric model of T-duality that includes constructions of nilmanifolds from tori. This paper shows how one-dimensional foliations on manifolds may be used in a shear construction, which in algebraic form builds certain solvable Lie groups from Abelian ones. We discuss other examples of geo…
Link between Teichmüller and anti de Sitter geometry via length functions.
problem Understanding the geometry of Teichmüller space and anti de Sitter manifolds.
method Establishing a connection between Teichmüller space and anti de Sitter geometry through length functions.
result New purely anti de Sitter proofs of Teichmüller theory results.
We give parameterizations of homeomorphisms, quasisymmetric maps and symmetric maps of the unit circle in terms of shear coordinates for the Farey tesselation.
A new proof shows how to characterize maps using simple geometry.
problem Characterizing quasisymmetric maps on the unit circle.
method Elementary proof using normal family argument and hyperbolic geometry.
result Characterizes quasisymmetric maps via shear coordinates on the Farey tesselation.
Study circular foliations and shear-radius coordinates on hyperbolic cone surfaces.
problem Characterize Teichmüller spaces of hyperbolic cone surfaces.
method Construct circular foliations and shear-radius coordinates on Teichmüller spaces of hyperbolic cone surfaces.
result Shear-radius coordinates provide global coordinates on Teichmüller spaces and converge to specific metrics.
Bayesian neural networks (BNN) are the probabilistic model that combines the strengths of both neural network (NN) and stochastic processes. As a result, BNN can combat overfitting and perform well in applications where data is limited. Earthquake rupture study is such a problem where data is insufficient, and scientis…
The paper extends optimal transport for linear separability of sheared distributions in supervised learning.
problem Learning on the space of probability measures using shifts and scalings.
method Embedding probability measures into L2 spaces using optimal transport, then applying regular machine learning techniques. result Sheared distributions can be linearly separated under certain conditions, with bounds on transformations.
Classifies two-step solvable Lie groups with SKT structures.
problem Classifying Lie groups with SKT structures.
method Shear construction and analysis of SKT shear data on Abelian Lie algebras.
result Large part of the classification for two-step solvable SKT algebras of dimension six.
We present a procedure for asymptotic gluing of hyperboloidal initial data sets that preserves the shear-free condition. Our construction is modeled on a previous gluing construction by the last three named authors, but with significant modifications that incorporate the shear-free condition. We rely on the special Höl…
Shear moves connect square-tiled surfaces in quadratic differentials.
problem Connecting square-tiled surfaces via specific moves.
method Shear moves corresponding to diagonal flips preserving square-tiled properties.
result Connected components of reconfiguration problem are in bijection with moduli space of quadratic differentials.
Study quasisymmetric maps on hyperbolic plane boundaries.
problem Identify quasisymmetric maps corresponding to specific lambda lengths and flip distances.
method Analyze maps on Farey triangulation, relate to shearing coordinates and flip distance.
result Identify quasisymmetric maps corresponding to pinched lambda lengths and flip distances.
Given a semi-Riemannian manifold, we give necessary and sufficient conditions for a Riemannian submanifold of arbitrary co-dimension to be umbilical along normal directions. We do that by using the so-called \emph{total shear tensor}, i.e., the trace-free part of the second fundamental form. We define the \emph{shear s…
Enhanced Teichmüller space for surfaces with decorations and enhancements.
problem Parameterizing and understanding Teichmüller spaces with enhancements and decorations.
method Introduced a new variation of Teichmüller space, constructed parameterization, and introduced lamination space.
result Compatibility of shear coordinates and λ-length coordinates in the new deformation space.
Abstract: Poisson bracket on shear coordinates relates to Fenchel-Nielsen bracket on gluing parameters.
problem Relationship between Fenchel-Nielsen coordinates and shear coordinates on Riemann surfaces.
method Explicitly showed the Poisson bracket on shear coordinates induces the Fenchel-Nielsen bracket on gluing parameters.
result Poisson bracket on shear coordinates relates to Fenchel-Nielsen bracket on gluing parameters.
We show that any polyhomogeneous asymptotically hyperbolic constant-mean-curvature solution to the vacuum Einstein constraint equations can be approximated, arbitrarily closely in Hölder norms determined by the physical metric, by shear-free smoothly conformally compact vacuum initial data.
We prove that shear-free perfect fluid solutions of Einstein's field equations must be either expansion-free or non-rotating (as conjectured by Treciokas and Ellis) for all linear equations of state p=wρ except for six values of w.
We start by describing how ideal triangulations on a surface degenerate under pinching of a multicurve. We use this process to construct a homomorphism from the Ptolemy groupoid of a surface to that of a pinched surface which is natural with respect to the action of the mapping class group. We then apply this construct…
Geometric model of unbounded sl3 laminations with tropical coordinates.
problem Modeling unbounded laminations in cluster varieties.
method Introducing tropical cluster coordinates and geometric gluing procedures.
result Established a geometric gluing procedure for unbounded sl3 laminations.
We show that the length function of a measured geodesic lamination is convex in Thurston's shear coordinates over Teichmüller space and strictly convex for generic laminations. We give some consequences of this result in the context of Thurston's asymmetric metric on Teichmüller space.
The paper models financial order books using geometric shears and directional liquidity.
problem Understanding the geometry and dynamics of financial order books.
method Structural framework modeling liquidity as emergent observables, geometric shears, and directional imbalances.
result The geometry of financial order books can be described by a rigid drift and geometric shear, leading to a gamma-like profile of projected liquidity.
New method connects veering triangulations to dynamic pairs.
problem Understanding veering triangulations and their properties.
method Shearing decomposition of veering triangulations.
result Canonically associated dynamic pairs of branched surfaces.