Study on buckling of cylindrical shells using elastic energy scaling.
problem Buckling behavior of cylindrical shells under compression.
method Scaling analysis and solution of an obstacle problem for minimal elastic energy.
result Explicit bifurcation point between compression and buckling determined.
Paper proves rigidity estimates for hyperbolic shells and applies them to \(Γ\)-limit theory.
problem Rigidity of hyperbolic shells and their \(Γ\)-limit behavior.
method Nonlinear rigidity estimates for \(H^1\) deformations and hyperbolic shells with clamped lateral boundary.
result Derives the optimal exponent \(h^{-4/3}\) for hyperbolic shells.
Shells resist three out of six possible loads if simply connected.
problem Understanding the load resistance of shells.
method Formal mathematical analysis of shell strains and deflections.
result The space of strains is three-dimensional for simply-connected shells.
Symmetries in shell theory lead to multiple deformation possibilities.
problem Understanding symmetries in thin shell deformation theory.
method Analyzing symmetries in the context of linear theory of thin shells.
result Infinitely many deformations without shear strains and twisting.
The writhe polynomial invariant is proven for virtual knots via shell moves.
problem Determining equivalence of oriented virtual knots using writhe polynomials.
method Introducing shell moves to prove equivalence of writhe polynomials.
result Two virtual knots are equivalent if they can be transformed by shell moves.
Discrete Morse functions induce shellings with critical tiles corresponding to function's critical faces.
problem Mapping discrete Morse functions to shellings for topological analysis.
method Inducing Morse shellings on the second barycentric subdivision of a simplicial complex.
result Critical tiles of induced shellings correspond to critical faces of the discrete Morse function.
Method designs lightweight, structurally robust shell objects.
problem Designing lightweight, structurally robust shell objects under external forces.
method Shape parametrization based on Laplace's equation for smooth, intersection-free boundaries; gradient-free optimization algorithm.
result Practical solution to structural design of hollow objects with single inner cavity.
New method extends discrete Morse theory to simplicial complexes.
problem Discrete Morse theory on simplicial complexes.
method Morse shellings and compatible discrete Morse functions.
result Triangulated surfaces and manifolds have Morse shellable triangulations.
Extends Penrose's method to null shells with pressure and energy flux.
problem Constructing null thin shells with arbitrary gravitational/matter content.
method Derive locally Lipschitz metric and coordinate transformation.
result Example of null shell with non-trivial energy density, flux, and pressure in Minkowski space.
The paper proves rigidity for shells in non-Euclidean spaces.
problem Proving rigidity for shells in non-Euclidean spaces.
method Analyzing a stretching plus bending functional of an elastic shell in a Riemannian manifold.
result A sequence of immersions of asymptotically vanishing energy converges to an isometric immersion of the shell.
This paper studies singular improper affine spheres from Lagrangian submanifolds, classifying stable singularities.
problem Understanding singularities of improper affine spheres from Lagrangian submanifolds.
method Analyzes canonical improper affine spheres and their on-shell singularities from Lagrangian submanifolds in arbitrary even dimensions.
result Classifies stable Lagrangian/Legendrian singularities on shell for improper affine spheres.
We introduce a method to learn a mixture of submodular "shells" in a large-margin setting. A submodular shell is an abstract submodular function that can be instantiated with a ground set and a set of parameters to produce a submodular function. A mixture of such shells can then also be so instantiated to produce a mor…
New concept of effective isometries for compliant shells.
problem Inadequate classification of isometric deformations for compliant shells.
method Introduce effective isometric deformations defined by first-order isometry in a small scale separation parameter.
result Effective isometries are solutions to a quasilinear second-order PDE.
Paper derives formulas for surface variations in shell theory.
problem Deriving first variation formulas for surfaces in thin shell theory.
method Using strain-displacement relations from thin shell theory.
result Provides formulas for linear Weingarten surfaces as stationary points.
We describe an end-to-end real-time S&P futures trading system. Inner-shell stochastic nonlinear dynamic models are developed, and Canonical Momenta Indicators (CMI) are derived from a fitted Lagrangian used by outer-shell trading models dependent on these indicators. Recursive and adaptive optimization using Adaptive …
Off-shell (4,0) supermultiplets in 2-dimensions are formulated. These are used to construct sigma models whose target spaces are vector bundles over manifolds that are hyperkähler with torsion. The off-shell supersymmetry implies that the complex structures are simultaneously integrable and allows us to write actions…
Semichiral sigma models with a four-dimensional target space do not support extended N=(4,4) supersymmetries off-shell arXiv:0903.2376, arXiv:0912.4724. We contribute towards the understanding of the non-manifest on-shell transformations in (2,2) superspace by analyzing the extended on-shell supersymmetry of such model…
NSBI approach detects Higgs trilinear coupling with high luminosity upgrade constraints.
problem Determining the Higgs trilinear self-coupling via off-shell Higgs production.
method Hybrid neural simulation-based inference (NSBI) incorporating SMEFT and quantum interference effects.
result NSBI achieves sensitivity close to theoretical optimum for Higgs trilinear self-coupling.
Study cylindrical symmetric Finsler metrics with vanishing Douglas curvature.
problem Understanding Finsler metrics with specific curvature properties.
method Analyzing cylindrically symmetric Finsler metrics and solving differential equations.
result Differential equations for cylindrically symmetric Finsler metrics with vanishing Douglas curvature.
We discuss several issues regarding material homogeneity and strain compatibility for materially uniform thin elastic shells from the viewpoint of a 3-dimensional theory, with small thickness, as well as a 2-dimensional Cosserat theory. A relationship between inhomogeneity and incompatibility measures under the two des…
Asymptotically cylindrical Ricci-flat manifolds play a key role in constructing Topological Quantum Field Theories. It is particularly important to understand their behavior at the cylindrical ends and the natural restrictions on the geometry. In this paper we show that an orientable, connected, asymptotically cylindri…
Study resolves flow through cylindrical singularities, proving nonfattening.
problem Analyzing free boundary flow through cylindrical singularities.
method Foundational results for free boundary Brakke flows and classification of ancient flows.
result Proves all cylindrical singularities have a mean-convex neighborhood, leading to well-posed flow.
The paper introduces surfaces with constant solid angle for designing shell structures.
problem Designing shell structures with balanced structural, spatial, aesthetic, and construction requirements.
method Proposes surfaces defined by constant solid angle at all points, using Gauss-Bonnet theorem and Newton's method.
result Constant solid angle surfaces enable control over boundary slope and span-to-height ratio, making them structurally viable.
We study gluings of asymptotically cylindrical special Lagrangian submanifolds in asymptotically cylindrical Calabi--Yau manifolds. We prove both that there is a well-defined gluing map, and, after reviewing the deformation theory for special Lagrangians, prove that this gluing map defines a local diffeomorphism from m…
Study cylindrical symmetric Finsler metrics that are projectively flat.
problem Characterize Finsler metrics that are projectively flat.
method Solve the system of differential equations for cylindrical symmetric Finsler metrics.
result Provide a family of solutions for the projectively flat Finsler metrics.
This paper studies mean curvature flows near cylindrical singularities.
problem Understanding the behavior of mean curvature flows near cylindrical singularities.
method Proved the rescaled flow converges to a graph over a cylinder, defined nondegeneracy, and showed properties of nondegenerate singularities.
result Nondegenerate cylindrical singularities are isolated, have a mean convex neighborhood, and are type-I.
In an earlier paper, we proved that, under certain hypotheses, the moduli space of an asymptotically cylindrical special Lagrangian submanifold with fixed boundary of an asymptotically cylindrical Calabi-Yau 3-fold is a smooth manifold. Here we prove the analogous result for an asymptotically cylindrical special Lagran…
Optimizing shapes for a specific eigenvalue problem involving two balls.
problem Optimizing shapes for the first mixed Steklov-Dirichlet eigenvalue.
method Geometric proof based on Newton's shell theorem.
result Geometric insight into eigenvalue optimization.
A classical result by Pachner states that two d-dimensional combinatorial manifolds with boundary are PL homeomorphic if and only they can be connected by a sequence of shellings and inverse shellings. We prove that for balanced, i.e., properly (d+1)-colored, manifolds such a sequence can be chosen such that bala…
Study explores kinematics of surfaces under metric restrictions.
problem Understanding the kinematics of surfaces under metric constraints.
method Analyzed three energy contents: stretching, drilling, and bending.
result Metric restrictions can hinder the elastic response of a shell.
Shows uniqueness of cylindrical blowups in mean curvature flow.
problem Uniqueness of cylindrical blowups in mean curvature flow in higher codimension.
method Developed new methods to prove uniqueness of cylindrical blowups.
result Implication of regularity of the singular set for the system.
Finite number of eigenvalues found in cylindrical surface.
problem Finding eigenvalues in manifolds with cylindrical ends.
method Constructing a surface with a cylindrical end attached to a hyperbolic torus.
result First example of a finite and nonzero number of embedded eigenvalues in a cylindrical manifold.
Study on parabolic points and cylindrical surfaces in Euclidean 3-space.
problem Characterizing parabolic points and their geometric properties.
method Introducing contact cylindrical surfaces and analyzing their properties.
result Characterization of A-singularity through projections. We study the deformations of an asymptotically cylindrical Cayley submanifold inside an asymptotically cylindrical Spin(7)-manifold. We prove an index formula for the operator of Dirac type that arises as the linearisation of the deformation map and show that if the Spin(7)-structure is generic, then there are no obstr…
FGSV defends against shell company attacks in group data valuation.
problem Shell company attacks on group-level data valuation.
method Developed a provably fast and accurate approximation algorithm for FGSV.
result Empirical results show significant improvement in computational efficiency and accuracy.
Cylindrical contact homology studied for a specific class of 3-manifolds.
problem Calculating the cylindrical contact homology for a specific class of 3-manifolds.
method Using cylindrical contact homology, a relatively simple version of symplectic field theory.
result Complete description of cylindrical contact homology for a specific class of 3-manifolds.
Proves uniqueness of cylindrical tangent flows in mean curvature flow.
problem Proving uniqueness of cylindrical singularity models in mean curvature flow.
method Inspired by Székelyhidi's approach, uses a different method to prove uniqueness.
result Proves uniqueness of cylindrical tangent flows.
We solve the long standing problem of finding an off-shell supersymmetric formulation for a general N = (2, 2) nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates; these correspond to particular superfields that allow for a superspace descriptio…
Theoretical study explains grokking in neural networks.
problem Understanding the abrupt transition from fitting to generalizing in neural networks.
method Characterized a shell-core topological configuration of the solution space induced by Adam's optimization dynamics.
result Derived grokking scaling laws for learning rate, batch size, and regularization coefficient.
Extends ASD connection existence to 4-manifolds with cylindrical ends.
problem Existence of ASD connections on 4-manifolds with specific ends.
method Extends gluing theorems to cylindrical ends, using mASD connections.
result Establishes existence of ASD connections on 4-manifolds with cylindrical ends.
We study a class of asymptotically cylindrical Ricci-flat Kähler metrics arising on quasiprojective manifolds. Using the Calabi--Yau geometry and analysis and the Kodaira--Kuranishi--Spencer theory and building up on results of N.Koiso for the case of compact manifolds, we show that under rather general hypotheses any …
Paper proves strong uniqueness of cylindrical tangent flows near singularity in Ricci flow.
problem Proving strong uniqueness of cylindrical tangent flows near singularity in Ricci flow.
method Established Lojasiewicz inequality for pointed W-entropy under cylindrical geometry assumption. result Strong uniqueness of cylindrical tangent flows at first singular time of Ricci flow proved.
Chern-Simons gauge theories in 3 dimensions and the Poisson Sigma Model (PSM) in 2 dimensions are examples of the same theory, if their field equations are interpreted as morphisms of Lie algebroids and their symmetries (on-shell) as homotopies of such morphisms. We point out that the (off-shell) gauge symmetries of th…
Unique cylindrical tangent cone for Simons' hypersurface found.
problem Uniqueness of cylindrical tangent cones for area-minimizing hypersurfaces.
method Developed a new Lojasiewicz inequality for non-isolated singularities.
result Cylindrical tangent cone for Simons' hypersurface is unique.
Uniqueness proven for cylindrical tangent cones in high dimensions.
problem Proving uniqueness of cylindrical tangent cones in high dimensions.
method Analyzing area-minimizing hypersurfaces in R^9.
result Uniqueness of cylindrical tangent cones Cp,qimesR in R9. We prove that for a 7-dimensional manifold M with cylindrical ends the moduli space of exponentially asymptotically cylindrical torsion-free G_2 structures is a smooth manifold (if non-empty), and study some of its local properties. We also show that the holonomy of the induced metric of an exponentially asymptotically…
We develop some consequences of the connection between Calabi-Yau structures and torsion-free G2 structures on compact and asymptotically cylindrical six- and seven-dimensional manifolds. Firstly, we improve the known proof that matching asymptotically cylindrical Calabi-Yau threefolds can be glued. Secondly, we giv…
New special Lagrangian submanifolds with cylindrical tangent cones are constructed.
problem Constructing special Lagrangian submanifolds with specific geometric properties.
method Constructing examples in a neighborhood of the origin with an isolated singularity and cylindrical tangent cone.
result Existence of special Lagrangian submanifolds with cylindrical tangent cones, including examples with transverse planes.