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.
Symmetries in shell theory lead to multiple deformation possibilities.
We consider the two logarithmic strain measures\[ω_{\rm iso}=\|\mathrm{dev}_n\log U\|=\|\mathrm{dev}_n\log \sqrt{F^TF}\|\quad\text{ and }\quad ω_{\rm vol}=|\mathrm{tr}(\log U)|=|\mathrm{tr}(\log\sqrt{F^TF})|\,,\]which are isotropic invariants of the Hencky strain tensor , and show that they can be uniquely char…
Shells resist three out of six possible loads if simply connected.
We study the problem of finding strain-minimising stream surfaces in a divergence-free vector field. These surfaces are generated by motions of seed curves that propagate through the field in a strain minimising manner, i.e., they move without stretching or shrinking, preserving the length of their arbitrary arc. In ge…
This paper presents a proof-of-concept demonstration of triaxial strain tomography from Bragg-edge neutron imaging within a three-dimensional sample. Bragg-edge neutron transmission can provide high-resolution images of the average through thickness strain within a polycrystalline material. This poses an associated ric…
Study of circle homeomorphisms with square summable diamond shears.
Unified framework for strain-gradient plasticity from dislocations.
Invariants of braids found using shear coordinates in hyperbolic geometry.
Given a distribution of defects on a structured surface, such as those represented by 2-dimensional crystalline materials, liquid crystalline surfaces, and thin sandwiched shells, what is the resulting stress field and the deformed shape? Motivated by this concern, we first classify, and quantify, the translational, ro…
Bounding shears in ideal triangulations on hyperbolic surfaces.
New model reduces bias in cosmic shear measurements.
Recently, several algorithms for strain tomography from energy-resolved neutron transmission measurements have been proposed. These methods assume that the stress-free lattice spacing is a known constant limiting their application to the study of stresses generated by manufacturing and loading methods that do not…
The paper proves properties of strain tensors on surfaces with changing Gauss curvature.
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…
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.
Unified theory solves strain compatibility and elasticity of origami metamaterials.
We consider various notions of strains; quantitative measures for the deviation of a linear transformation from an isometry. The main approach, which is motivated by physical applications and follows the work of Patrizio Neff and co-workers , is to select a Riemannian metric on , and use its induced geodes…
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 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 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 …
Emergenet predicts animal influenza strain emergence, outperforming current methods.
Geodesic patterns, shears, and Anosov representations of the modular group.
Ultrasound elastography is used to estimate the mechanical properties of the tissue by monitoring its response to an internal or external force. Different levels of deformation are obtained from different tissue types depending on their mechanical properties, where stiffer tissues deform less. Given two radio frequency…
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.
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.
Paper derives formulas for surface variations in shell theory.
Sparse regression models CMs from oscillatory shear data efficiently.
The entropy models have been recently adopted in many studies to evaluate the distribution of the shear stress in circular channels. However, the uncertainty in their predictions and their reliability remains an open question. We present a novel method to evaluate the uncertainty of four popular entropy models, includi…
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…
Shear stress distribution prediction in open channels is of utmost importance in hydraulic structural engineering as it directly affects the design of stable channels. In this study, at first, a series of experimental tests were conducted to assess the shear stress distribution in prismatic compound channels. The shear…
Study circular foliations and shear-radius coordinates on hyperbolic cone surfaces.
TIER uses extended strain data to improve gravitational wave detection sensitivity.
Model trains passing events on a bridge using multilevel Gaussian process.
The paper extends optimal transport for linear separability of sheared distributions in supervised learning.
Classifies two-step solvable Lie groups with SKT structures.
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.
Study quasisymmetric maps on hyperbolic plane boundaries.
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.
Abstract: 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 except for six values of .
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.