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.
Characterizes null Lagrangians in Cosserat elasticity.
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…
We suggest an alternative mathematical model for the massless neutrino. Consider an elastic continuum in 3-dimensional Euclidean space and assume that points of this continuum can experience no displacements, only rotations. This framework is a special case of the so-called Cosserat theory of elasticity. Rotations of p…
The paper deals with the Weyl equation which is the massless Dirac equation. We study the Weyl equation in the stationary setting, i.e. when the spinor field oscillates harmonically in time. We suggest a new geometric interpretation of the stationary Weyl equation, one which does not require the use of spinors, Pauli m…
The paper deals with the Weyl equation which is the massless Dirac equation. We study the Weyl equation in the stationary setting, i.e. when the the spinor field oscillates harmonically in time. We suggest a new geometric interpretation of the stationary Weyl equation, one which does not require the use of spinors, Pau…
The paper introduces new uniformity and homogeneity concepts for Cosserat media.
Closed-form relations and approximations for SE(3) derivatives for robust numerical simulations.
We discuss how the shape of a special Cosserat rod can be represented as a path in the special Euclidean algebra. By shape we mean all those geometric features that are invariant under isometries of the three-dimensional ambient space. The representation of the shape as a path in the special Euclidean algebra is intrin…
New equations for Cosserat media motions derived from bundle automorphisms.
Study Bernstein-Gelfand-Gelfand complexes on Lipschitz domains, computing cohomology and applying to elasticity models.
We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis which give…
The purpose of this short notice is to present an elementary summary of a few recent results obtained through the application of the formal theory of systems of partial differential equations and Lie pseudo groups to engineering (elasticity theory, electromagnetism, coupling phenomena) and mathematical (gauge theory, g…
We start recalling with critical eyes the mathematical methods used in gauge theory and prove that they are not coherent with continuum mechanics, in particular the analytical mechanics of rigid bodies or hydrodynamics, though using the same group theoretical methods and despite the well known couplings existing betwee…
We suggest an alternative mathematical model for the electron in which the dynamical variables are a coframe (field of orthonormal bases) and a density. The electron mass and external electromagnetic field are incorporated into our model by means of a Kaluza-Klein extension. Our Lagrangian density is proportional to ax…
Geometrically reformulates Cosserat solid mechanics using differential geometry.
A Lie groupoid, called \textit{second-order non-holonomic material Lie groupoid}, is associated in a natural way to any Cosserat media. This groupoid is used to give a new definition of homogeneity which does not depend on a reference crystal. The corresponding Lie algebroid, called \textit{second-order non-holonomic m…
In-plane drill rotations are impossible for smooth shells.
The Spencer operator, introduced by D.C. Spencer fifty years ago, is rarely used in mathematics today and, up to our knowledge, has never been used in engineering applications or mathematical physics. The main purpose of this paper, an extended version of a lecture at the second workshop on Differential Equations by Al…
In 1870, R. Clausius found the virial theorem which amounts to introduce the trace of the stress tensor when studying the foundations of thermodynamics, as a way to relate the absolute temperature of an ideal gas to the mean kinetic energy of its molecules. In 1901, H. Poincar{é} introduced a duality principle in analy…
The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential equations and Lie pseudogroups in order to revisit the mathematical foundations of general relativity. Other engineering examples (contro…
Analyzes properties of stiffness tensors for elastic wave imaging.
This paper introduces an elasticity reconstruction method based on local displacement observations of elastic bodies. Sparse reconstruction theory is applied to formulate the underdetermined inverse problems of elasticity reconstruction including unobserved areas. An online local clustering scheme called a superelement…
Elastic Cash adjusts money supply to stabilize interest rates.
Approximate 3D elastic curves with exact constraints
In this paper we will discuss some new developments in the design of numerical methods for optimal control problems of Lagrangian systems on Lie groups. We will construct these geometric integrators using discrete variational calculus on Lie groups, deriving a discrete version of the second-order Euler-Lagrange equatio…
The paper studies rigidity and continuity in nonlinear elasticity on manifolds and hypersurfaces.
Study preserves planar and graphical properties of curves under elastic flow.
The paper studies the free elastic flow of closed curves and finds their asymptotic shape converges to a circle.
Motivated by the problem of finding an explicit description of a developable narrow Moebius strip of minimal bending energy, which was first formulated by M. Sadowsky in 1930, we will develop the theory of elastic strips. Recently E.L. Starostin and G.H.M. van der Heijden found a numerical description for an elastic Mo…
Study on migrating elastic flows of curves across half-planes.
Study gauge freedoms in elastic wave equations and Dirichlet-to-Neumann map.
Solves curve migration problem with elastic flows.
New insights into stability of special curves on spheres.
Due to the advantage of achieving a better performance under weak regularization, elastic net has attracted wide attention in statistics, machine learning, bioinformatics, and other fields. In particular, a variation of the elastic net, adaptive elastic net (AEN), integrates the adaptive grouping effect. In this paper,…
Symmetric elastic knots are found for certain classes with dihedral symmetry.
We study a class of elastic energy functionals for maps between planar domains (among them the so-called squared distance functional) whose critical points (elastic maps) allow a far more complete theory than one would expect from general elasticity theory. For some of these functionals elastic maps even admit a "Weier…
Study of elastic models in non-Euclidean spaces via Γ-convergence.
New discrete curves defined in space forms with geometric properties.
Demand variance can result in a mismatch between planned supply and actual demand. Demand shaping strategies such as pricing can be used to shift elastic demand to reduce the imbalance. In this work, we propose to consider elastic demand in the forecasting phase. We present a method to reallocate the historical elastic…
The elastic flow, which is the -gradient flow of the elastic energy, has several applications in geometry and elasticity theory. We present stable discretizations for the elastic flow in two-dimensional Riemannian manifolds that are conformally flat, i.e.\ conformally equivalent to the Euclidean space. Examples in…
Unified survey of elastic flow for curves and networks.
Study on elastic curves with variable stiffness, derived from bending energy.
Study on closed -elastic curves in hyperbolic and de Sitter planes.
In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, . We prove the -convergence of elastic energies for configurations of a converging sequence, , of body manifolds. This convergence result …
Study on Transfer Elastic Net error bounds and grouping effect.
Study shows global invertibility in nonlinear elasticity with vanishing self-repulsion term.
Study on spectral asymptotics in elasticity on smooth manifolds.
Study on surfaces minimizing elastic energy with boundary constraints.