arXiv research

Solves the Poisson problem for elastic plates with specific boundary conditions.

We derive a dimensionally-reduced limit theory for an $n$-dimensional nonlinear elastic body that is slender along $k$ dimensions. The starting point is to view an elastic body as an $n$-dimensional Riemannian manifold together with a not necessarily isometric $W^{1,2}$-immersion in $n$-dimensional Euclidean space. The…

Novel defects in hyperbolic sheets explain complex wrinkling patterns in nature.

Sophie Germain's mean curvature deserves recognition as a surface shape measure.

The elastic energy functional of a thin elastic rod or sheet is generalized to the case of an M-dimensional manifold in N-dimensional space. We derive potentials for the stress field and curvatures and find the generalized von Karman equations for a manifold in elastic equilibrium. We perform a scaling analysis of an M…

We prove a relation between the scaling $h^β$ of the elastic energies of shrinking non-Euclidean bodies $S_h$ of thickness $h\to 0$, and the curvature along their mid-surface $S$. This extends and generalizes similar results for plates [BLS16, LRR] to any dimension and co-dimension. In particular, it proves that the na…

The edge of torn elastic sheets and growing leaves often form a hierarchical buckling pattern. Within non-Euclidean plate theory this complex morphology can be understood as low bending energy isometric immersions of hyperbolic Riemannian metrics. With this motivation we study the isometric immersion problem in strip a…

New solutions found for bending of flat surfaces and origami structures.

In Chinese societies, superstition is of paramount importance, and vehicle license plates with desirable numbers can fetch very high prices in auctions. Unlike other valuable items, license plates are not allocated an estimated price before auction. I propose that the task of predicting plate prices can be viewed as a …

The game of plates and olives, introduced by Nicolaescu, begins with an empty table. At each step either an empty plate is put down, an olive is put down on a plate, an olive is removed, an empty plate is removed, or the olives on two plates that both have olives on them are combined on one of the two plates, with the …

The paper sets lower bounds for Laplacian eigenvalues and clamped plate problem eigenvalues.

Tensor variable elimination for plated factor graphs enables exact inference in models with repeated structure.

High throughput screening of compounds (chemicals) is an essential part of drug discovery [7], involving thousands to millions of compounds, with the purpose of identifying candidate hits. Most statistical tools, including the industry standard B-score method, work on individual compound plates and do not exploit cross…

Estimates for plate eigenvalues with nonzero Poisson's ratio.

In earlier work, we provided a general description of the forces of attraction and repulsion, encountered by two parallel vertical plates of infinite extent and of possibly differing materials, when partially immersed in an infinite liquid bath and subject to surface tension forces. In the present study, we examine som…

Extends plate problems to differential forms on manifolds.

Affirm Lord Rayleigh's conjecture on curved spaces for clamped plates.

In this paper, we study eigenvalues of a clamped plate problem. We obtain a lower bound for eigenvalues, which gives an important improvement of results due to Levine and Protter.

Un sous-système de dimension différentielle au plus 2 d'une extension plate est plate. Si un tel système plat est stationnaire, il admet des sorties plates indépendantes du temps. A subsystem of a flat system of differential dimension at most 2 is flat. Furthermore, if such a flat system is stationary, we show that the…

Recent work by Jaffe and Scardicchio has expressed the optical approximation to the Casimir effect as a sum over geometric quantities. The first two authors have developed a technique which uses the complex geometry of the space of oriented affine lines in ${\Bbb{R}}^3$ to describe reflection of rays off a surface. Thi…

In this paper, we study estimates for eigenvalues of the clamped plate problem. A sharp upper bound for eigenvalues is given and the lower bound for eigenvalues in [10] is improved.

For a bounded domain $Ω$ in a complete Riemannian manifold $M^n$, we study estimates for lower order eigenvalues of a clamped plate problem. We obtain universal inequalities for lower order eigenvalues. We would like to remark that our results are sharp.

PAVI speeds up Bayesian inference for large datasets.

This research optimizes plate structures to reduce vibrations in vehicles and aircraft.

New isoperimetric inequality for clamped plates in RCD(0,N) spaces, sharp and stable.

This paper studies eigenvalues of the clamped plate problem on a bounded domain in an $n$-dimensional Euclidean space. We give an estimate for the gap between $\sqrt {Γ_{k+1}-Γ_{1}}$ and $\sqrt {Γ_{k}-Γ_{1}}$, for any positive integer $k$. According to the asymptotic formula of Agmon and Pleijel, we know, the gap betwe…

Study develops efficient algorithm for probabilistic penetration response of composite plates.

The study introduces a new stickiness parameter for stock prices using a non-linear model.

Study fundamental tones of clamped plates on curved spaces.

The paper studies eigenvalue inequalities for a clamped plate problem involving a generalized elliptic differential operator.

Proves Payne conjecture for buckling and membrane eigenvalues.

We study the conformal plate buckling equation (Laplace--Beltrami)^2 u =1, where the L-B operator is for the metric g = e^{2u}g_0, with $g_0$ the standard Euclidean metric on R^2. This conformal elliptic PDE of fourth order is equivalent to the nonlinear system of elliptic PDEs of second order, Delta u +K_g e^(2u)=0, D…

Paper studies eigenvalues of a specific operator on Riemannian manifolds.

Develops control and observer methods for complex systems.

PAVI speeds up VI for large-scale studies by sharing parameterization across i.i.d. variables.

This paper focuses on the port-Hamiltonian formulation of systems described by partial differential equations. Based on a variational principle we derive the equations of motion as well as the boundary conditions in the well-known Lagrangian framework. Then it is of interest to reformulate the equations of motion in a …

Paper tackles vehicle make & model classification with improved accuracy.

This research uses Siamese networks to identify partial mouse brain images from the Allen atlas.

This work develops a high precision fault diagnosis classifier using XAI insights.

Shells resist three out of six possible loads if simply connected.

Sparse elasticity reconstruction from local displacements reduces error.

Six AI solutions accurately detect growth plate planes in mice bone scans.

Analyzes properties of stiffness tensors for elastic wave imaging.

Elastic Cash adjusts money supply to stabilize interest rates.

Proposes using elastic demand to improve forecasting accuracy.

Sharp spectral gap estimates for higher-order operators on hyperbolic spaces.

Characterizes null Lagrangians in Cosserat elasticity.

In the first part of this article we revisit the theory of weighted spinors on conformal manifolds. In the second part we introduce the notions of asymptotically flat Weyl structures and of associated mass, and we prove a conformal version of the positive mass theorem on conformal spin manifolds.