The paper analyzes defects on structured surfaces and calculates stress and shape.
problem Analyzing defects on structured surfaces and their effects on stress and shape.
method Classified and quantified defects, derived strain incompatibility relations, and applied to shells.
result Determined internal stress field and deformed shape for shells with defects.
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…
Unified framework for strain-gradient plasticity from dislocations.
problem Deriving strain-gradient plasticity from edge-dislocations.
method Γ-limit derivation in a continuum framework with smooth frame fields and dislocation circulation.
result Unified strain-gradient model with new geometric rigidity estimates.
We develop a theory to represent dislocated single crystals at the mesoscopic scale by considering concentrated effects, governed by the distribution theory combined with multiple-valued kinematic fields. Our approach gives a new understanding of the continuum theory of defects as developed by Kroener (1980) and other …
Paper demonstrates triaxial strain tomography using neutron imaging.
problem Reconstructing full triaxial strain field from Bragg-edge neutron images.
method Gaussian process based approach ensuring equilibrium and boundary conditions.
result Validation of reconstruction through comparison with conventional strain scans and simulations.
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…
New method reconstructs strain and lattice spacing from neutron data.
problem Jointly reconstructing strain and lattice spacing from neutron data.
method Solves non-linear problem ensuring strain field equilibrium with knowledge of boundary conditions.
result Demonstrates ability to jointly reconstruct strain and lattice spacing from simulated data.
Incompatible operations affect Khovanov homology and spectral sequences.
problem Incompatibility between operations and spectral sequences.
method Observation of obstructions to integral lifting and spectrification.
result Lipshitz-Sarkar Steenrod operations are incompatible with Szabo's spectral sequence.
The paper proves properties of strain tensors on surfaces with changing Gauss curvature.
problem Regularity of solutions to strain tensor equations on surfaces with variable Gauss curvature.
method Proof of regularity, density property, and matching property.
result Established matching property and density of smooth infinitesimal isometries.
Unified theory solves strain compatibility and elasticity of origami metamaterials.
problem Understanding and controlling the morphing paths of origami metamaterials.
method Unified theory for a wide array of origami tessellations, solving strain compatibility and elasticity.
result Origami metamaterials exhibit equal but opposite in-plane and out-of-plane Poisson's ratios and bending energy depends on strain gradient.
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 GLn, and use its induced geodes…
CNN improves frame selection for ultrasound elastography.
problem Choosing suitable frames for accurate strain estimation in ultrasound elastography.
method Convolutional Neural Network (CNN) for frame selection.
result CNN selects frames in 5.4 ms for high-quality strain images.
Emergenet predicts animal influenza strain emergence, outperforming current methods.
problem Limited ability to quantitatively assess animal influenza strain emergence.
method Infer digital twin of sequence evolution using 220,151 HA sequences.
result Emergenet predictions outperform WHO seasonal vaccine recommendations and CDC IRAT scores.
This paper reviews incompatibilities of comonotonic risk measures.
problem Incompatibilities of comonotonic risk measures with central properties.
method Literature review and Choquet representation of comonotonic additive risk measures.
result Comonotonic additive risk measures cannot be surplus invariant.
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 logU, and show that they can be uniquely char…
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.
TIER uses extended strain data to improve gravitational wave detection sensitivity.
problem Improving gravitational wave detection sensitivity using extended strain data.
method TIER framework using machine learning to capture extended strain data features.
result Up to 20% improvement in sensitive volume time in LIGO-Virgo-Kagra O3 data.
Model trains passing events on a bridge using multilevel Gaussian process.
problem Represent aggregate train-passing events from a bridge monitoring system.
method Formulate a combined model with low-rank approximation hierarchical Gaussian process, incorporating domain expertise as constraints.
result Allow for simulation of previously unobserved train types.
Differentiable sorting and rank normalization are incompatible, with specific conditions for admissibility.
problem Incompatibility between differentiable sorting and rank normalization.
method Formalized admissibility through monotone invariance, batch independence, and rank-space stability conditions.
result Different gap-sensitive and batchwise relaxations of rank normalization violate the conditions for admissibility.
The paper explores the incompatibility between fair privacy, need-to-know, and fairness in classifier outputs.
problem The interaction between fair privacy, need-to-know, and fairness in classifier outputs.
method Formulated and explored the interaction between fair privacy, need-to-know, and fairness in classifier outputs.
result Optimal classifiers are generally incompatible with fair privacy and need-to-know.
Defense against backdoor attacks by clustering incompatible data subsets.
problem Backdoor poisoning attacks on deep neural networks.
method Incompatibility clustering of data subsets during training.
result Successfully reduces attack success rate to below 1%.
Physics-informed deep learning approximates strain gradient plasticity solutions.
problem Stiffness and computational challenges in solving strain gradient plasticity models.
method Physics-informed deep learning (PIDL) with modified loss functions and optimization schemes.
result PIDL methods address stiffness and computational challenges in strain gradient plasticity.
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.
We derive a continuum model from discrete elastic models on smooth manifolds.
problem Modeling stress-free configurations in geometrically-incompatible elastic systems.
method Variational convergence of discrete models to a continuum model.
result No stress-free configurations unless the manifold is flat.
The paper develops GPR models for hyperelastic materials, improving accuracy and rotational invariance.
problem Modeling stress tensors of hyperelastic materials with fewer training examples and higher accuracy.
method Developed three approaches: direct stress tensor modeling, embedding rotational invariance, and recovering strain-energy density.
result Improved GPR models achieve higher accuracy and rotational invariance with fewer training examples.
TANNs integrate thermodynamics into ANN models for accurate, consistent predictions.
problem Lack of rigorous physics-based approach in ANN constitutive modeling.
method TANNs encode thermodynamics principles in neural network architecture using automatic differentiation.
result TANNs produce thermodynamically consistent predictions without requiring large datasets.
Unified theory for curved shell deformations with elastic and inelastic components.
problem Coupled nonlinear elastic and inelastic deformations of curved thin shells.
method Multiplicative decomposition of surface deformation gradient, detailed kinematics analysis, surface balance laws, constitutive relations derived from thermodynamics.
result Unified constitutive relations for growth, chemical swelling, thermoelasticity, viscoelasticity and elastoplasticity of shells.
Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is developed to analytically predict the equilibrium deformed helical shape of an initiall…
A new method quantifies uncertainty in brain injury simulations.
problem High computational cost and high-dimensional inputs/outputs limit traditional UQ methods for biofidelic head models.
method Two-stage, data-driven manifold learning framework using Gaussian kernel-density estimation, diffusion maps, and Grassmannian diffusion maps.
result Surrogate models reduce computational cost while providing highly accurate approximations of the computational model.
Gradient flows for knot energies ensure long-term existence of knotted loops.
problem Ensuring long-term existence of knotted loops under various energies.
method Banach gradient flows, curves of maximal slope, logarithmic strain control.
result Established long-time existence of gradient flows for knot energies.
Deep learning speeds up gravitational wave analysis.
problem Computational challenge in analyzing gravitational wave data.
method Trained a neural-network to model posterior probability distributions over 15-dimensional system parameters.
result Generated accurate posterior samples at high speed.
Geometrically reformulates Cosserat solid mechanics using differential geometry.
problem Formalizing Cosserat solid mechanics in modern differential geometry.
method Formulation as a principal fibre bundle, using Cartan's magic formula, and integrating infinitesimal strains.
result Reveals strain as a Lie algebra-valued one-form and finite strain through integration.
Study shows incompatibility of certain scalar curvatures on manifolds.
problem Incompatibility of scalar curvatures on manifolds.
method Analyzing closed manifolds with positive Yamabe invariant and positive Morse functions.
result Existence of energetically bounded solutions for related candidate functions.
New path integrals for elasticity derived from differential complex theory.
problem Deriving path integrals for elasticity equations.
method Using Bernstein-Gelfand-Gelfand (BGG) construction and properties of the de Rham complex, derived path integral operators for elasticity.
result Path integral operators P for elasticity satisfying DP+PD=id and P2=0. For a bounded N-dimensional domain with Lipschitz boundary we extend Korn's first inequality to incompatible tensor fields. For compatible tensor fields our estimate reduces to a non-standard variant of the well known Korn's first inequality. On the other hand, for skew-symmetric tensor fields our new estimate turns to…
Improved VAE models avoid posterior collapse in text modeling.
problem Posterior collapse in VAEs leads to poor data manifold parameterization.
method Coupled-VAE couples a VAE with a deterministic autoencoder to improve encoder and decoder parameterizations.
result Coupled-VAE consistently improves results in probability estimation and latent space richness.
Study of elastic models in non-Euclidean spaces via Γ-convergence.
problem Elasticity in non-Euclidean ambient spaces with incompatible local rest distances.
method Γ-convergence to derive a limit elastic model, relating minimum energy to curvature discrepancy.
result Linearized version of a conjecture in elasticity confirmed, linking energy to curvature.
The fixed-point index of a homeomorphism of Jordan curves measures the number of fixed-points, with multiplicity, of the extension of the homeomorphism to the full Jordan domains in question. The now-classical Circle Index Lemma says that the fixed-point index of a positive-orientation-preserving homeomorphism of round…
New method shows ignoring morphological graph info improves reinforcement learning performance.
problem Improving reinforcement learning performance in incompatible environments.
method Transformer-based approach (Amorpheus) that ignores morphological graph information.
result Transformer-based approach outperforms GNN-based methods that use morphological information.
We derive a new model for pre-strained thin films, which consists of minimizing a biharmonic energy of deformations v∈W2,2 satisfying the Monge-Ampère constraint det∇2v=f. We further discuss multiplicity properties of the minimizers of this model, in some special cases.
Paper introduces a streaming compression method for monitoring pedestrian events on footbridges.
problem Storage and analysis of high-rate sensor data from instrumented infrastructure is computationally challenging.
method Develops a streaming feature-based compression method to preserve key patterns and features of pedestrian events.
result Demonstrates the trade-off between compression and accuracy during and between pedestrian events.
Non-Euclidean, or incompatible elasticity is an elastic theory for pre-stressed materials, which is based on a modeling of the elastic body as a Riemannian manifold. In this paper we derive a dimensionally-reduced model of the so-called membrane limit of a thin incompatible body. By generalizing classical dimension red…
Cartesian neural network models learn soft tissue mechanical properties without shape assumptions.
problem Model-based methods limit elastography to imaging linear-elastic parameters.
method Data-driven neural network constitutive models (NNCMs) learn stress-strain relationships from force-displacement data.
result NNCMs can characterize mechanical properties and their spatial distribution without prior shape knowledge.
Cincer cleans both new and past data by identifying and relabeling suspicious and counter-examples.
problem Sequential learning under label noise, especially in applications with human supervision.
method Cincer uses example-based explanations to identify and relabel suspicious and counter-examples, leveraging Fisher information matrix approximation.
result Cincer achieves better data and models by clarifying the model's suspicions, especially with FIM approximation.
Affinity propagation is an exemplar-based clustering algorithm that finds a set of data-points that best exemplify the data, and associates each datapoint with one exemplar. We extend affinity propagation in a principled way to solve the hierarchical clustering problem, which arises in a variety of domains including bi…
A new model for simulating cloth manipulation in robots, accurate to within 1cm.
problem Accurately simulating cloth manipulation in robots, especially in moderate stress environments.
method A continuous, isometric strain model for textiles, treating them as inextensible surfaces with only isometric motions. Aerodynamic effects are incorporated through virtual uncoupling of mass.
result Simulations are accurate to within 1cm compared to real-world manipulation, even with coarse meshes.
This work extends elasticity theory to curved spaces, solving stress potentials.
problem Addressing elasticity in curved spaces with boundary.
method Using double forms and bilaplacian operator regularity, solving biharmonic equations.
result Stress potentials can be used in non-Euclidean geometries.
New method weaves paper strips for designing curved surfaces with elasticity.
problem Designing general curved surfaces with geometrical elasticity.
method Shape optimization of paper strips using nonlinear elasticity theory.
result Demonstrated creation of catenoid and helicoid surfaces with 54 paper strips.