The paper explores strain measures and geodesic distances in the general linear group.
problem Quantifying the deviation of linear transformations from isometries.
method Geometric derivation and analysis of various distance functions on GL_n.
result No bi-invariant distances exist on GL_n, but inverse-invariant distances yield valid strain measures.
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.
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…
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…
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.
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…
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.
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.
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.
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.
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.
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.
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.
New indicator detects financial strain through smart meter data.
problem Fuel poverty in households, affecting millions.
method Smart meters and machine learning for behavior measurement.
result Early detection of financial strain in households.
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 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 …
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.
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. 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.
Bayesian model updating uses VAEs to approximate likelihood with small data.
problem Approximating likelihood for small data sets in structural analysis.
method Uses multimodal VAEs to approximate likelihood, suitable for high-dimensional correlated observations.
result Demonstrates computational efficiency and accuracy compared to original VAE approach.
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.
Study of regular points in extremal subsets of Alexandrov spaces.
problem Characterizing extremal subsets in Alexandrov spaces.
method Definition and analysis of regular points, properties of neighborhoods, and applications to convergence and fibration structures.
result Regular points have full measure and are dense in extremal subsets, with applications to convergence and fibration structures.
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.
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.
PIMA autoencoders discover shared features in multimodal scientific data.
problem Discovering shared information in high-throughput scientific datasets.
method Physics-informed multimodal autoencoders (PIMA) with Gaussian mixture prior and product of experts formulation.
result Accurate cross-modal inference between images and mechanical stress-strain response in lattice metamaterials.
PIE-PINN estimates elastic properties from noisy, low-res displacement data.
problem Estimating heterogeneous elastic properties from low-resolution, noisy data.
method Probabilistic Physics-Informed Neural Network (PIE-PINN) framework combining B-spline and hierarchical scale model.
result Robust estimation of Young's modulus and Poisson's ratio from noisy, low-resolution displacement data.
Paper presents a method for imputing and forecasting structural response from incomplete sensor data.
problem Missing sensor data in structural health monitoring (SHM).
method Incremental Bayesian tensor learning for spatiotemporal missing data reconstruction and forecasting.
result The proposed method achieves accurate and robust imputation and prediction even with high rates of missing data.
Self-supervised learning improves RUL prediction with limited data in fatigue damage prognosis.
problem Limited labelled data for RUL prediction in fatigue damage prognosis.
method Pre-training deep learning models on unlabelled sensor data using self-supervised learning.
result Self-supervised pre-trained models significantly outperform non-pre-trained models in RUL prediction with scarce labelled data.
New method bypasses global fit for LISA's Galactic binaries, extracting population parameters directly.
problem Disentangling LISA's Galactic binary sources from backgrounds in a computationally intensive process.
method Simulation-based approach using normalizing flow to infer population parameters.
result Direct inference of population parameters from LISA's frequency strain series.
Local laGPR speeds up multiscale mechanics simulations without neural networks.
problem High computational costs in multiscale mechanics simulations.
method Local approximate Gaussian process regression (laGPR) combined with FE schemes.
result laGPR offers better accuracy than neural networks for stress predictions.
Observation of the workings of productive organizations shows that the characteristics of a trade, backed by nature given to a technological environment, determine the productive combination implemented by the decision maker, and the structure of the operating cycle which is related. The choice of the production functi…
A new method represents rod shapes as paths in special Euclidean algebra.
problem Representing the shapes of rods and framed curves for mechanical analysis.
method Representing shapes as paths in the special Euclidean algebra.
result The method avoids expensive reconstruction and interpolation in rod mechanics.
Reformulates elasticity complex with new differential and Hodge star operators.
problem Elasticity complex and compatibility condition reformulation.
method Generalized differential complex of Dubois-Violette-Henneaux.
result Integrating formula to recover displacement from strain.
Study variational problem for time-like curves in Einstein universe.
problem Variational problem for time-like curves in Einstein universe.
method Conformally invariant variational problem, analysis of stationary curves, integration by quadratures.
result Stationary curves are trapped into Einsetin universes of dimension 2, 3, or 4.
Study how large-scale flows align small-scale vortices in 3D Euler equations.
problem Understanding how large-scale flows align small-scale vortices in 3D Euler equations.
method Constructing a Lagrangian coordinate to identify when the Lie bracket is zero and investigating the locality of the pressure term.
result Clarified conditions under which small-scale vortices are aligned by large-scale flows.
Neural networks improve gravitational-wave parameter estimation.
problem Estimating parameters of binary black hole systems from gravitational-wave data.
method Autoregressive normalizing flows for likelihood-free inference.
result Performance comparable to current best deep-learning approaches, with fast sampling.