New material groupoid theory subdivides non-uniform bodies into smoothly uniform parts and isolated points.
problem Lack of differentiability in material bodies leads to non-uniformity.
method Introducing material groupoid and material distribution to study non-uniform bodies rigorously.
result Material bodies can be subdivided into smoothly uniform parts and isolated points.
Study on materials with disclinations, limiting their size.
problem Limiting the size of disclinations in materials with symmetries.
method Defining material-uniform hyperelastic bodies with disclinations, rigorously analyzing their properties.
result The size of disclinations is limited by the symmetries of the constitutive relation.
Study uniformity of material bodies using groupoids.
problem Understanding uniformity and homogeneity of material bodies.
method Using groupoids and algebraic subgroupoids to analyze material bodies.
result Uniform material bodies can be covered by transitive material foliations and their leaves generate transitive Lie groupoids.
Study material evolution using groupoids to track intrinsic properties.
problem Tracking material evolution without considering the whole body.
method Construct a groupoid encoding intrinsic properties and characteristic foliations.
result Define the evolution equation for material points.
Unified framework for non-uniform materials evolving over time.
problem Dealing with non-uniform materials evolving over time.
method Constructing a material groupoid and material distribution.
result Unified framework for general non-uniform evolution materials.
A Lie groupoid, called \textit{material Lie groupoid}, is associated in a natural way to any elastic material. The corresponding Lie algebroid, called \textit{material algebroid}, is used to characterize the uniformity and the homogeneity properties of the material. The relation to previous results in terms of G−stru…
MPM-ParVI uses particle sampling for variational inference.
problem Variational inference for complex probabilistic models.
method Material Point Method (MPM) for particle-based simulation.
result Deterministic sampling and inference for intractable densities.
A geometrical interpretation of the G-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of homogeneity, the corresponding inhomogeneity conditions are obtained
Material properties linked to Lie groupoids and algebroids in continuum mechanics.
problem Understanding material properties through groupoids and algebroids.
method Intuitive treatment of material groupoids and their algebroids.
result Material groupoids and algebroids are linked to material properties and their deformations.
Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a configuration of a body in classical elasticity is the sum of local contributions …
Establishes inequalities linking body size, mass, angular momentum, and charge.
problem Understanding the relationship between a body's size, mass, angular momentum, and charge.
method Analyzes axisymmetric initial data sets for the Einstein equations, using a computable notion of size.
result Provides black hole existence criteria even in the time-symmetric case.
A novel method computes Wigner kernels for atomic environments, achieving state-of-the-art accuracy.
problem Efficiently describing local atomic environments in materials science.
method Computes fully equivariant and body-ordered kernels iteratively, independent of basis.
result Achieves state-of-the-art accuracy on the QM9 benchmark dataset.
Paper explores limits of distributed dislocations in geometric and constitutive paradigms.
problem Understanding limits of distributed dislocations in geometric and constitutive paradigms.
method Review and comparison of geometric and constitutive paradigms, analysis of edge dislocations in both paradigms.
result Homogenization theories in geometric and constitutive paradigms are consistent and identical in the case of constitutive relations having discrete symmetries.
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…
Machine learning predicts electron correlations in disordered materials.
problem Predicting electron correlations in disordered materials.
method Combining neural networks with many-body techniques to learn electron behavior in the Anderson-Hubbard model.
result A neural network accurately predicts electron correlation properties in disordered systems.
Paper learns particle dynamics for versatile object manipulation.
problem Challenges in traditional rigid-body physics engines for complex scenes.
method Combines learning with particle-based systems for versatile object manipulation.
result Robots achieve complex manipulation tasks using the learned simulator.
MACE uses higher-order messages to create fast, accurate force fields.
problem Creating fast and accurate force fields in computational chemistry and materials science.
method Introducing MACE, an equivariant MPNN model that uses four-body messages.
result MACE reduces the required number of message passing iterations to just two, achieving state-of-the-art accuracy.
Mathematician summarizes protein geometry and mutation effects.
problem Understanding how proteins mutate and their structure-function relationship.
method Mathematical analysis of protein structures and functions, focusing on hydrogen bonds and secondary structure.
result Protein secondary structure regulates mutation by stabilizing or destabilizing regions.
In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric represents the evolution of the stress-free (natural) configuration of the body in response to changes in mass density and "shape". We show t…
Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are defining a mapping of an input function to an output function, and distinguishing metallic from insulating solutions. Both meta…
In this paper we propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds associated to the extended musculo-skeletal configuration…
The study of isospectral surfaces in Euclidean and hyperbolic geometries.
problem Existence of non-isometric surfaces with identical chord length distributions.
method Construction of isospectral pairs of hyperbolic surfaces without common covers.
result Found isospectral pairs of hyperbolic surfaces with no common cover.
PSI-KT improves KT accuracy and interpretability in learning materials.
problem Optimizing learning materials selection and timing for understanding and retention.
method Hierarchical generative approach using Bayesian inference.
result Superior multi-step predictive accuracy and scalable inference.
Paper proposes a new method for designing materials using deep learning.
problem Designing high-performance material distributions from given distributions.
method Iterative process of selecting, generating, and merging material distributions using a deep generative model.
result The method improves material performance through iterative refinement.
DECT-MULTRA improves material decomposition in CT images.
problem Noise and artifacts degrade material images in DECT imaging.
method Combines PWLS estimation with MULTRA model for efficient clustering and sparse coding.
result Superior material image quality and decomposition accuracy compared to other methods.
MatGAN uses GAN to efficiently generate new inorganic materials.
problem Efficiently searching the vast chemical design space for new materials.
method Generative adversarial network (GAN) trained on ICSD materials database.
result 92.53% novelty and 84.5% chemically valid samples generated.
Deep learning model reconstructs material microstructures from feature representations.
problem Reconstructing complex material microstructures accurately and efficiently.
method Convolutional deep belief network for automated feature learning and dimension reduction.
result Material reconstructions preserve microstructural features and material properties.
New sensor placement affects robot controller learnability.
problem Catastrophic forgetting in neural controllers for robots.
method Demonstrated how sensor placement alters loss function manifolds.
result Sensor placement can reduce or induce catastrophic forgetting.
Predicts fracture evolution and material failure in brittle materials.
problem Predicting how fractures propagate and materials fail in brittle materials.
method Recurrent graph convolutional neural networks trained on simulation data.
result Predictions within 3% for fracture damage and 15% for time to failure.
New illumination bodies defined for ball-convex shapes, proving convexity and establishing surface area measures.
problem Characterizing properties of ball-convex shapes.
method Introducing illumination bodies and weighted illumination bodies, proving convexity, and establishing surface area measures.
result Illumination bodies are convex and provide surface area measures for ball-convex shapes.
Robots can classify household materials using spectroscopy.
problem Estimating the material of household objects during manipulation.
method Used spectroscopy to estimate material classification of 50 flat objects.
result Achieved 94.6% material classification accuracy with one spectral sample per object.
System learns user preferences to synthesize materials quickly.
problem Slow material synthesis for novice and expert users.
method Gaussian Process Regression for user preferences, neural network for real-time image predictions.
result Real-time material synthesis enables novice users to generate hundreds of models.
Study improves material similarity measures considering distinctiveness.
problem Improving similarity measures for materials science applications.
method Used machine learning techniques with specific descriptors and kernels.
result Minimizing loss of distinctiveness improves prediction accuracy.
Calibrating materials to engineering targets improves wind turbine design.
problem Separate material and mechanical design processes lead to uncertainty.
method Repurpose calibration techniques to integrate material and mechanical design.
result Materials can be designed with specific engineering targets in mind.
The paper proves a conjecture about the shape of floating bodies.
problem The shape of bodies of flotation and buoyancy.
method Modern differential geometry techniques.
result If a body of flotation is homothetic to a body of buoyancy, it must be an ellipse.
Robots learn material recognition from unlabeled data using GANs.
problem Difficulties in collecting labeled training data for robots.
method Semi-supervised learning with GANs for haptic features.
result Achieves ~90% accuracy in material estimation with 92% unlabeled data.
Model predicts multiple material properties with reduced error.
problem Limited materials data and lack of universal material descriptors.
method Integrates CGCNN with multi-task learning.
result Reduces test error by up to 8% for correlated properties.
The paper studies properties of Orlicz-Petty bodies and related geometric areas.
problem Properties of Orlicz-Petty bodies and related geometric areas.
method Established properties through the existence and uniform boundedness of Orlicz-Petty bodies.
result Geominimal surface areas are continuous under certain conditions on convex bodies.
New index characterizes non-smooth Zoll convex bodies.
problem Characterizing non-smooth Zoll convex bodies.
method Defining systolic S1-index and using it to introduce generalized Zoll convex bodies. result Generalized Zoll convex bodies coincide with classical ones under certain conditions.
Deep learning model predicts material microstructures from processing methods.
problem Linking processing conditions to material properties for material design.
method Conditional image synthesis using Wasserstein GAN with gradient penalty.
result Deep learning model synthesizes high-quality microstructures for given cooling methods.
New algorithm improves materials discovery using max K-Armed Bandit.
problem Maximizing material breakthroughs in materials discovery.
method Proposed a search algorithm based on max K-Armed Bandit (MKB) for materials discovery.
result Stable performance in late search stages, outperforming other bandit algorithms.
Infinite diameter found in compression body graph.
problem Determining the diameter of compression body graphs.
method Analyzing the structure and connections within compression body graphs.
result The compression body graph has infinite diameter.
New surface area measures defined for ball-convex bodies, leading to entropy and inequalities.
problem Defining and analyzing surface area measures for ball-convex bodies.
method Introducing Lp relative surface areas, proving invariance and inequalities, and using geometric interpretations. result Established inequalities and a new notion of entropy for ball-convex bodies.
IRNet improves material property prediction from composition and crystal structure.
problem Predicting material properties from composition and crystal structure.
method Deep residual regression network with individual residual learning.
result IRNet outperforms state-of-the-art machine learning approaches in predicting material properties.
Geometrically reformulates elasticity theory using exterior calculus.
problem Formulating nonlinear elasticity theory geometrically.
method Using exterior calculus and bundle-valued differential forms.
result Equivalence to standard tensor calculus formulations.
New method integrates latent variables for Bayesian Optimization of materials with both qualitative and quantitative factors.
problem Bayesian Optimization for materials design with mixed qualitative and quantitative variables.
method Integrates latent variables for mixed-variable Gaussian process modeling within the Bayesian Optimization framework.
result LVGP provides superior modeling accuracy compared to existing methods for mixed-variable problems.
Deep neural networks predict material properties from images.
problem Tailoring material properties for advanced turbomachinery.
method Developed deep convolutional neural networks to predict processing-structure-property relations.
result Models accurately predict material properties from images, surpassing current methods.
Model predicts DFT formation energies without atomic positions.
problem Fast prediction of material properties without atomic positions.
method Symmetry-labeled graphs and message passing neural network.
result Mean absolute error below 0.1 eV for selenides.