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.
Paper recovers material parameters in transversely isotropic media under specific conditions.
Model for material elasticity and plasticity using networks.
Researchers recover material parameters in transversely isotropic media from travel times of qP and qSV waves.
Elasticity images map biomechanical properties of soft tissues to aid in the detection and diagnosis of pathological states. In particular, quasi-static ultrasonic (US) elastography techniques use force-displacement measurements acquired during an US scan to parameterize the spatio-temporal stress-strain behavior. Curr…
Analyzes properties of stiffness tensors for elastic wave imaging.
Metric anomalies arising from a distribution of point defects (intrinsic interstitials, vacancies, point stacking faults), thermal deformation, biological growth, etc. are well known sources of material inhomogeneity and internal stress. By emphasizing the geometric nature of such anomalies we seek their representation…
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…
4-dim intrinsic (material) Riemannian metric of the material 4-D space-time continuum is utilized as the characteristic of the aging processes developing in the material. Manifested through variation of basic material characteristics such as density, moduli of elasticity, yield stress, strength, and toughness.,…
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 stru…
A geometrical interpretation of the -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
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 …
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…
Study on evolving interfaces with complex curvature and density effects.
Physics-constrained GP predicts material states under shockwave conditions.
Lie groupoids and their associated algebroids arise naturally in the study of the constitutive properties of continuous media. Thus, Continuum Mechanics and Differential Geometry illuminate each other in a mutual entanglement of theory and applications. Given any material property, such as the elastic energy or an inde…
Study on materials with disclinations, limiting their size.
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…
The notions of uniformity and homogeneity of elastic materials are reviewed in terms of Lie groupoids and frame bundles. This framework is also extended to consider the case Functionally Graded Media, which allows us to obtain some homogeneity conditions.
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…
Physics-informed GANs estimate elastic moduli from mechanical tests.
Wavelet scattering predicts material properties beyond training data.
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…
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…
Sparse elasticity reconstruction from local displacements reduces error.
Geometrically reformulates elasticity theory using exterior calculus.
Proposes VEESA pipeline for interpreting ML models with functional data.
Approximate 3D elastic curves with exact constraints
Neural network solves inverse problem in multiscale mechanics.
For curves of prescribed length embedded into the unit disc in two dimensions, we obtain scaling results for the minimal elastic energy as the length just exceeds and in the large length limit. In the small excess length case, we prove convergence to a fourth order obstacle type problem with integral constraint on…
Paper presents a new approach to continuum mechanics using port-Hamiltonian framework.
Machine learning predicts failure in brittle materials with high accuracy.
Researchers reconstruct stiffness tensors from limited data in anisotropic elasticity.
New solutions for soft materials' nonlinear behavior in growing spheroidal inclusions.
Study on elastic curves pinned at the boundary, focusing on minimizers and their interaction with obstacles.
Theory models nonlinear soft tissue elasticity and remodeling using extended Finsler geometry.
Unified treatment of elastic metrics for curves in any dimension.
Study gauge freedoms in elastic wave equations and Dirichlet-to-Neumann map.
The paper classifies and analyzes the stability of elastic curves with fixed endpoints.
Dematerialization is the reduction in the quantity of materials needed to produce something useful over time. Dematerialization fundamentally derives from ongoing increases in technical performance but it can be counteracted by demand rebound - increases in usage because of increased value (or decreased cost) that also…
A new method distills material models from noisy data without prior selection.
Efficiently estimates material parameter space with multifidelity Gaussian process modeling.
EVCL combines VCL and EWC to prevent forgetting new tasks.
Given a distribution of defects on a structured surface, such as those represented by 2-dimensional crystalline materials, liquid crystalline surfaces, and thin sandwiched shells, what is the resulting stress field and the deformed shape? Motivated by this concern, we first classify, and quantify, the translational, ro…
It is well known that the out-of-sample performance of Markowitz's mean-variance portfolio criterion can be negatively affected by estimation errors in the mean and covariance. In this paper we address the problem by regularizing the mean-variance objective function with a weighted elastic net penalty. We show that the…
In order to study a one-dimensional analogue of the spontaneous curvature model for two-component lipid bilayer membranes we consider planar curves that are made of a material with two phases. Each phase induces a preferred curvature to the curve, and these curvatures as well as phase boundaries may lead to the develop…
GPR enhances materials discovery by automating parameter space exploration.
Calibrating materials to engineering targets improves wind turbine design.