相关论文: Numerical Fr\'echet derivatives of the displacemen…

We analyze the Fr\'echet derivative $F$, that maps a perturbation in conductivity to the linearized change in boundary measurements governed by the conductivity equation. The domain is taken to be the unit ball $B \subset \mathbb{R}^d$ with…

We consider the Cosserat continuum in its finite strain setting and discuss the dislocation density tensor as a possible alternative curvature strain measure in three-dimensional Cosserat models and in Cosserat shell models. We establish a…

A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual…

The quality factor (Q) links seismic wave energy dissipation to physical properties of the Earth's interior, such as temperature, stress and composition. Frequency independence of Q, also called constant Q for brevity, is a common…

This paper deals with the numerical modeling of transient mechanical waves in linear viscoelastic solids. Dissipation mechanisms are described using the generalized Zener model. No time convolutions are required thanks to the introduction…

The tensor t-function, a formalism that generalizes the well-known concept of matrix functions to third-order tensors, is introduced in [K. Lund, The tensor t-function: a definition for functions of third-order tensors, Numer. Linear…

An experiment was performed using Dual-plane-SPIV in the LMFL boundary layer facility to determine all of the derivative moments needed to estimate the average dissipation rate of the turbulent kinetic energy, $\varepsilon$, and its…

We develop a novel data-driven approach to modeling the atmospheric boundary layer. This approach leads to a nonlocal, anisotropic synthetic turbulence model which we refer to as the deep rapid distortion (DRD) model. Our approach relies on…

Deep Neural Networks (DNNs) are a powerful and flexible tool for information extraction and modeling. In this study, we use DNNs to extract the Sivers functions by globally fitting Semi- Inclusive Deep Inelastic Scattering (SIDIS) and…

Surface wave dispersion curve inversion is crucial for estimating subsurface shear-wave velocity (vs), yet traditional methods often face challenges related to computational cost, non-uniqueness, and sensitivity to initial models. While…

The present article is the third part of a series of papers devoted to the shallow water wave modelling. In this part, we investigate the derivation of some long wave models on a deformed sphere. We propose first a suitable for our purposes…

Seismic noise cross correlations are used to image crustal structure and heterogeneity. Typically, seismic networks are only anisotropically illuminated by seismic noise, a consequence of the non-uniform distribution of sources. Here, we…

With the rapid development of data collection techniques, complex data objects that are not in the Euclidean space are frequently encountered in new statistical applications. Fr\'echet regression model (Peterson & M\"uller 2019) provides a…

Stochastic gradient descent (SGD) is a key ingredient in the training of deep neural networks and yet its geometrical significance appears elusive. We study a deterministic model in which the trajectories of our dynamical systems are…

Traditional free vibration-based forward models generate theoretical dispersion curves under the assumption of planar waves, neglecting the influence of the actual source-receiver configuration. While 2D/3D numerical wavefield modeling…

In this paper, we propose a novel one-dimensional (1D) discrete differential geometry (DDG)-based numerical method for geometrically nonlinear mechanics analysis (e.g., buckling and snapping) of axisymmetric shell structures. Our numerical…

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…

A novel approach was derived to compute the elastic displacement field from a measured elastic deformation field (i.e., deformation gradient or strain). The method is based on integrating the deformation field using Finite Element…

Objective: Most deep neural network-based diffusion tensor imaging methods require the diffusion gradients' number and directions in the data to be reconstructed to match those in the training data. This work aims to develop and evaluate a…

In this work, dislocation master-equations valid for anisotropic materials are derived in terms of kernel functions using the framework of micromechanics. The second derivative of the anisotropic Green tensor is calculated in the sense of…