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The paper deals with the approximate solution of integro-differential equations of Prandtl's type. Quadrature methods involving ``optimal'' Lagrange interpolation processes are proposed and conditions under which they are stable and…
In this paper, we describe a new scalable and modular material point method (MPM) code developed for solving large-scale problems in continuum mechanics. The MPM is a hybrid Eulerian-Lagrangian approach, which uses both moving material…
We present in this article a novel Lagrangian measurement technique: an instrumented particle which continuously transmits the force/acceleration acting on it as it is advected in a flow. We develop signal processing methods to extract…
Extracting information on fluid motion directly from images is challenging. Fluid flow represents a complex dynamic system governed by the Navier-Stokes equations. General optical flow methods are typically designed for rigid body motion,…
In this work, we extend a phase-field approach for pressurized fractures to non-isothermal settings. Specifically, the pressure and the temperature are given quantities and the emphasis is on the correct modeling of the interface laws…
Thermal multi-phase flow simulations are indispensable to understanding the multi-scale and multi-physics phenomena in metal additive manufacturing (AM) processes, yet accurate and robust predictions remain challenging. This book chapter…
A scheme is developed which shows how one would, given a light-front Hamiltonian for QCD, extract the $Q\overline{Q}$ potential, i.e. the quantity which corresponds to the potential between two infinitely heavy quarks in a rest frame, from…
When a large body of data from diverse experiments is analyzed using a theoretical model with many parameters, the standard error matrix method and the general tools for evaluating errors may become inadequate. We present an iterative…
Machine Learning tools are nowadays widely applied extensively to the prediction of the properties of molecular materials, using datasets extracted from high-throughput computational models. In several cases of scientific and technological…
This paper deals with the estimation of multiantenna channels in the line-of-sight conditions that are prevalent in the near field. By expressing the curved wavefront as a polynomial via a power series expansion of a sphere, the estimation…
Computational fluid dynamics (CFD) simulations of complex fluid flows in energy systems are prohibitively expensive due to strong nonlinearities and multiscale-multiphysics interactions. In this work, we present a transformer-based modeling…
In this paper we develop a conservative sharp-interface method dedicated to simulating multiple compressible fluids. Numerical treatments for a cut cell shared by more than two materials are proposed. First, we simplify the interface…
The paper introduces a multi-scale processing method for quantitative study and visualization of convective heat transfer using diffractive optical element based background-oriented schlieren technique. The method relies on robust…
In the present paper, we propose a novel generalization of the celebrated MMP algorithm in order to find the wavefront propagation and the cut-locus on a convex polyhedron with an emphasis on actual implementation for instantaneous…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the fourth paper, the application of the Fourier series multiscale method to the…
We propose a novel iterative numerical method to solve the three-dimensional inverse obstacle scattering problem of recovering the shape of the obstacle from far-field measurements. To address the inherent ill-posed nature of the inverse…
Computational fluid dynamics plays a key role in the design process across many industries. Recently, there has been increasing interest in data-driven methods, in order to exploit the large volume of data generated by such computations.…
High-throughput data generation methods and machine learning (ML) algorithms have given rise to a new era of computational materials science by learning relationships among composition, structure, and properties and by exploiting such…
Modeling of fluid flows requires corresponding adequate and effective approaches that would account for multiscale nature of the considered physics. Despite the tremendous growth of computational power in the past decades, modeling of fluid…
We describe a new data collection scheme for optical diffusion tomography in which plane wave illumination is combined with multiple projections in the slab imaging geometry. Multiple projection measurements are performed by rotating the…