Related papers: Computing material fronts with a Lagrange-Projecti…
Suspensions with fiber-like particles in the low Reynolds number regime are modeled by two different approaches that both use a Lagrangian representation of individual particles. The first method is the well-established formulation based on…
We present a method for computing projective isomorphisms between rational surfaces that are given in terms of their parametrizations. The main idea is to reduce the computation of such projective isomorphisms to five base cases by…
We describe a method for modeling the geometry of porous materials. The approach enables the independent selection of crucial parameters, including porosity, pore size distribution, pore shape, and connectivity. Consequently, it can…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
We present the error analysis of Lagrange interpolation on triangles. A new \textit{a priori} error estimate is derived in which the bound is expressed in terms of the diameter and circumradius of a triangle. No geometric conditions on…
In this note, we present a new look at translationally equivariant minimal Lagrangian surfaces in the complex projective plane via the loop group method.
We present a method to project a hypercube of arbitrary dimension on the plane, in such a way as to preserve, as well as possible, the distribution of distances between vertices. The method relies on a Montecarlo optimization procedure that…
We introduce a new numerical method for the computation of the inverse nonlinear Fourier transform and compare its computational complexity and accuracy to those of other methods available in the literature. For a given accuracy, the…
In this paper we present advanced representation learning study on integrating deep learning techniques and sparse approximation, including diffusion models, for advanced flow field analysis and reconstruction. Key applications include…
Laser material processing has emerged as a versatile and indispensable tool in various industries, including manufacturing, healthcare, and materials science. However, the interaction of a lasers with surfaces is highly dependent on a large…
This paper provides a short overview of how to use machine learning to build data-driven models in fluid mechanics. The process of machine learning is broken down into five stages: (1) formulating a problem to model, (2) collecting and…
Fluid discontinuities, such as shock fronts and vortex sheets, can reflect waves and become unstable to corrugation. Analytical calculations of these phenomena are tractable in the simplest cases only, while their numerical simulations are…
The optimization of an optical system benefits greatly from a study of its aberrations and an identification of each of its elements' contribution to the overall aberration figures. The matrix formalism developed by one of the authors was…
Crack fronts deform due to heterogeneities, and inspecting these deformations can reveal local variations of material properties, and help predict out of plane damage. Current models neglect the influence of a finite dissipation…
As we look to the next generation of adaptive optics systems, now is the time to develop and explore the technologies that will allow us to image rocky Earth-like planets; wavefront control algorithms are not only a crucial component of…
We introduce Lagrange2D, a Mathematica package for analysis and characterization of complex fluid flows using Lagrangian transport metrics. Lagrange2D includes built-in functions for integrating ensembles of trajectories subject to…
The Lagrange-mesh method is a powerful method to solve eigenequations written in configuration space. It is very easy to implement and very accurate. Using a Gauss quadrature rule, the method requires only the evaluation of the potential at…
Large language models have steadily increased in size to achieve improved performance; however, this growth has also led to greater inference time and computational demands. Consequently, there is rising interest in model size reduction…
An efficient method for calculating inclusive conventional and prompt atmospheric leptons fluxes is presented. The coupled cascade equations are solved numerically by formulating them as matrix equation. The presented approach is very…
Morphing is a long-standing problem in vision and computer graphics, requiring a time-dependent warping for feature alignment and a blending for smooth interpolation. Recently, multilayer perceptrons (MLPs) have been explored as implicit…