Related papers: Vertex and front-tracking methods for the modeling…
Foundation models (FMs) have emerged as a powerful paradigm, enabling a diverse range of data analytics and knowledge discovery tasks across scientific fields. Inspired by the success of FMs, particularly large language models, researchers…
Parametric finite elements lead to very efficient numerical methods for surface evolution equations. We introduce several computational techniques for curvature driven evolution equations based on a weak formulation for the mean curvature.…
In this paper, we present a flexible and probabilistic framework for tracking topological features in time-varying scalar fields using merge trees and partial optimal transport. Merge trees are topological descriptors that record the…
This paper presents a novel sharp front-tracking method designed to address limitations in classical front-tracking approaches, specifically their reliance on smooth interpolation kernels and extended stencils for coupling the front and…
The large models, as predicted by scaling raw forecasts, have made groundbreaking progress in many fields, particularly in natural language generation tasks, where they have approached or even surpassed human levels. However, the…
We analyze the transition between pulled and pushed fronts both analytically and numerically from a model-independent perspective. Based on minimal conceptual assumptions, we show that pushed fronts bifurcate from a branch of pulled fronts…
Understanding the fracture mechanisms in composite materials across scales, from nano- to micro-scales, is essential for an in-depth understanding of the reinforcement mechanisms and designing the next generation of lightweight,…
Material properties controlled by evolving defect structures, such as mechanical response, often involve processes spanning many length and time scales which cannot be modeled using a single approach. We present a variety of new results…
This paper presents a modular, extensible and highly efficient open source framework for registration based tracking called Modular Tracking Framework (MTF). Targeted at robotics applications, it is implemented entirely in C++ and designed…
Reconstructing the surfaces of deformable objects from correspondences between a 3D template and a 2D image is well studied under Shape-from-Template (SfT) methods; however, existing approaches break down when topological changes accompany…
Despite the massive success of fine-tuning Pre-trained Language Models (PLMs), they remain susceptible to out-of-distribution input. Dataset cartography is a simple yet effective dual-model approach that improves the robustness of…
Phase-field modeling is an elegant and versatile computation tool to predict microstructure evolution in materials in the mesoscale regime. However, these simulations require rigorous numerical solutions of differential equations, which are…
Fluid flow applications can involve a number of coupled problems. One is the simulation of free-surface flows, which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled…
We present a multi-scale computational framework suitable for designing solid lubricant interfaces fully in silico. The approach is based on stochastic thermodynamics founded on the classical thermally activated two-dimensional…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
Simulating the long-term dynamics of multi-scale and multi-physics systems poses a significant challenge in understanding complex phenomena across science and engineering. The complexity arises from the intricate interactions between scales…
Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic- and microscales are tightly coupled. The PFC…
Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…
A hybrid sharp-interface immersed-boundary/front-tracking (IB/FT) method is developed for interface-resolved simulation of evaporating droplets in incompressible multiphase flows. A one-field formulation is used to solve the flow, species…
Phase-Field Crystal (PFC) models are able to resolve atomic length scale features of materials during temporal evolution over diffusive time scales. Traditional PFC models contain solid and liquid phases, however many important materials…