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Over the last half-century, linear viscoelastic models for crack growth in soft solids have flourished but their predictions have rarely been compared to experiments. In fact, most available models are either very approximate or cast in…
Discrete simulation methods are efficient tools to investigate the complex behaviors of complex fluids made of either dry granular materials or dilute suspensions. By contrast, materials made of soft and/or concentrated units (emulsions,…
In this paper, we develop a new reduced basis (RB) method, named as Single Eigenvalue Acceleration Method (SEAM), for second-order parabolic equations with homogeneous Dirichlet boundary conditions. The high-fidelity numerical method adopts…
We introduce a new measure of the structure of a liquid which is the softness of the mean-field potential developed by us earlier. We find that this softness is sensitive to small changes in the structure. We then study its correlation with…
We present a Newton-Krylov solver for a viscous-plastic sea-ice model. This constitutive relation is commonly used in climate models to describe the material properties of sea ice. Due to the strong nonlinearity introduced by the material…
We extend the phase-field approach to model the solidification of faceted materials. Our approach consists of using an approximate gamma-plot with rounded cusps that can approach arbitrarily closely the true gamma-plot with sharp cusps that…
Most heat transfer models for bulk crystal growth rely on the classical Stefan formulation to evaluate interface motion during phase change. However, when the interface is non-smooth the use of the classical Stefan formulation may lead to…
In this paper, we study the problem of weakly-supervised temporal grounding of sentence in video. Specifically, given an untrimmed video and a query sentence, our goal is to localize a temporal segment in the video that semantically…
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…
For the first time we introduce an error estimator for the numerical approximation of the equations describing the dynamics of sea ice. The idea of the estimator is to identify different error contributions coming from spatial and temporal…
The basal sliding of glaciers and ice sheets can constitute a large part of the total observed ice velocity, in particular in dynamically active areas. It is therefore important to accurately represent this process in numerical models. The…
Climate simulations, at all grid resolutions, rely on approximations that encapsulate the forcing due to unresolved processes on resolved variables, known as parameterizations. Parameterizations often lead to inaccuracies in climate models,…
The modeling and forecasting of sea ice conditions in the Arctic region are important tasks for ship routing, offshore oil production, and environmental monitoring. We propose the adaptive surrogate modeling approach named LANE-SI…
A rigorous derivation and validation for linear fluid-structure-interaction (FSI) equations for a rigid-body-motion problem is performed in an Eulerian framework. We show that the added-stiffness terms arising in the formulation of Fanion…
A stable partitioned algorithm for fluid-structure interaction (FSI) problems that couple viscous incompressible flow with structural shells or beams is described. This added-mass partitioned (AMP) scheme uses Robin (mixed) interface…
We discuss applications of a recently developed method for model reduction based on linear response theory of weakly coupled dynamical systems. We apply the weak coupling method to simple stochastic differential equations with slow and fast…
Introduced by Beck and Teboulle, FISTA (for Fast Iterative Shrinkage-Thresholding Algorithm) is a first-order method widely used in convex optimization. Adapted from Nesterov's accelerated gradient method for convex functions, the generated…
Sea ice is a mushy layer, a porous material whose properties depend on the relative proportions of solid and liquid. The growth of sea ice is governed by heat transfer through the ice together with appropriate boundary conditions at the…
Given the massive cost of language model pre-training, a non-trivial improvement of the optimization algorithm would lead to a material reduction on the time and cost of training. Adam and its variants have been state-of-the-art for years,…
As a first step towards the numerical analysis of the stochastic primitive equations of the atmosphere and oceans, we study their time discretization by an implicit Euler scheme. From deterministic viewpoint the 3D Primitive Equations are…