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The enforcement of global energy conservation in phase-field fracture simulations has been an open problem for the last 25 years. Specifically, the occurrence of unstable fracture is accompanied by a loss in total potential energy, which…
Molecular simulations of the forced unfolding and refolding of biomolecules or molecular complexes allow to gain important kinetic, structural and thermodynamic information about the folding process and the underlying energy landscape. In…
We consider large-scale Markov decision processes (MDPs) with a risk measure of variability in cost, under the risk-aware MDPs paradigm. Previous studies showed that risk-aware MDPs, based on a minimax approach to handling risk, can be…
Time Series Forecasting (TSF) faces persistent challenges in modeling intricate temporal dependencies across different scales. Despite recent advances leveraging different decomposition operations and novel architectures based on CNN, MLP…
In molecular simulations, efficient methods for investigating equilibration and slow relaxation in dense systems are crucial yet challenging. This study focuses on the diffusional characteristics of monodisperse hard disk systems at…
This paper explores a geometric approach to constructing quasi-sure solutions for $G$-stochastic differential equations (G-SDEs) under model uncertainty. We propose a pathwise patching methodology that systematically combines…
This paper develops a parameter-free adaptive proximal bundle method with two important features: 1) adaptive choice of variable prox stepsizes that "closely fits" the instance under consideration; and 2) adaptive criterion for making the…
In this paper, we develop a novel unfitted multiscale framework that combines two separate scales represented by only one single computational mesh. Our framework relies on a mixed zooming technique where we zoom at regions of interest to…
The fracture simulation of random particle reinforced composite structures remains a challenge. Current techniques either assumed a homogeneous model, ignoring the microstructure characteristics of composite structures, or considered a…
Equation-free methods make possible an analysis of the evolution of a few coarse-grained or macroscopic quantities for a detailed and realistic model with a large number of fine-grained or microscopic variables, even though no equations are…
We study the evolution of step bunches on vicinal surfaces using a thermodynamically consistent step-flow model that (i) circumvents the quasistatic approximation that prevails in the literature by accounting for the dynamics of adatom…
An approach for quantitatively evaluating overshooting oscillations is designed to characterize the performance of shock-capturing schemes. Specifically, following our previous work focused on cases with only discontinuities, now we account…
In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by representing the solution as a suitable frame decomposition, i.e., a complete, stable,…
We present a fully adaptive multiresolution scheme for spatially one-dimensional quasilinear strongly degenerate parabolic equations with zero-flux and periodic boundary conditions. The numerical scheme is based on a finite volume…
The implementation of optimization-based motion coordination approaches in real world multi-agent systems remains challenging due to their high computational complexity and potential deadlocks. This paper presents a distributed model…
We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle…
Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of…
The increasing number of protein-based metamaterials demands reliable and efficient theoretical and computational methods to study the physicochemical properties they may display. In this regard, we develop a simulation strategy based on…
We present the Multi-Particle-Collision (MPC) dynamics approach to simulate properties of low-dimensional systems. In particular, we illustrate the method for a simple model: a one-dimensional gas of point particles interacting through…
This paper develops three linear and energy-stable schemes for a modified phase field crystal model with a strong nonlinear vacancy potential (VMPFC model). This sixth-order phase-field model enables realistic crystal growth simulation.…