Related papers: An Improved Normal Compliance Method for Dynamic H…
We introduce a new methodology for adding localized, space-time smooth, artificial viscosity to nonlinear systems of conservation laws which propagate shock waves, rarefactions, and contact discontinuities, which we call the $C$-method. We…
It is well known that for solutions of semi-linear parabolic PDEs, there are equivalent probabilistic interpretations, which yields the so called nonlinear Feymman-Kac formula. By adopting such formula, we consider in this work a novel…
In this paper, we present a method of applying integral action to enhance the robustness of energy shaping controllers for underactuated mechanical systems with matched disturbances. Previous works on this problem have required a number of…
Inactive constraints do not contribute to the solution of an optimal control problem, but increase the problem size and burden the numerical computations. We present a novel strategy for handling inactive constraints efficiently by…
We present a practical framework for ideal hyperelasticity in numerical relativity. For this purpose, we recast the formalism of Carter and Quintana as a set of Eulerian conservation laws in an arbitrary 3+1 split of spacetime. The…
We introduce a methodology for seeking conservation laws within a Hamiltonian dynamical system, which we term ``neural deflation''. Inspired by deflation methods for steady states of dynamical systems, we propose to {iteratively} train a…
Small-scale plasticity problems are often characterised by different patterning behaviours ranging from macroscopic down to the atomistic scale. In successful models of such complex behaviour, its origin lies within non-convexity of the…
In this study, we propose a safety-critical compliant control strategy designed to strictly enforce interaction force constraints during the physical interaction of robots with unknown environments. The interaction force constraint is…
Dynamic simulation of elastic bodies is a longstanding task in engineering and computer graphics. In graphics, numerical integrators like implicit Euler and BDF2 are preferred due to their stability at large time steps, but they tend to…
Plasticity-stability dilemma is a main problem for incremental learning, where plasticity is referring to the ability to learn new knowledge, and stability retains the knowledge of previous tasks. Many methods tackle this problem by storing…
Accurate frictional contact is critical in simulating the assembly of rod-like structures in the practical world, such as knots, hairs, flagella, and more. Due to their high geometric nonlinearity and elasticity, rod-on-rod contact remains…
Modeling contact mechanics with high contrast coefficients presents significant mathematical and computational challenges, especially in achieving strongly symmetric stress approximations for mixed formulations. Due to the inherent…
For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each…
A new interior-exterior penalty method for solving quasi-variational inequality and pseudo-monotone operators arising in two-dimensional point contact problem has been analyzed and developed in discontinuous Galerkin finite volume method…
This work presents an Iterative Constraint Energy Minimizing Generalized Multiscale Finite Element Method (ICEM-GMsFEM) for solving the contact problem with high contrast coefficients. The model problem can be characterized by a variational…
A mechanical system consisting of an elastic beam under harmonic excitation and an attached sliding body is investigated. Recent experimental observations suggest that the system passively (self-)adapts the axial location of the slider to…
In this two part series, we present a contact model able to capture the response of interacting adhesive elastic-perfectly plastic particles under a variety of loadings. In Part I, we focus on elastic through fully-plastic contact with and…
Accurate numerical modeling of compressible flows, particularly in the turbulent regime, requires a method that is non-dissipative and stable at high Reynolds ($Re$) numbers. For a compressible flow, it is known that discrete conservation…
For over 30 years, mode-coupling theory (MCT) has been the de facto theoretic description of dense fluids and the liquid-glass transition. MCT, however, is limited by its ad hoc construction and lacks a mechanism to institute corrections.…
This paper considers the leader-follower tracking control problem for linear interconnected systems with undirected topology and linear dynamic coupling. Interactions between the systems are treated as linear dynamic uncertainty and are…