Related papers: Finite-time stability of polyhedral sweeping proce…
In this letter, we develop a framework to study the mechanical response of athermal amorphous solids via a coupling of mesoscale and microscopic models. Using measurements of coarse grained quantities from simulations of dense disordered…
This paper deals with asymptotic stability of a class of dynamical systems in terms of smooth Lyapunov pairs. We point out that well known converse Lyapunov results for differential inclusions cannot be applied to this class of dynamical…
We discuss how matrix-free/timestepper algorithms can efficiently be used with dynamic non-Newtonian fluid mechanics simulators in performing systematic stability/bifurcation analysis. The timestepper approach to bifurcation analysis of…
Two finite element approximations of the Oldroyd-B model for dilute polymeric fluids are considered, in bounded 2- and 3-dimensional domains, under no flow boundary conditions. The pressure and the symmetric conformation tensor are…
We study the stability of explicit one-step integration schemes for the linear finite element approximation of linear parabolic equations. The derived bound on the largest permissible time step is tight for any mesh and any diffusion matrix…
Computational formulations for large strain, polyconvex, nearly incompressible elasticity have been extensively studied, but research on enhancing solution schemes that offer better tradeoffs between accuracy, robustness, and computational…
This paper establishes a far-reaching connection between the Finite-Difference Time-Domain method (FDTD) and the theory of dissipative systems. The FDTD equations for a rectangular region are written as a dynamical system having the…
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…
We analyse three time integration schemes for unfitted methods in fluid structure interaction. In Alghorithm 1 we propose a fully discrete monolithic algorithm with P1 P1 stabilized finite elements for the fluid problem; for this alghorithm…
A dynamic linear thermo-poroelasticity model, containing inertial and relaxation terms with second-order time derivatives, is investigated in this paper. The mathematical and numerical analysis of this model is performed in the frequency…
Consideration is given to the effects of inhomogeneous shear flow (both regular and chaotic) on nematic liquid crystals in a planar geometry. The Landau--de Gennes equation coupled to an externally-prescribed flow field is the basis for the…
The elastic response of mechanical, chemical, and biological systems is often modeled using a discrete arrangement of Hookean springs, either representing finite material elements or even the molecular bonds of a system. However, to date,…
We prove a version of the Poincar\'e-Bendixson theorem for certain classes of curves on the 2-sphere which are not required to be the trajectories of an underlying flow or semiflow on the sphere itself. Using this result we extend the…
A Finite Element procedure based on a full implicit backward Euler predictor/corrector scheme for the Cosserat continuum is here presented. Since this is based on invariants of the stress and couple stress tensors and on the spectral…
The sweeping process was proposed by J. J. Moreau as a general mathematical formalism for quasistatic processes in elastoplastic bodies. This formalism deals with connected Prandtl's elastic-ideal plastic springs, which can form a system…
We consider a simple lattice spring model in which every spring is elastoplastic and is capable to conduct current. The elasticity bounds of spring $i$ are taken as $[-c_i,c_i]$ and the resistance of spring $i$ is taken as $1/c_i$, which…
In this paper, we present new results on finite- and fixed-time convergence for dynamical systems using LaSalle-like invariance principles. In particular, we provide first and second-order non-smooth Lyapunov-like results for finite- and…
The Polyhedral Escape Problem for continuous linear dynamical systems consists of deciding, given an affine function $f: \mathbb{R}^{d} \rightarrow \mathbb{R}^{d}$ and a convex polyhedron $\mathcal{P} \subseteq \mathbb{R}^{d}$, whether, for…
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…
The paper addresses stability and finite element analysis of the stationary two-phase Stokes problem with a piecewise constant viscosity coefficient experiencing a jump across the interface between two fluid phases. We first prove a priori…