Related papers: On multi-time-step monolithic coupling algorithms …
Simulating physical problems involving multi-time scale coupling is challenging due to the need of solving these multi-time scale processes simultaneously. In response to this challenge, this paper proposed an explicit multi-time step…
We present a novel formulation for parametric finite element methods to approximate two-phase Stokes flow. The new formulation is based on the classical Stokes equation in the bulk and a novel choice of interface conditions with additional…
We present a novel thermodynamically guided, low-noise, time-scale bridging, and pertinently efficient strategy for the dynamic simulation of microscopic models for complex fluids. The systematic coarse-graining method is exemplified for…
This paper presents a novel parallel splitting algorithm for solving quasi-static multiple-network poroelasticity (MPET) equations. By introducing a total pressure variable, the MPET system can be reformulated into a coupled…
We consider a system of coupled nonlinear Schr{\"o}dinger equations in one space dimension. First, we prove the existence of multi-speed solitary waves, i.e solutions to the system with each component behaving at large times as a solitary…
We develop a moment equation closure minimization method for the inexpensive approximation of the steady state statistical structure of nonlinear systems whose potential functions have bimodal shapes and which are subjected to correlated…
We develop a linearly-scaling variant of the Force Coupling Method [K. Yeo and M. R. Maxey, J. Fluid Mech. 649, 205-231 (2010)] for computing hydrodynamic interactions among particles confined to a doubly-periodic geometry with either a…
When liquid-crystal elastomers are prepared without any alignment, disordered polydomain structures emerge as the materials are cooled into the nematic phase. These polydomain structures have been attributed to quenched disorder in the…
We propose a numerical methodology for the numerical simulation of distinct, interacting physical processes described by a combination of compressible, inert and reactive forms of the Euler equations, multiphase equations and elastoplastic…
We consider the development of high order asymptotic-preserving linear multistep methods for kinetic equations and related problems. The methods are first developed for BGK-like kinetic models and then extended to the case of the full…
We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and…
The study of the long time conservation for numerical methods poses interesting and challenging questions from the point of view of geometric integration. In this paper, we analyze the long time energy and magnetic moment conservations of…
We study two coupled cavities with a single two-level system in each and a second-order non-linear process in one of the cavities. Introduction of a harmonic time dependence on the non-linear coupling is utilized for the preservation of…
In the present study we investigate electrostatic stabilization mechanisms acting on stratified fluids. Electric fields have been shown to control and even suppress the Rayleigh-Taylor instability when a heavy fluid lies above lighter…
Elastic contact in hydrodynamic environments is a complex multiphysics phenomenon and can be found in applications ranging from engineering to biological systems. Understanding the intricacies of this coupled problem requires the…
We demonstrate how to construct dynamic phase diagrams for complex fluids that undergo transitions under flow, in which the conserved composition variable and the broken-symmetry order parameter (nematic, smectic, crystalline, etc.) are…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
A consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The consistency of mass conservation and the…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
We model polydomain liquid-crystal elastomers by extending the neo-classical soft and semi-soft free energies used successfully to describe monodomain samples. We show that there is a significant difference between polydomains cross-linked…