相关论文: A Structure-Preserving Stagewise Rescaling Algorit…
We study the Duffing equation and its generalizations with polynomial nonlinearities. Recently, we have demonstrated that metamorphoses of the amplitude response curves, computed by asymptotic methods in implicit form as $F\left( \Omega ,\…
Autonomous oscillators, such as clocks and lasers, produce periodic signals \emph{without} any external frequency reference. In order to sustain stable periodic motions, there needs to be external energy supply as well as nonlinearity built…
The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution…
We investigate the increase in efficiency of simulated and parallel tempering MCMC algorithms when using non-reversible updates to give them "momentum". By making a connection to a certain simple discrete Markov chain, we show that, under…
Metasurfaces have provided a novel and promising platform for the realization of compact and large-scale optical devices. The conventional metasurface design approach assumes periodic boundary conditions for each element, which is…
In distributed model predictive control (DMPC), where a centralized optimization problem is solved in distributed fashion using dual decomposition, it is important to keep the number of iterations in the solution algorithm, i.e. the amount…
The Equation-Free approach to efficient multiscale numerical computation marries trusted micro-scale simulations to a framework for numerical macro-scale reduction -- the patch dynamics scheme. A recent novel patch scheme empowered the…
A first-principles based methodology for efficiently and accurately finding thermodynamically stable and metastable atomic structures is introduced and benchmarked. The approach is demonstrated for gas-phase metal-oxide clusters in…
Exponential decay estimates of a general linear weakly damped wave equation are studied with decay rate lying in a range. Based on the $C^0$-conforming finite element method to discretize spatial variables keeping temporal variable…
Locally refined meshes impose severe stability constraints on explicit time-stepping methods for the numerical simulation of time dependent wave phenomena. Local time-stepping methods overcome that bottleneck by using smaller time-steps…
Spatially confined rigid membranes reorganize their morphology in response to the imposed constraints. A crumpled elastic sheet presents a complex pattern of random folds focusing the deformation energy while compressing a membrane resting…
We propose a continuous-time scheme for large-scale optimization that introduces individual, adaptive momentum coefficients regulated by the kinetic energy of each model parameter. This approach automatically adjusts to local landscape…
This paper extends the high-order entropy stable (ES) adaptive moving mesh finite difference schemes developed in [14] to the two- and three-dimensional (multi-component) compressible Euler equations with the stiffened equation of state.…
The dynamical and stationary behaviors of a fourth-order equation in the unit ball with clamped boundary conditions and a singular reaction term are investigated. The equation arises in the modeling of microelectromechanical systems (MEMS)…
In the current work we study a nonlocal parabolic problem with Robin boundary conditions. The problem arises from the study of an idealized electrically actuated MEMS (Micro-Electro-Mechanical System) device. Initially we study the…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems…
While elastic metasurfaces offer a remarkable and very effective approach to the subwalength control of stress waves, their use in practical applications is severely hindered by intrinsically narrow band performance. This work introduces…
In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced-order methods are demanded. Combining these…
In this paper we study the local wellposedness of the solution to a non-linear parabolic-dispersive coupled system which models a Micro-Electro-Mechanical System (MEMS). A simple electrostatically actuated MEMS capacitor device has two…