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Analysis of a force-based quasicontinuum approximation
We analyze a force-based quasicontinuum approximation to a one-dimensional system of atoms that interact by a classical atomistic potential. This force-based quasicontinuum approximation can be…
An Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation
We derive a model problem for quasicontinuum approximations that allows a simple, yet insightful, analysis of the optimal-order convergence rate in the continuum limit for both the energy-based…
Accuracy of quasicontinuum approximations near instabilities
Stability, Instability, and Error of the Force-based Quasicontinuum Approximation
Due to their algorithmic simplicity and high accuracy, force-based model coupling techniques are popular tools in computational physics. For example, the force-based quasicontinuum (QCF)…
Using coupling methods to estimate sample quality for stochastic differential equations
- M. Dobson, Jiayu Zhai, Yao Li
- Mathematics, Computer ScienceSIAM/ASA J. Uncertain. Quantification
- 21 December 2019
A probabilistic approach for estimating sample qualities for stochastic differential equations and finds that suitable numerical coupling methods can effectively estimate the rate of contraction of the transition kernel of the SDE, which gives the distance between two invariant probability measures.
A multilattice quasicontinuum for phase transforming materials: Cascading Cauchy Born kinematics
The quasicontinuum (QC) method is applied to materials possessing a multilattice crystal structure. Cauchy-Born (CB) kinematics, which accounts for the shifts of the crystal basis, is used in…
AN ANALYSIS OF THE EFFECT OF GHOST FORCE OSCILLATION ON QUASICONTINUUM ERROR
The atomistic to continuum interface for quasicontinuum energies exhibits nonzero forces under uniform strain that have been called ghost forces. In this paper, we prove for a linearization of a…
Sharp Stability Estimates for the Force-Based Quasicontinuum Approximation of Homogeneous Tensile Deformation
This work forms a simple one-dimensional model problem and gives a detailed analysis of the linear stability of the force-based quasicontinuum (QCF) method at homogeneous deformations, and investigates in detail for which choices of “function spaces” the QCF operator is stable, uniformly in the size of the atomistic system.
SN 2019ehk: A Double-peaked Ca-rich Transient with Luminous X-Ray Emission and Shock-ionized Spectral Features
We present panchromatic observations and modeling of the Calcium-rich supernova 2019ehk in the star-forming galaxy M100 (d$\approx$16.2 Mpc) starting 10 hours after explosion and continuing for ~300…
A deep learning method for solving Fokker-Planck equations
A mesh-free Fokker-Planck solver is proposed, in which the solution to the Fokkersonian equation is now represented by a neural network, and the presence of the differential operator in the loss function improves the accuracy of the neural network representation and reduces the demand of data in the training process.