RT Journal Article
ID 18c89b39628de94f
A1 Salloum, Maher
A1 Templeton, Jeremy A.
T1 INFERENCE AND UNCERTAINTY PROPAGATION OF ATOMISTICALLY-INFORMED CONTINUUM CONSTITUTIVE LAWS, PART 1: BAYESIAN INFERENCE OF FIXED MODEL FORMS
JF International Journal for Uncertainty Quantification
JO IJUQ
YR 2014
FD 2014-04-17
VO 4
IS 2
SP 151
OP 170
K1 constitutive law
K1 continuum
K1 atomistic
K1 Bayesian inference
K1 uncertainty
K1 Fourier model
K1 polynomial chaos expansion
AB Uncertainty quantification techniques have the potential to play an important role in constructing constitutive relationships applicable to nanoscale physics. At these small scales, deviations from laws appropriate at the macroscale arise due to insufficient scale separation between the atomic and continuum length scales, as well as fluctuations due to thermal processes. In this work, we consider the problem of inferring the coefficients of an assumed constitutive model form using atomistic information and propagation of the associated uncertainty. A nanoscale heat transfer problem is taken as the model, and we use a polynomial chaos expansion to represent the thermal conductivity with a linear temperature dependence. A Bayesian inference method is developed to extract the coefficients in this expansion from molecular dynamics (MD) samples at prescribed temperatures. Importantly, the atomistic data are incompatible with the continuum model because of the finite probability of heat flowing in the opposite direction of the temperature gradient; we present a method to account for this in the model. The fidelity and uncertainty in these techniques are then examined. Validation is provided by comparing a continuum Fourier model against a larger all MD simulation representing the true solution.
PB Begell House
LK http://dl.begellhouse.com/journals/52034eb04b657aea,14db5d4c2510c6cc,18c89b39628de94f.html