TY - JOUR
T1 - Nonlinear constitutive models for nano-scale heat conduction
AU - Chu, Weiqi
AU - Li, Xiantao
N1 - Funding Information:
\ast Received by the editors April 22, 2019; accepted for publication (in revised form) January 27, 2021; published electronically March 24, 2021. https://doi.org/10.1137/19M1257664 Funding: This research was supported by the NSF under grants DMS-1522617 and DMS-1619661. \dagger Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095 USA ([email protected]). \ddagger Department of Mathematics, Pennsylvania State University, University Park, PA 16802 USA ([email protected]).
Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics.
PY - 2021
Y1 - 2021
N2 - We present a first-principle based approach that leads from a many-particle description to a nonlinear, stochastic constitutive relation for the modeling of transient heat conduction processes at the nano-mechanical scale. By enforcing statistical consistency, in that the statistics of local energy is consistent with that from an all-atom description, we identify the driving force as well as the model parameters in these generalized constitutive models. The connections to established generalized constitutive relations, including Cattaneo-Vernotte-type models, will be demonstrated.
AB - We present a first-principle based approach that leads from a many-particle description to a nonlinear, stochastic constitutive relation for the modeling of transient heat conduction processes at the nano-mechanical scale. By enforcing statistical consistency, in that the statistics of local energy is consistent with that from an all-atom description, we identify the driving force as well as the model parameters in these generalized constitutive models. The connections to established generalized constitutive relations, including Cattaneo-Vernotte-type models, will be demonstrated.
UR - http://www.scopus.com/inward/record.url?scp=85104652767&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85104652767&partnerID=8YFLogxK
U2 - 10.1137/19M1257664
DO - 10.1137/19M1257664
M3 - Article
AN - SCOPUS:85104652767
SN - 1540-3459
VL - 19
SP - 533
EP - 549
JO - Multiscale Modeling and Simulation
JF - Multiscale Modeling and Simulation
IS - 1
ER -