Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures
Abstract
An efficient adjoint design sensitivity analysis method is developed for reduced atomic systems. A reduced atomic system and the adjoint system are constructed in a locally confined region, utilizing generalized Langevin equation (GLE) for periodic lattice structures. Due to the translational symmetry of lattice structures, the size of time history kernel function that accounts for the boundary effects of the reduced atomic systems could be reduced to a single atom’s degrees of freedom. For the problems of highly nonlinear design variables, the finite difference method is impractical for its inefficiency and inaccuracy. However, the adjoint method is very efficient regardless of the number of design variables since one additional time integration is required for the adjoint GLE. Through numerical examples, the derived adjoint sensitivity turns out to be accurate and efficient through the comparison with finite difference sensitivity.
 Authors:
 National Creative Research Initiatives Center for Isogeometric Optimal Design and Department of Naval Architecture and Ocean Engineering, Seoul National University, 1 Gwanakro, Gwanakgu, Seoul 151744 (Korea, Republic of)
 Publication Date:
 OSTI Identifier:
 22233570
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics; Journal Volume: 240; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; DEGREES OF FREEDOM; DESIGN; FINITE DIFFERENCE METHOD; FUNCTIONS; KERNELS; LANGEVIN EQUATION; NONLINEAR PROBLEMS; PERIODICITY; SENSITIVITY ANALYSIS; SYMMETRY
Citation Formats
Kim, MinGeun, Jang, HongLae, and Cho, Seonho, Email: secho@snu.ac.kr. Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures. United States: N. p., 2013.
Web. doi:10.1016/J.JCP.2013.01.020.
Kim, MinGeun, Jang, HongLae, & Cho, Seonho, Email: secho@snu.ac.kr. Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures. United States. doi:10.1016/J.JCP.2013.01.020.
Kim, MinGeun, Jang, HongLae, and Cho, Seonho, Email: secho@snu.ac.kr. 2013.
"Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures". United States.
doi:10.1016/J.JCP.2013.01.020.
@article{osti_22233570,
title = {Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures},
author = {Kim, MinGeun and Jang, HongLae and Cho, Seonho, Email: secho@snu.ac.kr},
abstractNote = {An efficient adjoint design sensitivity analysis method is developed for reduced atomic systems. A reduced atomic system and the adjoint system are constructed in a locally confined region, utilizing generalized Langevin equation (GLE) for periodic lattice structures. Due to the translational symmetry of lattice structures, the size of time history kernel function that accounts for the boundary effects of the reduced atomic systems could be reduced to a single atom’s degrees of freedom. For the problems of highly nonlinear design variables, the finite difference method is impractical for its inefficiency and inaccuracy. However, the adjoint method is very efficient regardless of the number of design variables since one additional time integration is required for the adjoint GLE. Through numerical examples, the derived adjoint sensitivity turns out to be accurate and efficient through the comparison with finite difference sensitivity.},
doi = {10.1016/J.JCP.2013.01.020},
journal = {Journal of Computational Physics},
number = ,
volume = 240,
place = {United States},
year = 2013,
month = 5
}

Secondquantized molecular time scale generalized Langevin equation (MTGLE) theory is applied to the computation of time correlation functions for a finite system and shown to be convergent as a function of temperature and nonlinear coupling parameter. The system chosen is a simple nonlinear or quartic oscillator in which the rotating wave approximation has been made. The effect of this approximation in the context of an MTGLE approach to computing dipole spectra is explored. As a consequence of these computations, a new pathology of the MTGLE approach is uncovered; namely, coupling frequencies {omega}{sup 4}{sub {ital c}{sub {ital n}}} can become negative.more »

Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems With Switching [Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems]
Sensitivity analysis is an important tool for describing power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. The existing approaches for sensitivity calculations, namely, finitedifference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. In this paper, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The proposed approach is highly efficient for calculating sensitivities of larger systems and is consistent, within machine precision, with the function whosemore » 
Reply to: ''Comment on 'A critique of the Brownian approximation to the generalized Langevin equation in lattice dynamics' ''
The comments of P. Mark Rodger ( ref.3) on the authors paper (ref.1) are answered. It is contended that the comments address a more general phenomenon than was analyzed in the authors article. (AIP) 
Critique of the Brownian approximation to the generalized Langevin equation in lattice dynamics
We consider the classical motion of a harmonic lattice in which only those atoms in a certain subset of the lattice (primary zone) may interact with an external force. The formally exact generalized Langevin equation (GLE) for the primary zone is an appropriate description of the dynamics. We examine a previously proposed Brownian, or frictional damping, approximation that reduces the GLE to a set of coupled ordinary Langevin equations for the primary atoms. It is shown that the solution of these equations can contain undamped motion if there is more than one atom in the primary zone. Such motion ismore » 
Automated divertor target design by adjoint shape sensitivity analysis and a oneshot method
As magnetic confinement fusion progresses towards the development of first reactorscale devices, computational tokamak divertor design is a topic of high priority. Presently, edge plasma codes are used in a forward approach, where magnetic field and divertor geometry are manually adjusted to meet design requirements. Due to the complex edge plasma flows and large number of design variables, this method is computationally very demanding. On the other hand, efficient optimizationbased design strategies have been developed in computational aerodynamics and fluid mechanics. Such an optimization approach to divertor target shape design is elaborated in the present paper. A general formulation ofmore »