Communications in Mathematical Sciences

Volume 15 (2017)

Number 6

Sensitivity analysis and optimization of reaction rate

Pages: 1507 – 1525

DOI: http://dx.doi.org/10.4310/CMS.2017.v15.n6.a2

Authors

Shuting Gu (Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong)

Ling Lin (Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong)

Xiang Zhou (Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong)

Abstract

The chemical reaction rate from reactant to product depends on the geometry of potential energy surface (PES) as well as the temperature. We consider a design problem of how to choose the best PES from a given family of smooth potential functions in order to maximize (or minimize) the reaction rate for a given chemical reaction. By utilizing the transition-path theory, we relate reaction rate to committor functions which solves boundary-value elliptic problems, and perform the sensitivity analysis of the underlying elliptic equations via adjoint approach. We derive the derivative of the reaction rate with respect to the potential function. The shape derivative with respect to the domains defining reactant and product is also investigated. The numerical optimization method based on the gradient is applied for two simple numerical examples to demonstrate the feasibility of our approach.

Keywords

rare event, reaction rate, transition path theory, sensitivity analysis

2010 Mathematics Subject Classification

49Q12, 82C80

Full Text (PDF format)

This research of X. Zhou was supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. City U 11304314, 109113,11304715). L. Lin acknowledges the partial financial support of the DRS Fellowship Program of Freie Universität Berlin.

Paper received on 23 February 2016.