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# Correction: Generalized Langevin dynamics: construction and numerical integration of non-Markovian particle-based models

Gerhard Jung *ab, Martin Hanke c and Friederike Schmid a
aInstitut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55128 Mainz, Germany. E-mail: jungge@uni-mainz.de; friederike.schmid@uni-mainz.de
bGraduate School of Excellence Materials Science in Mainz, Staudingerweg 9, 55128 Mainz, Germany
cInstitut für Mathematik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55128 Mainz, Germany. E-mail: hanke@mathematik.uni-mainz.de

Received 16th November 2018 , Accepted 16th November 2018

First published on 30th November 2018

Correction for ‘Generalized Langevin dynamics: construction and numerical integration of non-Markovian particle-based models’ by Gerhard Jung et al., Soft Matter, 2018, DOI: 10.1039/c8sm01817k.

Algorithm 1 presented in the manuscript on page 4 contains a significant typographical error which was introduced in the typesetting process. Line 13 of Algorithm 1 in the published manuscript is: and has been corrected to . The full and correct algorithm is repeated below.
 Algorithm 1: Generating correlated random numbers FI,n with the distribution 〈FI,n+mFJ,n〉 = KIJ,m 1: Inputs: KIJ,m for m = 0,…,mmax − 1 with KIJ,m = KIJ,−m WI,n with 〈WI,n+mWJ,n〉 = δm0δIJ 2: Initialize: 3: forω = 0 to mmax − 1 do 4:  set v0I = 0, β0 = 0, v1I = ŴI,ω/‖Ŵω‖, k = 1, Δ = 1 5:  compute α1 = v1IIJ,ωv1J 6:  whileΔ > toldo 7:   compute rk+1I = IJ,ωvkJ − αkvkI − βk−1vk−1I 8:   set βk = ‖rk+1‖ 9:   set vk+1I = rk+1I/βk 10:   compute αk+1 = vk+1IIJ,ωvk+1J 11:   define Vk+1Ip = vpI, p = 1,…,k + 1 12:   construct tridiagonal Hk+1pq with diagonal elements equal to (α1,…,αk+1) and super- and sub-diagonal elements equal to (β1,…,βk) 13:   compute , with e01 = 1 and e0q = 0, q = 2,…,k + 1 14:   set Δ = ‖xk+1 − xk‖ 15:   set k = k + 1 16:  end while 17:  set I,ω = xkI 18: end for 19:

The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers.

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