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DOI: 10.1039/C8SM90228C (Correction) Soft Matter, 2018, 14, 9973-9974

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

Abstract

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: image file: c8sm90228c-t1.tif and has been corrected to image file: c8sm90228c-t2.tif. 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:
  [thin space (1/6-em)]KIJ,m for m = 0,…,mmax − 1 with KIJ,m = KIJ,−m
  [thin space (1/6-em)]WI,n with 〈WI,n+mWJ,n〉 = δm0δIJ
2: Initialize:
  [thin space (1/6-em)]image file: c8sm90228c-t3.tif
  [thin space (1/6-em)]image file: c8sm90228c-t4.tif
3: forω = 0 to mmax − 1 do
4:  [thin space (1/6-em)]set v0I = 0, β0 = 0, v1I = ŴI,ω/‖Ŵω‖, k = 1, Δ = 1
5:  [thin space (1/6-em)]compute α1 = v1I[K with combining circumflex]IJ,ωv1J
6:  [thin space (1/6-em)]whileΔ > toldo
7:   [thin space (1/6-em)]compute rk+1I = [K with combining circumflex]IJ,ωvkJ − αkvkI − βk−1vk−1I
8:   [thin space (1/6-em)]set βk = ‖rk+1‖
9:   [thin space (1/6-em)]set vk+1I = rk+1I/βk
10:   [thin space (1/6-em)]compute αk+1 = vk+1I[K with combining circumflex]IJ,ωvk+1J
11:   [thin space (1/6-em)]define Vk+1Ip = vpI, p = 1,…,k + 1
12:   construct tridiagonal Hk+1pq with diagonal
    [thin space (1/6-em)]elements equal to (α1,…,αk+1) and super- and
    [thin space (1/6-em)]sub-diagonal elements equal to (β1,…,βk)
13:   compute image file: c8sm90228c-t5.tif,
   [thin space (1/6-em)][thin space (1/6-em)]with e01 = 1 and e0q = 0, q = 2,…,k + 1
14:   [thin space (1/6-em)]set Δ = ‖xk+1 − xk‖
15:   [thin space (1/6-em)]set k = k + 1
16:  [thin space (1/6-em)]end while
17:  [thin space (1/6-em)]set [F with combining circumflex]I,ω = xkI
18: end for
19: image file: c8sm90228c-t6.tif

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

This journal is © The Royal Society of Chemistry 2018