Errata – Book “Simulation of Complex Systems”

Link to the Notes and Comments page.

  • Chapter 1, page 13, Exercise 1.8, formula after the sentence Numerically, MSD(nΔt) is calculated as follows:
    N   →   Np
  • Chapter 1, page 13, Exercise 1.8, sentence after MSD(nΔt) formula:
    Note   →   where Np is the number of points in the trajectory of the large particle. Note
  • Chapter 5, page 5-7, caption Fig. (5.4):
    with inertia (equation 5.6, black dashed line)   →   with inertia (equation 5.6, cyan solid line)
    without inertia (equation 5.7, cyan solid line)   →   without inertia (equation 5.7, black dashed line)
  • Chapter 5, page 5-7, Exercise 5.3c:
    This shows that the motion of a Brownian particle is ergodic.   →   This shows that the motion of a Brownian particle is ergodic. [Hint: The numerical definition of the time-averaged MSDs and the ensemlbe-averaged MSDs is given in Chapter 6, Eqs. (6.2-6.3). The numerical definition of time-averaged MSDs is given also in Exercise 1.8 point b.]
  • Chapter 6, page 6-3, paragraph after Eq. (6.3):
    where τi is a reference time at which to calculate the square displacements of the particle.   →   where τi is a reference time at which to calculate the square displacements of the particle and n is the number of elements in the summation (note: this number depends on τi).
  • Chapter 7, page 7-4, Exercise 7.3, paragraph after Eq. (7.8):
    σ( −L ⁄ 2 )=0.1 and σ( −L ⁄ 2 )=1.9   →   σ( −L ⁄ 2 )=0.1 and σ( L ⁄ 2 )=1.9
  • Chapter 7, page 7-5, paragraph after Eq. (7.4):
    a standard deviation of σ√(2jΔt)   →   a standard deviation of σ√(jΔt)
  • Chapter 7, page 7-7, Eq. (7.11), right hand side:
    ασ(xt) dσ(xt)/dx Δt±σ√(Δt)   →   ασ(xj) dσ(xj)/dx Δt±σ(xj)√(Δt)
  • Chapter 7, page 7-9, Exercise. 7.6, end of the initial paragraph:
    […] and with multiplicative noise (as in exercise 7.3).   →   […] and with multiplicative noise (as in exercise 7.4b).
  • Chapter 7, page 7-12, Eq. (7.22), third equation, right hand side:
    dWx,t   →   dWz,t
  • Chapter 8, page 8-3, Eq. (8.3):
    vj,n+1   →   vj,n
  • Chapter 11, page 11-2, bottom line:
    with some probability 1∸   →   with some probability 1−d
  • Chapter 14, page 14-8, Eq. (14.11) (second equation, for yn+1):
    yn+1 = yn + (δxnyn+1-γyn) Δt   →   yn+1 = yn + (δxnyn+1-γyn+1) Δt
  • Chapter 14, page 14-8, Eq. (14.12) (second equation, for yn+1):
    yn+1 = yn + (δxn+1yn-γyn+1) Δt   →   yn+1 = yn + (δxn+1yn-γyn) Δt
  • Chapter 14, page 14-12, Eq. (14.19):
    xeq = (α1r1+β12r1)/(α1α2-β12β21)   →   xeq = (α2r1+β12r1)/(α1α2-β12β21)
  • Chapter 15, page 15-5, Exercise 14.2a:
    Create the corresponding distance matrix M   →   Create the corresponding connection matrix M