Figure 3
Mean-field and discrete results for a range of adhesive strengths: (a)–(f) extreme adhesion
, (g)–(l) strong adhesion
, and (m)–(r) modest adhesion
. (a), (b); (g), (h); (m), (n) For each adhesive strength, two snapshots of the discrete process are shown at
and
, respectively. All discrete results correspond to
; simulations are performed on a lattice with
and periodic boundary conditions. Discrete snapshots show 20 identically prepared realizations of the same one-dimensional process in the region
. (d), (j), (p) Comparisons of averaged density profiles (red), the initial condition (black dashed), and the solution of Eq. (
2) (blue). (e), (k), (q) Comparisons of averaged density profiles (red), the initial condition (black dashed), and the solution of Eq. (
4) (blue). (f), (l), (r) Comparisons of averaged density profiles (red), the initial condition (black dashed), and the solution of Eq. (
8) (blue). All discrete simulation results and mean-field solutions were obtained using periodic boundary conditions. (c), (i), (o) Show the nonlinear diffusivity function,
, associated with Eq. (
2). Results for extreme
and strong
adhesion show that
becomes negative in some interval
while results for the modest adhesion
show that
for all
. (s), (t) Continuum (blue) and discrete (red) profiles of
and
, respectively. In each plot, profiles of the correlation function are given for extreme
, strong
, and modest adhesion
with the arrow showing the direction of increasing
. (u) The error profile
as a function of the adhesion parameter
at
. Error profiles are given for Eqs. (
2) (blue dashed), (
4) (blue), and (
8) (red). All numerical solutions of Eq. (
2) correspond to
,
, and
. All numerical solutions of Eqs. (
4) and (
8) correspond to
.
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