The unit cell of the D3Q27 lattice. The nearest neighbors, next-nearest neighbors and next-next nearest neighbors are shown in green, blue, and red, respectively. The weighting factors, w i , for the D3Q27 are: w 0 = 8/27 (the cell-center), w i = 2/27 (i = 1 − 6), w i = 1/54 (i = 7 − 18), and w i = 1/216 (i = 19 − 26).
Tetrahedral representation of water-like molecules sitting at lattice site x and its neighbor x i . The four arms are denoted by the corresponding normals n k , k = 1, 4 (unprimed) and n l , l = 1, 4 (primed), respectively. Blue and red code for donor and acceptor arms, respectively. Here the index i corresponds to i = 23 in Fig. 1 .
Radial shape functions for the case σ R = 0.28 and . Note that nearest-neighbor interactions are roughly an order of magnitude weaker than next and next-next nearest neighbor ones.
The angular potential V ikl for σθ = 0.28. θ ik and θ il are shown in degrees.
The torque acting on the arm n k has two components in the direction of e ϕ(n k ) and e θ(n k ). The total torque acting on the tetrahedron is then the vector sum of the torques acting on all 4 arms.
Time evolution of the total potential energy vs the LB time steps together with the number of hydrogen bonds for four different effective temperatures, at (a) β−1 = 10−4, (b) β−1 = 4 × 10−4, (c) β−1 = 5.5 × 10−4, and (d) β−1 = 7 × 10−4. Main parameters are as follows N = 103, σ R = 0.28, σθ = 0.28, and .
(a) Initial random distribution of tetrahedrons and the corresponding final distribution at steady state with and without thermal fluctuations in (b) and (c), respectively.
Comparison of LB-ADR (blue) and MC (green) simulated annealing as energy minimizers. Main parameters are as follows N = 63, , σ R = 0.28, σθ = 0.28.
Extremal values of the angular potential , corresponding to cos θ ik = 1, 0, −1 and cos θ il = − 1, 0, 1 for the case σθ = 1.
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