# Interdisciplinary Applied Mathematics

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The temperature of fluid is regulated to 300 K by using a Berendsen thermostat with a time constant of 0.1 ps (see Section 16.1.3 on thermostats). When setting up the simulation, the molecules were randomly positioned. An energy minimization was performed to remove the local contacts. To start the simulation, an initial velocity sampled from a Maxwellian distribu-

TABLE 12.1. Parameters for the Lennard-Jones potential U(r) =

 Interaction Cq (kJ • nm6/mol)) Ci2 (kJ • nm12/mol) a (nm)j 0-0 0.2617 x КГ2 0.2633 x КГ5 0.317 O-Si 0.6211 x КГ2 0.7644 x КГ5 0.327 O-Cl 0.6011 x КГ2 0.1678 x НГ4 0.375 O-Na 0.4343 x КГ3 0.2352 x НГ6 0.286 Cl-Cl 0.1380 x КГ1 0.1069 x НГ3 0.445 Cl-Si 0.1426 x КГ1 0.4871 x КГ4 0.388 Cl-Na 0.9974 x КГ3 0.1499 x НГ5 0.339 Na-Na 0.7206 x КГ4 0.2101 x НГ7 0.257 Na-Si 0.1031 x КГ2 0.6829 x НГ6 0.295

I a is the separation distance between atoms where the potential energy is zero.

tion at 300 K was assigned to each molecule in the system. The system was simulated for a time period of 1 ns to 2 ns, so that the system has reached steady state. A production run of 1 ns to 7 ns (depending on the system to be simulated) was performed to gather the statistics of various quantities, e.g., streaming velocity. The density and velocity profile across the channel were computed using the binning method as described in Chapter 16. The flow is driven by an external electric field Eext, applied along the channel in the x-direction. Because of the extremely high thermal noise, a strong electric field    is    required    so    that    the    fluid    velocity can be    retrieved    with

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