  ## Diffusive System Parameters

These parameters set up cases where steady state diffusion is present in the physical problem. Note these are steady state calculations only. A time-dependent DFT is not implement as of the v2.1 release of Tramonto.

### Basic Diffusion Parameters

These parameters turn on the diffusion capability in Tramonto and set up the computational strategy.

• Lsteady_state(int): Logical (0=FALSE, 1=TRUE) that indicates whether this run is a steady state calculation that requires inhomogeneous boundary conditions.
• Grad_dim(int): The dimension in which the chemical potential of the fluid varies (only 1D diffusion is currently implemented).
• L1D_bc(int): A logical (0=TRUE; 1=FALSE) that indicates if a 1D boundary conditions should be applied at some distance from the ends of the boundary in the Grad_dim directions. This can be helpful in speeding up a 3D calculation where there is some region that is exactly or approximately 1D outside of a central diffusion region.
• X_1D_bc(real): The distance over which the 1D boundary should be applied. Only applies when L1D_bc=TRUE.
• x_const_mu(real): A distance in the Grad_dim dimension measured from the edges of the computational domain where the chemical potential is held constant. These constant regions (on either side of the computational domain) will be treated as a bulk fluid regions.
• ### Parameters for transport through a pore - treated as a 1-dimensional problem

Transport through a nanopore can be treated as a 1D problem as has been done for ion channels (see: for example). Several parameters are needed to set up these kinds of problems depending on if the pore has a constant radius or varies in size down the length of the pore. The parameters are as follows:

• Geom_Flag(int): This flag indicates whether we are doing a nanopore calculation in this way and whether the area of the pore varies in the Grad_dim dimension. Options are:
• 0: unit area - not performing nanopore calculation
• 1: cylindrical pore - uniform area finite length
• 2: pore composed of a sequence of tapered segments
• Nseg(int): This constant sets how many pore segments of different geometry there are for a given pore. For example a cylindrical pore with tapered ends might have be three segments.
• Radius_L[Nseg](vector real): Stores the radius of the left side of each pore segment (use when Geom_Flag=2).
• Radius_R[Nseg](vector real): Stores the radius of the right side of each pore segment (use when Geom_Flag=2).
• Length[Nseg](vector real): Stores the length of each pore segment (use when Geom_Flag=1 or 2).
• ### Define state points and transport coefficients

For steady state diffusion, there must two bulk regions where the (electro)chemical potentals differ. These parameters replace the Rho_b parameters in defining the state point of the diffusing fluid in the two regions. Note that in all cases if Tripathi-Chapman polymers are being studied, replace the Ncomp with Npol_comp in the vectors below. Also note that diffusion can not be done for CMS polymers because an explict calculation of the chemical potential is never done.

• Rho_b_LBB[Ncomp](vector real): The density on the left (x0), bottom (x1), or back (x2) of the computational domain depending on the direction Grad_dim.
• Rho_b_RTF[Ncomp](vector real): The density on the right (x0), top (x1), or front (x2) of the computational domain depending on the direction Grad_dim.
• D_coeff[Ncomp](vector real): The diffusion coefficient for each species in the problem of interest. Given the assumptions of ideal diffusion and steady state, these constants are only used in post processing a flux: they are not needed in the calculation of density an chemical potential profiles.
• Elec_pot_LBB[Ncomp](vector real): The electrostatic potential on the left (x0), bottom (x1), or back (x2) of the computational domain depending on the direction Grad_dim.
• Elec_pot_RTF[Ncomp](vector real): The electrostatic potential on the right (x0), top (x1), or front (x2) of the computational domain depending on the direction Grad_dim.
• Velocity(real): A constant that accounts for center of mass motion in steady state transport.