A LinearRamp allows a user to vary a set of one or more parameters over the course of a simulation, such that each of the chosen parameters varies linear with the simulation step counter. This is the default ramp algorithm for both pscf_pc and pscf_pg, and so may be selected by including a parameter file block with either the specific label "LinearRamp" or the generic label "Ramp" in the appropriate location within a BdSimulator or McSimulator parameter file block.

See also

Parameter File Format

The parameter file format for a LinearRamp is closely analogous to that used for SCFT calculations by the LinearSweep class.

A simple example of the parameter file block for a LinearRamp is shown below:

LinearRamp{
   nParameters      2
   parameters[
      chi            0     1    2.0
      v_monomer                 0.005
   ]
}

This parameter file block varies the parameter chi(0,1) (i.e., the Flory-Huggins interaction parameter controlling interactions between monomers of types \( 0 \) and \( 1 \), and the length of block 1 of polymer species 1 (i.e., the second block of the first species). The last parameter in each line specifies how much the associated parameter will be changed over the course of a simulation.

The parameter file format for a LinearRamp is specified below:

LinearRamp{
   nParameter        int
   parameters        Array [ RampParameter ]
}

Each element of the "parameters" array is stored internally in an instance of a class RampParameter, as discussed in more detail below. The meaning of the two parameters are described in the following table:

Label	Description
nParameter	number of parameters that are modified during the ramp
parameters	Array in which each element specifies a parameter and the amount it should be changed over the course of the simulation

The array "parameters" must contain nParameter lines, each on a separate line, each of which contains an identifier for a single parameter and a value for the amount that parameter will be changed over the course of a simulation. Parameters that are not listed in this array are not modified during the simulation.

Technical comment (for users who read the source code): The "parameters" array is implemented as an array in which each element is an instance of a class RampParameter<D>, which is defined by a class template RampParameter that takes the dimension D of space as a template argument. The information about a single parameter given in each line of the "parameters" array in parameter file is read into and stored by a corresponding RampParameter<D> object. Class RampParameter<D> has an overloaded stream extraction (>>) operator that defines the allowed text format for each line in this array.

Ramp Parameters

The file format each line of the "parameters" array (corresponding to a single parameter) in a LinearRamp contains an identifier for a specific input parameter followed by amount by which the value of that parameter should change over the course of a simulation. The parameter identifier in each such entry contains a name string that identifies the type of variable, such as "block" for a block length or "chi" for an interaction parameter. This string is followed by zero, one or two integer indices that specify which variable of that type should be changed. For example, the string "block" must be followed by two integers, the first of which is an index for the polymer species the block belongs to, and the second of which is an index for that block within that polymer. Some other types of parameter can be uniqued identified using only a single index. For example the description of a parameter that specifies a volume fraction or chemical potential of a polymer or solvent molecular species requires a single index to identify the polymer or solvent species of interest. Other parameters, such as v_monomer, do not have any associated indices.

The general format for a line in the parameters array for a parameter that is specified by two indices is:

type id0 id1 change

where "type" denotes the parameter type identifier string (e.g., block or chi), "id0" and "id1" denote associated integer indices, and "change" is a real number that specifies the total amount that the specified parameter should be changed over the course of the ramp. The format for a parameter that has only one associated index (such as a molecular volume fraction) simply omits the second integer index.

The table shown below gives all allowed values for the parameter type string identifer for a LinearRamp for a periodic microstructure with with the number and meaning of any associated index or indices. All but one of these types of parameter are also valid in a linear ramp performed by pscf_1d one-dimensional finite difference program, as discussed below. To indicate the meaning of each index in this table, we use the following notation:

mId denote a monomer type index
pId denotes a polymer species index
bId denote the index of a block within a polymer
sId denotes a solvent species index
uId denotes an index for a unit cell parameter for a periodic structure.

If only one index is required for a particular parameter type, then no entry is is given for the the second index.

Type	Meaning	id0	id1
kuhn	monomer segment length	mId
chi	Flory-Huggins parameter	mId	mId
block	block length	pId	bId
solvent	solvent size	sId
phi_polymer	polymer volume fraction	pId
mu_polymer	polymer chemical potential	pId
phi_solvent	solvent volume fraction	sId
mu_solvent	solvent chemical potential	sId
cell_param	unit cell lattice parameter	uId
v_monomer	monomer reference volume
lambda_pert	perturbation parameter

The two indices for a Flory-Huggins chi parameter refer to indices in the chi matrix maintained by Interaction. Changes to element chi(i, j) automatically also update chi(j, i) for \( i \neq j \), thus preserving the symmetry of the chi matrix. The parameter types v_monomer and lambda_pert are global values that are not associated with any indices. All other parameter types are identified by at least one associated index.

Perturbation Parameter

The parameter type "lambda_pert" is designed specifically for use with a Perturbation, and allows the user to ramp the value of the parameter that controls the strength of a perturbation, denoted by "lambda". This parameter may not be used if the parameter file does not contain a Perturbation block.

The most important use of a linear ramp with parameter type lambda_pert is to perform continuous Einstein crystal integration.