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Ramp Concept

The "ramp" is an optional feature of PSCF allows a user to perform a FTS in which one or more of the parameters of the model vary continuously over the course of the simulation. The main uses for parameter ramps are:

To approximately identify the location of an equilibrium phase transition, such as an order-disorder transition, by inducing a spontaneous phase transformation during a slow parameter ramp.
To evaluate the integral of some ensemble average with respect to changes in a model parameter in order to implement continuous thermodynamic integration.

A parameter ramp is enabled by adding an optional, selectable Ramp block within the Simulator block of the parameter file. When present, this Ramp block must appear within the BdSimulator or McSimulator block after the Compressor block, and after any Perturbation block, as discussed previously.

The Ramp block has been programmed as a selectable block to allow for later extension, but only one ramp algorithm is provided with the current version of PSCF, as discussed below.

Linear Ramp

The only type ramp that is currently available is a linear ramp algorithm that is implemented by class LinearRamp. The LinearRamp class allows a user to perform a simulation in which almost any physical parameter of the Hamiltonian that is represented by a real number, or any set of these parameters, can be chosen to vary linearly with the number of simulation steps completed since the beginning of the simulation. The design and interface of the LinearRamp class are closely analogous to those of the LinearSweep class, which is used to program SCFT parameter sweeps. Because the LinearRamp class is the default Ramp algorithm (since it is currently the only one), the opening line of a parameter block for this class may contain either the generic block label "Ramp" (thereby choosing the default) or the specific class name "LinearRamp".

A full description of the parameter file format for a LinearRamp block is given in a separate page . As already noted, the required format is closely analogous to that of the LinearSweep class. The parameter block contains an 1D array in which each line contains an identifier for a parameter that should ramped and a parameter value that indicates how much that parameter should be changed. This more detailed description includes a complete list of the string labels that are used to specify different types of parameters that should be varied during such a ramp.

The initial value of each parameter that is varied by a LinearRamp is equal to the value that would have been used in the simulation if the Ramp block were absent. This value is usually known from the values of rameters defined earlier in the parameter file. In the case of unit cell parameters, it may instead be set to values given in the header of a field file that contains the initial field configuration, which must be read before beginning a simulation. The final value at the end of a simulation is given by the sum of that initial value and the change specified in the Ramp block. The change per step required to accomplish this is computed for each ramped parameter just before beginning a simulation, based on the planned number of steps for the simulation The number of BD or MC steps is given as a parameter to the SIMULATE command in the command file.

See also: LinearRamp (manual page)

Example

Below, we show an example of parameter file for BD simulation for a symmetric diblock copolymer melt containing chains of total length 1.0 in which the chi parameter is ramped from chi = 14 to 18 over the course of a simulation. The main difference from previous examples is the presence of a Ramp subblock within the BdSimulation block. In this example, the Ramp block appears immediately after the Compressor block, and the generic block label "Ramp" in order to choose a LinearRamp by default.

System{
  Mixture{
    nMonomer  2
    monomers[
             1.0  
             1.0 
    ]
    nPolymer  1
    Polymer{
      type    linear
      nBlock  2
      blocks[
              0   0.5
              1   0.5
      ]
      phi     1.0
    }
    vMonomer  0.01
    ds   0.02
  }
  Interaction{
    chi(
        1   0   14.0
    )
  }
  Domain{
    mesh         40    40    40
    lattice      cubic   
  }
  BdSimulator{
    seed           486893701
    BdStep{
      mobility  5.0E-2
    }
    Compressor{
      epsilon      1.0e-4
      maxHist      40
    }
    Ramp{
       nParameter  1 
       parameters[
          chi     0    1   4.0
       ]
    }
    AnalyzerManager{
 
      StepLogger{
        interval        20
      }
 
      MaxOrderParameter{
        interval         10
        outputFileName   out/maxOrderParameter
      }
 
      HamiltonianAnalyzer{
        interval         10
        outputFileName   out/hamiltonian
      }
 
    }
  }
}

Discussion : Within the Ramp block, the first parameter, named nParameter, gives the number of parameters that will be varied during the simulation. In this example, nParameter = 1 because we only want to vary a single chi parameter. The next element is an array named parameters[ ... ] in which each line specifies a parameter that will be varied, and how much it should be changed. The number of elements (or lines) in this array must be equal to nParameter. In this example, because nParameter = 1 , the array only contains one line, which specifies that the chi parameter chi(0, 1) that controls interaction between monomers of types 0 and 1 (i.e., A and B) should be increased by 4.0 over the course of the simulation. Because chi(0,1) is given an initial value of 14.0 in the Interaction block, this chi parameter will thus be increased from 14 to 18 over the course of a simulation.

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