topoparam Namespace Reference

Functions
double	normHeightPercent (molSys::PointCloud< molSys::Point< double >, double > *yCloud, int nPrisms, double avgPrismHeight)
std::vector< double >	calcCoverageArea (molSys::PointCloud< molSys::Point< double >, double > *yCloud, std::vector< std::vector< int >> rings, double sheetArea)
std::vector< double >	projAreaSingleRing (molSys::PointCloud< molSys::Point< double >, double > *yCloud, std::vector< int > ring)
	Calculates the projected area on the XY, YZ and XZ planes. More...

Function Documentation

calcCoverageArea()

std::vector< double > topoparam::calcCoverageArea	(	molSys::PointCloud< molSys::Point< double >, double > *	yCloud,
		std::vector< std::vector< int >>	rings,
		double	sheetArea
	)

Calculates the coverage area%, an area-based measure of relative proportion of monolayer ices.

The average height of prism blocks remains relatively constant. We have observed a average prism heights of 2.7-2.85 Angstrom for prisms irrespective of the number of nodes. The equation is given by:

\[ Height_{n}% = \frac{N_n}{N_{max}} \times 100 \]

Here, \(N_{max} = H_{SWCT}/h_{avg}f$ and \)N_{n}$ is the number of prism blocks for n-sided prismatic phase.

This means that the normalization factor, is the same for every node number \(n\).

Definition at line 70 of file order_parameter.cpp.

                                                       {
  //
  double areaXY, areaXZ, areaYZ;   // Total coverage area
  std::vector<double> singleAreas; // Area of single rings
 
  // ---------------------------------------
  // Initialization
  areaXY = 0.0;
  areaXZ = 0.0;
  areaYZ = 0.0;
  // ---------------------------------------
  // Loop through all the rings
  for (int iring = 0; iring < rings.size(); iring++) {
    // Get the coverage area for the current ring
    singleAreas = topoparam::projAreaSingleRing(yCloud, rings[iring]);
    // Add these to the total coverage area
    areaXY += singleAreas[0];
    areaXZ += singleAreas[1];
    areaYZ += singleAreas[2];
  } // end of loop through all the rings
  // ---------------------------------------
  // Normalize the coverage area by the sheet area
  areaXY = areaXY / sheetArea * 100.0;
  areaXZ = areaXZ / sheetArea * 100.0;
  areaYZ = areaYZ / sheetArea * 100.0;
 
  return {areaXY, areaXZ, areaYZ};
}

normHeightPercent()

double topoparam::normHeightPercent	(	molSys::PointCloud< molSys::Point< double >, double > *	yCloud,
		int	nPrisms,
		double	avgPrismHeight
	)

Calculates the height%, an average measure of filled volume. The average height of a prism can be taken to be 2.75-2.85 Angstrom. (Koga et. al., 2001)

The average height of prism blocks remains relatively constant. We have observed a average prism heights of 2.7-2.85 Angstrom for prisms irrespective of the number of nodes. The equation is given by:

\[ Height_{n}% = \frac{N_n}{N_{max}} \times 100 \]

Here, \(N_{max} = H_{SWCT}/h_{avg}f$ and \)N_{n}$ is the number of prism blocks for n-sided prismatic phase.

This means that the normalization factor, is the same for every node number \(n\).

Definition at line 32 of file order_parameter.cpp.

                           {
  //
  double hPercent;       // Normalized height percent
  double nanoTubeHeight; // Height of the SWCT
  double numberMax; // Maximum number possible, given the average prism height
 
  // ---------------------------------------
  // Calculate the height of the SWCT
  // This is the longest dimension of the simulation box
  nanoTubeHeight = *max_element(yCloud->box.begin(), yCloud->box.end());
  // ---------------------------------------
  // Calculate the maximum possible height, given the average prism height
  // and the height of the nanotube
  numberMax = nanoTubeHeight / avgPrismHeight;
  // ---------------------------------------
  // Calculate the normalized height percentage
  hPercent = nPrisms / numberMax * 100.0;
 
  return hPercent;
}

projAreaSingleRing()

std::vector< double > topoparam::projAreaSingleRing	(	molSys::PointCloud< molSys::Point< double >, double > *	yCloud,
		std::vector< int >	ring
	)

Calculates the projected area on the XY, YZ and XZ planes.

Calculates the coverage area/ projected area of a single ring given the ring and the PointCloud.

Definition at line 105 of file order_parameter.cpp.

                         {
  //
  int iatomIndex, jatomIndex; // Atom indices of the i^th and j^th atoms
  int ringSize = ring.size(); // Number of nodes in the ring
  double areaXY, areaXZ, areaYZ;
  double x_iatom, y_iatom, z_iatom; // Coordinates of iatom
  double x_jatom, y_jatom, z_jatom; // Coordinates of jatom
  // ----------------------------------------
  // Calculate projected area onto the XY, YZ and XZ planes for basal1
 
  // Init the projected area
  areaXY = 0.0;
  areaXZ = 0.0;
  areaYZ = 0.0;
 
  jatomIndex = ring[0];
 
  // All points except the first pair
  for (int k = 1; k < ringSize; k++) {
    iatomIndex = ring[k]; // Current vertex
 
    // --------------------------------------------------------------------
    // SHIFT PARTICLES TEMPORARILY (IN CASE OF UNWRAPPED COORDINATES)
    gen::unwrappedCoordShift(yCloud, iatomIndex, jatomIndex, &x_iatom, &y_iatom,
                             &z_iatom, &x_jatom, &y_jatom, &z_jatom);
    // --------------------------------------------------------------------
 
    // Add to the polygon area
    // ------
    // XY plane
    areaXY += (x_jatom + x_iatom) * (y_jatom - y_iatom);
    // ------
    // XZ plane
    areaXZ += (x_jatom + x_iatom) * (z_jatom - z_iatom);
    // ------
    // YZ plane
    areaYZ += (y_jatom + y_iatom) * (z_jatom - z_iatom);
    // ------
    jatomIndex = iatomIndex;
  }
 
  // Closure point
  iatomIndex = ring[0];
  // Unwrapped coordinates needed
  gen::unwrappedCoordShift(yCloud, iatomIndex, jatomIndex, &x_iatom, &y_iatom,
                           &z_iatom, &x_jatom, &y_jatom, &z_jatom);
  // ------
  // XY plane
  areaXY += (x_jatom + x_iatom) * (y_jatom - y_iatom);
  // ------
  // XZ plane
  areaXZ += (x_jatom + x_iatom) * (z_jatom - z_iatom);
  // ------
  // YZ plane
  areaYZ += (y_jatom + y_iatom) * (z_jatom - z_iatom);
  // ------
  // The actual projected area is half of this
  areaXY *= 0.5;
  areaXZ *= 0.5;
  areaYZ *= 0.5;
 
  // Absolute area
  areaXY = fabs(areaXY);
  areaXZ = fabs(areaXZ);
  areaYZ = fabs(areaYZ);
 
  return {areaXY, areaYZ, areaXZ};
}