GraphenePotential Class Reference

The smooth non-corregated version of the helium-carbon nanotube potential. More...

#include <potential.h>

Inheritance diagram for GraphenePotential:

Collaboration diagram for GraphenePotential:

Public Member Functions
	GraphenePotential (const double, const double, const double, const double, const double)
	Constructor.
	~GraphenePotential ()
	Destructor.
double	V (const dVec &r)
	Return the value of the van der Waals' interaction between a graphene sheet and a helium adatom at a position, r, above the sheet. More...
Array< dVec, 1 >	initialConfig (const Container *, MTRand &, const int)
	Initial configuration corresponding to graphene-helium vdW potential. More...
Public Member Functions inherited from PotentialBase
	PotentialBase ()
	Constructor.
virtual	~PotentialBase ()
	Destructor.
virtual double	V (const dVec &, const dVec &)
	The effective potential for the pair product approximation.
virtual dVec	gradV (const dVec &)
	The gradient of the potential.
virtual double	grad2V (const dVec &)
	Grad^2 of the potential.
virtual double	dVdlambda (const dVec &, const dVec &)
	The derivative of the effective potential with respect to lambda and tau.
virtual double	dVdtau (const dVec &, const dVec &)
void	output (const double)
	A debug method that output's the potential to a supplied separation. More...
virtual Array< double, 1 >	getExcLen ()
	Array to hold data elements. More...

Additional Inherited Members
Data Fields inherited from PotentialBase
double	tailV
	Tail correction factor.
Protected Member Functions inherited from PotentialBase
double	deltaSeparation (double sep1, double sep2) const
	Return the minimum image difference for 1D separations.

Detailed Description

The smooth non-corregated version of the helium-carbon nanotube potential.

See also

http://prb.aps.org/abstract/PRB/v62/i3/p2173_1

Returns van der Waals' potential between a helium adatom and a graphene sheet using summation in reciprocal space.

Author: Nathan Nichols Returns the potential energy resulting from a van der Waals' interaction between a helium adatom and a fixed infinite graphene lattice

Definition at line 1174 of file potential.h.

Member Function Documentation

initialConfig()

Array< dVec, 1 > GraphenePotential::initialConfig ( const Container *  boxPtr, MTRand &  random, const int  numParticles  )

virtual

Initial configuration corresponding to graphene-helium vdW potential.

Return an initial particle configuration.

We create particles at random locations above the graphene sheet.

Reimplemented from PotentialBase.

Definition at line 2571 of file potential.cpp.

                                {
 
    /* The particle configuration */
    Array<dVec,1> initialPos(numParticles);
    initialPos = 0.0;
    double initSideCube = 1.0*numParticles;
    
    for (int i = 0; i < NDIM - 1; i++) {
        initSideCube /= boxPtr->side[i];
    }
 
    initSideCube /= ((boxPtr->side[NDIM-1] / 2.0) - 6.0);
 
    /* Get the linear size per particle, and the number of particles */
    double initSide = pow((initSideCube),-1.0/(1.0*NDIM));
 
    /* We determine the number of initial grid boxes there are in 
     * in each dimension and compute their size */
    int totNumGridBoxes = 1;
    iVec numNNGrid;
    dVec sizeNNGrid;
 
    for (int i = 0; i < NDIM - 1; i++) {
        numNNGrid[i] = static_cast<int>(ceil((boxPtr->side[i] / initSide) - EPS));
 
        /* Make sure we have at least one grid box */
        if (numNNGrid[i] < 1)
            numNNGrid[i] = 1;
 
        /* Compute the actual size of the grid */
        sizeNNGrid[i] = boxPtr->side[i] / (1.0 * numNNGrid[i]);
 
        /* Determine the total number of grid boxes */
        totNumGridBoxes *= numNNGrid[i];
    }
 
    numNNGrid[NDIM-1] = static_cast<int>(ceil(((boxPtr->side[NDIM-1] - 12.0) / (2.0 * initSide)) - EPS));
 
    /* Make sure we have at least one grid box */
    if (numNNGrid[NDIM-1] < 1)
        numNNGrid[NDIM-1] = 1;
 
    /* Compute the actual size of the grid */
    sizeNNGrid[NDIM-1] = (boxPtr->side[NDIM-1] - 12.0) / (2.0 * numNNGrid[NDIM-1]);
 
    /* Determine the total number of grid boxes */
    totNumGridBoxes *= numNNGrid[NDIM-1];
 
    /* Now, we place the particles at the middle of each box */
    PIMC_ASSERT(totNumGridBoxes>=numParticles);
    dVec pos;
    for (int n = 0; n < totNumGridBoxes; n++) {
 
        iVec gridIndex;
        for (int i = 0; i < NDIM; i++) {
            int scale = 1;
            for (int j = i+1; j < NDIM; j++) 
                scale *= numNNGrid[j];
            gridIndex[i] = (n/scale) % numNNGrid[i];
        }
 
        for (int i = 0; i < NDIM - 1; i++) 
            pos[i] = (gridIndex[i]+0.5)*sizeNNGrid[i] - 0.5*boxPtr->side[i];
        
        pos[NDIM - 1] = (gridIndex[NDIM - 1]+0.5)*sizeNNGrid[NDIM - 1] + 3.0;
 
        boxPtr->putInside(pos);
 
        if (n < numParticles)
            initialPos(n) = pos;
        else 
            break;
    }
    return initialPos;
}

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V()

double GraphenePotential::V ( const dVec &  r )

virtual

Return the value of the van der Waals' interaction between a graphene sheet and a helium adatom at a position, r, above the sheet.

Parameters

r	the position of a helium particle

Returns

the van der Waals' potential for graphene-helium

Reimplemented from PotentialBase.

Definition at line 2526 of file potential.cpp.

                                         {
 
    double z = r[2] + Lzo2;
 
    /* We take care of the particle being in a forbidden region */
    if (z < 1.5) 
        return 40000.;
    if (z > Lz-0.05)
        return 40000.;
 
    double x = r[0];
    double y = r[1];
    double g = 0.;
    double gdotb1 = 0.;
    double gdotb2 = 0.;
    double k5term = 0.;
    double k2term = 0.;
    double prefactor = 0.;
    double v_g = 0.;
    double v = (4.*M_PI/A)*epsilon*sigma*sigma*( ((2./5.)*pow((sigma/z),10)) - pow((sigma/z),4) );
 
    for (double m = -1; m < 1+1; m++) {
        for (double n = -1; n < 1+1; n++) {
            if ((m != 0) || (n != 0)){
                g = sqrt(pow((m*g1x + n*g2x),2.) + pow((m*g1y + n*g2y),2.));
                gdotb1 = ((m*g1x + n*g2x)*(b1x+x)) + ((m*g1y + n*g2y)*(b1y+y));
                gdotb2 = ((m*g1x + n*g2x)*(b2x+x)) + ((m*g1y + n*g2y)*(b2y+y));
                k5term = pow((g*sigma*sigma/2./z),5.)*boost::math::cyl_bessel_k(5., g*z)/30.;
                k2term = 2.*pow((g*sigma*sigma/2./z),2.)*boost::math::cyl_bessel_k(2., g*z);
                prefactor = epsilon*sigma*sigma*2.*M_PI/A;
 
                v_g = prefactor*(k5term-k2term);
                v += (cos(gdotb1)+cos(gdotb2))*v_g;
            }
        }
    }
 
    return v;
 
}

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The documentation for this class was generated from the following files:

• include/potential.h
• src/potential.cpp