LJCylinderPotential Class Reference

Computes the value of the external wall potential for a cylindrical cavity. More...

#include <potential.h>

Inheritance diagram for LJCylinderPotential:

Collaboration diagram for LJCylinderPotential:

Public Member Functions
	LJCylinderPotential (const double)
	Constructor. More...
	~LJCylinderPotential ()
	Destructor.
double	V (const dVec &r)
	The integrated LJ Wall potential.
dVec	gradV (const dVec &)
	Return the gradient of aziz potential for separation r using a lookup table.
double	grad2V (const dVec &)
	Return the Laplacian of aziz potential for separation r using a lookup table.
Array< dVec, 1 >	initialConfig (const Container *, MTRand &, const int)
	Initial configuration corresponding to the LJ cylinder 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 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...
Public Member Functions inherited from TabulatedPotential
	TabulatedPotential ()
	Constructor.
virtual	~TabulatedPotential ()
	Destructor.

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.
Protected Member Functions inherited from TabulatedPotential
void	initLookupTable (const double, const double)
	Given a discretization factor and the system size, create and fill the lookup tables for the potential and its derivative.
virtual double	newtonGregory (const Array< double, 1 > &, const TinyVector< double, 2 > &, const double)
	Use the Newton-Gregory forward difference method to do a 2-point lookup on the potential table. More...
virtual double	direct (const Array< double, 1 > &, const TinyVector< double, 2 > &, const double)
	Use a direct lookup for the potential table. More...
Protected Attributes inherited from TabulatedPotential
Array< double, 1 >	lookupV
	A potential lookup table.
Array< double, 1 >	lookupdVdr
	A lookup table for dVint/dr.
Array< double, 1 >	lookupd2Vdr2
	A lookup table for d2Vint/dr2.
double	dr
	The discretization for the lookup table.
int	tableLength
	The number of elements in the lookup table.
TinyVector< double, 2 >	extV
	Extremal value of V.
TinyVector< double, 2 >	extdVdr
	Extremal value of dV/dr.
TinyVector< double, 2 >	extd2Vdr2
	Extremal value of d2V/dr2.

Detailed Description

Computes the value of the external wall potential for a cylindrical cavity.

Definition at line 535 of file potential.h.

Constructor & Destructor Documentation

LJCylinderPotential()

LJCylinderPotential::LJCylinderPotential

(

const double

radius

)

Constructor.

We create a Lennard-Jones cylinder, which uses a lookup table to hold the value of the integrated 6-12 potential for helium atoms interacting with a silicon nitride cylinder.

See also

C. Chakravarty J. Phys. Chem. B, 101, 1878 (1997).

Parameters

radius

The radius of the cylinder

Definition at line 1027 of file potential.cpp.

                                                            : 
    PotentialBase(),
    TabulatedPotential()
{
 
    /* The radius of the tube */
    R = radius;
 
    /* The density of nitrogen in silicon nitride */
    density = 0.078; // atoms / angstrom^3
//  density = 0.008; // atoms / angstrom^3
 
    /* We define the values of epsilon and sigma for N and He */ 
//  double epsilonHe = 10.216;  // Kelvin
//  double sigmaHe   = 2.556;   // angstroms
//  double sigmaN    = 3.299;   // angstroms
//  double epsilonN  = 36.2;    // Kelvin
//  epsilon = sqrt(epsilonHe*epsilonN);
//  sigma = 0.5*(sigmaHe + sigmaN);
 
    /* We operate under the assumption that the silicon can be neglected in the 
     * silicon-nitride, and thus only consider the Nitrogen.  We use a
     * Kiselov type model to extract the actual parameters.  We assume that
     * silicate and silicon-nitride are roughly equivalent. */
    epsilon = 10.22;    // Kelvin
    sigma   = 2.628;    // angstroms
 
//  epsilon = 32;   // Kelvin
//  sigma   = 3.08; // angstroms
 
    /* We choose a mesh consisting of 10^6 points, and create the lookup table */
    dR = (1.0E-6)*R;
 
    initLookupTable(dR,R);
    
    /* Find the minimun of the potential */
    minV = 1.0E5;
    for (int n = 0; n < tableLength; n++) {
        if (lookupV(n) < minV)
            minV = lookupV(n);
    }
 
    /* The extremal values for the lookup table */
    extV = valueV(0.0),valueV(R);
    extdVdr = valuedVdr(0.0),valuedVdr(R);
}

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Member Function Documentation

initialConfig()

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

virtual

Initial configuration corresponding to the LJ cylinder potential.

Return an initial particle configuration.

Return a set of initial positions inside the cylinder.

Reimplemented from PotentialBase.

Definition at line 1191 of file potential.cpp.

                                {
 
    /* The particle configuration */
    Array<dVec,1> initialPos(numParticles);
    initialPos = 0.0;
 
    /* We shift the radius inward to account for the excluded volume from the
     * hard wall.  This represents the largest prism that can be put
     * inside a cylinder. */
    dVec lside;
    lside[0] = lside[1] = sqrt(2.0)*(R-sigma);
    lside[2] = boxPtr->side[NDIM-1];
 
    /* Get the linear size per particle */
    double initSide = pow((1.0*numParticles/product(lside)),-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; i++) {
        numNNGrid[i] = static_cast<int>(ceil((lside[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] = lside[i] / (1.0 * numNNGrid[i]);
 
        /* Determine the total number of grid boxes */
        totNumGridBoxes *= numNNGrid[i];
    }
 
    /* 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; i++) 
            pos[i] = (gridIndex[i]+0.5)*sizeNNGrid[i] - 0.5*lside[i];
 
        boxPtr->putInside(pos);
 
        if (n < numParticles)
            initialPos(n) = pos;
        else 
            break;
    }
 
    return initialPos;
}

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

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