/**
* Constructs OscillatorsMode with the given mode and number of particles.
*
* <p>The particle separation is one in this model.
*
* @param mode int
* @param N int
*/
OscillatorsMode(int mode, int N) {
amplitude = Math.sqrt(2.0 / (N + 1));
omega = 2 * Math.sqrt(OMEGA_SQUARED) * Math.abs(Math.sin(mode * Math.PI / N / 2));
wavenumber = Math.PI * mode / (N + 1);
functionDrawer = new FunctionDrawer(this);
functionDrawer.initialize(0, N + 1, 300, false); // draws the initial displacement
functionDrawer.color = Color.LIGHT_GRAY;
}
/**
* Creates an AffineMatrix representing a rotation about the origin by some angle around the given
* axis.
*
* @param theta double
* @param axis double[]
* @return AffineMatrix
*/
public static Affine3DMatrix Rotation(double theta, double[] axis) {
Affine3DMatrix at = new Affine3DMatrix(null);
double[][] atMatrix = at.matrix;
double norm = Math.sqrt(axis[0] * axis[0] + axis[1] * axis[1] + axis[2] * axis[2]);
double x = axis[0] / norm, y = axis[1] / norm, z = axis[2] / norm;
double c = Math.cos(theta), s = Math.sin(theta);
double t = 1 - c;
// matrix elements not listed are zero
atMatrix[0][0] = t * x * x + c;
atMatrix[0][1] = t * x * y - s * z;
atMatrix[0][2] = t * x * y + s * y;
atMatrix[1][0] = t * x * y + s * z;
atMatrix[1][1] = t * y * y + c;
atMatrix[1][2] = t * y * z - s * x;
atMatrix[2][0] = t * x * z - s * y;
atMatrix[2][1] = t * y * z + s * x;
atMatrix[2][2] = t * z * z + c;
atMatrix[3][3] = 1;
return at;
}
/**
* Evaluates the displacement for an oscillator at postion x
*
* @param x postion along chain
* @return the displacement
*/
public double evaluate(double x) {
return amplitude * Math.sin(x * wavenumber);
}
public double cosh(double x) {
double ex, mex;
ex = Math.exp(x);
mex = 1 / ex;
return (ex + mex) / 2;
}
public double tanh(double x) {
double ex, mex;
ex = Math.exp(x);
mex = 1 / ex;
return (ex - mex) / (ex + mex);
}
public double freeenergy(double x) {
return 0.5 * Jq * x * x - 1.0 / beta * Math.log(2 * cosh(beta * (Jq * x + b)));
}