public static Vector BrownianSolution(double mass, double Temp, double relaxTime, double prevPosition, double prevVelocity, double timeStep, SolutionDimension XorY)
{
Vector result;
Random random = new Random();
//Calculate G
double U1, U2, G;
U1 = random.NextDouble();
U2 = random.NextDouble();
if (XorY == SolutionDimension.X)
G = Math.Sqrt(-2 * (Math.Log(U1))) * Math.Cos(2 * Math.PI * U2);
else
G = Math.Sqrt(-2 * (Math.Log(U1))) * Math.Sin(2 * Math.PI * U2);
//Calculate S
double S;
double k = 1.3806488E-23;
S = (2 * k * Temp) / (Math.PI * mass * relaxTime);
//Calculate n_x(t)
double n = G * Math.Sqrt((Math.PI * S) / timeStep);
//perform 4th order Runge-Kutta scheme on (2)
double k1, k2, k3, k4, newVelocity;
k1 = n + (1 / relaxTime) * prevVelocity;
k2 = n + (1 / relaxTime) * (prevVelocity + (timeStep / 2) * k1);
k3 = n + (1 / relaxTime) * (prevVelocity + (timeStep / 2) * k2);
k4 = n + (1 / relaxTime) * (prevVelocity + timeStep * k3);
newVelocity = prevVelocity + (1.0 / 6.0) * timeStep * (k1 + 2 * k2 + 2 * k3 + k4);
//perform forward Euler scheme on (1)
double newPosition;
newPosition = prevPosition + timeStep * newVelocity;
return result = new Vector(newPosition, newVelocity);
}
public static Vector BrownianSolution(double mass, double Temp, double relaxTime, double prevPosition, double prevVelocity, double timeStep, SolutionDimension XorY)
{
Vector result;
Random random = new Random();
//Calculate G
double U1, U2, G;
U1 = random.NextDouble();
U2 = random.NextDouble();
if (XorY == SolutionDimension.X)
{
G = Math.Sqrt(-2 * (Math.Log(U1))) * Math.Cos(2 * Math.PI * U2);
}
else
{
G = Math.Sqrt(-2 * (Math.Log(U1))) * Math.Sin(2 * Math.PI * U2);
}
//Calculate S
double S;
double k = 1.3806488E-23;
S = (2 * k * Temp) / (Math.PI * mass * relaxTime);
//Calculate n_x(t)
double n = G * Math.Sqrt((Math.PI * S) / timeStep);
//perform 4th order Runge-Kutta scheme on (2)
double k1, k2, k3, k4, newVelocity;
k1 = n + (1 / relaxTime) * prevVelocity;
k2 = n + (1 / relaxTime) * (prevVelocity + (timeStep / 2) * k1);
k3 = n + (1 / relaxTime) * (prevVelocity + (timeStep / 2) * k2);
k4 = n + (1 / relaxTime) * (prevVelocity + timeStep * k3);
newVelocity = prevVelocity + (1.0 / 6.0) * timeStep * (k1 + 2 * k2 + 2 * k3 + k4);
//perform forward Euler scheme on (1)
double newPosition;
newPosition = prevPosition + timeStep * newVelocity;
return(result = new Vector(newPosition, newVelocity));
}