/* 
 *  Solves the Schroedinger equation for a wavepacket inside
 *  a square-well.
 *  Observe how the dymanical development of the wavefunction 
 *  displays the several square-well energy components of the wave.
 *  Sqwell.html: <applet code= HeatDiff.class width=600 height=450></applet>
 *  by C.A. Bertulani, 08/15/2000
 */
import java.awt.*;
import java.applet.*;

public class HeatDiff extends Applet implements Runnable {
  Thread runstring;
  private Image offScreenImage;
  int ixmesh0, ixmeshN; 
  double y0, yN;
  double Stretchxx,Coefxx,Stretchyy,Coefyy,pi,k0,dx;
  double ro,sph,diffk,cons,dt,el,xx;
  double thk,divi,u[][];
  int AppletHeight, AppletWidth;
  // Labels in applet
  String graphLabel1 = "Two bars with different temperatures in contact";
  String graphLabel2 = "(watch and see evolution of heat diffusion)";
  // Font for caption
  Font smallArialFont = new Font("Arial", Font.PLAIN, 15);
  int jj;

  public void start()
  {
    if(runstring==null);
    {
     runstring=new Thread(this);
     runstring.start();
    }
  }

  public void stop()
  {
     if(runstring != null){
       runstring.stop();
       runstring=null;
     }
  }

  public void run()
  {
    while(true){
      repaint();
      try{ Thread.sleep(350);
      }
      catch(InterruptedException e){ }
    }
  }
  
  public void update(Graphics g)  //To avoid flicker
  {
    Graphics offScreenGraphics=offScreenImage.getGraphics();
	 //Erase the previous image
	Dimension d = size();
    offScreenGraphics.setColor(getBackground());
    offScreenGraphics.fillRect(0,0,AppletWidth,AppletHeight);
    offScreenGraphics.setColor(g.getColor());
	 //Paint the frame into the image
    paint(offScreenGraphics);
    g.drawImage(offScreenImage,0,0,this);

  }
   
  private int pixx(int ivalue)  { 
    // Given the  index of the mesh-xpoint return the pixel equivalent 
    int jvalue = (int)(Stretchxx*ivalue + Coefxx);
    return jvalue; 
  }  

  private int pixy(double yvalue)  { 
    // Given the y-value in desired scale, return the pixel equivalent 
	int jvalue = (int)(Stretchyy*yvalue + Coefyy);
    return jvalue; 
  }  

   void CoordUndo(double ixmesh0,double ixmeshN,double y0,double yN)
  {  // changes x-mesh-indexing and y-coordinate definition into
     // java applet coordinate system of pixels	   
    double W = AppletWidth;
    double H = AppletHeight;
	// put graph within a margin from applet window
	double margin = 0.2;  // percent used in margin
    double xxmax = (1.0-margin)*W; // right x-pixel-limit  
    double xxmin = margin*W; // left x-pixel-limit
    double yymin = (1.0-margin)*H; // upper y-pixel-limit
    double yymax = margin*H; // lower y-pixel-limit
	// fit data within graph axis 
	// first transform mesh indices into x-window-pixel coordinates
    Stretchxx = (xxmax-xxmin)/(ixmeshN-ixmesh0);
    Coefxx = (xxmin*ixmeshN-xxmax*ixmesh0)/(ixmeshN-ixmesh0);
	// now transform graph y-values to y-window-pixel coordinates
    Stretchyy = (yymax-yymin)/(yN-y0);
    Coefyy = (yymin*yN-yymax*y0)/(yN-y0);
  }
     
  void axisg(int ix1,int ix2,double y1,double y2,Graphics g)
  {
    // Plot the axis with desired cordinates
    int xpix1,xpix2,ypix1,ypix2;
    xpix1 = pixx(ix1); 
	xpix2 = pixx(ix2);
	ypix1 = pixy(y1);
	ypix2 = pixy(y2);
	int dtick = AppletHeight/50;
	g.drawLine(xpix1,ypix1,xpix2,ypix1);
    g.drawLine(xpix1,ypix1,xpix1,ypix2);
    double yincr = (y1-y2)/5.0;
	// ticks, marks and label in vertical axis
	for (int i=0; i<6; i++){
		int tick = pixy(y2+yincr*i);
		g.drawLine(xpix1-dtick,tick,xpix1,tick);
		double ytick = y2+yincr*i;
		if(Math.abs(ytick)<0.01)ytick=0.0;
		g.drawString(Double.toString(ytick),xpix1-5*dtick,tick);
		g.drawString("Temperature in C",xpix1-5*dtick,ypix2-3*dtick);
  }
 }

  public void HeatDiffplot(Graphics g, int jj)
  {
    int j;
    int nmaxi,k,i,il,km,ii;
    int pixx1,pixx2,pixy1,pixy2,tone;
    // At t=0 ( j=0) all points are at 100 C 
    for(i=0;i<ixmeshN;i++){
      if(i>=ixmeshN/2)u[i][0]=yN;
      if(i<ixmeshN/2)u[i][0]=yN/2.0;
    }
    // in i=0 and i=100 (ends) U=0 for all times
    for(j=0;j<2;j++){
      u[0][j]=0.0;
      u[ixmeshN-1][j]=0.0;
    }
    /* solves numerically the heat partial differential equation
    el,ro,sph,thk,diffk,cons,dx,dt */
    //  loop over time      
    for(k=1; k<jj+1; k++){
      //loop over space, end points not included (they are known)      
      for(i=1; i<ixmeshN-1; i++){
        u[i][1]=u[i][0] + cons*(u[i+1][0]+u[i-1][0]-2*u[i][0]);
      }
      // we want to know the temperatures every 10 000 time steps 
       if(k==jj)
      {
         for(j=0; j<ixmeshN; j++){
           tone = (int)(2.55*u[j][1]);
           Color redi = new Color(tone,0,0);
           g.setColor(redi);
		   int RectHeight = AppletHeight/20; 
           int RectWidth = (pixx(ixmeshN)-pixx(ixmesh0))/ixmeshN; 
           int RectTop = AppletHeight-AppletHeight/6; 
           int RectLeft = pixx(j); 
           g.drawRect(RectLeft,RectTop,RectWidth,RectHeight);
           g.fillRect(RectLeft,RectTop,RectWidth,RectHeight);
           g.setColor(redi);
		   g.drawRect(pixx(ixmeshN/2),RectTop-10,1,RectHeight+20);
        }
         for(i=0; i<ixmeshN; i++) 
         { 
          if(i>0){
          tone=(int)(2.55*u[i][1]);
          Color redi=new Color(tone,0,0);
          g.setColor(redi);
		  // transform coordinates to pixel coordinates			 
          pixx1=pixx(i-1);
		  pixx2=pixx(i);
		  pixy1=pixy(u[i-1][1]);
		  pixy2=pixy(u[i][1]);
          g.drawLine(pixx1,pixy1,pixx2,pixy2); // plot it
          }
         }  //for i
      }
     // recycle, new values are now old.  
     for(i=0;i<ixmeshN-1;i++)u[i][0]=u[i][1];
   }
 }

  public void init()
  {
   // create an image with the same size of the applet area
   // How big is the applet? 
   Dimension d = size(); 
   AppletHeight = d.height; 
   AppletWidth  = d.width; 
   offScreenImage = createImage(AppletWidth,AppletHeight);
   jj=1;   
   // limits on x-mesh and on desired y-values
   ixmesh0 = 0; 
   ixmeshN = 101; 
   y0 = 0.0; 
   yN = 100.0; 
   u=new double[101][2];
   /* specific heat, thermal conductivity and density for iron
   next three comments. */
   sph=0.217;
   thk=0.49;
   ro=2.7;
   diffk=thk/(sph*ro);
   el=50.0;
   // The bar is divided in ixmeshN parts (divi)     
   divi=ixmeshN;
   cons=0.1;
   dx=el/divi;
   dt=cons*dx*dx/diffk ;
   CoordUndo(ixmesh0,ixmeshN,y0,yN); // transform pixels to coordinates
  }

  public void paint(Graphics g){
    axisg(ixmesh0,ixmeshN,y0,yN,g); // plot axis
	// find position for caption in pixels			 
    int pixxL =pixx(ixmesh0);
	int pixyL = AppletHeight - AppletHeight/20;
	g.setColor(Color.blue);
	g.setFont(smallArialFont);
    g.drawString(graphLabel1,pixxL,pixyL);  // draw caption
    g.drawString(graphLabel2,pixxL,pixyL+pixyL/20);  
    HeatDiffplot(g,jj);  //plot graphics
    jj=jj+50;
 }
}