particles simulation (gravity and collision) bug - simulation

Question

1.The particles seems to have an excess y-direction movement, but i didn't add a background gravity for them.
2.The particles seems to move too fast when they're getting closer and closer, (because I don't know how to handle the issue of collision?)
I calculate the location by adding the corresponding force it experienced , how can i know if they collided with other? for example:
stage 1
particle1 [1,1]
particle2 [1,9]
stage 2
particle1 [9,9]
particle2 [1,9]
If I plot a graph of the path belonging to each particle, I can see if the graph of paths intercept with other, but the path intercept doesn't 100% means they'll collide, as they can have different speed.
I've tried to debug but just cannot find out where is going wrong.
in version 0 they tend to fail down (not my wish)
in version 1 they tend to fail to the right (i swap the x y) (simplified version)
here is the url of the bin and source (in pascal): stack_exchange_particle_gravity_collision.zip
here is the source code of version 0 in case you do not want to download the zip:
program ParticlesV0;
uses
graph;
const
pi=3.14159265358979;
n=500;
defaultSpeed=1;
defaultRadius=2;
defaultDensity=1e4;
energyLoss=0.50;
dotStyle=1;
backGroundLevel=0;
type
ParticleType=record
x,y,dr,dd,dx,dy,dfr,dfd:real;
color:word;
radius,mass:real;
end;
var
gd,gm:smallint;
PathToDriver:string;
l:longint;
particle:array[1..n]of ParticleType;
////////////////////////////////////////////////////////////////
procedure backGround(i:smallint);
var
y:smallint;
s,t:string;
w,ori:word;
begin
ori:=GetColor;
SetColor(10);
while i>0 do begin
for y:=0 to (GetMaxY div 10) do begin
s:='';
for w:=0 to 255 do begin
str(random(10),t);
s:=s+t;
end;
OutTextXY(5,y*10,s);
end;
dec(i);
end;
SetColor(ori);
end;
procedure line(x1,y1,x2,y2:smallint);
var
x,y:smallint;
begin
x:=getx;
y:=gety;
moveto(x1,y1);
lineto(x2,y2);
moveto(x,y);
end;
function rx(x:real):real;
begin
rx:=x+(GetMaxX div 2);
end;
function ry(y:real):real;
begin
ry:=y+(GetMaxY div 2);
end;
function s(r:real):smallint;
begin
s:=round(r);
end;
function distance(p1,p2:ParticleType):real;
var
x,y:real;
begin
x:=p1.x-p2.x;
y:=p1.y-p2.y;
distance:=sqrt(x*x+y*y);
end;
function degree(p1,p2:ParticleType):real;
var
x,y,d:real;
begin
x:=p2.x-p1.x;
y:=p2.y-p1.y;
if x0 then d:=arctan(y/x)
else if (yGetMaxX) then begin
dx:=-dx;
x:=GetMaxX-(x-GetMaxX);
end;
if (xGetMaxY) then begin
dy:=-dy;
y:=GetMaxY-(y-GetMaxY);
end;
if (y0) then begin
tfr:=G*p.mass*particle[l].mass/sqr(r);
tfd:=degree(p,particle[l]);
tdx:=tfr*cos(tfd);
tdy:=tfr*sin(tfd);
dx:=dx+tdx;
dy:=dy+tdy;
// tdx:=
end;
p.dx:=p.dx+dx;
p.dy:=p.dy+dy;
end;
end;
//++++++++++++++++++++++++++++++//
////////////////////////////////////////////////////////////////
begin
gd:=detect; { highest possible resolution }
gm:=0; { not needed, auto detection }
PathToDriver:=' '; { path to BGI fonts, drivers aren't needed }
InitGraph(gd,gm,PathToDriver);
if (GraphResult=grok) then begin
writeln('gd ',gd);
writeln('GetMaxX ',GetMaxX);
writeln('GetMaxY ',GetMaxY);
writeln('GetMaxColor ',GetMaxColor);
backGround(backGroundLevel);
line(0, 0, GetMaxX, GetMaxY);
SetFillStyle(HatchFill,13);
FillEllipse(s(rx(0)),s(ry(0)),10,10);
for l:=1 to n do initp(particle[l]);
repeat
for l:=1 to n do begin
calp(particle[l]);
movep(particle[l]);
end;
until false;
readln;
CloseGraph; { restores the old graphics mode }
end else writeln('Graphic not supported.');
readln;
end.
sorry for the poor formatting

Answer 1

If you want to remove a particle when it get too close, this line should do the job:
procedure calp(var p:ParticleType);
...
e:=*put a number here witch scales with mass or something esle, you can even use defaultradius constant*;
if (r>e) then begin
...
else mass:=0 <- this now means it won't pull others particles, and won't be pulled either, ideally now you need to check everywhere for 0-os, alternatively
you can place the particle randomly on the screen again, but it can cause some funny stuff, becouse of leftover vectors.