1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
|
<HTML>
<HEAD>
<TITLE>Package edu.rit.hyb.antimatter</TITLE>
</HEAD>
<BODY>
Package edu.rit.hyb.antimatter
provides the Antimatter Simulation,
an example of an <I>N</I>-body problem.
<P>
The Antimatter Simulation program
calculates the motion of a number of antiprotons
moving in a two-dimensional plane.
The antiprotons have equal, negative charges.
Each antiproton experiences a repulsive force
from every other antiproton
that is directly proportional
to the product of the antiprotons' charges
and is inversely proportional
to the square of the distance
between the antiprotons.
The antiprotons are surrounded by an "antiproton trap" --
a square metal cage with sides of length <I>R</I>,
extending from coordinates (0,0) to (<I>R,R</I>)
in the (<I>x,y</I>) plane.
The antiproton trap has a negative charge.
Thus, each antiproton experiences a repulsive force
away from the sides of the trap.
Since the antiprotons are repelled from the sides of the trap,
the antiprotons will never touch the trap
and matter-antimatter annihilation will not happen.
<P>
The Antimatter Simulation program
maintains each antiproton's position and velocity.
The program calculates the positions and velocities
as a function of time
by doing a series of discrete time steps.
At each time step,
the program calculates the total force on each antiproton
(repulsive forces from all other antiprotons
plus repulsive forces from the sides of the trap),
updates the velocity based on the force,
and updates the position based on the velocity and force:
<BR>
<BR><B>V'</B> = <B>V</B> + <B>F</B> Δt
<BR>
<BR><B>P'</B> = <B>P</B> + <B>V</B> Δt + 1/2 <B>F</B> Δt<SUP>2</SUP>
<BR>
<BR>where <B>F</B> is the vector force on the antiproton,
<B>V</B> is the antiproton's vector velocity before the time step,
<B>V'</B> is the antiproton's vector velocity after the time step,
<B>P</B> is the antiproton's vector position before the time step,
<B>P'</B> is the antiproton's vector position after the time step,
and Δt is the size of the time step.
(These formulas represent the first few terms
in the Taylor series expansions
for velocity and position as a function of time.)
<P>
The hybrid SMP cluster parallel programs in this package use Parallel Java (PJ)
in package <A HREF="../../pj/package-summary.html">edu.rit.pj</A>.
</BODY>
</HTML>
|
