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<TITLE>Package edu.rit.clu.antimatter</TITLE>
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Package edu.rit.clu.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.
A magnetic field is imposed
perpendicular to the plane of the antiprotons.
As each antiproton moves,
the magnetic field exerts a force on the antiproton
that bends its path into a circle.
<P>
The Antimatter Simulation program
maintains each antiproton's position, velocity, and acceleration.
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 acceleration of each antiproton
(due to repulsive forces from all other antiprotons
plus the magnetic force),
updates the velocity based on the acceleration,
and updates the position based on the velocity and acceleration:
<BR>
<BR><B>v'</B> = <B>v</B> + <I>δ</I> <B>a</B>
<BR>
<BR><B>p'</B> = <B>p</B> + <I>δ</I> <B>v</B> + 1/2 <I>δ</I><SUP>2</SUP> <B>a</B>
<BR>
<BR>where <B>a</B> is the acceleration,
<B>v</B> is the velocity before the time step,
<B>v'</B> is the velocity after the time step,
<B>p</B> is the position before the time step,
<B>p'</B> is the position after the time step,
and <I>δ</I> 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 cluster parallel programs in this package use Parallel Java (PJ)
in package <A HREF="../../pj/package-summary.html">edu.rit.pj</A>.
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