# AiS Challenge Team Interim Report

**Team Number: **006

**School Name: **Albuquerque

**Area of Science: **Computer Science/Physics

**Project Title: **Brittle object collision using smooth particle
hydrodynamics

**Project Definition:**
We are seeking to use the theories of smooth particle
hydrodynamics to calculate in either a general or specific sense the
relative positions and motions of a massive number of objects, in the
most specific sense representing individual particles of matter. Using
a fractal analysis, possibly in conjunction with the artificial
intelligence methods of swarm intelligence and genetic algorithms, we
will evaluate the state of the particles in a brittle object after a
collision with a resilient inelastic object. Considering that an
object will contain millions of individual particles, using
conventional methods to approximate the final position of those
particles after an indeterminate number of small collisions is
essentially impossible and even a very inaccurate approximation is
extremely inefficient. We need to form a method of more efficiently
managing this computer science problem.
**Problem Solution:**
The problem we have selected to work on is one that is
impossible to model exactly, and very difficult to achieve good
approximations to. This aspect of it comes from the fact that since it
is a simulation of a physical event, there are so many small factors
that affect the system, and the complexity and quantity of particles
that make up the structure of a brittle material make it unrealistic
to attempt to account for everything. However, using smooth particle
hydrodynamics the actual number of particles the program will use in
calculating the final state of the object is relative to the desired
accuracy of the results. In addition, many of the particles more
distant from the collision may be disregarded or combined into a
smaller set of particles. Our concept of using a fractal-based
analysis will allow us to be even more efficient. By modeling a
fractal to approximate a real world based situation, we can disregard
a massive amount of extraneous information and allow a minimum of
required computing power. However, we need to initially model a
fractal based on the results of a more complex collision. To do this
we will attempt to use genetic algorithms reducing the time needed to
create such models as well as increasing the accuracy of the fractal.
Further utilizing swarm intelligence will enable us to test multiple
fractals and verify the results. This problem should lend itself well
to being paralleled, since it is possible to isolate particles, and
calculate the forces acting on them at a given time interval
independently of the rest of the system since the system at a point in
time is completely static. Using these methods will make a much more
accurate program, but even more importantly we hope that by combining
them we will be able to create a general method of solving an entire
set of previously extremely complex problems, especially in the field
of hydrodynamics.
**Progress to Date:**
Primarily as of now we have been researching the problem and
various solutions. We contacted multiple physicists and professors,
both scientists that work in the field and teachers of college level
hydrodynamics. Through the Internet we have found a basic program
written in Fortran that models a brittle collision in one-dimension,
along with multiple equations that would help model the collision. We
hope to be able to modify the code to work in more dimensions as well
as more complexly analyze the solution.
We have conducted research of the subject of smooth particle
hydrodynamics and have begun to code the program to run our
simulations. Our research has included studying several papers on
smooth particle hydrodynamics, books on fluid mechanics, physics, and
the mathematics required to deal with this type of problem. We have
coded a lot of the fundamental mathematical functionality for the
project, and we are currently attempting to decide what the most
efficient and useful structures are for representing data such as the
particles and forces acting on those particles.
Our next step after we decide upon the proper data structures is to
integrate all of the components of the program. Then we will be ready
to test the program. We will test our results against other similar
simulations, and actual data taken from the collision of objects with
the properties that we specify in our program. Once we are satisfied
that our program is functioning properly, we will work on
paralleling our algorithms, and generally improving the efficiency
of our code.
**Expected Results:**
Our program should be able to accurately predict the resultant
particle movement based on the collision. By plotting the positions of
the particles through time as the collision progresses we will be able
to benchmark important calculations and compare them to previous
experiments, thus making it possible to know that our program will
truly represent the collision. The use of genetic algorithms will
reduce the time and space required to track the individual particles.
Once we have finished, our program will simulate the collisions of
brittle objects with rigid objects with high accuracy. It will predict
how and where the brittle object will break, and the distribution of
pieces after the collision. Our program will be capable of providing
useful information about this type of collision in a reasonable amount
of time.

**Team Members**

Team Mail

**Sponsoring Teacher(s)**

**Project Mentor(s)**