# 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)

• Jim Mims
• David Bizzozero