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Department of Chemistry
Princeton University Princeton, NJ 08540 |
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Another project
The objective is to find inherent structures (potential energy minima, mechanically stable arrangements) for a set of attracting particles that initially are widely dispersed. For ease of visualization, the initial phase of this study was confined to two dimensions; currently the three dimensional case is being explored. Random initial configurations of the N particles will be mapped onto the final inherent structure configurations by a numerical steepest descent on the potential energy surface. This procedure involves simultaneously moving all particles in directions, and at rates, proportional to the forces that they experience. Interest centers around the final (approximate) inherent structure arrangement and its potential energy value. An objective is to determine if the arrangements are compact and convex, or are irregular "fractal" shapes. You can watch particles move according to the steepest descent algorithm from an initial diffuse random array towards a more compact array with lower potential energy. A fortran program called MINOP from time to time grabs a particle array in the steepest descent sequence and produces an associated array, the "inherent structure," with potential energy at a local minimum. MINOP was written by Linda C. Kaufman (currently at William Paterson University) and is based on her discussion of a quasi-Newton trust region algorithm in SIAM J. OPTIM. Vol. 10, No. 1, pp. 56-69 (1999). Watch the Movie 3D Case: 400 particles from initial three dimensional random configuration to final configuration with lowest potential energy. |
Initial random configuration of 400 particles. ![]() |
Intermediate configuration. ![]() |
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Intermediate configuration near the end. ![]() |
Final configuration - lowest potential energy. ![]() |
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