The underlying physics of dislocation ordering in deforming metals was explored, where attention was focused on the competing role of energy relaxation and the noise in the local stress-field. The competition was investigated by using a simple 2-dimensional model that exhibited the essential physics while avoiding extraneous mechanisms that might confuse the situation. It was shown that noise and energetics were equally important in determining the final state of the system. Quantitative functions for the energetic driving force for ordering and the resistive force owing to the noise were developed that balanced each other in the relaxed state. These features resulted from the system being scale-invariant, with power-law dependences of the macro-variables upon the number of relaxing dislocations.

Modeling Energetics and Noise in Dislocation Patterning. R.Thomson, M.Koslowski, R.LeSar: Physical Review B, 2006, 73[2], 024104 (7pp)