2007/07/31 by V. M. Kenkre, Kenkre, V. M. · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Computational Drug Discovery Methods #Graph theory and applications #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.0708.0034
4 pages, 1 fig
arxiv created 2007/08/06 · arxiv updated 2009/12/01
An analytic formulation of memory-possessing random walks introduced recently [Cressoni et al., Phys. Rev. Lett. 98, 070603 (2007) and Schütz and Trimper, Phys. Rev. E 70, 045101 (2004)] for Alzheimer behavior and related phenomena is provided along with exact solutions on the basis of Fokker-Planck equations. The solution of a delay-differential equation derived for the purpose is shown to produce log-periodic oscillations and to coincide rather accurately with previously published computer simulation results. Generalizations along several directions are also constructed on the basis of the formalism.