2008/01/04 by Vasily E. Tarasov, Vasily E Tarasov · 12 citations
Environmental Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Chain (unit) #Coagulation and Flocculation Studies #Dispersion (optics) #Exponential function #Fractal #Fractional Differential Equations Solutions #Particle (ecology) #Type (biology) #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8113/41/3/035101
published in Journal of Physics A Mathematical and Theoretical 41(3), 035101 (Institute of Physics) · 9 pages, LaTeX
openalex publication_date 2008/01/04 · arxiv created 2008/04/03 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Chains with long-range interactions are considered. The interactions are defined such that each nth particle interacts only with chain particles with the numbers n+a(m) and n-a(m), where m=1,2,3,... and a(m) is an integer-valued function. Exponential type functions a(m)=bm, where b=2,3,.., are discussed. The correspondent pseudodifferential equations of chain oscillations are obtained. Dispersion laws of the suggested chains are described by the Weierstrass and Weierstrass-Mandelbrot functions.