Scale invariant forces in one-dimensional shuffled lattices

@article{citeulike:2502312, abstract = {We present a detailed and exact study of the probability density function P(F) of the total force F acting on a point particle belonging to a perturbed lattice of identical point sources of a power-law pair interaction. The main results concern the large-F tail of P(F) for which two cases are mainly distinguished: (i) Gaussian-like fast decreasing P(F) for lattice with perturbations forbidding any pair of particles to be found arbitrarily close to one each other and (ii) L\évy-like power-law decreasing P(F) when this possibility is instead permitted. It is important to note that in the second case the exponent of the power-law tail of P(F) is the same for all perturbations (apart from very singular cases) and is in a one-to-one correspondence with the exponent characterizing the behavior of the pair interaction with the distance between the two particles.}, author = {Gabrielli, Andrea }, citeulike-article-id = {2502312}, doi = {http://dx.doi.org/10.1103/PhysRevE.72.066113}, journal = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)}, keywords = {2005, cosmological\_dynamics, gabrielli, nonlinear\_physics, stochastic\_processes}, number = {6}, posted-at = {2008-03-10 16:49:48}, priority = {2}, publisher = {APS}, title = {Scale invariant forces in one-dimensional shuffled lattices}, url = {http://dx.doi.org/10.1103/PhysRevE.72.066113}, volume = {72}, year = {2005} }

TY - JOUR ID - citeulike:2502312 L3 - citeulike-article-id:2502312 N2 - We present a detailed and exact study of the probability density function P(F) of the total force F acting on a point particle belonging to a perturbed lattice of identical point sources of a power-law pair interaction. The main results concern the large-F tail of P(F) for which two cases are mainly distinguished: (i) Gaussian-like fast decreasing P(F) for lattice with perturbations forbidding any pair of particles to be found arbitrarily close to one each other and (ii) Lévy-like power-law decreasing P(F) when this possibility is instead permitted. It is important to note that in the second case the exponent of the power-law tail of P(F) is the same for all perturbations (apart from very singular cases) and is in a one-to-one correspondence with the exponent characterizing the behavior of the pair interaction with the distance between the two particles. IS - 6 JF - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) TI - Scale invariant forces in one-dimensional shuffled lattices PB - APS VL - 72 KW - 2005 KW - cosmological_dynamics KW - gabrielli KW - nonlinear_physics KW - stochastic_processes AU - Gabrielli, Andrea PY - 2005/// UR - http://dx.doi.org/10.1103/PhysRevE.72.066113 ER -