Spring-block Models and Highway Traffic

Abstract

A brief review on the applicability of spring-block type models for describing various complex systems is given. Pattern formation in drying granular materials, capillarity driven self-organization of nano-particles and magnetization phenomena of ferromagnetic materials are examples in such sense. We learn from these that the spring-block stick-slip model family is especially useful for those phenomena where avalanche-like jumps or self-organized criticality is present. As a novel application, in the present study, a simple one-dimensional spring-block chain with asymmetric interactions is used to model the motion of a queue of cars. Within the model the spring-block chain is dragged with constant velocity through the first block. As a result of this, the blocks in the chain will move in avalanches of widely different magnitudes. For a given parameter range and certain blocks in the system self-organized criticality and disorder-driven dynamical phase transitions are observed.