Assortative Exchange Processes

Abstract

In exchange processes clusters composed of elementary building blocks, monomers, undergo binary exchange in which a monomer is transferred from one cluster to another. In assortative exchange only clusters with comparable masses participate in exchange events. We study maximally assortative exchange processes in which only clusters of equal masses can exchange monomers. A mean-field framework based on rate equations is appropriate for spatially homogeneous systems in sufficiently high spatial dimension. For diffusion-controlled exchange processes, the mean-field approach is erroneous when the spatial dimension is smaller than critical; we analyze such systems using scaling and heuristic arguments. Apart from infinite-cluster systems we explore the fate of finite systems and study maximally assortative exchange processes driven by a localized input.

14 pages, 3 figures

References in corpus (10)

• Burgers Turbulence
• Nuclear Structure of Bound States of Asymmetric Dark Matter
• Exchange Driven Growth
• An $H$ theorem for Boltzmann's equation for the Yard-Sale Model of asset exchange
• Heat transport in stochastic energy exchange models of locally confined hard spheres
• Explosive condensation in symmetric mass transport models
• On the limiting Markov process of energy exchanges in a rarely interacting ball-piston gas
• Hydrodynamics of granular particles on a line
• Mass Exchange Processes with Input
• Dynamical contribution to the heat conductivity in stochastic energy exchanges of locally confined gases

Cited by in corpus (1)

• A combined model of aggregation, fragmentation, and exchange processes: insights from analytical calculations