Abstract
We study the transient dynamics of an A+B→0 process on a pair of randomly coupled networks, where reactants are initially separated. We find that, for sufficiently small fractions q of cross couplings, the concentration of A (or B) particles decays linearly in a first stage and crosses over to a second linear decrease at a mixing time tx. By numerical and analytical arguments, we show that for symmetric and homogeneous structures tx((k)/q)log((k)/q) where (k) is the mean degree of both networks. Being this behavior is in marked contrast with a purely diffusive process, where the mixing time would go simply like (k)/q, we identify the logarithmic slowing down in tx to be the result of a spontaneous mechanism of repulsion between the reactants A and B due to the interactions taking place at the networks' interface. We show numerically how this spontaneous repulsion effect depends on the topology of the underlying networks.
Original language | English |
---|---|
Article number | 040301 |
Journal | Physical Review E |
Volume | 97 |
Issue number | 4 |
DOIs | |
State | Published - 4 Apr 2018 |
Bibliographical note
Publisher Copyright:©2018 American Physical Society.
Funding
Acknowledgments . Results presented in this work have been produced using the European Grid Infrastructure (EGI) through the National Grid Infrastructures N G I _ G R N E T (HellasGrid) as part of the SEE Virtual Organization. This research was supported by European Commission FP7-FET Project Multiplex No. 317532. S.H. acknowledges the ISF, ONR Global, the Israel-Italian collaborative project NECST, Japan Science Foundation, BSF-NSF, and DTRA (Grant No. HDTRA-1-10-1-0014), together with the Israeli Ministry of Science, Technology and Space (MOST, Grant No. 3-12072) for financial support. This research was supported by European Commission FP7-FET Project Multiplex No. 317532. S.H. acknowledges the ISF, ONR Global, the Israel-Italian collaborative project NECST, Japan Science Foundation, BSF-NSF, and DTRA (Grant No. HDTRA-1-10-1-0014), together with the Israeli Ministry of Science, Technology and Space (MOST, Grant No. 3-12072) for financial support.
Funders | Funder number |
---|---|
BSF-NSF | |
European Commission FP7-FET | |
Japan Science Foundation | |
NECST | |
Office of Naval Research | |
Defense Threat Reduction Agency | HDTRA-1-10-1-0014 |
Seventh Framework Programme | 317532 |
Ministry of Science, Technology and Space | |
Ministry of Science and Technology of the People's Republic of China | |
Ministry of Science and Technology | 3-12072 |
Israel Science Foundation |