About: We study the transient dynamics of an [Formula: see text] process on a pair of randomly coupled networks, where reactants are initially separated. We find that, for sufficiently small fractions [Formula: see text] of cross couplings, the concentration of [Formula: see text] (or [Formula: see text]) particles decays linearly in a first stage and crosses over to a second linear decrease at a mixing time [Formula: see text]. By numerical and analytical arguments, we show that for symmetric and homogeneous structures [Formula: see text] where [Formula: see text] 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 [Formula: see text] , we identify the logarithmic slowing down in [Formula: see text] to be the result of a spontaneous mechanism of repulsion between the reactants [Formula: see text] and [Formula: see text] 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.   Goto Sponge  NotDistinct  Permalink

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  • We study the transient dynamics of an [Formula: see text] process on a pair of randomly coupled networks, where reactants are initially separated. We find that, for sufficiently small fractions [Formula: see text] of cross couplings, the concentration of [Formula: see text] (or [Formula: see text]) particles decays linearly in a first stage and crosses over to a second linear decrease at a mixing time [Formula: see text]. By numerical and analytical arguments, we show that for symmetric and homogeneous structures [Formula: see text] where [Formula: see text] 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 [Formula: see text] , we identify the logarithmic slowing down in [Formula: see text] to be the result of a spontaneous mechanism of repulsion between the reactants [Formula: see text] and [Formula: see text] 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.
Subject
  • Topology
  • Symmetry
  • Concepts in physics
  • Markov processes
  • Mathematical structures
  • Quantum phases
  • Theoretical physics
  • Standard Model
  • Quantum field theory
  • Dimensional analysis
  • Quantum chromodynamics
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