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(Color online) Efficiency versus temperature for various fractions of deep sites. Left column ∆E = 250 K, middle ∆E = 750 K, right ∆E = 1500 K. Randomly assigned energies (blue line, diamonds), longhop dynamics (red line, circles). Only for ∆E = 750 K: sublattice (orange dashed line, crosses), and cluster (black line, squares). Vertical green line at T eq. The first row shows the results for homogeneous systems of only standard or only deep sites, respectively.
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Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous desorption of particles. Hopping and desorption are taken to be thermally activated processes. The activation energies...
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Context 1
... importantly, we provide detailed explanations and analytic results which ex- plain all notable features of the simulation outcome in terms of microscopic physical processes. Figure 2 shows the results of our simulations. For each ∆E, we simulated systems with 1, 4, 25 and 50% of strong-binding sites. ...
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Citations
... We identify a uniform mechanism facilitating a high reaction rate even in temperature regions where a system without disorder performs poorly. This part is based on the publications [89,90] and contains further efforts on general discrete binding energy distributions and multiple-species systems. ...
... Thus, we must not replace the reaction term 2A i N 2 i for 'homogeneous' reactions by the -on first sight more intuitive -term 2A i N i (N i − 1), as the reaction term then could become negative. As mentioned in the introductory section 8.2.1 for the homogeneous system and argued in detail in [89], the assumption that the reaction rate can be written as above is at the heart of the rate equation approach. Equations (9.13) are easily derived from the full master equation using this assumption in the forms N i (N i − 1) ≈ N 2 i and N 1 N 2 ≈ N 1 N 2 (where the expectation is over the joint probability distribution P (N 1 , N 2 ) and the r.h.s. ...
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We study the steady state of a stochastic particle system on a
two-dimensional lattice, with particle influx, diffusion and desorption, and
the formation of a dimer when particles meet. Surface processes are thermally
activated, with (quenched) binding energies drawn from a \emph{continuous}
distribution. We show that sites in this model provide either coverage or
mobility, depending on their energy. We use this to analytically map the system
to an effective \emph{binary} model in a temperature-dependent way. The
behavior of the effective model is well-understood and accurately describes key
quantities of the system: Compared with discrete distributions, the temperature
window of efficient reaction is broadened, and the efficiency decays more
slowly at its ends. The mapping also explains in what parameter regimes the
system exhibits realization dependence.
