Efficient stochastic simulations of complex reaction networks on surfaces

Barzel, Baruch; Biham, Ofer

doi:10.1063/1.2789417

Cited by 21 publications

(42 citation statements)

References 67 publications

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“…The network that involves H, O, and CO molecules, from which ice mantles containing H 2 O, CO 2 and CH 3 OH are formed by successive hydrogenation and oxydation reactions, is promising (Barzel & Biham 2007b). Unlike the H and D atoms, these heavier atoms and molecules are more strongly bound to both the surface and each other and do not exhibit the Langmuir rejection property.…”

Section: Discussionmentioning

confidence: 99%

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Incorporation of stochastic chemistry on dust grains in the Meudon PDR code using moment equations

Petit¹,

Barzel

Biham

et al. 2009

A&A

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Context. Unlike gas-phase reactions, chemical reactions taking place on interstellar dust grain surfaces cannot always be modeled by rate equations. Because of the small grain sizes and low flux, these reactions may exhibit large fluctuations and thus require stochastic methods such as the moment equations. Aims. We evaluate the formation rates of H 2 , HD, and D 2 molecules on dust grain surfaces and their abundances in the gas phase under interstellar conditions. Methods. We incorporate the moment equations into the Meudon PDR code and compare the results with those obtained from the rate equations. Results. We find that within the experimental constraints on the energy barriers for both diffusion and desorption and the density of adsorption sites on the grain surface, H 2 , HD and D 2 molecules can be formed efficiently on dust grains. Conclusions. In a wide range of conditions, the moment equation results agree with those obtained from the rate equations. However, for a range of relatively high grain temperatures, there are significant deviations: the rate equations fail, while the moment equations provide accurate results. The incorporation of the moment equations into the PDR code can be extended to other reactions taking place on grain surfaces.

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Section: Discussionmentioning

confidence: 99%

“…We apply the same technique as in Barzel & Biham (2007b) to derive the corresponding moment equations when the additional terms introduced by the Langmuir rejection are included. The time derivatives of the moments introduced by the term proportional to f I are…”

Section: Moment Equationsmentioning

confidence: 99%

Incorporation of stochastic chemistry on dust grains in the Meudon PDR code using moment equations

Petit¹,

Barzel

Biham

et al. 2009

A&A

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“…In spite of its good accuracy for grain surfaces, this method can only be used for small chemical networks since the number of equations grows exponentially with the number of species. Lipshtat & Biham (2003) have thus introduced another method based on the time derivatives of the moments to study the formation of molecular hydrogen, while Barzel & Biham (2007) have extended this method for more complex chemical networks. The comparisons between the methods introduced here show that the rate equations method tends to overestimate the reaction rates and the abundance of the reactants, especially when they are in low quantities.…”

Section: The Computational Methodsmentioning

confidence: 99%

Multilayer modeling of porous grain surface chemistry

Taquet

Ceccarelli

Kahane

2012

A&A

141

157

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Context. Mantles of iced water mixed with carbon monoxyde, formaldehyde, and methanol are formed during the so-called prestellar core phase. In addition, radicals are also thought to be formed on the grain surfaces, and to react to form complex organic molecules later on, during the so-called warm-up phase of the protostellar evolution. Aims. We aim to study the formation of the grain mantles during the prestellar core phase and the abundance of formaldehyde, methanol, and radicals trapped in them. Methods. We have developed a macrosopic statistic multilayer model that follows the formation of grain mantles with time and that includes two effects that may increase the number of radicals trapped in the mantles: i) during the mantle formation, only the surface layer is chemically active and not the entire bulk; and ii) the porous structure of grains allows the trapping reactive particles. The model considers a network of H, O, and CO forming neutral species such as water, CO, formaldehyde, and methanol, plus several radicals. We ran a large grid of models to study the impact of the mantle multilayer nature and grain porous structure. In addition, we explored how the uncertainty of other key parameters influences the mantle composition. Results. Our model predicts relatively high abundances of radicals, especially of HCO and CH 3 O (10 −9 −10 −7 ). In addition, the multilayer approach enables us to follow the chemical differentiation within the grain mantle, showing that the mantles are far from being uniform. For example, methanol is mostly present in the outer layers of the mantles, whereas CO and other reactive species are trapped in the inner layers. The overall mantle composition depends on the density and age of the prestellar core as well as on some microscopic parameters, such as the diffusion energy and the hydrogenation reactions activation energy. Comparison with observations allows us to constrain the value of the last two parameters (0.5-0.65 and 1500 K, respectively) and provide some indications on the physical conditions during the formation of the ices.

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“…Moreover, in practice one can obtain accurate results using surprisingly low values of the cutoffs. In fact, in an earlier version of this formulation, it was shown that for a broad range of conditions the cutoff C = 2 is sufficient [13,14]. In this case, the equations include first order moments that account for the average population sizes and second order moments that account for the number of pairs of species X i and X j in the system, from which the reaction rates are evaluated.…”

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confidence: 99%

“…The difficulty with moment equations is that higher order moments appear on the right hand side of each equation. To obtain a closed set of equations one needs to apply a suitable truncation scheme, in which the higher order moments are expressed in terms of low order moments [11][12][13][14]. In practice, the truncation is typically done at the level of third order moments, namely only the first and second order moments are taken into account.…”

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confidence: 99%

Binomial Moment Equations for Stochastic Reaction Systems

Barzel

Biham

2011

Phys. Rev. Lett.

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A highly efficient formulation of moment equations for stochastic reaction networks is introduced.It is based on a set of binomial moments that capture the combinatorics of the reaction processes.The resulting set of equations can be easily truncated to include moments up to any desired order. The number of equations is dramatically reduced compared to the master equation. This formulation enables the simulation of complex reaction networks, involving a large number of reactive species much beyond the feasibility limit of any existing method. It provides an equationbased paradigm to the analysis of stochastic networks, complementing the commonly used Monte Carlo simulations.

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Efficient stochastic simulations of complex reaction networks on surfaces

Cited by 21 publications

References 67 publications

Incorporation of stochastic chemistry on dust grains in the Meudon PDR code using moment equations

Incorporation of stochastic chemistry on dust grains in the Meudon PDR code using moment equations

Multilayer modeling of porous grain surface chemistry

Binomial Moment Equations for Stochastic Reaction Systems

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