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Sergey P Verevkin - One of the best experts on this subject based on the ideXlab platform.
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experimental and theoretical study of chemical equilibria in the Reacting System of the di alkyl carbonate synthesis
Industrial & Engineering Chemistry Research, 2011Co-Authors: Sergey P Verevkin, Vladimir N Emelyanenko, Svetlana A Kozlova, Irina Smirnova, Wolfgang ArltAbstract:The chemical equilibrium of the reactive System (propylene carbonate + butanol = dibutyl carbonate +1,2-propanediol) was studied in the temperature range (303 to 373) K in the liquid phase using the method of sealed ampules using K2CO3 as heterogeneous catalyst. This reactive System exhibits a strong nonideal behavior of the mixture compounds in the liquid phase. The knowledge of the activity coefficients is required in order to obtain the thermodynamic equilibrium constants Ka. A well established procedure, COSMO-RS, has been used to assess activity coefficients of the reaction participants in the liquid phase. Enthalpies of reactions of the dialkyl carbonate synthesis reaction in the liquid phase were obtained from temperature dependences of the corresponding thermodynamic equilibrium constants. For the sake of comparison, high-level ab initio calculations of the reaction participants have been performed using the GAUSSIAN-03 program package. Absolute electronic energy values of the molecules have been ...
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comprehensive experimental and theoretical study of chemical equilibria in the Reacting System of the tert amyl methyl ether synthesis
Journal of Physical Chemistry B, 2007Co-Authors: Andreas Heintz, Simon Kapteina, Sergey P VerevkinAbstract:: The chemical equilibrium of the reactive System (methanol+isoamylenes methyl tert-amyl ether) was studied in the temperature range 298-393 K in the liquid phase using the method of sealed ampoules as well as in the gaseous phase using a tubular flow reactor in the temperature range 355-378 K. In both cases, a cation exchanger Amberlist-15 was used as a heterogeneous catalyst. The reactive System of the methyl tert-amyl ether synthesis exhibits a strong nonideal behavior of the mixture compounds in the liquid phase. The knowledge of the activity coefficients is required in order to obtain the thermodynamic equilibrium constants Ka. Two well-established procedures, UNIFAC and COSMO-RS, have been used to assess activity coefficients of the reaction participants in the liquid phase. Thermodynamic equilibrium constants KP measured in the gaseous phase together with the vapor pressures of the pure compounds have been used to obtain Ka in the liquid phase on a consistent experimental basis in order to check the results obtained from the UNIFAC and COSMO-RS methods. Enthalpies of reactions DeltarH degrees of the methyl tert-amyl ether synthesis reaction in the gaseous and in the liquid phase were obtained from temperature dependences of the corresponding thermodynamic equilibrium constants. Consistency of the experimental data of DeltarH degrees was verified with help of enthalpies of formation and enthalpies of vaporization of methyl tert-amyl ether, methanol, and methyl-butenes, available from the literature. For the sake of comparison, high-level ab initio calculations of the reaction participants have been performed using the Gaussian-03 program package. Absolute electronic energy values, normal frequencies (harmonic approximation), and moments of inertia of the molecules have been obtained using G2(MP2), G3(MP2), and G3 levels. Using these results, calculated equilibrium constants and the enthalpy of reaction of the methyl tert-amyl ether synthesis in the gaseous phase based on the principles of statistical thermodynamics are found to be in acceptable agreement with the data obtained from the thermochemical measurements.
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thermochemistry of branched ethers experimental study of chemical equilibrium in the Reacting System of tert amyl alkyl ether synthesis
Journal of Chemical & Engineering Data, 2004Co-Authors: Sergey P VerevkinAbstract:The chemical equilibrium of the reactive Systems (alkanol + methylbutenes ⇔ alkyl tert-amyl ether) with the following alkyl substituents: ethyl, propyl, butyl, iso-propyl, sec-butyl, and cyclohexyl, were studied in the liquid phase. Reactions were investigated in the screwed vials in the temperature range (298 to 393) K, and a cation exchanger Amberlist 15 was used as heterogeneous catalyst. Enthalpies of reactions of tert-amyl alkyl ethers synthesis in the liquid phase were obtained from the temperature dependence of the equilibrium constants and used to derive standard enthalpies of formation, , of tert-amyl alkyl ethers. For the sake of comparison, these enthalpies of formation have been calculated using improved Benson's increments. Calculated values are in close agreement with those from thermochemical measurements.
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chemical equilibrium study in the Reacting System of the 1 alkoxyethyl benzene synthesis from alkanols and styrene
Journal of Chemical & Engineering Data, 2001Co-Authors: Sergey P Verevkin, Andreas HeintzAbstract:The chemical equilibrium of the reactive System alkanol + styrene ⇔ (1-alkoxyethyl)benzene (where alkyl is methyl, ethyl, propyl, and butyl) was studied in the liquid phase in the temperature range (343 to 423) K using a cation exchanger as the heterogeneous catalyst. Enthalpies of reactions Δ r H° m of (1-alkoxyethyl)benzene synthesis in the liquid phase were obtained from the temperature dependence of equilibrium constants measured in the reactive mixtures with an excess of alkanol and showed a good agreement with those reaction enthalpies derived from values of the enthalpies of formation Δ f H° m (l) of the reactions participants measured for (1-methoxyethyl)benzene and (1-butoxyethyl)benzene by combustion calorimetry. The standard molar enthalpies of vaporization of (1-alkoxyethyl)benzenes were obtained from the temperature dependence of the vapor pressure measured by using the transpiration method. Resulting values of Δ f H° m (g) were used to prove the consistency of the experimental data and to derive strain enthalpies of (1-alkoxyethyl)benzenes. The strain effects were discussed in terms of deviations of Δ f H° m (g) from the group additivity rules.
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simultaneous study of chemical and vapour liquid equilibria in the Reacting System of the methyl cumyl ether synthesis from methanol and α methyl styrene
Fluid Phase Equilibria, 2001Co-Authors: Andreas Heintz, Sergey P VerevkinAbstract:Abstract The chemical equilibrium of the reactive System methanol+α-methyl-styrene⇔methyl cumyl ether was studied in the liquid and gaseous phase in the temperature range 313–328 K using a static vapour–liquid equilibrium (static VLE) method. A cation exchanger resin immersed in the liquid phase was used as heterogeneous catalyst. Equilibrium concentrations were measured chromatographically in the liquid and the vapour phase. From these data activity coefficients and thermodynamic equilibrium constants in the liquid K a and vapour phase K P were determined. Plots of ln K a and ln K P versus 1/ T result in straight lines, from which the enthalpy of reaction Δ r H m 0 of methyl cumyl ether (MCE) synthesis in the liquid and gaseous phase was obtained. The consistency of these results was verified by comparison with the data of the reaction enthalpy calculated from the formation enthalpies of the reaction participants obtained by combustion calorimetry. Since the enthalpies of formation and vapourisation of methanol and α-methyl-styrene (α-MS) are known from the literature, the investigation was focused on the MCE. The standard molar enthalpy of formation Δ f H m 0 (l) for MCE at 298.15 K was measured by means of a precise combustion calorimeter. The standard molar enthalpy of vapourisation of MCE was obtained from the temperature dependence of the vapour pressure measured by using the transpiration method. Values obtained for the enthalpy of reaction Δ r H m 0 of the MCE synthesis in the liquid and gaseous phase were found to be in excellent agreement with the values derived from the chemical and phase equilibria study, indicating internal thermodynamic consistency of the whole procedure.
Andreas Heintz - One of the best experts on this subject based on the ideXlab platform.
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comprehensive experimental and theoretical study of chemical equilibria in the Reacting System of the tert amyl methyl ether synthesis
Journal of Physical Chemistry B, 2007Co-Authors: Andreas Heintz, Simon Kapteina, Sergey P VerevkinAbstract:: The chemical equilibrium of the reactive System (methanol+isoamylenes methyl tert-amyl ether) was studied in the temperature range 298-393 K in the liquid phase using the method of sealed ampoules as well as in the gaseous phase using a tubular flow reactor in the temperature range 355-378 K. In both cases, a cation exchanger Amberlist-15 was used as a heterogeneous catalyst. The reactive System of the methyl tert-amyl ether synthesis exhibits a strong nonideal behavior of the mixture compounds in the liquid phase. The knowledge of the activity coefficients is required in order to obtain the thermodynamic equilibrium constants Ka. Two well-established procedures, UNIFAC and COSMO-RS, have been used to assess activity coefficients of the reaction participants in the liquid phase. Thermodynamic equilibrium constants KP measured in the gaseous phase together with the vapor pressures of the pure compounds have been used to obtain Ka in the liquid phase on a consistent experimental basis in order to check the results obtained from the UNIFAC and COSMO-RS methods. Enthalpies of reactions DeltarH degrees of the methyl tert-amyl ether synthesis reaction in the gaseous and in the liquid phase were obtained from temperature dependences of the corresponding thermodynamic equilibrium constants. Consistency of the experimental data of DeltarH degrees was verified with help of enthalpies of formation and enthalpies of vaporization of methyl tert-amyl ether, methanol, and methyl-butenes, available from the literature. For the sake of comparison, high-level ab initio calculations of the reaction participants have been performed using the Gaussian-03 program package. Absolute electronic energy values, normal frequencies (harmonic approximation), and moments of inertia of the molecules have been obtained using G2(MP2), G3(MP2), and G3 levels. Using these results, calculated equilibrium constants and the enthalpy of reaction of the methyl tert-amyl ether synthesis in the gaseous phase based on the principles of statistical thermodynamics are found to be in acceptable agreement with the data obtained from the thermochemical measurements.
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chemical equilibrium study in the Reacting System of the 1 alkoxyethyl benzene synthesis from alkanols and styrene
Journal of Chemical & Engineering Data, 2001Co-Authors: Sergey P Verevkin, Andreas HeintzAbstract:The chemical equilibrium of the reactive System alkanol + styrene ⇔ (1-alkoxyethyl)benzene (where alkyl is methyl, ethyl, propyl, and butyl) was studied in the liquid phase in the temperature range (343 to 423) K using a cation exchanger as the heterogeneous catalyst. Enthalpies of reactions Δ r H° m of (1-alkoxyethyl)benzene synthesis in the liquid phase were obtained from the temperature dependence of equilibrium constants measured in the reactive mixtures with an excess of alkanol and showed a good agreement with those reaction enthalpies derived from values of the enthalpies of formation Δ f H° m (l) of the reactions participants measured for (1-methoxyethyl)benzene and (1-butoxyethyl)benzene by combustion calorimetry. The standard molar enthalpies of vaporization of (1-alkoxyethyl)benzenes were obtained from the temperature dependence of the vapor pressure measured by using the transpiration method. Resulting values of Δ f H° m (g) were used to prove the consistency of the experimental data and to derive strain enthalpies of (1-alkoxyethyl)benzenes. The strain effects were discussed in terms of deviations of Δ f H° m (g) from the group additivity rules.
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simultaneous study of chemical and vapour liquid equilibria in the Reacting System of the methyl cumyl ether synthesis from methanol and α methyl styrene
Fluid Phase Equilibria, 2001Co-Authors: Andreas Heintz, Sergey P VerevkinAbstract:Abstract The chemical equilibrium of the reactive System methanol+α-methyl-styrene⇔methyl cumyl ether was studied in the liquid and gaseous phase in the temperature range 313–328 K using a static vapour–liquid equilibrium (static VLE) method. A cation exchanger resin immersed in the liquid phase was used as heterogeneous catalyst. Equilibrium concentrations were measured chromatographically in the liquid and the vapour phase. From these data activity coefficients and thermodynamic equilibrium constants in the liquid K a and vapour phase K P were determined. Plots of ln K a and ln K P versus 1/ T result in straight lines, from which the enthalpy of reaction Δ r H m 0 of methyl cumyl ether (MCE) synthesis in the liquid and gaseous phase was obtained. The consistency of these results was verified by comparison with the data of the reaction enthalpy calculated from the formation enthalpies of the reaction participants obtained by combustion calorimetry. Since the enthalpies of formation and vapourisation of methanol and α-methyl-styrene (α-MS) are known from the literature, the investigation was focused on the MCE. The standard molar enthalpy of formation Δ f H m 0 (l) for MCE at 298.15 K was measured by means of a precise combustion calorimeter. The standard molar enthalpy of vapourisation of MCE was obtained from the temperature dependence of the vapour pressure measured by using the transpiration method. Values obtained for the enthalpy of reaction Δ r H m 0 of the MCE synthesis in the liquid and gaseous phase were found to be in excellent agreement with the values derived from the chemical and phase equilibria study, indicating internal thermodynamic consistency of the whole procedure.
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chemical equilibria study of the Reacting System of the alkyl cumyl ether synthesis from n alkanols and α methylstyrene
Journal of Chemical & Engineering Data, 2001Co-Authors: Andreas HeintzAbstract:The chemical equilibrium of the reactive Systems n-alkanol + α-methylstyrene ⇔ alkyl cumyl ether (alkyl is ethyl, propyl, and butyl) was studied in the liquid phase in the temperature range (300 to 383) K using a cation exchanger as heterogeneous catalyst. Equilibrium ratios Kx obtained from concentrations of the reaction participants in the mixtures with an excess amount of alkanol are practically independent of the reactive mixture composition and can be identified with the thermodynamic equilibrium constant Ka. Enthalpies of reactions of alkyl cumyl ether synthesis in the liquid phase were obtained from the temperature dependence of Ka and showed a good agreement with those reaction enthalpies derived from the values of the reactions participants measured for alkyl cumyl ethers by combustion calorimetry. The standard molar enthalpies of vaporization of alkyl cumyl ethers were obtained from the temperature dependence of the vapor pressure measured by using the transpiration method. Resulting values of w...
Jingde Cheng - One of the best experts on this subject based on the ideXlab platform.
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An anticipatory reasoning-Reacting System for defending against malice anticipatorily
2013 IEEE 4th International Conference on Software Engineering and Service Science, 2013Co-Authors: Bo Wang, Yuichi Goto, Jingde ChengAbstract:Today, information security of information Systems is no longer about confidentiality, integrity and availability, but about ensuring that the Systems are predictably dependable in the face of all sorts of malice. Although intrusion detection Systems (IDS) make big progress on defending against computing malice, there is still a gap between current IDSs and ideal malice defense Systems. On the other hand, anticipatory reasoning-Reacting Systems (ARRS) were proposed as a high secure System with the ability to defend against malice anticipatorily, however, until now, there is no concrete implementation of ARRS for security, as well as no evidence showing the practical usefulness of anticipatory computing for security. As a step towards to ideal secure Systems, we designed and implemented an ARRS for malice defense, which can adapt to different application by configuring different information source, anticipatory model, and anticipatory actions. We also evaluated our System by KDD99 dataset and a case study of web server. This paper proposes what features ideal malice defense Systems should have, points out the gap between current IDSs and ideal malice defense Systems, shows why some advantages of ARRSs could contribute ideal malice defense Systems, and presents and evaluates a practical implementation of ARRS for security.
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development of a decision maker in an anticipatory reasoning Reacting System for terminal radar control
Hybrid Artificial Intelligence Systems, 2009Co-Authors: Natsumi Kitajima, Yuichi Goto, Jingde ChengAbstract:Terminal radar control is more and more complex in recent years. To reduce human errors in terminal radar control, an automatic System to support conflict detection and conflict resolution is required for reliable and safe terminal radar control. An anticipatory reasoning-Reacting System for terminal radar control is a hopeful candidate for such Systems. This paper proposes a methodology of decision-making in an anticipatory reasoning-Reacting System for terminal radar control, presents a prototype of decision-maker, and shows that it can make appropriate decisions in anticipatory reasoning-Reacting System for terminal radar control.
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HAIS - Development of a Decision-Maker in an Anticipatory Reasoning-Reacting System for Terminal Radar Control
Lecture Notes in Computer Science, 2009Co-Authors: Natsumi Kitajima, Yuichi Goto, Jingde ChengAbstract:Terminal radar control is more and more complex in recent years. To reduce human errors in terminal radar control, an automatic System to support conflict detection and conflict resolution is required for reliable and safe terminal radar control. An anticipatory reasoning-Reacting System for terminal radar control is a hopeful candidate for such Systems. This paper proposes a methodology of decision-making in an anticipatory reasoning-Reacting System for terminal radar control, presents a prototype of decision-maker, and shows that it can make appropriate decisions in anticipatory reasoning-Reacting System for terminal radar control.
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a prototype implementation of an anticipatory reasoning Reacting System
COMPUTING ANTICIPATORY SYSTEMS: CASYS'05 - Seventh International Conference, 2006Co-Authors: Feng Shang, Yuichi Goto, Shinsuke Nara, Jingde ChengAbstract:This paper presents the first prototype of anticipatory reasoning‐Reacting System (ARRS). First, we briefly analyze implementation issues of an ARRS, present our considerations on the implementation of the first prototype, and implementation issues under these considerations; second, we introduce the architecture of the prototype System we implemented, the important components, the problems we met and solutions adopted in these components; and then, we present a case study to show and discuss some primitive experimental results on the prototype System; finally, we briefly compare our prototype System with several other computing anticipatory Systems from the viewpoints of basic approaches and application fields.
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A Prototype Implementation of an Anticipatory Reasoning‐Reacting System
AIP Conference Proceedings, 2006Co-Authors: Feng Shang, Yuichi Goto, Shinsuke Nara, Jingde ChengAbstract:This paper presents the first prototype of anticipatory reasoning‐Reacting System (ARRS). First, we briefly analyze implementation issues of an ARRS, present our considerations on the implementation of the first prototype, and implementation issues under these considerations; second, we introduce the architecture of the prototype System we implemented, the important components, the problems we met and solutions adopted in these components; and then, we present a case study to show and discuss some primitive experimental results on the prototype System; finally, we briefly compare our prototype System with several other computing anticipatory Systems from the viewpoints of basic approaches and application fields.
Michel Weibel - One of the best experts on this subject based on the ideXlab platform.
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unifying redox kinetics for standard and fast nh3 scr over a v2o5 wo3 tio2 catalyst
Aiche Journal, 2009Co-Authors: Isabella Nova, Cristian Ciardelli, Enrico Tronconi, Daniel Chatterjee, Michel WeibelAbstract:A dynamic Mars–van Krevelen kinetic model that unifies Standard and Fast SCR reactions into a single redox approach is herein proposed for V-based catalysts for NOx removal from Diesel exhausts. Such a mechanistic model is consistent with the detailed catalytic chemistry proposed for the NH3-NO/NO2 Reacting System in which NO2 disproportionates to form nitrites and nitrates, nitrates are reduced by NO to nitrites in a key redox step, and nitrites react with NH3 to form N2 via decomposition of unstable ammonium nitrite. Intrinsic kinetic parameters were estimated by global multiresponse nonlinear regression of 42 transient runs. The model accounts for stoichiometry, selectivity, and kinetics of the global SCR process, reproducing successfully both the steady-state and transient behaviors of the SCR Reacting System over the full range (0–1) of NO2/NOx feed ratios in the 175–425°C temperature range. © 2009 American Institute of Chemical Engineers AIChE J, 2009
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nh3 scr of nox for diesel exhausts aftertreatment role of no2 in catalytic mechanism unsteady kinetics and monolith converter modelling
Chemical Engineering Science, 2007Co-Authors: Cristian Ciardelli, Isabella Nova, Enrico Tronconi, Daniel Chatterjee, Thomas Burkhardt, Michel WeibelAbstract:A chemically consistent dynamic kinetic model of the NH3–NO/NO2NH3–NO/NO2 Reacting System was developed on the basis of an extensive fundamental research carried out over a commercial V2O5–WO3/TiO2V2O5–WO3/TiO2 selective catalytic reduction (SCR) catalyst for automotive applications. Intrinsic kinetics of all the selective and non-selective reactions were estimated by fitting a Systematic set of transient runs over the powdered catalyst. The resulting model accounts for the complex SCR chemistry over a wide range of experimental conditions (T=160–450∘C; NO/NO2=0→∞NO/NO2=0→∞): in particular, it takes into account formation, storage, decomposition and reaction of NH4NO3NH4NO3, which resulted in a good description of the selectivity to all the major N-containing products (N2N2, NH4NO3NH4NO3, HNO3HNO3, N2ON2O). The model was validated by independent dynamic runs both over powdered catalyst at the microreactor scale and over monolith catalysts in engine test bench runs at the full scale.
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reactivity of no no2 nh3 scr System for diesel exhaust aftertreatment identification of the reaction network as a function of temperature and no2 feed content
Applied Catalysis B-environmental, 2007Co-Authors: Cristian Ciardelli, Isabella Nova, Enrico Tronconi, Daniel Chatterjee, Michel Weibel, Brigitte Bandlkonrad, Bernd KrutzschAbstract:Abstract We present a Systematic study of the NH3-SCR reactivity over a commercial V2O5–WO3/TiO2 catalyst in a wide range of temperatures and NO/NO2 feed ratios, which cover (and exceed) those of interest for industrial applications to the aftertreatment of exhaust gases from diesel vehicles. The experiments confirm that the best deNOx efficiency is achieved with a 1/1 NO/NO2 feed ratio. The main reactions prevailing at the different operating conditions have been identified, and an overall reaction scheme is herein proposed. Particular attention has been paid to the role of ammonium nitrate, which forms rapidly at low temperatures and with excess NO2, determining a lower N2 selectivity of the deNOx process. Data are presented which show that the chemistry of the NO/NO2–NH3 Reacting System can be fully interpreted according to a mechanism which involves: (i) dimerization/disproportion of NO2 and reaction with NH3 and water to give ammonium nitrite and ammonium nitrate; (ii) reduction of ammonium nitrate by NO to ammonium nitrite; (iii) decomposition of ammonium nitrite to nitrogen. Such a scheme explains the peculiar deNOx reactivity at low temperature in the presence of NO2, the optimal stoichiometry (NO/NO2 = 1/1), and the observed selectivities to all the major N-containing products (N2, NH4NO3, HNO3, N2O). It also provides the basis for the development of a mechanistic kinetic model of the NO/NO2–NH3 SCR Reacting System.
Daniel T. Gillespie - One of the best experts on this subject based on the ideXlab platform.
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Refining the weighted stochastic simulation algorithm
Journal of Chemical Physics, 2009Co-Authors: Daniel T. Gillespie, Linda R. PetzoldAbstract:The weighted stochastic simulation algorithm (wSSA) recently introduced by Kuwahara and Mura [J. Chem. Phys. 129, 165101 (2008)] is an innovative variation on the stochastic simulation algorithm (SSA). It enables one to estimate, with much less computational effort than was previously thought possible using a Monte Carlo simulation procedure, the probability that a specified event will occur in a chemically Reacting System within a specified time when that probability is very small. This paper presents some procedural extensions to the wSSA that enhance its effectiveness in practical applications. The paper also attempts to clarify some theoretical issues connected with the wSSA, including its connection to first passage time theory and its relation to the SSA.
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stochastic simulation of chemical kinetics
Annual Review of Physical Chemistry, 2007Co-Authors: Daniel T. GillespieAbstract:Stochastic chemical kinetics describes the time evolution of a wellstirred chemically Reacting System in a way that takes into account the fact that molecules come in whole numbers and exhibit some degree of randomness in their dynamical behavior. Researchers are increasingly using this approach to chemical kinetics in the analysis of cellular Systems in biology, where the small molecular populations of only a few reactant species can lead to deviations from the predictions of the deterministic differential equations of classical chemical kinetics. After reviewing the supporting theory of stochastic chemical kinetics, I discuss some recent advances in methods for using that theory to make numerical simulations. These include improvements to the exact stochastic simulation algorithm (SSA) and the approximate explicit tau-leaping procedure, as well as the development of two approximate strategies for simulating Systems that are dynamically stiff: implicit tau-leaping and the slow-scale SSA.
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efficient step size selection for the tau leaping simulation method
Journal of Chemical Physics, 2006Co-Authors: Daniel T. Gillespie, Linda R. PetzoldAbstract:The tau-leaping method of simulating the stochastic time evolution of a well-stirred chemically Reacting System uses a Poisson approximation to take time steps that leap over many reaction events. Theory implies that tau leaping should be accurate so long as no propensity function changes its value “significantly” during any time step τ. Presented here is an improved procedure for estimating the largest value for τ that is consistent with this condition. This new τ-selection procedure is more accurate, easier to code, and faster to execute than the currently used procedure. The speedup in execution will be especially pronounced in Systems that have many reaction channels.
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Approximate accelerated stochastic simulation of chemically Reacting Systems
Journal of Chemical Physics, 2001Co-Authors: Daniel T. GillespieAbstract:The stochastic simulation algorithm (SSA) is an essentially exact procedure for numerically simulating the time evolution of a well-stirred chemically Reacting System. Despite recent major improvements in the efficiency of the SSA, its drawback remains the great amount of computer time that is often required to simulate a desired amount of System time. Presented here is the “τ-leap” method, an approximate procedure that in some circumstances can produce significant gains in simulation speed with acceptable losses in accuracy. Some primitive strategies for control parameter selection and error mitigation for the τ-leap method are described, and simulation results for two simple model Systems are exhibited. With further refinement, the τ-leap method should provide a viable way of segueing from the exact SSA to the approximate chemical Langevin equation, and thence to the conventional deterministic reaction rate equation, as the System size becomes larger.
