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B Nowakowski - One of the best experts on this subject based on the ideXlab platform.
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master equation for a bistable Chemical System with perturbed particle velocity distribution function
Physical Review E, 2012Co-Authors: Piotr Dziekan, B Nowakowski, Annie LemarchandAbstract:We present a modified master equation for a homogeneous gaseous reactive System which includes nonequilibrium corrections due to the reaction-induced perturbation of the particle velocity distribution function. For the Schl\"ogl model, the modified stochastic approach predicts nonequilibrium-induced transitions between different dynamical regimes, including the transformation of a monostable System into a bistable one, and vice versa. These predictions are confirmed by the comparison with microscopic simulations using the direct simulation Monte Carlo method. Compared to microscopic simulations of the particle dynamics, the modified master equation approach proves to be much more efficient.
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perturbation of particle velocity distribution in a bistable Chemical System
Physica A-statistical Mechanics and Its Applications, 1999Co-Authors: Annie Lemarchand, B NowakowskiAbstract:Departure from Maxwellian particle velocity distribution induced by Chemical reactions is studied in a bistable homogeneous System maintained out of Chemical equilibrium. In the vicinity of the bifurcation associated with the coalescence of two stationary states, the dynamics of the System is very sensitive to small perturbations originating from the deformations of particle velocity distribution. An analytical approach of Boltzmann equations and microscopic simulations show that the perturbation of velocity distribution results in a significant deformation of the bifurcation diagram.
Khaled M Saad - One of the best experts on this subject based on the ideXlab platform.
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a comparative study on solving fractional cubic isothermal auto catalytic Chemical System via new efficient technique
Chaos Solitons & Fractals, 2020Co-Authors: Necdet Bildik, Khaled M Saad, Sinan DenizAbstract:Abstract In this paper, we examine a cubic isothermal auto-catalytic Chemical System (CIACS) with the help of the newly developed technique. Classical model of this System is transformed into a new fractional forms by using three different and special fractional operators. The new model is therefore called as fractional cubic isothermal auto-catalytic Chemical System (FCIACS). Then, the new Systems are solved by optimal perturbation iteration method. Obtained results are compared to get an idea about the new derivative operators and optimal perturbation iteration method.
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analysis of reaction diffusion System via a new fractional derivative with non singular kernel
Physica A-statistical Mechanics and Its Applications, 2018Co-Authors: Khaled M Saad, J F GomezaguilarAbstract:Abstract In this paper, we obtain analytical solutions for the fractional cubic isothermal auto-catalytic Chemical System with Caputo–Fabrizio and Atangana–Baleanu fractional time derivatives in Liouville–Caputo sense. We utilize the q-homotopy analysis transform method to compute the approximate solutions. We find the optimal values of h so we assure the convergence of the approximate solutions. Finally, we compare our results numerically with the finite difference method and excellent agreement is found.
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comparing the caputo caputo fabrizio and atangana baleanu derivative with fractional order fractional cubic isothermal auto catalytic Chemical System
European Physical Journal Plus, 2018Co-Authors: Khaled M SaadAbstract:In this work we extend the standard model for a cubic isothermal auto-catalytic Chemical System (CIACS) to a new model of a fractional cubic isothermal auto-catalytic Chemical System (FCIACS) based on Caputo (C), Caputo-Fabrizio (CF) and Atangana-Baleanu in the Liouville-Caputo sense (ABC) fractional time derivatives, respectively. We present approximate solutions for these extended models using the q -homotopy analysis transform method (q -HATM). We solve the FCIACS with the C derivative and compare our results with those obtained using the CF and ABC derivatives. The ranges of convergence of the solutions are found and the optimal values of h , the auxiliary parameter, are derived. Finally, these solutions are compared with numerical solutions of the various models obtained using finite differences and excellent agreement is found.
Hong Qian - One of the best experts on this subject based on the ideXlab platform.
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stochastic dynamics and non equilibrium thermodynamics of a bistable Chemical System the schlogl model revisited
Journal of the Royal Society Interface, 2009Co-Authors: Melissa Vellela, Hong QianAbstract:Schlogl's model is the canonical example of a Chemical reaction System that exhibits bistability. Because the biological examples of bistability and switching behaviour are increasingly numerous, this paper presents an integrated deterministic, stochastic and thermodynamic analysis of the model. After a brief review of the deterministic and stochastic modelling frameworks, the concepts of Chemical and mathematical detailed balances are discussed and non-equilibrium conditions are shown to be necessary for bistability. Thermodynamic quantities such as the flux, Chemical potential and entropy production rate are defined and compared across the two models. In the bistable region, the stochastic model exhibits an exchange of the global stability between the two stable states under changes in the pump parameters and volume size. The stochastic entropy production rate shows a sharp transition that mirrors this exchange. A new hybrid model that includes continuous diffusion and discrete jumps is suggested to deal with the multiscale dynamics of the bistable System. Accurate approximations of the exponentially small eigenvalue associated with the time scale of this switching and the full time-dependent solution are calculated using Matlab. A breakdown of previously known asymptotic approximations on small volume scales is observed through comparison with these and Monte Carlo results. Finally, in the appendix section is an illustration of how the diffusion approximation of the Chemical master equation can fail to represent correctly the mesoscopically interesting steady-state behaviour of the System.
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oscillations and multiscale dynamics in a closed Chemical reaction System second law of thermodynamics and temporal complexity
Journal of Chemical Physics, 2008Co-Authors: Hong QianAbstract:We investigate the oscillatory reaction dynamics in a closed isothermal Chemical System: the reversible Lotka-Volterra model. The second law of thermodynamics dictates that the System ultimately reaches an equilibrium. Quasistationary oscillations are analyzed while the free energy of the System serves as a global Lyapunov function of the dissipative dynamics. A natural distinction between regions near and far from equilibrium in terms of the free energy can be established. The dynamics is analogous to a nonlinear mechanical System with time-dependent increasing damping. Near equilibrium, no oscillation is possible as dictated by Onsager's reciprocal symmetry relation. We observe that while the free energy decreases in the closed System's dynamics, it does not follow the steepest descending path.
David M. Jenkins - One of the best experts on this subject based on the ideXlab platform.
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dehydration and partial melting of tremolitic amphibole coexisting with zoisite quartz anorthite diopside and water in the System h 2 o cao mgo al 2 o 3 sio 2
Contributions to Mineralogy and Petrology, 1998Co-Authors: Diane M Quirion, David M. JenkinsAbstract:The greenschist to amphibolite transition as modeled by the reaction zoisite+tremolite + quartz= anorthite+diopside+water has been experimentally investigated in the Chemical System H2O−CaO− MgO−Al2O3−SiO2 over the range of 0.4–0.8 GPa. This reaction is observed to lie within the stability fields of anorthite + water and of zoisite + quartz, in accord with phase equilibrium principles, and its position is in excellent agreement with the boundary calculated from current internally-consistent data bases. The small dP/dT slope of 0.00216 GPa/K (21.6 bars/K) observed for this reaction supports the pressure-dependency of this transition in this Chemical System. Experimental reversals of the Al content in tremolitic amphibole coexisting with zoisite, diopside, quartz, and water were obtained at 600, 650, and 700°C and indicated Al total cations (atoms per formula unit, apfu) of only up to 0.5±0.08 at the highest temperature. Thermodynamic analysis of these and previous compositional reversal data for tremolitic amphibole indicated that, of the activity/composition relationships considered, a two-site-coupled cation substitution model yielded the best fit to the data and a S0 (1 bar, 298 K) of 575.4±1.6 J/K · mol for magnesio-hornblende. The calculated isopleths of constant Al content in the amphibole are relatively temperature sensitive with Al content increasing with increasing temperature and pressure. Finally, several experiments in the range of 1.0–1.3 GPa were conducted to define the onset of melting, and thus the upper-thermal limit, for this mineral assemblage, which must involve an invariant point located at approximately 1.05 GPa and 770°C.
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dehydration and partial melting of tremolitic amphibole coexisting with zoisite quartz anorthite diopside and water in the System
1998Co-Authors: Diane M Quirion, David M. JenkinsAbstract:The greenschist to amphibolite transition as modeled by the reaction zoisitea tremolitea quartza anorthitea diopsidea water has been experimentally investigated in the Chemical System H2O-CaO- MgO-Al2O3-SiO2 over the range of 0.4-0.8 GPa. This reaction is observed to lie within the stability fields of anorthite + water and of zoisite + quartz, in accord with phase equilibrium principles, and its position is in excellent agreement with the boundary calculated from current internally-consistent data bases. The small dP=dT slope of 0.00216 GPa/K (21.6 bars/K) observed for this reaction supports the pressure-dependency of this transition in this Chemical System. Experimental reversals of the Al content in tremolitic amphibole co- existing with zoisite, diopside, quartz, and water were obtained at 600, 650, and 700C and indicated Al total cations (atoms per formula unit, apfu) of only up to 0:5 0:08 at the highest temperature. Thermodynamic analysis of these and previous compositional reversal data for tremolitic amphibole indicated that, of the ac- tivity/composition relationships considered, a two-site- coupled cation substitution model yielded the best fit to the data and a S 0 (1 bar, 298 K) of 575:4 1:6 J/K AE mol for magnesio-hornblende. The calculated isopleths of constant Al content in the amphibole are relatively temperature sensitive with Al content increasing with increasing temperature and pressure. Finally, several experiments in the range of 1.0-1.3 GPa were conducted to define the onset of melting, and thus the upper-ther- mal limit, for this mineral assemblage, which must in- volve an invariant point located at approximately 1.05 GPa and 770C.
Annie Lemarchand - One of the best experts on this subject based on the ideXlab platform.
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master equation for a bistable Chemical System with perturbed particle velocity distribution function
Physical Review E, 2012Co-Authors: Piotr Dziekan, B Nowakowski, Annie LemarchandAbstract:We present a modified master equation for a homogeneous gaseous reactive System which includes nonequilibrium corrections due to the reaction-induced perturbation of the particle velocity distribution function. For the Schl\"ogl model, the modified stochastic approach predicts nonequilibrium-induced transitions between different dynamical regimes, including the transformation of a monostable System into a bistable one, and vice versa. These predictions are confirmed by the comparison with microscopic simulations using the direct simulation Monte Carlo method. Compared to microscopic simulations of the particle dynamics, the modified master equation approach proves to be much more efficient.
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perturbation of particle velocity distribution in a bistable Chemical System
Physica A-statistical Mechanics and Its Applications, 1999Co-Authors: Annie Lemarchand, B NowakowskiAbstract:Departure from Maxwellian particle velocity distribution induced by Chemical reactions is studied in a bistable homogeneous System maintained out of Chemical equilibrium. In the vicinity of the bifurcation associated with the coalescence of two stationary states, the dynamics of the System is very sensitive to small perturbations originating from the deformations of particle velocity distribution. An analytical approach of Boltzmann equations and microscopic simulations show that the perturbation of velocity distribution results in a significant deformation of the bifurcation diagram.