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A class of processes for which the problem of species balance can be solved without using any assumptions concerning the mechanism of the chemical event of the reaction was found in the problem of species balance in the reaction zone. The mathematical statement of the problem in this case was discussed; it was shown that the solution is mainly determined by the system geometry. The method for reducing the problem to determination of the probability of species entering the chemical event zone is substantiated; this can be done by the Green function method. 相似文献
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Models of chemical kinetics in which some reactions are much faster than others are often treated by a type of quasi-steady-state
approximation (QSSA). The total QSSA (tQSSA) was introduced for models of Michaelis-Menten enzyme kinetics and shown to be valid over a wider parameter regime
than the usual QSSA. Here, we extend the tQSSA to the Mitogen-Activated Protein Kinase Cascade, an important signaling system
in cell biochemistry. These approximations were first developed in a deterministic setting, but here we also describe how
to incorporate this approximation into the discrete and stochastic framework of the Chemical Master Equation (CME). The CME
gives rise to a large-scale matrix exponential that can be solved by Krylov methods in combination with operator splitting
and the tQSSA.
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T细胞同祖细胞在骨髓中的发育一样在胸腺中分裂、分化、并最终发育成为成熟的T细胞.研究人员通过建立一类描述T细胞增殖、分化、死亡的微分方程模型来估计胸腺细胞总量及各种未成熟或成熟细胞所占的比例.本文在利用准静态近似法的基础之上,采用微分方程稳定性理论中的有关方法对这类微分方程模型的稳定性等问题进行了完整的理论分析,所获得的其平衡位置为全局渐近稳定的结论为有关文献中采用数值模拟所预测的结论的正确性提供了理论依据. 相似文献
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搅拌摩擦焊接过程中的材料塑性变形流场与温度场对焊接接头的组织演化及最终的力学性能有着十分重要的影响,许多学者对此进行了大量的研究.近年来的研究结果表明,该过程是一个极其复杂的热力耦合过程,温度场与材料塑性变形流场之间具有相互耦合效应.运用流体力学和传热学原理对准稳态热力耦合过程进行了数值模拟研究,通过计算得到了焊件材料的流场和温度场分布,并设计了相关实验对温度场进行了验证,结果表明该计算结果可以较准确地描述搅拌摩擦焊准稳态热力耦合状态. 相似文献
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《Mendeleev Communications》2023,33(1):103-106
Sufficient conditions for the validity of the quasi-steady-state approximation widely used in chemical kinetics are considered by means of the qualitative geometric theory of differential equations with small parameters. 相似文献
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