作为表征动力破碎的重要参数之一,平均破碎块度的研究对于揭示岩石破碎机理具有重要意义。尽管进行了大量理论与实验研究,但是还缺乏从裂纹动力学角度来澄清岩石破碎和块度形成机理。基于动态荷载作用下翼型裂纹扩展模型和J. R. Gladde...作为表征动力破碎的重要参数之一,平均破碎块度的研究对于揭示岩石破碎机理具有重要意义。尽管进行了大量理论与实验研究,但是还缺乏从裂纹动力学角度来澄清岩石破碎和块度形成机理。基于动态荷载作用下翼型裂纹扩展模型和J. R. Gladden柱体动力屈曲失稳模型,提出了一种预测岩石平均破碎块度的方法,并探究了应变率对动态强度和平均破碎块度的影响。研究结果表明,随着应变率的增加,动态强度增加,平均破碎块度减小,且应变率依赖性逐渐降低。模型平均破碎块度预测与实验数据吻合良好。展开更多
The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain.The simulations of this stochastic process and its i...The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain.The simulations of this stochastic process and its invariant measure are of interest.In this paper,we propose a numerical scheme for both the simulation of the process and the computation of the invariant measure,and show that under appropriate assumptions,the numerical chain converges to the continuous growth-fragmentation chain with an explicit error bound.With a triangle inequality argument,we are also able to quantitatively estimate the distance between the invariant measures of these two Markov chains.展开更多
We propose a kinetic aggregation model where species A aggregates evolve by the catalysis-coagulation and the catalysis-fragmentation, while the catalyst aggregates of the same species B or C perform self-coagulation ...We propose a kinetic aggregation model where species A aggregates evolve by the catalysis-coagulation and the catalysis-fragmentation, while the catalyst aggregates of the same species B or C perform self-coagulation processes. By means of the generalized Smoluchowski rate equation based on the mean-field assumption, we study the kinetic behaviours of the system with the catalysis-coagulation rate kernel K（i,j;l） l^v and the catalysis-fragmentation rate kernel F（i,j; l） l^μ, where l is the size of the catalyst aggregate, and v and μ are two parameters reflecting the dependence of the catalysis reaction on the size of the catalyst aggregate. The relation between the values of parameters v and μ reflects the competing roles between the two catalysis processes in the kinetic evolution of species A. It is found that the competing roles of the catalysis-coagulation and catalysis-fragmentation in the kinetic aggregation behaviours are not determined simply by the relation between the two parameters v and μ, but also depend on the values of these two parameters. When v 〉 μ and v ≥0, the kinetic evolution of species A is dominated by the catalysis-coagulation and its aggregate size distribution αk（t） obeys the conventional or generalized scaling law; when v 〈 μ and v ≥ 0 or v 〈 0 but μ≥ 0, the catalysis-fragmentation process may play a dominating role and ak（t） approaches the scale-free form; and in other cases, a balance is established between the two competing processes at large times and ακ（t） obeys a modified scaling law.展开更多
文摘作为表征动力破碎的重要参数之一,平均破碎块度的研究对于揭示岩石破碎机理具有重要意义。尽管进行了大量理论与实验研究,但是还缺乏从裂纹动力学角度来澄清岩石破碎和块度形成机理。基于动态荷载作用下翼型裂纹扩展模型和J. R. Gladden柱体动力屈曲失稳模型,提出了一种预测岩石平均破碎块度的方法,并探究了应变率对动态强度和平均破碎块度的影响。研究结果表明,随着应变率的增加,动态强度增加,平均破碎块度减小,且应变率依赖性逐渐降低。模型平均破碎块度预测与实验数据吻合良好。
基金partially supported by the National Key R&D Program of China,Project No.2020YFA0712000NSFC Grant No.12031013 and 12171013.
文摘The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain.The simulations of this stochastic process and its invariant measure are of interest.In this paper,we propose a numerical scheme for both the simulation of the process and the computation of the invariant measure,and show that under appropriate assumptions,the numerical chain converges to the continuous growth-fragmentation chain with an explicit error bound.With a triangle inequality argument,we are also able to quantitatively estimate the distance between the invariant measures of these two Markov chains.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10875086 and 10775104)
文摘We propose a kinetic aggregation model where species A aggregates evolve by the catalysis-coagulation and the catalysis-fragmentation, while the catalyst aggregates of the same species B or C perform self-coagulation processes. By means of the generalized Smoluchowski rate equation based on the mean-field assumption, we study the kinetic behaviours of the system with the catalysis-coagulation rate kernel K（i,j;l） l^v and the catalysis-fragmentation rate kernel F（i,j; l） l^μ, where l is the size of the catalyst aggregate, and v and μ are two parameters reflecting the dependence of the catalysis reaction on the size of the catalyst aggregate. The relation between the values of parameters v and μ reflects the competing roles between the two catalysis processes in the kinetic evolution of species A. It is found that the competing roles of the catalysis-coagulation and catalysis-fragmentation in the kinetic aggregation behaviours are not determined simply by the relation between the two parameters v and μ, but also depend on the values of these two parameters. When v 〉 μ and v ≥0, the kinetic evolution of species A is dominated by the catalysis-coagulation and its aggregate size distribution αk（t） obeys the conventional or generalized scaling law; when v 〈 μ and v ≥ 0 or v 〈 0 but μ≥ 0, the catalysis-fragmentation process may play a dominating role and ak（t） approaches the scale-free form; and in other cases, a balance is established between the two competing processes at large times and ακ（t） obeys a modified scaling law.
