KIO_3-KSCN-H~+反应体系的非线性动力学研究

研究了 KIO3-KSCN-H+反应体系在连续搅拌流动反应器 ( CSTR)中的非线性动力学行为 .在 CSTR中 ,该反应体系的 Pt电极电位显示出持续振荡现象 ,振荡的浓度范围非常宽 .通过酸度及各种金属离子对体系振荡行为影响的研究发现 ,对振荡体系具有催化作用的可能物种是 H+ 离子而不是金属离子     

KIO3-KSCN-H+反应体系的非线性动力学研究

研究了KIO₃-KSCN-H+反应体系在连续搅拌流动反应器(CSTR)中的非线性动力学行为.在CSTR中,该反应体系的Pt电极电位显示出持续振荡现象,振荡的浓度范围非常宽.通过酸度及各种金属离子对体系振荡行为影响的研究发现,对振荡体系具有催化作用的可能物种是H+离子而不是金属离子.     

铂电极BZ反应体系的系统动力学分析

在一定的条件下,将铂电极BZ化学反应的六变量高维动力学系约化为三变量体系,同时对该体系进行了全面的系统动力学分析.研究结果表明,通过改变耦合体系的外控参数条件,在将体相保持在均一稳定定态的参数范围内,电极反应相可能进入振荡区,而呈现出电极反应相与体相的动力学行为不一致性.进一步计算出体相处于非振荡状态时,电极反应相产生电化学振荡的外控参数区域.     

外控恒电流对BZ电化学反应体系动力学行为的影响

在使用探头对BZ反应体系进行观测时,原来纯粹的BZ反应系变成了由两个子系通过扩散过程耦合成的一类特殊电化学体系,所用的探头能否如实反映该体系的真实振荡行为值得探讨。本文基于FKN机理及Oregonator模型,分别对Pt电极BZ反应体系建立了动力学模型,讨论了两子系出现极限环振荡的动力学行为不一致性及外控电极电流的影响。     

高碘酸盐-亚硫酸盐反应体系的复杂动力学

研究了KIO4-Na2SO3-H2SO4 反应体系的复杂动力学，在酸性条件下（pH<3），发现碘电位、Pt电极电位和pH在封闭体系中显示单峰振荡以及半封闭体系和开放体系中的振荡现象.振荡现象受[Na2SO3]0/[KIO4]0比值以及体系的酸度影响.实验结果表明该体系可能为I2生成和I2消耗所驱动的振荡反应；所拟的反应机理解释了体系所显示的复杂动力学现象.     

反应NH~4ClO~4+Mg+K~2Cr~2O~7的非线性化学动力学2: 固相 振荡燃烧的化学模 型

建立了NH~4ClO~4+Mg+K~2Cr~2O~7固相振荡燃烧体系的非吸热三变量立方自催化化学模型,应用非线性数学分析方法,研究了固相振荡燃烧的非线性化学动力学机理,并对此进行了数值模拟,结果反映了这一振荡燃烧体系所具有的非线性化学动力学特性。     

反应NH~4ClO~4+Mg+K~2Cr~2O~7的非线性化学动力学2: 固相 振荡燃烧的化学模 型

建立了NH~4ClO~4+Mg+K~2Cr~2O~7固相振荡燃烧体系的非吸热三变量立方自催化化学模型,应用非线性数学分析方法,研究了固相振荡燃烧的非线性化学动力学机理,并对此进行了数值模拟,结果反映了这一振荡燃烧体系所具有的非线性化学动力学特性。     

B-Z反应对ki(T)的响应行为

众所周知,B-Z反应体系的振荡行为与温度的关系极为密切,如反应体系只在一定的温区内发生振荡行为;振荡频率ω随温度的升高而加快等。Sφrensen等人都曾根据Arrhenius定理定性地解释了系统的ω随温度的变化而连续改变的现象,但不能解释温度对振荡体系的类似开关的控制作用。本文以体系的速率系数K_i为参数,通过K_i与温度的关联,运用动力学稳定性理论研究体系的振荡行为随温度变化的规律,得到较为满意的结果。类似     

多定态转变化学反应体系与环境传热-扩散耦合导致的环面型化学振荡

以Schlögl模型作为多定态转变化学反应体系的范例, 研究了通过传热及扩散与环境耦合的多定态转变化学反应体系中诱发的新动力学行为, 其中特别重要的是沿慢变量方向的环面型化学振荡的出现. 建立了慢流型上的准定态的线形化稳定性分析法, 揭示了由极限环振荡蜕变为环面型振荡的动力学机制, 不同于小寄生参数存在引起的非连续极限环振荡. 通过以慢流型上准定态稳定性分区为基础的定性分析, 进一步揭示了该类体系中可能出现间歇性、反复持续式和骤发式3种亚类环面振荡. 最后以第三亚类作为示例, 以相应的计算机模拟证实理论分析的正确性.     

反应NH4ClO4+Mg+K2Cr2O7的非线性化学动力学Ⅱ.固相振荡燃烧的化学模型

建立了NH4ClO4+Mg+K2Cr2O7固相振荡燃烧体系的非吸热三变量立方自催化化学模型,应用非线性数学分析方法,研究了固相振荡燃烧的非线性化学动力学机理,并对此进行了数值模拟,结果反映了这一振荡燃烧体系所具有的非线性化学动力学特性.     

Atoms of multistationarity in chemical reaction networks

Chemical reaction systems are dynamical systems that arise in chemical engineering and systems biology. In this work, we consider the question of whether the minimal (in a precise sense) multistationary chemical reaction networks, which we propose to call ‘atoms of multistationarity,’ characterize the entire set of multistationary networks. Our main result states that the answer to this question is ‘yes’ in the context of fully open continuous-flow stirred-tank reactors (CFSTRs), which are networks in which all chemical species take part in the inflow and outflow. In order to prove this result, we show that if a subnetwork admits multiple steady states, then these steady states can be lifted to a larger network, provided that the two networks share the same stoichiometric subspace. We also prove an analogous result when a smaller network is obtained from a larger network by ‘removing species.’ Our results provide the mathematical foundation for a technique used by Siegal- Gaskins et al. of establishing bistability by way of ‘network ancestry.’ Additionally, our work provides sufficient conditions for establishing multistationarity by way of atoms and moreover reduces the problem of classifying multistationary CFSTRs to that of cataloging atoms of multistationarity. As an application, we enumerate and classify all 386 bimolecular and reversible two-reaction networks. Of these, exactly 35 admit multiple positive steady states. Moreover, each admits a unique minimal multistationary subnetwork, and these subnetworks form a poset (with respect to the relation of ‘removing species’) which has 11 minimal elements (the atoms of multistationarity).     

从多重定态经复杂奇点向极限环型化学振荡的跃迁

在文Ⅰ~[1]的相平面分析的基础上, 利用线性稳定性分析和数值模拟的方法进一步分析了Schlögl模型在CSTR中的行为, 发现在适当条件下可以发生从定态向振荡态的不连续的突然跃迁现象。认为这种突然跃迁现象是通过鞍点-结点型复杂奇点的形成和消失而实现的。分析了这种鞍点-结点型跃迁与亚临界Hopf分支现象的差别, 并讨论了这种跃迁现象和实验上发现的某些突变型化学振荡现象之间的联系。     

Entropy production in a mesoscopic chemical reaction system with oscillatory and excitable dynamics

Stochastic thermodynamics of chemical reaction systems has recently gained much attention. In the present paper, we consider such an issue for a system with both oscillatory and excitable dynamics, using catalytic oxidation of carbon monoxide on the surface of platinum crystal as an example. Starting from the chemical Langevin equations, we are able to calculate the stochastic entropy production P along a random trajectory in the concentration state space. Particular attention is paid to the dependence of the time-averaged entropy production P on the system size N in a parameter region close to the deterministic Hopf bifurcation (HB). In the large system size (weak noise) limit, we find that P ～ N(β) with β = 0 or 1, when the system is below or above the HB, respectively. In the small system size (strong noise) limit, P always increases linearly with N regardless of the bifurcation parameter. More interestingly, P could even reach a maximum for some intermediate system size in a parameter region where the corresponding deterministic system shows steady state or small amplitude oscillation. The maximum value of P decreases as the system parameter approaches the so-called CANARD point where the maximum disappears. This phenomenon could be qualitatively understood by partitioning the total entropy production into the contributions of spikes and of small amplitude oscillations.     

Fast determination of lead in lake sediment samples using electrothermal atomic absorption spectrometry with slurry samples introduction

An analytical method for the determination of glutamic acid by the sequential perturbation caused by different amounts of glutamic acid on the oscillating chemical system involving the Cu(II)-catalyzed oscillating reaction between hydrogen peroxide and sodium thiocyanate in an alkaline medium is proposed. The method relies on the linear relationship between the changes in the oscillation amplitude of the chemical system and the concentration of glutamic acid. The reaction is implemented in a continuous-flow stirred-tank reactor, and changes in the oscillation amplitude on each perturbation are proportional to the glutamic acid concentration. The use of the analyte pulse perturbation (APP) technique permits sequential determinations on the same oscillating system owing to the expeditiousness with which the steady state is regained after each perturbation. The dynamic range lies between 2.5x10(-6) and 3.2x10(-4) M of glutamic acid, with the regression coefficient is 0.9987. The precision is excellent (less than 0.68% as relative standard deviation (R.S.D.)). Some aspects of the potential mechanism of action of glutamic acid on the oscillating system are discussed.     

The energy pump and the origin of the non-equilibrium flux of the dynamical systems and the networks

The global stability of dynamical systems and networks is still challenging to study. We developed a landscape and flux framework to explore the global stability. The potential landscape is directly linked to the steady state probability distribution of the non-equilibrium dynamical systems which can be used to study the global stability. The steady state probability flux together with the landscape gradient determines the dynamics of the system. The non-zero probability flux implies the breaking down of the detailed balance which is a quantitative signature of the systems being in non-equilibrium states. We investigated the dynamics of several systems from monostability to limit cycle and explored the microscopic origin of the probability flux. We discovered that the origin of the probability flux is due to the non-equilibrium conditions on the concentrations resulting energy input acting like non-equilibrium pump or battery to the system. Another interesting behavior we uncovered is that the probabilistic flux is closely related to the steady state deterministic chemical flux. For the monostable model of the kinetic cycle, the analytical expression of the probabilistic flux is directly related to the deterministic flux, and the later is directly generated by the chemical potential difference from the adenosine triphosphate (ATP) hydrolysis. For the limit cycle of the reversible Schnakenberg model, we also show that the probabilistic flux is correlated to the chemical driving force, as well as the deterministic effective flux. Furthermore, we study the phase coherence of the stochastic oscillation against the energy pump, and argue that larger non-equilibrium pump results faster flux and higher coherence. This leads to higher robustness of the biological oscillations. We also uncovered how fluctuations influence the coherence of the oscillations in two steps: (1) The mild fluctuations influence the coherence of the system mainly through the probability flux while maintaining the regular landscape topography. (2) The larger fluctuations lead to flat landscape and the complete loss of the stability of the whole system.     

循环伏安法用于化学振荡的研究

迄今为止,Belousov-Zhabotinskii(B-Z)振荡反应中Br~-浓度~CBr~-的变化主要用Br~-选择电极跟踪监测,取得了一定的成果。但是有一些研究表明,由于受到体系中KBrO_3等物种的干扰,Br~-选择电极的信号在定性和定量上都不一定是Br~-行为的真实反映。Noyes     

介观化学体系中的动力学尺度效应

以生命和表面催化体系为对象,研究了介观化学体系中内涨落对体系非线性动力学行为的调控作用。内涨落可以诱导随机振荡,其强度在体系处于最佳尺度时会出现一个甚至多个极大值,并且在耦合体系中会得到进一步增强,表现为尺度共振效应、尺度选择效应和双重尺度效应,揭示了介观化学体系中尺度效应的新机制。     

介观化学体系中的动力学尺度效应

以生命和表面催化体系为对象,研究了介观化学体系中内涨落对体系非线性动力学行为的调控作用。内涨落可以诱导随机振荡,其强度在体系处于最佳尺度时会出现一个甚至多个极大值,并且在耦合体系中会得到进一步增强,表现为尺度共振效应、尺度选择效应和双重尺度效应,揭示了介观化学体系中尺度效应的新机制。     

Some consequences of thermodynamic feasibility for chemical reaction networks

Power law dynamics is used to describe the stability behavior in metabolic networks such as chemical reaction networks (CRN’s). These systems allow multiple steady states within a single stoichiometric class. On the other side thermodynamic constraints such as loop-less fluxes represented by the Gorban theorem of alternatives applied to these networks reveal considerable restrictions to their dynamics by eliminating multistability of CRN’s in general. Thermodynamic feasible CRN’s are contained in the class of injective CRN’s. We can give an alternative proof of the detailed balance with Brewer’s Fixed Point Theorem. Furthermore we can derive by the loop-less principle the extended detailed balance. This paper establishes a link between recent research in CRN theory and thermodynamic basics. The result has also consequences for the picture of multiple steady states as assumed for cell differentiation and regulation. CRN’s provide from their perspective not enough means to maintain multistability without regulation or external control.

     

Closed and endoreversible chemical oscillation

Based on a simple nonideal chemical reaction model, the closed system with reversible nonideal reactions and illumination is shown to be able to exhibit sustained oscillation. The essential points in the occurrence of such oscillations are the nonideality of reacting media, which gives rise to multiple chemical equilibria, and the energy flow through illumination and heat conduction, which gives rise to spontaneous transitions repeatedly between the multiple equilibrium states. During the oscillation, reacting media undergo only reversible chemical transformation and all irreversibilities are restricted to the coupling of the system to external world. This oscillation provides an example of the so-called endoreversible machine and a possible way to convert radiation energy of the light directly into mechanical energy.