三种典型布朗马达的定向输运与非平衡态热力学分析
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摘要
在传统的热力学中,一旦知道系统的始态和终态能量以及连接两态的路径,便可确定系统对外作的功。事实上,两态的能量及系统与环境在路径上的交换热均有k_BT涨落,只是在玻耳兹曼统计中,这个量级的涨落被忽略了。如果系统很小,这样的涨落则不能被忽略。这类微观系统的统计热力学问题是纳米科学当前所面临的研究障碍。分子马达正是这样的微观系统,可为物理学家解决该问题提供一个理想的研究平台。
近年来噪声诱导定向输运的现象已经引起人们的广泛兴趣。这种现象已经被普遍地应用在物理、化学以及生物上。理论和实验上研究的都比较集中的一个系统是动蛋白马达或者力蛋白马达的定向运动。这类马达蛋白主要负责细胞器官的输送,它们的运动是随机的但平均来说是定向运动,并且可以用布朗棘轮来构建这样的模型。于是布朗马达的概念便被用来解释噪声诱导定向输运。
基于以上原因,本论文围绕几种典型的布朗马达模型进行讨论,研究了马达的定向输运行为。同时应用非平衡态热力学理论探索受不可逆因素影响的热驱动布朗马达系统的各种最优性能参量对马达性能的影响。主要研究内容如下:介绍了布朗运动的动力学理论,对定向输运系统(热力学棘齿)和布朗马达作一整体概述。详细介绍了分子马达的研究历史、分类、模型的构建以及理论框架,同时还对现有模型中马达模型研究的不足作了探讨和分析,期望对今后的研究有所启示。
研究了由两个相同周期不对称势垒构成的两态闪烁棘齿模型中布朗粒子的定向输运。采用幂级数展开的方法得到了几率流的解析式,给出几率流随外参数变化的特性曲线。详细地讨论了不对称参数,势垒高度以及两态间的跃迁率等因素对几率流的影响。发现几率流不但会受到不对称参数和势垒高度的影响,而且两态间的跃迁率同样会影响到几率流。当两态间的跃迁率不等时,还发现势垒高度不仅会改变几率流的大小而且还会改变几率流的方向。
基于一个更为普遍的布朗马达模型,解析求解了热驱动布朗马达的昂色格系数和普适效率。发现模型的昂色格系数满足倒易关系,由粒子运动产生的动能变化部分不会影响昂色格系数。仅当系统的热漏部分可以忽略时,昂色格系数行列式等于零。此外,详细地讨论了表征模型的各个参数对热布朗马达效率的影响。给出普适效率随系统参量变化的特性曲线,计算了效率的最大值和相应的优化参数。得到的计算结果更具有普遍意义,它们可以用来分析布朗马达在三个有趣条件下的性能特性:没有热漏情况,平均速度等于零的情况和线性响应区附近的情况。
在上述基础上,建立了一个等效的循环系统,运用非平衡态热力学理论计算了系统的昂色格系数和最大输出功率时的效率。发现模型的昂色格系数满足倒易关系,对于现实系统的不可逆因素同样会影响模型的昂色格系数。仅当热漏和粒子动能改变部分可以忽略时,昂色格系数行列式等于零。同时还发现在非平衡态热力学框架下,对于不可逆热布朗马达的输出功率和效率可以表述成和不可逆卡诺热机相同的形式,因此所得的结果更具有普遍意义。此外这些结论还可以用来分析一类热驱动布朗马达的性能特性。
基于理论上可以计算且实验上可以操作的双阱棘齿势,研究了延迟时间,粒子数,势垒的不对称参量对延迟反馈棘轮性能的影响。计算了布朗粒子的质心速度,平均有效扩散系数以及Pe数。详细地解释了这些参数不仅会受到延迟时间和粒子数的影响,而且还会受到双阱棘齿势的不对称参数的影响。很有趣地发现通过改变系统的粒子数可以获得定向流的反转。期望能够在某些物理和生物系统中观测到这些结果,因为本模型采用的是更为实际的并且可以在实验上实现的双阱棘齿势垒。
本论文所得的结果可作为进一步深入研究上述三种典型布朗马达的理论基础,也可为相关纳米机器的优化设计提供理论参考。
Once we know the initial and final energies of the system and the path between them, the work output of the system can be determined by classical thermodynamics.In fact, there exists the quantity of fluctuations with k_BT dominate in the energies of the two states and the exchange heat between the system and the environment.In the Boltzmann statistic the quantity of fluctuations is usually negligible.However,the fluctuations aren't negligible as the systems are very small.The statistical thermodynamic issues appearing in microscopic systems are becoming the holdback which has to be faced with in the nano science.Molecular motors are just such microscopic systems which may serve as the basis for physicists to solve the problems.
The phenomenon of noise induced directed transport has attracted much interest in recent years.It has widespread applications in physics,chemistry and biology.One particular system which has been intensively studied both theoretically and experimentally is the motion of motor proteins like kinesins or dyneins.These motor proteins are responsible for the transport of cell organelles along the cytosceleton.They move randomly but directly on average and have been modeled by Brownian ratchets,and consequently,the concept of Brownian motors has been used to illuminate the directed, noise-induced transport.
Based on the above reasons,this thesis is focused on the discussion of several typical Brownian models,and then the directed transports of Brownian motors are investigated. The performance parameters of the thermally driven Brownian motors systems under the influence of the irreversibilities are searched by using nonequilibrium thermodynamics. The main research contents are organized as follows:
The brief introduction of the dynamics theory of the Brownian motion and thermodynamic ratchets and Brownian motors are given.The research histories, classification,construction of the model and theory frame of the molecular motors are presented in detail.The insufficiency of the Brownian ratchet model in existence is explored and analyzed.It is expected that this discussion can give some inspire for future research.
The transport of Brownian particles in two-state flashing ratchets composed of two asymmetric potentials with the same period is investigated.The analytic expression of a probability current is derived by using the power series expansion method and used to generate the curve characteristics of the current varying with other parameters.The effects of the asymmetric parameters and heights of two potentials and the transition rates between two states on the probability current are discussed in detail.It is found that the current is affected by not only the asymmetric parameters and heights of two potentials but also the transition rates between two states.It is also found that the heights of two potentials may change the magnitude as well as the direction of the current when the transition rates between two states are not the same.
Based on a general model of Brownian motors,the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically.It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle's motion.Only when the heat leak in the system is negligible,can the determinant of the Onsager matrix vanish.Moreover,the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail.The characteristic curves of the generalized efficiency varying with these parameters are presented.The maximum generalized efficiency and the corresponding optimum parameters are determined.The results obtained here are of general significance.They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with the zero heat leak,zero average drift velocity or linear response relation.
An equivalent cycle system is established based on the above discussion and the Onsager coefficients and efficiency at the maximum power output of the system are analytically calculated from nonequilibrium thermodynamics.It is found that the Onsager reciprocity relation holds and the Onsager coefficients are affected by the main irreversibilities existing in practical systems.Only when the heat leak and the kinetic energy change of the particle in the system are negligible,can the determinant of the Onsager matrix vanish.It is also found that in the frame of nonequilibrium thermodynamics,the power output and efficiency of an irreversible Brownian motor can be expressed to be the same form as those of an irreversible Carnot heat engine,so the results obtained here are of general significance.Moreover,these results can be used to analyze the performance characteristics of a class of thermally driven Brownian motors.
On the basis of the double-well potential which can be calculated theoretically and implemented experimentally,the influence of the time delay,number of particles and asymmetric parameter of the potential on the performance of a delayed feedback ratchet is investigated.The center-of-mass velocity of Brownian particles,the average effective diffusion coefficient and Pe number are calculated.It is expounded that the parameters are affected by not only the time delay and number of particles but also the asymmetric parameter of the double-well ratchet potential.It is very interesting to find that the current transport reversal may be obtained by varying the number of particles of the system.It is expected that the results obtained here may be observed in some physical and biological systems because the double-well ratchet potential is realizable experimentally.
The results obtained in the thesis may provide some theoretical bases for the deep investigation on the three classes of typical Brownian motors mentioned above as well as some references for the optimal design of some relevant nano machines.
近年来噪声诱导定向输运的现象已经引起人们的广泛兴趣。这种现象已经被普遍地应用在物理、化学以及生物上。理论和实验上研究的都比较集中的一个系统是动蛋白马达或者力蛋白马达的定向运动。这类马达蛋白主要负责细胞器官的输送,它们的运动是随机的但平均来说是定向运动,并且可以用布朗棘轮来构建这样的模型。于是布朗马达的概念便被用来解释噪声诱导定向输运。
基于以上原因,本论文围绕几种典型的布朗马达模型进行讨论,研究了马达的定向输运行为。同时应用非平衡态热力学理论探索受不可逆因素影响的热驱动布朗马达系统的各种最优性能参量对马达性能的影响。主要研究内容如下:介绍了布朗运动的动力学理论,对定向输运系统(热力学棘齿)和布朗马达作一整体概述。详细介绍了分子马达的研究历史、分类、模型的构建以及理论框架,同时还对现有模型中马达模型研究的不足作了探讨和分析,期望对今后的研究有所启示。
研究了由两个相同周期不对称势垒构成的两态闪烁棘齿模型中布朗粒子的定向输运。采用幂级数展开的方法得到了几率流的解析式,给出几率流随外参数变化的特性曲线。详细地讨论了不对称参数,势垒高度以及两态间的跃迁率等因素对几率流的影响。发现几率流不但会受到不对称参数和势垒高度的影响,而且两态间的跃迁率同样会影响到几率流。当两态间的跃迁率不等时,还发现势垒高度不仅会改变几率流的大小而且还会改变几率流的方向。
基于一个更为普遍的布朗马达模型,解析求解了热驱动布朗马达的昂色格系数和普适效率。发现模型的昂色格系数满足倒易关系,由粒子运动产生的动能变化部分不会影响昂色格系数。仅当系统的热漏部分可以忽略时,昂色格系数行列式等于零。此外,详细地讨论了表征模型的各个参数对热布朗马达效率的影响。给出普适效率随系统参量变化的特性曲线,计算了效率的最大值和相应的优化参数。得到的计算结果更具有普遍意义,它们可以用来分析布朗马达在三个有趣条件下的性能特性:没有热漏情况,平均速度等于零的情况和线性响应区附近的情况。
在上述基础上,建立了一个等效的循环系统,运用非平衡态热力学理论计算了系统的昂色格系数和最大输出功率时的效率。发现模型的昂色格系数满足倒易关系,对于现实系统的不可逆因素同样会影响模型的昂色格系数。仅当热漏和粒子动能改变部分可以忽略时,昂色格系数行列式等于零。同时还发现在非平衡态热力学框架下,对于不可逆热布朗马达的输出功率和效率可以表述成和不可逆卡诺热机相同的形式,因此所得的结果更具有普遍意义。此外这些结论还可以用来分析一类热驱动布朗马达的性能特性。
基于理论上可以计算且实验上可以操作的双阱棘齿势,研究了延迟时间,粒子数,势垒的不对称参量对延迟反馈棘轮性能的影响。计算了布朗粒子的质心速度,平均有效扩散系数以及Pe数。详细地解释了这些参数不仅会受到延迟时间和粒子数的影响,而且还会受到双阱棘齿势的不对称参数的影响。很有趣地发现通过改变系统的粒子数可以获得定向流的反转。期望能够在某些物理和生物系统中观测到这些结果,因为本模型采用的是更为实际的并且可以在实验上实现的双阱棘齿势垒。
本论文所得的结果可作为进一步深入研究上述三种典型布朗马达的理论基础,也可为相关纳米机器的优化设计提供理论参考。
Once we know the initial and final energies of the system and the path between them, the work output of the system can be determined by classical thermodynamics.In fact, there exists the quantity of fluctuations with k_BT dominate in the energies of the two states and the exchange heat between the system and the environment.In the Boltzmann statistic the quantity of fluctuations is usually negligible.However,the fluctuations aren't negligible as the systems are very small.The statistical thermodynamic issues appearing in microscopic systems are becoming the holdback which has to be faced with in the nano science.Molecular motors are just such microscopic systems which may serve as the basis for physicists to solve the problems.
The phenomenon of noise induced directed transport has attracted much interest in recent years.It has widespread applications in physics,chemistry and biology.One particular system which has been intensively studied both theoretically and experimentally is the motion of motor proteins like kinesins or dyneins.These motor proteins are responsible for the transport of cell organelles along the cytosceleton.They move randomly but directly on average and have been modeled by Brownian ratchets,and consequently,the concept of Brownian motors has been used to illuminate the directed, noise-induced transport.
Based on the above reasons,this thesis is focused on the discussion of several typical Brownian models,and then the directed transports of Brownian motors are investigated. The performance parameters of the thermally driven Brownian motors systems under the influence of the irreversibilities are searched by using nonequilibrium thermodynamics. The main research contents are organized as follows:
The brief introduction of the dynamics theory of the Brownian motion and thermodynamic ratchets and Brownian motors are given.The research histories, classification,construction of the model and theory frame of the molecular motors are presented in detail.The insufficiency of the Brownian ratchet model in existence is explored and analyzed.It is expected that this discussion can give some inspire for future research.
The transport of Brownian particles in two-state flashing ratchets composed of two asymmetric potentials with the same period is investigated.The analytic expression of a probability current is derived by using the power series expansion method and used to generate the curve characteristics of the current varying with other parameters.The effects of the asymmetric parameters and heights of two potentials and the transition rates between two states on the probability current are discussed in detail.It is found that the current is affected by not only the asymmetric parameters and heights of two potentials but also the transition rates between two states.It is also found that the heights of two potentials may change the magnitude as well as the direction of the current when the transition rates between two states are not the same.
Based on a general model of Brownian motors,the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically.It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle's motion.Only when the heat leak in the system is negligible,can the determinant of the Onsager matrix vanish.Moreover,the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail.The characteristic curves of the generalized efficiency varying with these parameters are presented.The maximum generalized efficiency and the corresponding optimum parameters are determined.The results obtained here are of general significance.They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with the zero heat leak,zero average drift velocity or linear response relation.
An equivalent cycle system is established based on the above discussion and the Onsager coefficients and efficiency at the maximum power output of the system are analytically calculated from nonequilibrium thermodynamics.It is found that the Onsager reciprocity relation holds and the Onsager coefficients are affected by the main irreversibilities existing in practical systems.Only when the heat leak and the kinetic energy change of the particle in the system are negligible,can the determinant of the Onsager matrix vanish.It is also found that in the frame of nonequilibrium thermodynamics,the power output and efficiency of an irreversible Brownian motor can be expressed to be the same form as those of an irreversible Carnot heat engine,so the results obtained here are of general significance.Moreover,these results can be used to analyze the performance characteristics of a class of thermally driven Brownian motors.
On the basis of the double-well potential which can be calculated theoretically and implemented experimentally,the influence of the time delay,number of particles and asymmetric parameter of the potential on the performance of a delayed feedback ratchet is investigated.The center-of-mass velocity of Brownian particles,the average effective diffusion coefficient and Pe number are calculated.It is expounded that the parameters are affected by not only the time delay and number of particles but also the asymmetric parameter of the double-well ratchet potential.It is very interesting to find that the current transport reversal may be obtained by varying the number of particles of the system.It is expected that the results obtained here may be observed in some physical and biological systems because the double-well ratchet potential is realizable experimentally.
The results obtained in the thesis may provide some theoretical bases for the deep investigation on the three classes of typical Brownian motors mentioned above as well as some references for the optimal design of some relevant nano machines.
引文
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