等溫過程中平衡捷徑之實驗研究

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沙菈(Sarah Rizky Wulaningrum) 查詢紙本館藏

畢業系所

生物物理研究所

論文名稱

等溫過程中平衡捷徑之實驗研究
(Experimental study of shortcut to equilibration in isothermal process)

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摘要(中)

弛豫現象是自然系統或儀器中的一種內部性質，也就是在系統受到控制變因突然的刺激時，回復平衡的能力。根據傳統的熱力學，等溫轉換過程需要透過準靜態的調整規程是公認的事實。因此，
兩個平衡態之間的轉換時間幾乎需要無限長的時間才能完成。為了加速這個轉換過程，我們採用了由Li所提出的等溫過程中的平衡捷徑。優化這樣的轉換過程能夠提升布朗熱機的效率和功率。在此論文中，我們以實驗論證了在過阻尼系統中有限速率的等溫轉換過程。首先，我們用模擬建立了布朗運動模型，透過Langevin方程式的數值解來獲得各項優化轉換過程的數值。接著，我們用正弦輸出的光鉗使布朗粒子在兩個平衡態之間移動。透過以上的模擬數值和實驗操作，我們證實了此項調整規程能夠提供等溫過程中平衡的捷徑，使得光鉗的弛豫時間大大縮短。

摘要(英)

Relaxation is one of the intrinsic properties of any device and natural system, which is an ability to return to equilibrium after a sudden change of a control parameter. In conventional thermodynamics, it is widely acknowledged that the realization of an isothermal transition process requires aquasistatic controlling protocol. It takes an infinity long time to realize the transition between two equilibrium states. To accelerate
the transition, we use the shortcuts to isothermality protocol proposed by Li et al. Optimization of the transition process may increase efficiency and the power output of the Brownian heat engine. In this thesis, we experimentally demonstrate a finite-rate isothermal transition in the overdamped situation. First, we numerically simulate the Langevin equation for a Brownian dynamics to determine the optimized experimental control parameters. Next, we perform an experiment that a Brownian particle is shifted from one state to another state by the sinusoidally moving optical trap. We confirm that the shortcuts to isothermality protocol allow the isothermal transition between two equilibrium states even for the shorter time than the intrinsic relaxation
time of the optical trap.

關鍵字(中)

★ 弛豫
★ 平衡
★ 等溫
★ 光阱

關鍵字(英)

★ relaxation
★ equilibrium
★ isothermal
★ optical trap

論文目次

Abstract i
Acknowledgements iii
Contents v
List of Figures vii
List of Symbols ix
1 Introduction 1
2 Theoretical Background 5
2.1 Macroscopic and microscopic view...................... 5
2.1.1 Langevin equation........................... 6
2.1.2 Particle in a harmonic potential.................... 7
2.2 Stochastic thermodynamics.......................... 9
2.3 Shortcuts to Isothermality........................... 9
2.3.1 Definition of shortcuts to isothermality............... 9
2.3.2 Example of shortcut to isothermality................. 10
3 Simulation and Experimental Method 13
3.1 Simulation of shortcut to equilibration in isothermal process....... 13
3.2 Experimental method.............................. 14
3.2.1 Introduction of optical trap...................... 14
3.2.2 Experimental setup........................... 16
3.2.3 Experimental procedure........................ 17
4 Result and Discussion19
4.1 Calibration.................................... 19
4.1.1 CCD Image............................... 19
4.1.2 AOD calibration............................ 20
4.1.3 PSD calibration............................. 21
4.1.4 Stiffness Calibration.......................... 22
4.2 Test of the driving protocol on the system.................. 24
4.3 Shortcuts to Isothermality........................... 26
4.4 Nonequilibrium work relation......................... 29
5 Conclusions 35
Bibliography 37
Appendix 38
A Calculation 39
A.1 Free-energy difference from Hamiltonian equation............. 39
A.2 Work....................................... 40
B Python Code41
B.1 The python code for snapshot to create histogram............. 41
B.2 The Python code to calculate center position of the potential....... 42
B.3 The Python code of trajectory, free energy difference, and work..... 44
C Data of Calibration 47
C.1 CCD Camera Calibration...........................

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指導教授

田溶根(Yonggun Jun)

審核日期

2018-7-31

推文