122 research outputs found

    Finite-parameter feedback control for stabilizing the complex Ginzburg-Landau equation

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    In this paper, we prove the exponential stabilization of solutions for complex Ginzburg-Landau equations using finite-parameter feedback control algorithms, which employ finitely many volume elements, Fourier modes or nodal observables (controllers). We also propose a feedback control for steering solutions of the Ginzburg-Landau equation to a desired solution of the non-controlled system. In this latter problem, the feedback controller also involves the measurement of the solution to the non-controlled system.Comment: 20 page

    A study of poststenotic shear layer instabilities

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    Performance of a linear robust control strategy on a nonlinear model of spatially developing flows

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    International audienceThis paper investigates the control of self-excited oscillations in spatially developing flow systems such as jets and wakes using H 8 control theory on a complex Ginzburg-Landau (CGL) model. The coefficients used in this one-dimensional equation, which serves as a simple model of the evolution of hydrodynamic instability waves, are those selected by Roussopoulos & Monkewitz (Physica D 1996, vol. 97, p. 264) to model the behaviour of the near-wake of a circular cylinder. Based on noisy measurements at a point sensor typically located inside the cylinder wake, the compensator uses a linear H 8 filter based on the CGL model to construct a state estimate. This estimate is then used to compute linear H 8 control feedback at a point actuator location, which is typically located upstream of the sensor. The goal of the control scheme is to stabilize the system by minimizing a weighted average of the 'system response' and the 'control effort' while rigorously bounding the response of the controlled linear system to external disturbances. The application of such modern control and estimation rules stabilizes the linear CGL system at Reynolds numbers far above the critical Reynolds number Rec ˜ 47 at which linear global instability appears in the uncontrolled system. In so doing, many unstable modes of the uncontrolled CGL system are linearly stabilized by the single actuator/sensor pair and the model-based feedback control strategy. Further, the linear performance of the closed-loop system, in terms of the relevant transfer function norms quantifying the linear response of the controlled system to external disturbances, is substantially improved beyond that possible with the simple proportional measurement feedback proposed in previous studies. Above Re ˜ 84, the control designs significantly outperform the corresponding control designs in terms of their ability to stabilize the CGL system in the presence of worst-case disturbances. The extension of these control and estimation rules to the nonlinear CGL system on its attractor (a simple limit cycle) stabilizes the full nonlinear system back to the stationary state at Reynolds numbers up to Re ˜ 97 using a single actuator/sensor pair, fixed-gain linear feedback and an extended Kalman filter incorporating the system nolinearity. © 2004 Cambridge University Press

    강상 페λ₯΄λ―Έ 기체의 상전이 λ™μ—­ν•™μ—μ„œ ν‚€λΈ”-μ£Όλ ‰ κΈ°μž‘μ˜ λ³΄νŽΈμ„±

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    ν•™μœ„λ…Όλ¬Έ(박사)--μ„œμšΈλŒ€ν•™κ΅ λŒ€ν•™μ› :μžμ—°κ³Όν•™λŒ€ν•™ λ¬Όλ¦¬Β·μ²œλ¬Έν•™λΆ€(물리학전곡),2020. 2. μ‹ μš©μΌ.Understanding strongly correlated quantum many-body systems remains as one of the most challenging problems of modern physics. Ultracold atomic Fermi gases with strong interactions have arisen as a versatile platform where a variety of many-body phenomena can be studied owing to their favorable characteristics such as the clean environment, dynamics control, and high tunability, including the interactions, potential, and defects. This thesis concerns with three aspects: the achievement of large (10^6 atoms per spin state) strongly interacting fermionic superfluids of 6Li and two experiments with it. Standard laser cooling techniques and the sympathetic cooling by bosonic Na-23 cooled Li-6 atoms down to degeneracy, and they were subsequently brought to the strongly interacting regime by exploiting the magnetic Feshbach resonance that enables a free and precise control over the interactions via the s-wave scattering length. By an evaporative cooling in the regime, we obtained ultracold atomic Fermi superfluids of Li-6 with strong interactions at T/TF=0.1. Especially, the microscopic nature of superfluidity is dramatically but smoothly transformed from Bose-Einstein condensate (BEC) of tightly bound diatomic molecules to Bardeen-Cooper-Schrieffer (BCS) superfluid of long-range Cooper pairs across the BEC-BCS crossover. The dissipation through the nucleation of quantum vortices in a strongly interacting fermionic superfluid is investigated by measuring the critical velocity for vortex shedding as a function of the sweeping length in the BEC-BCS crossover. The large critical velocity near unitarity demonstrated the robustness of fermionic superfluidity in the regime, and our simple dissipation model explains the relation between the critical velocity and the sweeping length. The comparison between the vortex shedding critical velocity for an in nite sweeping distance and the Landau critical velocity in the crossover suggests the involvement of the pair-breaking mechanism in the vortex-shedding dynamics. The Kibble-Zurek universality in a strongly interacting Fermi superfluid is observed. The thermal quench across the normal to superfluid phase transition of a strongly interacting Fermi gas in the BEC-BCS crossover spontaneously created an unprecedentedly large number of quantized vortices by the Kibble-Zurek mechanism, where their statistics revealed di erent aspects of the mechanism. The characteristic power-law relation between the density of the created vortices and the quench rate for slow quenches showed that the Kibble-Zurek mechanism holds true in the strongly correlated regime including unitarity, and the constant exponents across the BEC-BCS crossover verified that BEC and BCS superfluids belong to the same universality class. The density deviates from the scaling and saturates for rapid quenches because of the destructive interactions among the vortices, where the saturated values in the BEC-BEC crossover reveal the coherence length of a strongly interacting fermionic superfluid in the crossover.κ°•ν•˜κ²Œ μƒκ΄€λœ μ–‘μž 닀체계 μ‹œμŠ€ν…œμ„ μ΄ν•΄ν•˜λŠ” 것은 ν˜„λŒ€λ¬Όλ¦¬ν•™μ˜ λ‚œμ œ 쀑 ν•˜λ‚˜λ‘œ λ‚¨μ•„μžˆλ‹€. κ°•ν•˜κ²Œ μƒν˜Έμž‘μš©ν•˜λŠ” κ·Ήμ €μ˜¨ 페λ₯΄λ―Έ μ›μž κΈ°μ²΄λŠ” 자유둜운 μƒν˜Έμž‘μš©, νΌν…μ…œ 및 결점의 쑰절 λ“± 높은 μžμœ λ„μ™€ κΉ¨λ—ν•œ ν™˜κ²½, 동적 ν†΅μ œ λ“±μ˜ μœ λ¦¬ν•œ νŠΉμ„±λ“€ λ•Œλ¬Έμ— λ‹€μ–‘ν•œ 닀체계 ν˜„μƒμ„ 연ꡬ할 수 μžˆλŠ” λ‹€λͺ©μ  ν”Œλž«νΌμœΌλ‘œ 뢀상해왔닀. 이 ν•™μœ„λ…Όλ¬Έμ€ 3가지 츑면을 닀룬닀: ν•œ μŠ€ν•€ μƒνƒœλ‹Ή 10^6 개의 μ›μžλ‘œ κ΅¬μ„±λœ μ»€λ‹€λž€ κ°•ν•˜κ²Œ μƒν˜Έμž‘μš©ν•˜λŠ” Li-6 페λ₯΄λ―Έ 초유체의 κ΅¬ν˜„, 그리고 이 μ‹œλ£Œλ₯Ό μ‚¬μš©ν•œ 두 가지 μ‹€ν—˜. ν‘œμ€€μ μΈ λ ˆμ΄μ € 냉각과 보쑴 Na-23λ₯Ό μ‚¬μš©ν•œ 동쑰냉각이 Li-6 μ›μžλ“€μ„ 좕퇴(degeneracy)μƒνƒœκΉŒμ§€ λƒ‰κ°μ‹œμΌ°κ³ , s-파 좩돌 거리λ₯Ό 톡해 μƒν˜Έμž‘μš©μ„ 자유둭게 μ‘°μ ˆν•˜κ²Œ ν•΄μ£ΌλŠ” μžμ„± Feshbach 곡진을 μ΄μš©ν•΄ λƒ‰κ°λœ Li-6 μ›μžλ“€μ„ κ°•ν•˜κ²Œ μƒν˜Έμž‘μš©ν•˜λŠ” μ˜μ—­μœΌλ‘œ 데렀왔닀. 이 μ˜μ—­μ—μ„œ 좔가적인 μ¦λ°œλƒ‰κ°μ„ 톡해 μš°λ¦¬λŠ” T/TF=0.1 λ₯Ό κ°€μ§€λŠ” κ°•ν•˜κ²Œ μƒν˜Έμž‘μš©ν•˜λŠ” κ·Ήμ €μ˜¨ Li-6 μ›μž 페λ₯΄λ―Έ 초유체λ₯Ό μ–»μ—ˆλ‹€. 특히, μ΄ˆμœ μ²΄μ„±μ˜ λ―Έμ‹œμ μΈ 근원이 BEC-BCS κ΅μ°¨μ˜μ—­μ„ μ§€λ‚˜λ©΄μ„œ κ°•ν•˜κ²Œ κ²°ν•©λœ μ΄μ›μž λΆ„μžλ“€μ˜ 보즈-μ•„μΈμŠˆνƒ€μΈ 응집체(BEC)μ—μ„œ κΈ΄ 거리의 Cooper μŒλ“€μ˜ BCS 초유체둜 κ·Ήμ μ΄μ§€λ§Œ λΆ€λ“œλŸ½κ²Œ λ³€ν•΄κ°„λ‹€. BEC-BCS κ΅μ°¨μ˜μ—­μ—μ„œ μ–‘μž μ†Œμš©λŒμ΄κ°€ μƒμ„±λ˜λŠ” μž„κ³„ 속도λ₯Ό μž₯애물이 μ›€μ§μ΄λŠ” 거리의 ν•¨μˆ˜λ‘œ μΈ‘μ •ν•¨μœΌλ‘œμ¨ 강상 페λ₯΄λ―Έ μ΄ˆμœ μ²΄μ—μ„œ μ–‘μž μ†Œμš©λŒμ΄μ˜ 생성을 ν†΅ν•œ μ—λ„ˆμ§€ μ†Œμ‹€μ„ μ—°κ΅¬ν–ˆλ‹€. Unitarity κ·Όμ²˜μ—μ„œμ˜ 큰 μž„κ³„ μ†λ„λŠ” 이 μ˜μ—­μ—μ„œ 페λ₯΄λ―Έ μ΄ˆμœ μ²΄μ„±μ΄ 탄탄함을 μž…μ¦ν–ˆκ³ , 우리의 κ°„λ‹¨ν•œ μ—λ„ˆμ§€ μ†Œμ‹€ λͺ¨λΈμ€ μž„κ³„ 속도와 μž₯애물이 움직인 거리 κ°„μ˜ 관계λ₯Ό μ„€λͺ…ν•΄λƒˆλ‹€. λ¬΄ν•œν•œ 거리에 λŒ€ν•œ μ–‘μž μ†Œμš©λŒμ΄ 생성 μž„κ³„ 속도와 Landau μž„κ³„ 속도 κ°„μ˜ λΉ„κ΅λŠ” μ–‘μž μ†Œμš©λŒμ΄ 생성 동역학에 쌍-λΆ€μ„œμ§(pair-breaking) κΈ°μž‘μ΄ μ—°κ΄€λ˜μ–΄ μžˆμŒμ„ μ‹œμ‚¬ν•œλ‹€. 강상 페λ₯΄λ―Έ μ΄ˆμœ μ²΄μ—μ„œ ν‚€λΈ”-μ£Όλ ‰(Kibble-Zurek)κΈ°μž‘μ˜ λ³΄νŽΈμ„±μ΄ κ΄€μΈ‘λ˜μ—ˆλ‹€. BEC-BCS κ΅μ°¨μ˜μ—­μ—μ„œ 강상 페λ₯΄λ―Έ 기체의 보톡-초유체 μƒνƒœ 상전이λ₯Ό κ°€λ‘œμ§€λ₯΄λŠ” 열적 ν€œμΉ˜(quench)λŠ” ν‚€λΈ”-μ£Όλ ‰ κΈ°μž‘μ„ 톡해 μ „λ‘€ μ—†λŠ” λ§Žμ€ 수의 μ–‘μž μ†Œμš©λŒμ΄λ“€μ„ λ§Œλ“€μ–΄λƒˆκ³ , μ΄λ“€μ˜ ν†΅κ³„λŠ” κΈ°μž‘μ˜ μ—¬λŸ¬ 면듀을 λ“œλŸ¬λƒˆλ‹€. 느린 ν€œμΉ˜μ—μ„œ λ‚˜νƒ€λ‚œ μƒμ„±λœ μ†Œμš©λŒμ΄λ“€μ˜ 밀도와 ν€œμΉ˜ 속도 κ°„μ˜ 멱법칙(power-law) κ΄€κ³„λŠ” ν‚€λΈ”-μ£Όλ ‰ κΈ°μž‘μ΄ unitarityλ₯Ό ν¬ν•¨ν•œ κ°•ν•˜κ²Œ μƒκ΄€ν•˜λŠ” μ˜μ—­μ—μ„œλ„ μ μš©λ¨μ„ λ³΄μ˜€κ³ , BEC-BCS κ΅μ°¨μ˜μ—­μ—μ„œ μΌμ •ν•œ λ©±λ²•μΉ™μ˜ μ§€μˆ˜λ“€μ€ BEC와 BCS μ΄ˆμœ μ²΄κ°€ 같은 λ³΄νŽΈμ„± λΆ€λ₯˜μ— μ†ν•œλ‹€λŠ” 것을 확인해 μ£Όμ—ˆλ‹€. λΉ λ₯Έ ν€œμΉ˜μ—μ„œλŠ” μ–‘μž μ†Œμš©λŒμ΄ κ°„μ˜ 좩돌 μ†Œλ©Έλ‘œ 인해 μ†Œμš©λŒμ΄μ˜ 밀도가 λ²•μΉ™μ—μ„œ λ²—μ–΄λ‚˜ ν¬ν™”λ˜κ³ , BEC-BCS κ΅μ°¨μ˜μ—­μ—μ„œ 이 ν¬ν™”λœ 값듀은 κ΅μ°¨μ˜μ—­μ—μ„œ 강상 페λ₯΄λ―Έ 초유체의 일관성 길이(coherence length)λ₯Ό λ“œλŸ¬λ‚Έλ‹€.Chapter 1 Introduction 1 1.1 Superfluidity of two types - BEC vs. BCS 2 1.1.1 Bose-Einstein condensate 2 1.1.2 Bardeen-Cooper-Schrieffer superfluid 3 1.1.3 BEC-BCS crossover 6 1.2 Ultracold atomic gases - a model system for bosonic and fermionic superfluids 9 1.3 My five and half years at Quantum Gas Laboratory 16 1.4 Outline 17 Chapter 2 The apparatus upgrades 18 2.1 Oven upgrade - from 23Na to 23Na-6Li 19 2.2 Laser system 24 2.2.1 6Li laser system 24 2.2.2 23Na laser system 40 2.3 Feshbach coil 42 2.4 Deeper optical dipole trap 49 2.5 Manipulating the hyperne states of 6Li 52 Chapter 3 Producing a large 106 strongly interacting Fermi superfluid of 6Li 57 3.1 Sympathetic cooling of 6Li by 23Na 58 3.2 Interacting Fermi mixture and its condensation 63 3.3 Time-of-flight imaging of 6Li condensate 67 Chapter 4 Critical vortex shedding in a strongly interacting fermionic superfluid 70 4.1 Quantum vortices and the dissipation of a superfluid 71 4.2 Speed of sound in the BEC-BCS crossover 75 4.2.1 Experimental measurement 76 4.2.2 Theoretical estimate 77 4.3 Critical vortex shedding across the BEC-BCS crossover 82 4.3.1 Measuring the critical velocity for vortex shedding 82 4.3.2 Characterization of the optical obstacle 86 4.3.3 Adiabaticity of the obstacle beam switch-off 87 4.4 Results: critical velocity for vortex shedding 89 4.5 Modeling the vortex shedding mechanism: involvement of pairbreaking? 93 4.6 Conclusion 97 Chapter 5 Kibble-Zurek universality in a strongly interacting Fermi superfluid 99 5.1 Kibble-Zurek mechanism and universality 99 5.1.1 The Kibble-Zurek mechanism .99 5.1.2 Universality of phase transition . 102 5.1.3 Kibble-Zurek universality and a strongly interacting Fermi gases 104 5.2 Thermal quench of a strongly interacting Fermi gas across the normal to superfluid phase transition and the creation of quantum vortices 105 5.3 Kibble-Zurek universality in the BEC-BCS crossover 116 5.4 Defect density saturation and the coherence length of a strongly interacting Fermi superfluid in the BEC-BCS crossover 119 5.5 Conclusion 122 Chapter 6 Conclusion and outlook 123 초둝 125 κ°μ‚¬μ˜ κΈ€ 127Docto

    Active feedback control of a wake flow via forced oscillations based on a reduced model

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    As it is well known, the flow past a cylinder consists of a symmetric recirculation bubble of vortices at small Reynolds numbers. As Reynolds number increases, the bubble becomes unstable and develops into a Karman vortex street of alternating vortices. This instability is responsible for the occurrence of large amplitude oscillations in the lift and an increase in the mean drag. It was previously shown by numerical simulation that the mechanism driving the bubble instability is well mimicked by Foppl\u27s four dimensional potential flow model where the bubble is represented by a saddle point. In this work, we design two active feedback control algorithms for the model based on small perturbations applied to the cylinder in order to control the flow slightly perturbed away from the fixed point. We use the domain perturbation method and asymptotic expansions to derive control algorithms analytically. In the first algorithm, we displace the cylinder by a small vertical distance such that the lift remains zero at all times. We also show by direct numerical simulation of the flow (based on the full N-S equations) that our feedback control system is capable of preventing vortex shedding from occurring in the impulsively started viscous flow at Reynolds number Re = 100. In the second algorithm, we deform the cylinder uniformly so that the drag remains the drag of the steady recirculation bubble
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