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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 闕志鴻 | |
| dc.contributor.author | Kuan-Wei Huang | en |
| dc.contributor.author | 黃冠維 | zh_TW |
| dc.date.accessioned | 2021-06-15T12:34:26Z | - |
| dc.date.available | 2016-08-24 | |
| dc.date.copyright | 2016-08-24 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2016-08-01 | |
| dc.identifier.citation | T. Chiueh. Dynamical quantum chaos as fluid turbulence. pre, 57:4150–4154, April 1998. doi: 10.1103/PhysRevE.57.4150.
W. Hu, R. Barkana, and A. Gruzinov. Fuzzy Cold Dark Matter: The Wave Properties of Ultralight Particles. Physical Review Letters, 85:1158–1161, August 2000. doi: 10.1103/PhysRevLett.85.1158. E. Madelung. Quantentheorie in hydrodynamischer Form. Zeitschrift fur Physik, 40: 322–326, March 1927. doi: 10.1007/BF01400372. H.-Y. Schive, Y.-C. Tsai, and T. Chiueh. GAMER: A Graphic Processing Unit Accelerated Adaptive-Mesh-Refinement Code for Astrophysics. apjs, 186:457–484, February 2010. doi: 10.1088/0067-0049/186/2/457. H.-Y. Schive, T. Chiueh, and T. Broadhurst. Cosmic structure as the quantum interference of a coherent dark wave. Nature Physics, 10:496–499, July 2014. doi: 10.1038/nphys2996. T.-P. Woo and T. Chiueh. High-Resolution Simulation on Structure Formation with Extremely Light Bosonic Dark Matter. apj, 697:850–861, May 2009. doi: 10.1088/0004-637X/697/1/850. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/50267 | - |
| dc.description.abstract | ψ 暗物質的動力學可用薛丁格–泊松 (Schrödinger-Poisson) 方程式加
以描述。我們使用 Lax–Wendroff 方法在流體形式下做數值計算。我們 以一些已知的解析解（如：平面波、微擾波、高斯波包、駐波、與漩 渦對）測試程式的準確度。演算法中產生的一些數值問題可以藉由數 值逸散、數學形式的改變、與通量項正規化加以改進。 | zh_TW |
| dc.description.abstract | The dynamics of the quantum wave dark matter (ψDM) can be described by the Schrödinger-Poisson equation. We numerically solve it in hydrodynamic form by the Lax–Wendroff method. The accuracy of the program is tested with several analytic solutions, e.g., plane wave, perturbation wave, Gaussian wave packet, standing wave, vortex pairs. We encounter some numerical problems so that we improve the algorithm by adding numerical diffusion, slightly changing the mathematical form, and regularizing the flux term. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T12:34:26Z (GMT). No. of bitstreams: 1 ntu-105-R03222078-1.pdf: 10552779 bytes, checksum: fab262ae7b3e132c9ea9cf556422a0b5 (MD5) Previous issue date: 2016 | en |
| dc.description.tableofcontents | 誌謝 v
摘要 vii Abstract ix 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Schrödinger-Poisson Equation . . . . . . . . . . . . . . . . . . . . . 2 1.3 Quantum Theory in Hydrodynamic Form . . . . . . . . . . . . . . . . . 2 1.3.1 Motive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3.2 The Madelung Transformation . . . . . . . . . . . . . . . . . . . 3 2 Numerical Scheme 5 2.1 Outline of the Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Discretization of the Main Equation . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Recall the Target Equations . . . . . . . . . . . . . . . . . . . . 7 2.2.2 Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Numerical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3.1 The Lax–Wendroff Method . . . . . . . . . . . . . . . . . . . . 8 2.3.2 Primary Array . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3.3 Flux for Half Step . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.4 Half Step Array and Evolution . . . . . . . . . . . . . . . . . . . 11 2.3.5 Flux for One Step . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.6 Full One Step Evolution . . . . . . . . . . . . . . . . . . . . . . 12 2.3.7 CFL Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3 Simulations and Results 15 3.1 Accuracy Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Traveling Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2.1 1D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2.2 3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 Gaussian Wave Packet . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.4 Perturbation Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.4.1 1D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.4.2 3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.5 Standing Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.6 Vortex Pair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4 Discussion 47 4.1 Analysis of the Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2 The Choice Between ∇sqrt(rho)∇sqrt(rho) and ∇(rho)∇(rho)/(4*rho). . . . . . . . . . . . . . . . 50 4.3 Numerical Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.4 The Vortex Pair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.4.1 Recall the Vortex Pair . . . . . . . . . . . . . . . . . . . . . . . 52 4.4.2 Regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.4.3 Smoothing the Flux . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.4.4 Results After Correction . . . . . . . . . . . . . . . . . . . . . . 56 5 Summary 59 6 Appendix 61 6.1 Pseudocode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.1.1 Primary Array for Density and Momentum . . . . . . . . . . . . 61 6.1.2 Flux for Half Step . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.1.3 Half Step Array and Evolution . . . . . . . . . . . . . . . . . . . 62 6.1.4 Flux for One Step . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6.1.5 Full One Step Evolution . . . . . . . . . . . . . . . . . . . . . . 64 Bibliography 65 | |
| dc.language.iso | en | |
| dc.subject | 暗物質 | zh_TW |
| dc.subject | 宇宙學 | zh_TW |
| dc.subject | 數值模擬 | zh_TW |
| dc.subject | 宇宙結構形成 | zh_TW |
| dc.subject | simulation | en |
| dc.subject | cosmic structure formation | en |
| dc.subject | cosmology | en |
| dc.subject | dark matter | en |
| dc.title | 使用數值方法解流體形式的薛丁格方程式 | zh_TW |
| dc.title | Numerically solving the Schrödinger equation in hydrodynamic form | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳宜良,薛克民 | |
| dc.subject.keyword | 數值模擬,宇宙學,暗物質,宇宙結構形成, | zh_TW |
| dc.subject.keyword | simulation,cosmology,dark matter,cosmic structure formation, | en |
| dc.relation.page | 65 | |
| dc.identifier.doi | 10.6342/NTU201601646 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2016-08-02 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理學研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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