Study of the connection between an ohmic damping system and a dispersive dissipative system.

• Other Authors: Kong, Wai.
• Format: Others
• Language: English; Chinese
• Published: 2006
• Subjects: System theory > Mathematical models
• Online Access: http://library.cuhk.edu.hk/record=b5896499; http://repository.lib.cuhk.edu.hk/en/item/cuhk-325775

Kong Wai = 歐姆阻尼系統與頻散耗散系統之連繫的研究 / 江偉. === Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. === Includes bibliographical references (leaves 72-73). === Text in English; abstracts in English and Chinese. === Kong Wai = Ou mu zu ni xi tong yu pin san hao san xi tong zhi lian xi de yan jiu / Jiang Wei. === Chapter 1 --- Introduction --- p.1 === Chapter 2 --- Review of ohmic systems and dispersive systems --- p.4 === Chapter 2.1 --- Damped ohmic systems --- p.4 === Chapter 2.1.1 --- Equations of motion --- p.4 === Chapter 2.1.2 --- Normal modes --- p.7 === Chapter 2.1.3 --- Bilinear mapping and general solutions --- p.8 === Chapter 2.2 --- Dissipative dispersive system --- p.10 === Chapter 2.2.1 --- Matrix representation --- p.13 === Chapter 2.2.2 --- Bilinear mapping and metric tensor --- p.14 === Chapter 2.2.3 --- Generalization to M relaxation frequencies --- p.16 === Chapter 3 --- Relation between dispersive and ohmic systems --- p.17 === Chapter 4 --- Odd dimension problem --- p.22 === Chapter 4.1 --- The ohmic system --- p.22 === Chapter 4.1.1 --- Fast mode --- p.22 === Chapter 4.1.2 --- e = 0 --- p.24 === Chapter 4.1.3 --- e→ 0 --- p.25 === Chapter 4.2 --- The dispersive system --- p.27 === Chapter 4.3 --- Connections in odd-dimensional case --- p.30 === Chapter 4.3.1 --- "Odd-dimensional cases, e = 0, ₁ت2= ´ؤi∞" --- p.30 === Chapter 4.3.2 --- "Limiting cases, e →0" --- p.31 === Chapter 4.4 --- Eigenvalues --- p.32 === Chapter 4.5 --- Conclusion --- p.34 === Chapter 5 --- Fluctuation-dissipation theorem --- p.35 === Chapter 5.1 --- FDT for a single damped oscillator --- p.35 === Chapter 5.2 --- FDT for two coupled ohmic oscillators --- p.38 === Chapter 5.3 --- Two couple damped oscillators in different baths --- p.40 === Chapter 5.3.1 --- Case I: Symmetric and T1 = T2 --- p.41 === Chapter 5.3.2 --- Case II: Symmetric and η2 = 0 --- p.42 === Chapter 5.3.3 --- Case III: Asymmetric and T1 = T2 --- p.44 === Chapter 5.3.4 --- Case IV: Asymmetric and η2 = 0 --- p.46 === Chapter 5.3.5 --- Discussion --- p.47 === Chapter 6 --- Pseudo-Boltzman distribution --- p.48 === Chapter 6.1 --- Fokker´ؤPlanck equation --- p.48 === Chapter 6.1.1 --- Single damped oscillator --- p.48 === Chapter 6.1.2 --- Two coupled damped oscillators --- p.50 === Chapter 6.2 --- Path integral method --- p.55 === Chapter 6.2.1 --- Single damped oscillator --- p.55 === Chapter 6.2.2 --- N coupled oscillators --- p.56 === Chapter 7 --- Energy stored in a dispersive system --- p.58 === Chapter 7.1 --- Correlations --- p.59 === Chapter 7.2 --- One-one mapping for N = 2 --- p.61 === Chapter 7.3 --- One-one mapping for N = 3 --- p.64 === Chapter 8 --- Conclusion --- p.70 === Bibliography --- p.72 === Chapter A --- Equipartition theorem --- p.74 === Chapter B --- General fluctuation-dissipation theorem --- p.76 === Chapter C --- Case I: Symmetric and T1 = T2 --- p.80 === Chapter D --- Fokker´ؤPlanck equation - Single damped oscillator --- p.82 === Chapter E --- Fokker-Planck equation - Two coupled damped oscillators --- p.86 === Chapter F --- Path integral method - Single damped oscillator --- p.88 === Chapter G --- Path integral method - N coupled oscillators --- p.90 === Chapter H --- Correlation of χ1χ1 --- p.94 === Chapter I --- Conditions for a dissipative dispersive system --- p.96 === Chapter J --- Solution of an ohmic system --- p.98