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

published_or_final_version / abstract / Mechanical Engineering / Doctoral / Doctor of Philosophy