<p> This thesis establishes the general Principle of Complementary Potential Energy for the finite deformations of an elastic continuum, in which the Lagrange stress tensor is employed as the stress variable. It is demonstrated that constitutive relations, formulated in terms of the Lagrange stress tensor and the deformation gradient, will admit inversion. Consequently, the present theorem and the theorem proposed by LEVINSON are established as valid principles. The complementary strain energy density of the present theorem, however, is shown to be Independent of rigid displacements, in contrast to that of the LEVINSON formulation. The general Principle is reduced to the form appropriate to finite elastic systems, and it is established that the present theorem reduces to, and therefore contains as a special case, the LIBOVE Theorem.</p> / Thesis / Doctor of Philosophy (PhD)

The dynamics of colloidal particles driven over optical potential energy landscapes is studied. Experiments are conducted using colloids driven by solvent flow or piezo-stage, optical tweezers, magnetic fields, and video-microscopy. Firstly, the properties of optical traps and potential energy landscapes are determined using driven colloidal particles and clusters. The trap stiffness and potential depth of single Gaussian traps are measured directly. It is shown that the nature of optical potential energy landscapes may be fully engineered and predicted using a sum of single Gaussian potentials. Next, the motion of colloidal particles driven by a constant force over a periodic optical potential energy landscape is considered. The average particle velocity is found as a function of the driving velocity, and the wavelength of the optical potential energy landscape, which is found to be sinusoidal at small trap spacings. The critical driving velocity required for a particle to move across the landscape is determined as a function of the wavelength. Brownian motion is found to have a significant effect on the critical driving velocity, but a negligible effect at high driving velocity. Subsequently, the dynamic mode locking caused by adding a modulation to the driving force is studied. This synchronisation manifests as a `Devil's staircase' in the average particle velocity as a function of driving velocity. The amplitude and frequency dependence of the mode locked steps are studied. Furthermore, particle trajectories are examined, and phase portraits show locked (unlocked) states as closed (open) loops in phase space. A state diagram of mode locked steps is constructed. Finally, driven systems of magnetically interacting colloidal particles are examined in potential energy landscapes. The critical driving velocity of a chain of coupled particles driven by a constant force is found to depend strongly on the chain length and the magnetic field. Secondly, a mobile density wave (kink) in an optically pinned chain of coupled particles is exposed to a constant and modulated drive. The kink is found to behave as a quasi-particle, exhibiting analogous dynamic mode locking behaviour to the single particle case. Finally, the mode locking of a finite mobile chain is considered, and found to be affected by the chain flexibility, which is a function of the magnetic field.

No description available.

Lau Kai-Chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references. / Abstracts in English and Chinese. / Abstract / Acknowledgements / Table of Contents / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Gaussian-2 Method / Chapter 1.2 --- The G2 Method with Reduced M φller-Plesset Order and Basis Set / Chapter 1.3 --- The Gaussian-3 Method / Chapter 1.4 --- Our Modified G2 Methods / Chapter 1.5 --- Calculation of Thermodynamical Data / Chapter 1.6 --- Scope of the Thesis / Chapter 1.7 --- Remark on the Location of Transition Structures / Chapter 1.8 --- References / Chapter Chapter 2 --- A Gaussian-2 Study of the [C2H5O-] Potential Energy Surface and the Fragmentation Pathways of the Ethoxide Anion --- p.7 / Chapter 2.1 --- Introduction / Chapter 2.2 --- Theoretical Methods / Chapter 2.3 --- Results and Discussion / Chapter 2.3.1 --- Stable Isomers and TSs for the [C2H50-] Anions / Chapter 2.3.2 --- Fragmentation Pathways of the Ethoxide Anion (1-) / Chapter 2.4 --- Conclusions / Chapter 2.5 --- Publication Note / Chapter 2.6 --- References / Chapter Chapter 3 --- A Gaussian-2 Study of Isomeric C2H2N and C2H2N+ --- p.20 / Chapter 3.1 --- Introduction / Chapter 3.2 --- Theoretical Methods / Chapter 3.3 --- Results and Discussion / Chapter 3.3.1 --- The C2H2N and C2H2N+ Isomers / Chapter 3.3.2 --- The Cyanomethyl Radical (1) and Cation (1+) / Chapter 3.3.3 --- The Isocyanomethyl Radical (2) and Cation (2+) / Chapter 3.3.4 --- The lH-Azirinyl Radical (5) and Cation (5+) / Chapter 3.3.5 --- Other C2H2N and C2H2N+ Isomers / Chapter 3.3.6 --- The Unidentified C2H2N Isomer Formed in N + CH=CH2 / Chapter 3.4 --- Conclusions / Chapter 3.5 --- Publication Note / Chapter 3.6 --- References / Chapter Chapter 4 --- A Gaussian-2 Study of the Photoionization and Dissociative Photoionization Channels of Ethylene Oxide --- p.35 / Chapter 4.1 --- Introduction / Chapter 4.2 --- Theoretical Methods / Chapter 4.3 --- Results and Discussion / Chapter 4.3.1 --- Bond Cleavage Reactions / Chapter 4.3.2 --- Dissociation Channels Involving Transition Structure(s) / Chapter 4.4 --- Conclusions / Chapter 4.5 --- Publication Note / Chapter 4.6 --- References / Chapter Chapter 5 --- A Gaussian-2 Study of the Photoionization and Dissociative Photoionization Channels of Propylene Oxide --- p.47 / Chapter 5.1 --- Introduction / Chapter 5.2 --- Theoretical Methods / Chapter 5.3 --- Results and Discussion / Chapter 5.3.1 --- Bond Cleavage Reactions / Chapter 5.3.2 --- Dissociation Channels Involving Transition Structure(s) / Chapter 5.4 --- Conclusions / Chapter 5.5 --- Publication Note / Chapter 5.6 --- References / Chapter Chapter 6 --- A Gaussian-3 Study of the Thermochemistry of Chlorofluoromethanes (CFnCl4-n) and Their Cations (CFnCl4_n+)， n =0-4 --- p.61 / Chapter 6.1 --- Introduction / Chapter 6.2 --- Theoretical Methods / Chapter 6.3 --- Results and Discussions / Chapter 6.3.1 --- Heats of Formation of Chlorofluoromethanes and Their Cations / Chapter 6.3.2 --- Ionization Energies of Chlorofluoromethanes / Chapter 6.3.3 --- Proton Affinities of Chlorofluoromethanes / Chapter 6.4 --- Conclusions / Chapter 6.5 --- Publication Note / Chapter 6.6 --- References / Chapter Chapter 7 --- "A Gaussian-2 and Gaussian-3 Study of the Energetics and Structures of Cl2On and Cl2On+, n = 1，4, 6，and7" --- p.69 / Chapter 7.1 --- Introduction / Chapter 7.2 --- Theoretical Methods / Chapter 7.3 --- Results and Discussion / Chapter 7.3.1 --- Cl20 and Cl20+ / Chapter 7.3.2 --- Cl204 and Cl204+ / Chapter 7.3.3 --- Cl206 and Cl206+ / Chapter 7.3.4 --- Cl207 and Cl207+ / Chapter 7.4 --- Conclusions / Chapter 7.5 --- Publication Note / Chapter 7.6 --- References / Chapter Chapter 8 --- Conclusions --- p.81 / Chapter Appendix A --- The Gaussian-n (n = 1 - 3) Theoretical Models --- p.82 / Chapter A.1 --- The G1 and G2 theories / Chapter A.2 --- The G2(MP2) theory / Chapter A.3 --- "The G2(MP2,SVP) theory" / Chapter A.4 --- The G3 theory / Chapter Appendix B --- "Calculation of Enthalpy at 298 K, H298" --- p.86

Orientador: Laurence Duarte Colvara / Banca: Percival Bueno de Araujo / Banca: George Lauro Ribeiro de Brito / Resumo: Este trabalho analisa a influência do FACTS TCSC na função energia do sistema, mais especificamente na energia potencial. Também é abordada a influência da compensação dinâmica do TCSC na trajetória do sistema frente a uma grande perturbação, visando a melhoria da estabilidade transitória. A energia potencial é avaliada no espaço das posições angulares dos rotores das máquinas em torno de um ponto de equilíbrio estável levando em conta os efeitos da ação do TCSC. A trajetória do sistema é sobrepostas às curvas equipotenciais, e com isso é possível a avaliar os efeitos da compensação dinâmica do dispositivo nas mesmas. Através das simulações de dois sistemas testes, um sistema considerado de pequeno porte (Sistema de Quatro Máquinas) e outro de maior porte (New England) quando expostos a uma grande perturbação avalia-se a estabilidade de primeira oscilação com o intuito de determinar o tempo crítico de eliminação de uma falta no sistema. Posteriormente verifica-se a possibilidade de deslocar a trajetória do sistema com o propósito de que ela percorra um caminho mais íngreme na superfície da energia potencial, ou seja, idealmente que ela tenha orientação coincidente do gradiente da energia potencial, e analisa-se qual a influência da compensação série na energia potencial, com o intuito de obter tal direcionamento / Abstract: This dissertation examines the influence of TCSC FACTS on the power system energy function, specifically on the potential energy. The influence of dynamic compensation of the TCSC in the trajectory of the system after a major disruption in order to improve transient stability is also approached. The potential energy is evaluated in the space of machines rotor angular positions around stable equilibrium point taking into account effects of the TCSC action and the trajectory of the system is superimposed with equipotential curves and so it is possible to evaluate the effects of the dynamic compensation. Simulations are performed with two test systems, one being a (four machines system) and the other being the well-know New England system submitted to great disturbances. The stability of the first oscillation in order to determine the critical fault clearing time, is assessed. It is possible to change the system trajectory in order to traverse a more steeply path, i.e. ideally matching orientation with the potential energy gradient. The influence of series compensation in potential energy is taken into account, in order to conduct the system trajectory to the potential energy gradient orientation / Mestre

Gravity waves in the atmosphere are the waves with gravity and buoyancy force as the restoring forces. Gravity waves will significantly impact the Mesosphere Lower / Thermosphere (MLT), and the breaking of gravity waves is the key factor to cause the cool summer and warm winter in the Mesopause region. Therefore, it is important for us to investigate gravity waves. In this dissertation, we mainly use USU Na lidar data to explore gravity waves in the MLT. The exploration is made up of two projects. One is the investigation of gravity wave breaking and the associated dynamic instability by USU Na Lidar and Advanced Mesosphere Temperature Mapper (AMTM). Another is the calculation of gravity wave temperature perturbations and potential energy density by least-squares fitting based on the data from the full-diurnal cycle observation of Na lidar. The sporadic sodium layer is the sharp increase of Na density in a small vertical range (several kilometers) above the Na main layer in the MLT. The formation of the sporadic sodium layer above 100 km remains unknown until now. Here we will investigate the mechanism of the generation of sporadic sodium layer using numeric modeling, including the effect of tide and gravity wave on the variation of Na density.

The vibrational potential energy surfaces in electronic ground and excited states of several ring molecules were investigated using several different spectroscopic methods, including far-infrared (IR), Raman, ultraviolet (UV) absorption, fluorescence excitation (FES), and single vibronic level fluorescence (SVLF) spectroscopies. Based on new information obtained from SVLF and millimeter wave spectra, the far-IR spectra of coumaran were reassigned and the one-dimensional ring-puckering potential energy functions for several vibrational states in the S0 ground state were determined. The barrier was found to be 154 cm-1 and the puckering angles to be ± 25°, in good agreement with the millimeter wave barrier of 152 cm-1 and puckering angles of ± 23°. Moreover, the UV absorption and FES spectra of coumaran allowed the one-dimensional ring-puckering potential energy functions in the S1 excited state to be determined. The puckering barrier is 34 cm-1 for the excited state and the puckering angles are ± 14°. Several calculations with different basis sets have been carried out to better understand the unusual vibrational frequencies of cyclopropenone. It was shown that there is strong interaction between the C=O and symmetric C-C stretching vibrations. These results differ quantitatively from a previous normal coordinate calculation and interpretation. The vapor-phase Raman spectrum of 3,7-dioxabicyclo[3.3.0]oct-1,5-ene was analyzed and compared to the predicted spectrum from DFT calculations. The spectrum further shows it has D2h symmetry, in which the skeletons of both rings are planar. The infrared and Raman spectra of vapor-phase and liquid-phase 1,4-benzodioxan and 1,2,3,4-tetrahydronaphthalene were collected and the complete vibrational assignments for both molecules were made. Theoretical calculations predicted the barriers to planarity to be 4809 cm-1 for 1,2,3,4-tetrahydonaphthalene and 4095 cm-1 for 1,4-benzodioxan. The UV absorption, FES, and SVLF spectra of both molecules were recorded and assigned. Both one and two-dimensional potential energy functions of 1,4-benzodioxan for the ring-twisting and ring-bending vibrations were carried out for the S0 and S1(π,π*) states, and these were consistent with the high barriers calculated for both states. The low-frequency spectra of 1,2,3,4-tetrahydronaphthalene in both S0 and S1(π,π*) states were also analyzed.

The virial equation of state p = ρRT[ 1 + B(T) ρ + C(T) ρ2 + · · ·] for high pressure and density gases is used for computing chemical equilibrium properties and mixture compositions of strong shock and detonation waves. The second and third temperature-dependent virial coefficients B(T) and C(T) are included in tabular form in computer codes, and they are evaluated by polynomial interpolation. A very accurate numerical integration method is presented for computing B(T) and its derivatives for tables, and a sophisticated method is introduced for interpolating B(T) more accurately and efficiently than previously possible. Tabulated B(T) values are non-uniformly distributed using an adaptive grid, to minimize the size and storage of the tables and to control the maximum relative error of interpolated values. The methods introduced for evaluating B(T) apply equally well to the intermolecular potentials of Lennard-Jones in 1924, Buckingham and Corner in 1947, and Rice and Hirschfelder in 1954.

The virial equation of state p = ρRT[ 1 + B(T) ρ + C(T) ρ2 + · · ·] for high pressure and density gases is used for computing chemical equilibrium properties and mixture compositions of strong shock and detonation waves. The second and third temperature-dependent virial coefficients B(T) and C(T) are included in tabular form in computer codes, and they are evaluated by polynomial interpolation. A very accurate numerical integration method is presented for computing B(T) and its derivatives for tables, and a sophisticated method is introduced for interpolating B(T) more accurately and efficiently than previously possible. Tabulated B(T) values are non-uniformly distributed using an adaptive grid, to minimize the size and storage of the tables and to control the maximum relative error of interpolated values. The methods introduced for evaluating B(T) apply equally well to the intermolecular potentials of Lennard-Jones in 1924, Buckingham and Corner in 1947, and Rice and Hirschfelder in 1954.

The Morse/Long Range (MLR) potential has become one of the most reliable and highly used potential energy functions for diatomic molecules. It includes the theoretical long range behaviour that diatomic molecules are known to exhibit as they approach the dissociation limit. Heavy alkali metals with adjacent electronic states often exhibit strong coupling between the spin and orbital angular momentum. The ground state X¹Σg⁺ and the lowest lying triplet state aᶟΣᵤ⁺ of Cs₂ exhibit such coupling effects and as a result, modeling the highest vibrational states of these states is a non-trivial problem. Utilizing scattering length values obtained from published analysis of 60 Feshbach resonances, the correct form of the potential energy function was determined. Moreover, the scattering length values were used to determine the correct leading dispersion coefficient that describes the true form of the long-range potential energy functions. All previous attempts to determine global potential energy functions for these states have considered only the optical spectroscopic data. This is the first ever effort attempting to use scattering lengths determined from cold atom collision experiments in a combined analysis with conventional spectroscopic data.