Coherent Phonons in Carbon Nanotubes and Graphene

We review recent studies of coherent phonons (CPs) corresponding to the radial breathing mode (RBM) and G-mode in single-wall carbon nanotubes (SWCNTs) and graphene. Because of the bandgap-diameter relationship, RBM-CPs cause bandgap oscillations in SWCNTs, modulating interband transitions at terahertz frequencies. Interband resonances enhance CP signals, allowing for chirality determination. Using pulse shaping, one can selectively excite speci!c-chirality SWCNTs within an ensemble. G-mode CPs exhibit temperature-dependent dephasing via interaction with RBM phonons. Our microscopic theory derives a driven oscillator equation with a density-dependent driving term, which correctly predicts CP trends within and between (2n+m) families. We also find that the diameter can initially increase or decrease. Finally, we theoretically study the radial breathing like mode in graphene nanoribbons. For excitation near the absorption edge, the driving term is much larger for zigzag nanoribbons. We also explain how the armchair nanoribbon width changes in response to laser excitation.Comment: 48 pages, 41 figure

Numerical stability of coupled differential equation with piecewise constant arguments

This paper deals with the stability of numerical solutions for a coupled differential equation with piecewise constant arguments. A sufficient condition such that the system is asymptotically stable is derived. Furthermore, when the linear  θ-method is applied to this system, it is shown that the linear θ-method is asymptotically stable if and only if 1/2<θ≤1. Finally, some numerical experiments are given

Formation Flight of Earth Satellites on Low-Eccentricity KAM Tori

The problem of Earth satellite constellation and formation flight is investigated in the context of Kolmogorov-Arnold-Moser (KAM) theory. KAM tori are constructed utilizing Wiesel’s Low-Eccentricity Earth Satellite Theory, allowing numerical representation of the perturbed tori describing Earth orbits acted upon by geopotential perturbations as sets of Fourier series. A maneuvering strategy using the local linearization of the KAM tangent space is developed and applied, demonstrating the ability to maneuver onto and within desired torus surfaces. Constellation and formation design and maintenance on KAM tori are discussed, along with stability and maneuver error concerns. It is shown that placement of satellites on KAM tori results in virtually no secular relative motion in the full geopotential to within computational precision. The effects of maneuver magnitude errors are quantified in terms of a singular value decomposition of the modal system for several orbits of interest, introducing a statistical distribution in terms of torus angle drift rates due to mismatched energies. This distribution is then used to create expectations of the steady-state station-keeping costs, showing that these costs are driven by operational and spacecraft limitations, and not by limitations of the dynamics formulation. A non-optimal continuous control strategy for formations based on Control Lyapunov Functions is also outlined and demonstrated in the context of formation reconfiguration

A pneumatic semi-active control methodology for vibration control of air spring based suspension systems

This research investigates a pneumatic suspension system containing an air spring, air flow valve, and an accumulator, where the spring and damping functions are combined into one package. The spring and accumulator provide the spring characteristics, and the computer controlled adjustable valve provides the damping characteristics by automatically adjusting the air flow between the air spring and the accumulator. An extensive analysis and investigation of the plant dynamics is performed. A dynamic plant model is developed and tuned to experimental data. The plant model is then used in the design of a semi-active control system. A detailed description of the model tuning procedure is provided. Based upon the insights gained through analysis and system identification, a semi-active control methodology is developed, which exploits certain unique features of the system. Three potential controllers are developed and compared, where each controller uses different measurement feedback signals. However, all three controllers measure direct force generation through a pressure feedback signal. Both experimental and simulation data for the controllers is provided. The first controller uses an LQI (Linear Quadratic Impulse) optimal solution, based on Covariance Control Theory, to generate an optimal active damping control force, along with a Set-Point plus PI tracking controller to adjust the valve opening to cause the system to track this desired force during a switching event or control window of opportunity. The second controller uses a Modified Skyhook solution to generate the ideal tracking signal, along with a Set-Point plus PI tracking controller. The LQI controller is used in simulation (offline) to aid in setting the skyhook gain on the Modified Skyhook controller. The third controller uses a Relative Displacement solution to generate the ideal tracking signal, along with a Set-Point plus PI tracking controller. The LQI controller is used (offline) to aid in setting the gain on the Relative Displacement controller. This controller is probably the most useful for vehicular applications, since only relative coordinates and a pressure are required for feedback. It was found that all three controllers could track an optimally generated active signal during the switching event, provided the proper gains were chosen

A fixed point approach for finding approximate solutions to second order non-instantaneous impulsive abstract differential equations

This paper is concerned with the approximation of solutions to a class of second order non linear abstract differential equations. The finite-dimensional approximate solutions of the given system are built with the aid of the projection operator. We investigate the connection between the approximate solution and exact solution, and the question of convergence. Moreover, we define the Faedo-Galerkin(F-G) approximations and prove the existence and convergence results. The results are obtained by using the theory of cosine functions, Banach fixed point theorem and fractional power of closed linear operators. At last, an example of abstract formulation is provided

Ultrafast lattice dynamics in excitonic self-trapping of quasi-one dimensional materials

This dissertation presents an investigation of the localization of electronic excitations via electron-lattice interactions. Electronic localization is an important fundamental process in molecular-based electronic materials. Femtosecond vibrationally impulsive excitation techniques were used to directly time-resolve the lattice motion associated with the self-trapping dynamics in halogen-bridged mixed-valence linear chain complexes, [Pt(en)2X2][Pt(en)2], en = ethylenediamine (C2H8N2) and (X = Br - and I - ), or PtX. Three sets of experimental studies were conducted: (1) The investigation of PtI, representing the weak electron-phonon coupling limit, revealed a low frequency modulation of the induced absorbance that was assigned to the motion that drives the system to the self-trapped state. A formation component, which decays within approximately a single period of the low frequency motion, is assigned to the transfer of population from the free exciton to the self-trapped state. Previous impulsive excitation measurements on PtBr and PtCl, in conjunction with the PtI measurements in this dissertation, uncover the dependence of the self-trapping dynamics on electron-phonon coupling strength.; (2) The vibrational frequency of a characteristic mode of the self-trapped exciton in its equilibrated structure was determined using a multiple pulse pump-pump-probe sequence. Timedomain excited state resonant stimulated impulsive Raman excitation of PtBr revealed a vibrational mode associated with the equilibrated self-trapped exciton at 125 cm-1. The upward shift in frequency from the final state of the intervalence charge transfer transition at 110 cm-1 to the equilibrated configuration is consistent with an increased degree of localization in the stabilized structure. (3) Low temperature pump-probe measurements on PtBr uncovered an acoustic phonon response seen as a large amplitude 11 cm-1 modulation of the induced absorbance. Using this frequency, the localized lattice deformation was estimated to have a spatial extent of ~ 5 unit cells, which reflects the size of the self-trapped exciton, consistent with theoretical models for polaron formation. An enhancement of the excited state wavepacket dephasing time indicates that the vibrational coherence properties of the exciton at room temperature are not simply limited by the excited state structural distortion

Relative Orbit Elements for Satellites in Elliptical Orbits

The purpose of this research was to describe the unperturbed relative motion of Earth satellites in elliptical orbits using a simple dynamics model whose parameters allow significant geometrical insight and operational efficacy. The goal was to retain the advantages of the Relative Orbit Elements (ROE) realization of the Hill-Clohessy-Wiltshire (HCW) equations, a linearized dynamics model for circular reference orbits. Specifically, this thesis analyzed the geometry of satellite rendezvous and proximity operations using the ROE parameters to characterize the model’s utility. Next, through a comprehensive literature review, this thesis sought possible approaches for developing a similarly useful parameterization for chief orbits with nonzero eccentricity. The approach selected was a novel linear time-varying system which requires both chief and deputy satellites to remain close to a virtual chief on a known circular orbit. The research derived and solved the equations of motion, expressing the solution in terms of simple geometric parameters. Numerical simulations compared the new model against both HCW and Keplerian two-body motion, revealing less accurate performance than HCW for some cases. Error analysis explained this behavior and found restricted regions where the new model performed accurately. Finally, this study identified new approaches for researching relative satellite motion on elliptical orbits