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  • 1
    Electronic Resource
    Electronic Resource
    Dynamic Displacement Tracking for Frame Structures with a Piezoelectric Patch Network Based on Plate Theory (2008)
    s.l. ; Stafa-Zurich, Switzerland
    Advances in science and technology Vol. 56 (Sept. 2008), p. 64-69 
    Details
    ISSN: 1662-0356
    Source: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Topics: Natural Sciences in General , Technology
    Notes: This paper is concerned with the design of a proper piezoelectric patch actuator networkin order to track the displacement of the sidewalls of a one-story frame structure; both, for the staticand the dynamic case. Weights for each network member found in our previous work were based onbeam theory; in the present paper a refinement of the weights by modeling the sidewalls of theframe structure as Kirchhoff plates is presented. For the sake of calculating the refined weightsapproximate solutions of the plate equations are calculated by an extended Galerkin method
    Type of Medium: Electronic Resource
    URL: http://www.tib-hannover.de/fulltexts/2011/0528/01/42/transtech_doi~10.4028%252Fwww.scientific.net%252FAST.56.64.pdf
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  • 2
    Electronic Resource
    Electronic Resource
    CH2I2 photodissociation: Dynamical modeling (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 3602-3611 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A full quantum mechanical calculation is carried out on the first excited state of CH2I2 to model the absorption and emission spectra and examine the photodissociation dynamics from a time dependent point of view. The dissociation at 355 nm is direct in the sense that the wave packet does not revisit the Franck–Condon region. The initial motion of the excited molecule is mainly along the CI2 symmetric stretch coordinate while simultaneously spreading in the antisymmetric stretch coordinate. The molecule then dissociates along a C–I "local'' mode; no I2 can be formed in this energy region. Vibrationally hot CH2I radical in the C–I mode is predicted. The model is in good agreement with available experimental results. A simple and intuitive method is presented to construct model potential energy surfaces for two chromophore systems from the potential energy surface and information known for the corresponding single chromophore. CH3I and CH2I2 are used as numerical illustrations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.454880
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  • 3
    Electronic Resource
    Electronic Resource
    Generalized Gaussian wave packet dynamics, Schrödinger equation, and stationary phase approximation (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 2003-2014 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We have recently published a new semiclassical method, generalized Gaussian wave packet dynamics, which extends Gaussian wave packet dynamics into complex phase space. Although we were able to give an accurate formulation of the method, we had at the time of writing that paper only an intuitive, heuristic understanding of the deeper causes which make the method work. A more mathematical understanding was needed. To close this gap we show in this paper the equivalence of the new method with a first order expansion of (h-dash-bar) of the Schrödinger equation. We further prove that the new method is equivalent to the stationary phase approximation, using the usual WKB formula for the propagator. The latter equivalence enables us to show that all the symmetry properties of time-dependent quantum mechanics also hold in the new semiclassical theory. Finally, we provide some elaboration of the method, and clarify several issues that were not discussed before. With this new insight we are able to formulate a simple rule for the calculation of semiclassical wave functions that contain contributions from more than one branch. This corrects for the divergence of semiclassical wave functions near caustics, a problem that we encountered in the preceding paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455714
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  • 4
    Electronic Resource
    Electronic Resource
    Hybrid mechanics: A combination of classical and quantum mechanics (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 4752-4760 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Because classical mechanics is so much easier to handle than quantum mechanics, the time evolution of wave functions for molecular dynamics is often calculated using semiclassical methods. The errors of such methods grow, in general, faster than linearly with time, although they may be quite small for small, but finite times. We therefore propose to use a semiclassical method to calculate the quantum mechanical time propagator for a finite time step (say 1/10 of a vibrational period) and to use this propagator and quantum mechanics for longer times. To describe the quantum time propagator we use a basis set that can describe regions in phase space that are not necessarily rectangular, but can have any shape, that will become important in applications to higher dimensions. We give numerical examples to demonstrate the accuracy of the method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455669
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  • 5
    Electronic Resource
    Electronic Resource
    Cross section and optical theorem for defects on a corrugated surface (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 2550-2557 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The definition for the surface scattering cross section of an object (defect, adatom, etc.) on a periodic surface in three dimensions is given. The analog of the Optical Theorem for gas phase scattering is derived. Calculations (made using semiclassical wave packets) are reported and compared to experiments for CO on Pt(111).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455050
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  • 6
    Electronic Resource
    Electronic Resource
    Generalized Gaussian wave packet dynamics (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 5302-5311 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We propose an extension of the semiclassical Gaussian wave packet dynamics to eliminate the three main restrictions of this method. The first restriction is that the wave packet is forced to remain Gaussian. This is correct only for quadratic, linear, or constant potentials. The second restriction is that the method is, in general, not able to treat most classically forbidden processes. The third restriction is that the norm is conserved only for Gaussian wave packets. For a superposition of Gaussians this is no longer true. We can eliminate these restrictions by an extension of the method into complex phase space, keeping time real.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.453647
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  • 7
    Electronic Resource
    Electronic Resource
    Hybrid mechanics. II (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 7317-7329 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We recently published a new method for the calculation of the time evolution of a wave function. We used an accurate approximate method to calculate the time propagator for a finite time Δt. Numerical calculations showed that this scheme works quite accurately, but that it is not more efficient than conventional methods. In this paper we propose to use a very fast and simple, but less accurate semiclassical method for the calculation of the time propagator. The approximation consists in the replacement of the Hamiltonian by a quadratic approximation around the center of the evolving wave packet called thawed Gaussian dynamics. We show by numerical examples in one and two dimensions that, despite this crude approximation, we achieve nearly the same accuracy as in the foregoing paper, but with an efficiency that is typically more than an order of magnitude better. We further show that the method is able to describe tunneling and long time dynamics (e.g., 1000 vibrational periods).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456211
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  • 8
    Electronic Resource
    Electronic Resource
    Semiclassical wave packet treatment of the rigid asymmetric rotor (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 1116-1129 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We discuss a semiclassical treatment of the rigid asymmetric rotor that delivers eigenenergies as well as eigenstates. We give possibilities to improve the semiclassical wave functions to any accuracy required. The method is devised so that inclusion of vibrations is possible. As no information about energetically lower states is included in the procedure, the calculation of highly excited states is easier than with conventional quantum methods. Calculation of quantum splitting from semiclassical eigenstates is treated. We give numerical examples for every procedure developed, so that the performance of the theory can be judged.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.453344
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  • 9
    Electronic Resource
    Electronic Resource
    Energies of vibrating and rotating molecules by ladder operators (1985)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 28 (1985), S. 245-267 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method which is well suited for calculating numerically the energies of the bent vibrating and rotating polyatomic molecule is given. By an analytical method using ladder operators the work of calculating the matrix elements of the Watson Hamiltonian is reduced to mere bookkeeping. This results in fast computation and good control of the errors introduced. To demonstrate the practical usefulness of the method, three test calculations on H2O and SO2 are reported and compared with results from the literature. It is intended to distribute the computer program developed to interested workers in the field.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560280208
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  • 10
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    Exoplanet orbital eccentricities derived from LAMOST–Kepler analysis (2016)
    National Academy of Sciences
    Details
    Publication Date: 2016-09-26
    Description: The nearly circular (mean eccentricity e¯≈0.06) and coplanar (mean mutual inclination i¯≈3°) orbits of the solar system planets motivated Kant and Laplace to hypothesize that planets are formed in disks, which has developed into the widely accepted theory of planet formation. The first several hundred extrasolar planets (mostly Jovian) discovered using the radial velocity (RV) technique are commonly on eccentric orbits (e¯≈0.3). This raises a fundamental question: Are the solar system and its formation special? The Kepler mission has found thousands of transiting planets dominated by sub-Neptunes, but most of their orbital eccentricities remain unknown. By using the precise spectroscopic host star parameters from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) observations, we measure the eccentricity distributions for a large (698) and homogeneous Kepler planet sample with transit duration statistics. Nearly half of the planets are in systems with single transiting planets (singles), whereas the other half are multiple transiting planets (multiples). We find an eccentricity dichotomy: on average, Kepler singles are on eccentric orbits with e¯≈ 0.3, whereas the multiples are on nearly circular (e¯=0.04−0.04+0.03) and coplanar (i¯=1.4−1.1+0.8 degree) orbits similar to those of the solar system planets. Our results are consistent with previous studies of smaller samples and individual systems. We also show that Kepler multiples and solar system objects follow a common relation [e¯≈(1–2)×i¯] between mean eccentricities and mutual inclinations. The prevalence of circular orbits and the common relation may imply that the solar system is not so atypical in the galaxy after all.
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
    Published by National Academy of Sciences
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