Search results for "Vibration"
showing 10 items of 823 documents
Rigidity and Dynamics of Random Spring Networks
1996
The static and dynamic elastic properties of two-dimensional random networks composed of Hookean springs are analyzed. These networks are proved to be nonrigid with respect to small deformations, and the floppy mode ratio is calculated exactly. The vibrational spectrum is shown to consist only of zero-frequency and localized modes. The exponential decay of the amplitude and velocity of the transient wave front are shown to be exactly described by a quasi-one-dimensional model of noninteracting paths of propagation.
Spectroscopy of XY2Z2 (C2v) Molecules: A Tensorial Formalism Adapted to the O(3)⊃Td⊃C2v Chain. Application to the Ground State of SO2F2
2002
Abstract A tensorial formalism adapted to the case of quasi-spherical XY 2 Z 2 asymmetric tops such as SO 2 F 2 has been developed as an extension of the usual one for the tetrahedral molecules. We use the O (3)⊃ T d ⊃ C 2 v group chain. All the coupling coefficients and formulas for the computation of matrix elements are given for this chain. Such relations are then deduced in the C 2 v group itself. We also present a development of the Hamiltonian, dipole moment, and polarizability operators for the molecules under consideration using this formalism. These operators are involved in the calculation of the energies and intensities of rovibrational transitions and are essential for spectrum …
Long Lived Acoustic Vibrational Modes of an Embedded Nanoparticle
2004
Classical continuum elastic calculations show that the acoustic vibrational modes of an embedded nanoparticle can be lightly damped even when the longitudinal plane wave acoustic impedances $Z_o=\rho v_L$ of the nanoparticle and the matrix are the same. It is not necessary for the matrix to be less dense or softer than the nanoparticle in order to have long lived vibrational modes. Continuum boundary conditions do not always accurately reflect the microscropic nature of the interface between nanoparticle and matrix, and a multi-layer model of the interface reveals the possibility of additional reduction of mode damping.
Longitudinal versus transverse spheroidal vibrational modes of an elastic sphere
2005
Analysis of the spheroidal modes of vibration of a free elastic sphere show that they can be qualitatively grouped into two categories: primarily longitudinal and primarily transverse. This is not a sharp distinction. However, there is a relatively stark contrast between the two kinds of modes. Primarily transverse modes have a small divergence and have frequencies that are almost functionally independent of the longitudinal speed of sound. Analysis of inelastic light scattering intensity from confined acoustic phonons in nanoparticles requires an understanding of this qualitative distinction between different spheroidal modes. In addition, some common misconceptions about spheroidal modes …
Circular dichroism in x-ray photoemission from core levels of nonmagnetic species
1992
Circular dichroism in the angular distribution of photoelectrons (CDAD) has been observed in core-level photoemission from spherically symmetric initial states of nonmagnetic species utilizing circularly polarized soft-x-ray radiation from BESSY. Up to now, CDAD was predicted and observed only for aligned initial states. The data for oriented CO molecules prove that circular x-ray dichroism in photoemission from core levels is a general phenomenon that is not restricted to ferromagnets. High asymmetries of 50% suggest future applications as an effective circular x-ray analyzer.
Propagation and localisation of vibrational modes in 3–dimensional disordered systems: the binary force constant model
1999
We consider a system of coupled harmonic oscillators on a cubic lattice. The force constants are supposed to take two distinct values at random according to a bond concentration x. The density of states (DOS) is evaluated both by numerical diagonalisation and in coherent-potential approximation (CPA). There is excellent agreement between the results of the two methods. Near the concentration, where the bonds with the larger force constants percolate, the DOS differs appreciably from the crystalline one and is anomalously enhanced at low frequencies as compared to Debye's ω2 law (“boson peak”). These features are shared with models with continuous distributions of force constants. The mean f…
Jahn-Teller effect in the phonon properties of defective SrTiO3from first principles
2012
the Jahn–Teller effect occurs, thus reducing the cubic symmetry of a perfect crystal and leading to the appearance of both Raman- and infrared-active vibrational modes. The calculated phonon densities of states and group-theoretical analysis of defect-induced phonon frequencies were used for the interpretation of the relevant experimental data, once defect-induced local modes are identified. The temperature dependence of the Vo formation energy based on the calculated Gibbs free energy was also compared with experiments, and the phonon contribution therein estimated.
A Tensorial Formalism Adapted to the Rovibronic Couplings in the Colored Hexafluorides: Application to the nu(5)(F(2g)) and nu(3)(F(1u)) Modes.
2000
A tensorial formalism adapted to the case of transition-metal hexafluorides in a degenerate electronic state has been developed on the basis of preceding works about spherical-top molecules in a nondegenerate electronic state. We have introduced electronic operators constructed using group theory features and some physical considerations. Vibronic couplings (Jahn-Teller effect, etc.) have been reviewed for the triply degenerate vibrational modes nu(5)(F(2g)) and nu(3)(F(1u)) leading to the identification of the main vibronic parameters. For the first time, an effective rovibronic Hamiltonian as well as the effective transition moment operators (dipole moment and polarizability) for rovibron…
Fractional mechanical model for the dynamics of non-local continuum
2009
In this chapter, fractional calculus has been used to account for long-range interactions between material particles. Cohesive forces have been assumed decaying with inverse power law of the absolute distance that yields, as limiting case, an ordinary, fractional differential equation. It is shown that the proposed mathematical formulation is related to a discrete, point-spring model that includes non-local interactions by non-adjacent particles with linear springs with distance-decaying stiffness. Boundary conditions associated to the model coalesce with the well-known kinematic and static constraints and they do not run into divergent behavior. Dynamic analysis has been conducted and both…
Improved Algorithms for the Modeling of Vibrational Polyads of Polyatomic Molecules: Application toT,O, andC3Molecules
1997
Abstract Improved algorithms for the construction of rovibrational operators of polyatomic molecules are presented. Vibrationally diagonal and off-diagonal terms are obtained by a specific coupling scheme of creation and annihilation elementary operators. Recursive procedures are used to generate all possible terms and associated basis functions as well as to calculate matrix elements and commutators. Explicit formulations are given forTd,Oh, andC3vmolecules.