Cartesian Dynamics of Simple Molecules IV Centrosymmetric Linear Quadratomics

A simple spring model for molecular vibrations, which uses Cartesian co-ordinates for both longitudinal and transverse displacements, is applied to centrosymmetric linear quadratomic molecules, such as cyanogen and acetylene and its halogenated derivatives. Analytical expressions for the three stretching and two bending mode frequencies are obtained in terms of five independent force constants. By substitution of Raman and infrared frequencies, values of these force constants are obtained and briefly discussed. The validity of the model is confirmed by the satisfactory agreement between calculated and observed frequencies of isotopic species.     

Cartesian Dynamics of Simple Molecules VI Centrosymmetric Linear Pentatomics

A simple spring model for molecular vibrations, which uses Cartesian co-ordinates for both longitudinal and transverse displacements, is applied to centresymmetric linear pentatomic molecules such as carbon suboxide and carbon subsulphide. Analytical expressions for the four stretching and three bending mode frequencies are derived in terms of seven independent force constants. By substitution of Raman and infrared frequencies, values of these force constants are obtained and briefly discussed. Eigenvectors of the normal modes and eigenfrequencies of various isotopic species are also calculated.     

Cartesian Dynamics of Simple Molecules II Non-Centrosymmetric Linear Triatomics

A simple spring model for molecular vibrations, which uses Cartesian co-ordinates for both longitudinal and transverse displacements, is applied to non-centrosymmetric linear triatomic molecules. Analytical expressions for the stretching and bending mode frequencies are obtained, which are equivalent to those derived by conventional methods. For most molecules, the effects of the interaction between the outside atoms are shown to be negligible, but for N₂O, complex solutions are obtained unless this is included. The validity of the model is demonstrated by the satisfactory agreement between calculated and observed frequencies of isotopic species. For N₂O, frequency shifts resulting from isotopic substitution are explained by reference to the calculated eigenvectors.     

Cartesian Dynamics of Simple Molecules X Linear Quadratomics (C∞v Symmetry)

The vibrations of linear ABC₂ type molecules with C_∞V point group are analysed in terms of Cartesian co-ordinates. Algebraic expressions for the three stretching and two bending normal mode frequencies are derived in terms of longitudinal and transverse force constants, atomic masses and bond lengths. Values of non-valence interaction parameters are transferred from A₂B₂ (D_∞h) molecules, and values of the principal force constants are adjusted to reproduce the observed frequencies for a number of asymmetric halogen derivatives of acetylene. Normal mode frequencies of various isotopic species are also calculated. The nature of the computed eigenvectors for these molecules is briefly discussed. It is found that the carbon-carbon and carbon-hydrogen valence interactions remain approximately constant for these molecules, whereas the carbon-halogen bonds show a weakening trend with increasing halogen mass.     

Cartesian Dynamics of Simple Molecules III Non-Linear Triatomics (C2v Symmetry)

A simple spring model for the molecular vibrations of non-linear triatomic molecules with C_2v symmetry is described in terms of Cartesian co-ordinates. Analytical expressions for the stretching and bending mode frequencies are obtained and compared with previous derivations. Optimized values of force constants are calculated for models involving two or three adjustable parameters. The validity of the model is demonstrated by the satisfactory agreement between calculated and observed frequencies of isotopic species. The model provides a simple explanation of the near degeneracy of the symmetric and asymmetric stretching frequencies of H₂S and H₂Se.     

Cartesian Dynamics of Simple Molecules. IX. Pyramidal Quadratomics (C3v Symmetry)

The vibrations of pyramidal AB₃ type molecules with C_3v symmetry are analyzed in terms of Cartesian co-ordinates, and analytical expressions for the four normal mode frequencies are derived as functions of two stretching and two bending force constants. Optimized values of these force constants are obtained for a number of tri-hydride and tri-halide molecules by substitution of available spectroscopic and geometric data. The physical validity of the model is confirmed by comparing the calculated and observed frequencies of several isotopic species.     

Transverse conductivity in the sliding charge-density-wave state of NbSe3

The dynamical properties of longitudinal and transverse conduction of NbSe3 single crystals have been simultaneously studied when the current is applied along the b axis (chain direction). In the vicinity of the threshold electric field for charge-density-wave sliding, the transverse conduction sharply decreases. When a rf field is applied, voltage Shapiro steps for longitudinal transport are observed as usual but also current Shapiro steps in the transverse direction. The possible mechanisms of this effect are discussed.     

Indirect nuclear spin coupling between Cu++ pair in copper acetate monohydrate

The methods of molecular dynamics has been used to investigate the behaviour of transverse and longitudinal current-current autocorrelation functions in a model liquid simulating molten strontium chloride. Examples of the spectra of these functions are given and it is shown that the liquid propagates shear waves in a manner not unlike transverse phonons in crystals. The spectra of the mass and charge density, related to the spectra of the longitudinal currents, were computed. In both cases a non-central peak indicative of propagating acoustic and optic-type modes was observed for small wavenumbers, the optic-type mode persisting for larger wavenumbers than the acoustic-type modes. The possibility of observing these modes in inelastic neutron scattering experiments is discussed briefly.     

Relaxation of quasi-transverse phonons in the Herring mechanism and ultrasound absorption in cubic crystals with positive and negative anisotropies of the second-order elastic moduli

The phonon relaxation and quasi-transverse ultrasound absorption in the course of Herring and Landau-Rumer anharmonic scattering processes in cubic crystals with positive (Ge, Si, diamond, InSb, LiF, MgO) and negative (KCl, NaCl, CaF₂) anisotropies of the second-order elastic moduli have been investigated. A new mechanism of transverse phonon relaxation, according to which the fusion of a transverse (slow or fast) phonon with a slow phonon generates a fast transverse phonon, has been considered in the long-wave-length approximation. This mechanism is similar to the Herring relaxation mechanism for longitudinal phonons. It has been demonstrated that, for crystals of the first group with a considerable anisotropy of the elastic energy (Ge, Si, InSb, LiF, MgO), “anomalous” relaxation processes in which the fusion of a slow transverse phonon with a fast phonon generates a slow transverse phonon are possible in contrast to the Herring relaxation mechanism for longitudinal phonons. These relaxation processes appear to be impossible for all crystals of the second group (KCl, NaCl, CaF₂), as well as for crystals of the first group with a small anisotropy of the elastic energy, such as diamond. The angular dependences of the ultrasound absorption coefficient for the Herring and Landau-Rumer mechanisms have been analyzed using the anisotropic-continuum model. It has been shown that, for the crystals of the first group under consideration, the contribution of the Herring mechanism to the long-wavelength ultrasound absorption is small compared to the contribution of the Landau-Rumer mechanism. However, for the KCl and NaCl crystals of the second group in directions of the [001] type, the contribution of the Herring mechanism can significantly exceed the contribution of the Landau-Rumer mechanism.     

横向电场对平面织构胆甾相液晶螺距及反射特性的影响

阐述一种理论模型,讨论共面转换（IPS）模式下横向电场对平面织构胆甾相液晶螺距及扭曲角的影响．利用琼斯矩阵法计算了光正入射情况下未加电场时胆甾相液晶的反射谱．在上述模型基础上,计算了施加电场后胆甾相液晶的反射峰值波长以及反射带宽随场强的变化关系．探讨了忽略锚定与强锚定两种边界条件下横向电场对平面织构胆甾相液晶螺距及反射特性的影响．所得结论在理论上证实：共面转换模式下电场可以调谐胆甾相液晶的反射光颜色,从而为基于电控螺距原理的胆甾相液晶反射式彩色显示方案提供了理论上的依据． 关键词： 胆甾相液晶 电控螺距 共面转换 琼斯矩阵法     

Polarization multiplexed fluorescence enhancer using a pixelated one-dimensional photonic band gap structure

Fluorescence enhancement using photonic crystals can produce a significant improvement in the signal-to-noise ratio for single molecule and low molecule-concentration fluorescence imaging in biological and biochemical studies. In this Letter, a pixelated one-dimensional photonic band gap structure was designed to enhance both transverse electric and transverse magnetic polarizations through a spatially multiplexed photonic crystal resonance. The average enhancement of 15.6 and 17.9 fold were experimentally verified for the transverse and longitudinal fields on the same substrate. This device may be used as an optical platform for molecular orientation determination.     

Magnetic properties of a mixed spin- 1/2 and spin- 3/2 transverse Ising model in a longitudinal magnetic field

The mixed spin- 1/2 and spin- 3/2 transverse Ising model in a longitudinal magnetic field is studied within the framework of the effective-field theory with correlations. In this approach the effective-field equations are derived by using a probability distribution method based on the generalized but approximated van der Waerden identities. The total longitudinal and transverse magnetizations, the transverse susceptibility and longitudinal susceptibility and the critical temperatures are obtained. We find a number of interesting phenomena in these quantities, due to the applied transverse field and the longitudinal field.     

Lattice Waves in Two-Dimensional Hexagonal Quantum Plasma Crystals

Lattice waves including a longitudinal wave and a transverse wave in two-dimensional hexagonal quantum plasma crystals are investigated by using the modified Debye-Hückel screening potential. It is shown that there exists an unstable region of lattice parameters, where the system will melt. The general dispersion relations are derived, and the waves propagating parallel to a primitive translation vector are discussed. We find that both the longitudinal and transverse waves are acoustic-like, and the longitudinal wave has a greater sound speed than that of the transverse wave in the long wavelength limit region.     

The effect of normal phonon-phonon scattering processes on the maximum thermal conductivity of isotopically pure silicon crystals

The effect of normal phonon-phonon scattering processes on the thermal conductivity of silicon crystals with various degrees of isotope disorder is considered. The redistribution of phonon momentum in normal scattering processes is taken into account within each oscillation branch (the Callaway generalized model), as well as between different oscillation branches of the phonon spectrum (the Herring mechanism). The values of the parameters are obtained that determine the phonon momentum relaxation in anharmonic scattering processes. The contributions of the drift motion of longitudinal and transverse phonons to the thermal conductivity are analyzed. It is shown that the momentum redistribution between longitudinal and transverse phonons in the Herring relaxation model represents an efficient mechanism that limits the maximum thermal conductivity in isotopically pure silicon crystals. The dependence of the maximum thermal conductivity on the degree of isotope disorder is calculated. The maximum thermal conductivity of isotopically pure silicon crystals is estimated for two variants of phonon momentum relaxation in normal phonon-phonon scattering processes.     

Spontaneous transition of one-dimensional plasma photonic crystal’s orientation in a dielectric barrier discharge

A novel one-dimensional plasma photonic crystal whose crystal orientation can change spontaneously is demonstrated using a dielectric barrier discharge with two liquid electrodes. The orientation of the plasma photonic crystal will vary from transverse to longitudinal or vary from longitudinal to transverse and then revert to longitudinal by self-adjustment, while the experimental conditions are kept fixed. The dispersion relation of these plasma photonic crystals are calculated, and the changes of the photonic band diagrams during the orientation transition are studied.     

Spontaneous transition of one-dimensional plasma photonic crystal's orientation in dielectric barrier discharge

A novel one-dimensional plasma photonic crystal whose crystal orientation can change spontaneously is demonstrated by using a dielectric barrier discharge with two liquid electrodes. The orientation of the plasma photonic crystal will vary from transverse to longitudinal or vary from longitudinal to transverse and then revert to longitudinal by self-adjustment, while the experimental conditions are kept fixed. The dispersion relations of these plasma photonic crystals are calculated, and the changes of photonic band diagrams during the orientation transition are studied.     

A modified analytical model of the alkali-metal atomic magnetometer employing longitudinal carrier field

Alkali-metal atomic magnetometers employing longitudinal carrier magnetic field have ultrahigh sensitivity to measure transverse magnetic fields and have been applied in a variety of precise-measurement science and technologies. In practice, the magnetometer response is not rigorously proportional to the measured transverse magnetic fields and the existing fundamental analytical model of this magnetometer is effective only when the amplitudes of the measured fields are very small. In this paper, we present a modified analytical model to characterize the practical performance of the magnetometer more definitely. We find out how the longitudinal magnetization of the alkali metal atoms vary with larger transverse fields. The linear-response capacity of the magnetometer is determined by these factors: the amplitude and frequency of the longitudinal carrier field, longitudinal and transverse spin relaxation time of the alkali spins and rotation frequency of the transverse fields. We give a detailed and rigorous theoretical derivation by using the perturbation-iteration method and simulation experiments are conducted to verify the validity and correctness of the proposed modified model. This model can be helpful for measuring larger fields more accurately and configuring a desirable magnetometer with proper linear range.     

VIBRATION OF A COMPLIANT TOWER IN THREE-DIMENSIONS

The three-dimensional motion of an offshore compliant tower using both rigid and flexible beam models is studied in this paper. The tower is modelled as a beam supported by a torsional spring at the base with a point mass at the free end. The torsional spring constant is the same in all directions. When the beam is considered rigid, the two-degree-of-freedom model is employed. The two degrees constitute the two angular degrees of spherical co-ordinates, and the resulting equations are coupled and non-linear. When the beam is considered as elastic, three displacements are obtained as functions of the axial co-ordinate and time; again with coupled and non-linear equations of motion. The free and the forced responses due to deterministic loads are presented. The free responses of the rigid and elastic beams show rotating elliptical paths when viewed from above. The rate at which the path rotates depends on the initial conditions. When a harmonic transverse loading is applied in one direction, the displacement in that direction shows subharmonic resonance of order 1/2 and 1/3 while the displacement in the perpendicular direction is affected minimally. Next, in addition to the harmonic load in one direction, a transverse load is applied in the perpendicular direction. The transverse load varies exponentially with depth but is constant with time. It is found that the transverse load affects the transverse displacements in the perpendicular direction minimally.     

High Frequency Current and Field Fluctuations in a Magnetized Plasma

The current density and electric field fluctuations at frequencies much above the ion plasma frequency are derived for a non-relativistic plasma of arbitrary density, using the Klimontovich approach. Both longitudinal and transverse components of the interaction forces between the electrons are taken into account. The error introduced by neglecting the transverse component is discussed.