Dipole Symmetry Research Articles

Relaxation mechanisms of multi-quantum coherences in the Zeeman structure of atomic Cs trapped in solid He

This paper extends our previous work on near-degenerate magnetic resonance transitions in alkali ground states involving the simultaneous absorption of multiple radio-frequency quanta. New experimental results with an improved spectral resolution were obtained with cesium atoms trapped in the cubic phase of a helium crystal. The main objective of the paper is a theoretical study of the influence of stochastic perturbations of given multipole orders on the various multi-photon coherences. Algebraic and numerical results for perturbations of both dipolar and quadrupolar symmetry are presented. The present experimental resolution does not yet allow us to distinguish between these two most likely relaxation mechanisms. Nonetheless, the experimental spectra are very well described when allowing in the calculations for a magnetic field inhomogeneity of 2×10-5.

Influence of charge distribution on the thermophysical and dynamical properties of polar linear molecules

Gibbs ensemble Monte Carlo and molecular dynamics simulations were used to study thermophysical and dynamical properties of Kihara fluids consisting of linear molecules with dipolar symmetry. Two models differing in the electrostatic part of the intermolecular potential have been considered. The first one is an ideal dipole (ID) model where electrostatic interactions are modeled as point dipoles placed on the molecular center of mass, and the second one is a discrete charge (DC) model with single positive and negative charges placed at opposite ends of the molecules. The magnitude of the charges and the distance between them were chosen to reproduce the dipole moment of the ID model. In addition, an effective ionic strength for the DC model has been defined. Simulations were performed at several densities and temperatures in a wide range of molecular lengths and at three dipole moments. For all the systems, vapor–liquid equilibrium, thermodynamic, and structural properties, autocorrelation functions, correlation times, and transport properties such as diffusion, shear viscosity, and thermal conductivity have been obtained and analyzed. The results of the present study are in agreement with those found in previous works and they confirm that, although differences between the DC model and the ID model are small for the lower molecular lengths, they become more pronounced at higher molecular lengths. Finally, the influence of the effective ionic strength on the different properties of the system is discussed.

Linear spin waves in a trapped Bose gas

An ultracold Bose gas of two-level atoms can be thought of as a spin-1/2 Bose gas. It supports spin-wave collective modes due to the exchange mean field. Such collective spin oscillations have been observed in recent experiments at JILA with ${}^{87}\mathrm{Rb}$ atoms confined in a harmonic trap. We present a theory of the spin-wave collective modes based on the moment method for trapped gases. In the collisionless and hydrodynamic limits, we derive analytic expressions for the frequencies and damping rates of modes with dipole and quadrupole symmetry. We find that the frequency for a given mode is given by a temperature-independent function of the peak density n, and falls off as $1/n.$ We also find that, to a very good approximation, excitations in the radial and axial directions are decoupled. We compare our model to the numerical integration of a one-dimensional version of the kinetic equation and find very good qualitative agreement. The damping rates, however, show the largest deviation for intermediate densities, where one expects Landau damping---which is unaccounted for in our moment approach---to play a significant role.

Convection-driven hydromagnetic waves in planetary fluid cores

We study hydromagnetic waves driven by thermal convection in a self-gravitating, rapidly rotating fluid spherical shell permeated by both poloidal and toroidal axisymmetric magnetic fields. The imposed magnetic fields satisfy electrically insulating boundary conditions at both surfaces of the shell and have an equatorial dipolar symmetry. The system is a model of the cores of the Earth and other planets, where magnetic fields are generated. We focus on the effect of poloidal magnetic fields at an asymptotically small Ekman number E = 10 −6. We find two new modes for convection-driven hydromagnetic waves. When the poloidal field is larger than the toroidal field, the waves propagate rapidly eastwards and concentrate just outside the “tangent cylinder”, which has axis parallel to the rotation axis and just encloses the inner sphere. When the poloidal field is comparable to the toroidal field the waves also propagate eastwards but concentrate inside the tangent cylinder. When the toroidal field is larger than the poloidal field the waves propagate slowly either eastwards or westwards and concentrate on lower to middle latitudes. In all the three cases, the flow approximately satisfies the two-dimensional Proudman-Taylor constraint, even though the theorem does not strictly apply because the magnetic forces are strong.

Correlation Between Cation Vacancies and Phase Transition Behavior in La-Modified Sodium Bismuth Titanate

In this study, the influence of cation vacancy on phase transition was investigated with the aid of dielectric spectroscopy. La ions were incorporated into (NBT) to cause A site vacancy (named as NBLT-A) or B site vacancy (named as NBLT-B). In NBLT-A, La modification reduced the degree of cation ordering in A-site and caused a dielectric relaxation in a transition from ferroelectric commensurate phase to incommensurate phase. However, NBLT-B (x=0.05) shows only diffuse phase transition between paraelectric and ferroelectric phase. The phenomenon was discussed in terms of the role of A-site cation ordering and vacancies on translational symmetry of dipoles.

Correlation Between Cation Vacancies and Phase Transition Behavior in La-Modified Sodium Bismuth Titanate

In this study, the influence of cation vacancy on phase transition was investigated with the aid of dielectric spectroscopy. La ions were incorporated into (NBT) to cause A site vacancy (named as NBLT-A) or B site vacancy (named as NBLT-B). In NBLT-A, La modification reduced the degree of cation ordering in A-site and caused a dielectric relaxation in a transition from ferroelectric commensurate phase to incommensurate phase. However, NBLT-B (x=0.05) shows only diffuse phase transition between paraelectric and ferroelectric phase. The phenomenon was discussed in terms of the role of A-site cation ordering and vacancies on translational symmetry of dipoles.

Launching of Jets and The Vertical Structure of Accretion Disk

The launching of magnetohydrodynamic outflows from accretion disks is considered. We formulate a model for the local vertical structure of a thin disk threaded by a poloidal magnetic field of dipolar symmetry. The model consists of an optically thick disk matched to an isothermal atmosphere. The disk is supposed to be turbulent and possesses an effective viscosity and an effective magnetic diffusivity. In the atmosphere, if the magnetic field lines are inclined sufficiently to the vertical, a magnetocentrifugal outflow is driven and passes through a slow magnetosonic point close to the surface. We determine how the rate of mass loss varies with the strength and inclination of the magnetic field. In particular, we find that for disks in which the mean poloidal field is sufficiently strong to stabilize the disk against the magnetorotational instability, the mass-loss rate decreases extremely rapidly with increasing field strength and is maximal at an inclination angle of 40°-50°. For turbulent disks with weaker mean fields, the mass-loss rate increases monotonically with increasing strength and inclination of the field, but the solution branch terminates before achieving excessive mass-loss rates. Our results suggest that efficient jet launching occurs for a limited range of field strengths and a limited range of inclination angles in excess of 30°. In addition, we determine the direction and rate of radial migration of the poloidal magnetic flux and discuss whether configurations suitable for jet launching can be maintained against dissipation.

Resonant Enhancements at Nonmagnetic Ions: New Possibilities for Magnetic X-Ray Scattering

Synchrotron experiments with uranium antiferromagnetic compounds have discovered large ( >1000) enhancements of the magnetic scattering intensities at the K edges of nominally nonmagnetic anions, e.g., Ga and As. The width in energy, the position with respect to the white line, and the azimuthal and polarization dependencies permit one to associate the signal with transitions of E1 dipole symmetry from 1s to 4p states. In momentum space, the signal exhibits long-range order at the antiferromagnetic wave vector. We discuss possible channels capable of generating the observed enhancements.

Supramolecular polar thin films built by surfactant liquid crystals: polarization-tunable multilayer self-assemblies with in-plane ferroelectric ordering of ion-based dipoles.

Polar order in the phosphonium liquid crystal thin films, which are composed of two-dimensional ion-pair-based domains separated by the insulating hydrocarbon layers, was probed by second harmonic generation (SHG) analysis. Despite the ordinary amphiphilic self-assemblies containing no pi-electron moieties, the solid-state thin films retaining a smectic layer structure showed clearly an SHG activity, while the disordered films without the layer structure were not active at all for the SHG. It was found that the multilayer structure plays a crucial role for the SHG from the phosphonium thin films and the ionic layers act as an SHG-active site. The most significant characteristic of this system is to possess an ability to control SHG intensity electrically. The efficiency of the SHG process in the thin-film assemblies was enhanced by applying an external electric field parallel to the layer plane. Furthermore, through evaluation of thermal stability of the sample films, it was revealed that the SHG signals were detected only in the solid-state temperature range and the disappearance of the SHG occurs earlier than the solid-to-liquid crystalline phase transition. These results demonstrated that the origin of polar order in the phosphonium thin films is due to in-plane noncentrosymmetric arrangement (ferroelectric ordering) of ion pairs as an electric dipole, that is, dipole symmetry in an ionic layer.

An unconventional accretion disc dynamo

In the light of recent results from numerical simulations of accretion disc MHD turbulence, we revisit the problem of the configuration of large-scale magnetic fields resulting from an αΩ dynamo operating in a thin accretion disc. In particular, we analyse the consequences of the peculiar sign of the α-effect suggested by numerical simulations. We determine the symmetry of the fastest-growing modes in the kinematic dynamo approximation and, in the framework of an ‘α-quenched’ dynamo model, study the evolution of the magnetic field. We find that the resulting field for this negative polarity of the α-effect generally has dipole symmetry with respect to the disc midplane, although the existence of an equilibrium configuration depends on the properties of the turbulence. The role of magnetic field dragging is discussed and, finally, the presence of an external uniform magnetic field is included to address the issue of magneto centrifugal wind launching from accretion discs.

Kinematic dynamo action in a sphere. II. Symmetry selection

The magnetic › elds of the planets are generated by dynamo action in their electrically conducting interiors. The Earth possesses an axial dipole magnetic › eld but other planets have other con› gurations: Uranus has an equatorial dipole for example. In a previous paper we explored a two-parameter class of ® ows, comprising convection rolls, di¬ erential rotation ( D) and meridional circulation ( M), for dynamo generation of steady › elds with axial dipole symmetry by solving the kinematic dynamo equations. In this paper we explore generation of the remaining three allowed symmetries: axial quadrupole, equatorial dipole and equatorial quadrupole. The results have implications for the fully nonlinear dynamical dynamo because the ® ows qualitatively resemble those driven by thermal convection in a rotating sphere, and the symmetries de› ne separable solutions of the nonlinear equations. Axial dipole solutions are generally preferred (they have lower critical magnetic Reynolds number) for D > 0, corresponding to westward surface drift. Axial quadrupoles are preferred for D 0), axial dipoles are preferred. The equatorial dipole must change sign between east and west hemispheres, and is not favoured by any elongation of the ® ux in longitude (caused by D) or polar concentrations (caused by M): they are preferred for small D and M. Polar and equatorial concentrations can be related to dynamo waves and the sign of Parker’s dynamo number. For the three-dimensional ® ow considered here, the sign of the dynamo number is related to the sense of spiralling of the convection rolls, which must be the same as the surface drift.

Kinematic dynamo action in a sphere. I. Effects of differential rotation and meridional circulation on solutions with axial dipole symmetry

A sphere containing electrically conducting fluid can generate a magnetic field by dynamo action, provided the flow is sufficiently complicated and vigorous. The dynamo mechanism is thought to sustain magnetic fields in planets and stars. The kinematic dynamo problem tests steady flows for magnetic instability, but rather few dynamos have been found so far because of severe numerical difficulties. Dynamo action might, therefore, be quite unusual, at least for large-scale steady flows. We address this question by testing a two-parameter class of flows for dynamo generation of magnetic fields containing an axial dipole. The class of flows includes two completely different types of known dynamos, one dominated by differential rotation (D) and one with none. We find that 36% of the flows in seven distinct zones in parameter space act as dynamos, while the remaining 64% either fail to generate this type of magnetic field or generate fields that are too small in scale to be resolved by our numerical method. The two previously known dynamo types lie in the same zone, and it is therefore possible to change the flow continuously from one to the other without losing dynamo action. Differential rotation is found to promote large-scale axisymmetric toroidal magnetic fields, while meridional circulation (M) promotes large-scale axisymmetric poloidal fields concentrated at high latitudes near the axis. Magnetic fields resembling that of the Earth are generated by D > 0, corresponding to westward flow at the surface, and M of either sign but not zero. Very few oscillatory solutions are found.

Theoretical study of short electrostatic lens for the Columbia ion microprobe

A short probe-forming system is developed for the Columbia Microprobe that includes four electrostatic quadrupoles with a Russian quadruplet configuration. The smallest beam spot size and appropriate optimal parameters of the probe-forming systems have been found. These parameters of the system are compared with appropriate parameters of other field configurations including the electrostatic and magnetic fields with dipole, quadrupole, and rotational symmetry. The new original construction of the electrostatic quadruplet has been manufactured. The sensitivity of this quadruplet to some misalignments of the construction is investigated.

Nonlinear magnetohydrodynamic convective flows in the Earth's fluid core

Convective motions in the Earth's fluid core are strongly affected by a combination of the Coriolis and magnetic forces. For a long-timescale phenomenon such as the geomagnetic reversals, the Earth's magnetic fields are generated by dynamo processes. For a shorter-timescale phenomenon such as the secular variation, dynamics of the Earth's fluid core can be understood by examining convective motions in the presence of an imposed magnetic field without involving the complex dynamo processes. The present paper investigates both linear and nonlinear convection in a rapidly rotating fluid spherical shell like the Earth's fluid core in the presence of a strong axisymmetric toroidal magnetic field with dipole symmetry. In our linear calculation, it is demonstrated that magnetoconvection is nearly independent of the Ekman number E when E≤10 −3. In our nonlinear calculation, which includes all nonlinear effects, two different types of magnetoconvection solutions are found. The primary nonlinear solution bifurcating from the onset of magnetoconvection corresponds to steadily travelling magnetoconvection waves with equatorial and azimuthal symmetries. The secondary solution after the instability of the steadily travelling waves is characterised by vacillating magnetoconvective motions which breaks both the temporal and azimuthal symmetries of the primary solution simultaneously. Implication of nonlinear solutions for the Earth's dynamo is also discussed.

Second-Order Nonlinear Optical Properties of the Four Tetranitrotetrapropoxycalix[4]arene Conformers

This paper reports a systematic experimental and theoretical study of the second-order nonlinear optical properties of multichromophoric molecules that range from dipolar symmetry to three-dimensional octupolar symmetry. The four possible conformers of tetranitrotetrapropoxycalix[4]arene (cone, pace, 1,2-air, 1,3-alt) were studied by nanosecond hyper-Rayleigh scattering and a newly developed time-resolved femtosecond hyper-Rayleigh scattering technique. The latter enables to correct for long-lived fluorescence contributions to the second harmonic scattering intensity. The depolarization ratios D-x/z prove the (partial) octupolar symmetry of the 1,2-alt and 1,3- alt conformers, and thus explain why their hyperpolarizabilities beta(FHRS) are of the same order of magnitude as those of the dipolar cone and pace conformers. The corresponding theoretical second-order nonlinear optical properties (both beta(FHRS) and D-x/z) were calculated using the conformations obtained from single-crystal X-ray diffraction, molecular mechanics (MM), and molecular dynamics (MD) calculations. In contrast with sum-over-state calculations presented in the literature, our theoretical method takes also into account octupolar contributions by linearly adding the NLO-properties of the separate chromophoric groups and using Bersohn's theory. The agreement between experimental and theoretical results is good both for the conformers having dipolar symmetry and for the conformers having (partly) three- dimensional octupolar symmetry. The 1,2-alt and 1,3-alt conformers of the tetranitrotetrapropoxycalix[4]arene represent the first examples of multichromophoric molecules that have high hyperpolarizabilities beta due to 3D octupolar symmetry.

Modulation and symmetry changes in stellar dynamos

Stellar dynamos are governed by non-linear partial differential equations (PDEs) which admit solutions with dipole, quadrupole or mixed symmetry (i.e. with different parities). These PDEs possess periodic solutions that describe magnetic cycles, and numerical studies reveal two different types of modulation. For modulations of Type 1 there are parity changes without significant changes of amplitude, while for Type 2 there are amplitude changes without significant changes in parity. In stars like the Sun, cyclic magnetic activity is interrupted by grand minima that correspond to Type 2 modulation. Although the Sun’s magnetic field has maintained dipole symmetry for almost 300 yr, there was a significant parity change at the end of the Maunder Minimum. We infer that the solar field may have flipped from dipole to quadrupole polarity (and back) after deep minima in the past and may do so again in the future. Other stars, with different masses or rotation rates, may exhibit cyclic activity with dipole, quadrupole or mixed parity. The origins of such behaviour can be understood by relating the PDE results to solutions of appropriate low-order systems of ordinary differential equations (ODEs). Type 1 modulation is reproduced in a fourth-order system while Type 2 modulation occurs in a third-order system. Here we construct a new sixth-order system that describes both types of modulation and clarifies the interactions between symmetry-breaking and modulation of activity. Solutions of these non-linear ODEs reproduce the qualitative behaviour found for the PDEs, including flipping of polarity after a prolonged grand minimum. Thus we can be confident that these patterns of behaviour are robust, and will apply to stars that are similar to the Sun.

Evaluation of the many-body contributions to the interionic interactions in MgO

The predictions of an “extended” ionic interaction model for the phonons and other properties of crystalline MgO are considered. In the extended model, the polarization interactions resulting from the dipoles and quadrupoles induced on the oxide ions by both Coulombic and short-range interactions with other ions are explicitly represented. Furthermore, the shapes of the oxide ions, as perceived through the short-range repulsive interactions with their immediate neighbors, are allowed to respond to their instantaneous coordination environment. Shape deformations of spherical (breathing), dipolar and quadrupolar symmetry are allowed. Each of these many-body effects is independently represented in the simulation model, so that the effect of each term on observed properties can be separately evaluated. It is shown how the polarization and breathing effects may be directly parametrized from ab initio electronic structure calculations. By consideration of the symmetry of the individual phonons at high symmetry points, it can be shown that the remaining effects may contribute only to particular phonons. Consequently, they may be assigned values in an unambiguous manner. The importance of each many-body effect for the different phonon branches is clearly delineated.

Acoustic Breathers in Two-Dimensional Lattices

The existence of breathers (time-periodic and spatially localized lattice vibrations) is well established for i) systems without acoustic phonon branches and ii) systems with acoustic phonons, but also with additional symmetries preventing the occurence of strains (dc terms) in the breather solution. The case of coexistence of strains and acoustic phonon branches is solved (for simple models) only for one-dimensional lattices. We calculate breather solutions for a two-dimensional lattice with one acoustic phonon branch. We start from the easy-to-handle case of a system with homogeneous (anharmonic) interaction potentials. We then easily continue the zero-strain breather solution into the model sector with additional quadratic and cubic potential terms with the help of a generalized Newton method. The lattice size is $70\times 70$. The breather continues to exist, but is dressed with a strain field. In contrast to the ac breather components, which decay exponentially in space, the strain field (which has dipole symmetry) should decay like $1/r^a, a=2$. On our rather small lattice we find an exponent $a\approx 1.85$.

Molecular dynamics simulations of dielectric properties of dimethyl sulfoxide: Comparison between available potentials

We present a molecular dynamics simulation study of the orientational correlations of molecular dipoles and dielectric properties of a series of recently proposed models for liquid dimethyl sulfoxide. The dipole–dipole correlations, as measured by the dipolar symmetry projections h110(r) and h112(r), are very similar for the models with four partially charged sites, but differ somewhat for the potential with no charges on the methyl groups. The effects of the charges on the methyl sites upon the local ordering of the molecular dipoles are discussed by comparing the h110(r) projections for two models which differ only in their site-charge assignments. The Kirkwood g factors for the simulated force fields turn out all greater than unity, in disagreement with some experimental estimates. The dielectric constants, however, are in good agreement with reported experimental data. In addition, we discuss the wave vector (k) dependence of the longitudinal static dielectric responses and also the single-particle molecular reorientation dynamics, which is found to differ from model to model. Likely consequences of that to the dielectric relaxation of these models are briefly discussed.

Orientational ordering of a polymer chain in a strong dipole field. Tetrahedral lattice model

AbstractOrientational and conformational properties have been investigated of a rotational isomeric model of a polar polymer chain on a tetrahedral lattice in a strong electric or mechanical field of dipole symmetry. Two types of dipole moment distribution along the chain are discussed: (A) constant signs of longitudinal components of the dipole moments, and (B) alternating signs of the longitudinal components of the dipole moments. The second case represents polymer chains such as \documentclass{article}\pagestyle{empty}\begin{document}$ \rlap{--} ({\rm CH}_{\rm 2} \hbox{---} {\rm CR}_{\rm 2} {\rm \rlap{--} )}_n $\end{document}>/UEQN> when the dipole moments are oriented along the bisector of the CR2‐angle, i.e., normal to the extended trans‐chain conformation. It is shown that only a discrete most probable orientation of the lattice relative to the field should be considered, namely that coinciding with one of the symmetry axes of the lattices. The average dipole order parameter and dichroic functions (quadrupole order parameter) are calculated in a strong external dipole field for unit vectors with different orientation relative to the chain backbone. The quadrupole order parameter for different unit vectors is obtained also as a function of chain elongation. The polarizability induced by an additional weak dipole field is calculated as a function of the magnitude of the strong external dipole field. For the model considered here the order parameters are more strongly influenced by the external field than those for the freely jointed chain (FJC) model having the same distribution of dipole moments along the chain. The orientational ordering of the chain in a dipole field is higher than in a quadrupole field of the same magnitude.