Polarization Quantities Research Articles

Patterns of shear zones in granular bodies within a polar hypoplastic continuum

The paper deals with numerical investigations on the patterning of shear zones in granular bodies. The behavior of dry sand during plane strain compression tests was numerically modelled with a finite element method using a hypoplastic constitutive relation within a polar (Cosserat) continuum. The constitutive relation was obtained through an extension of a non-polar one by polar quantities, viz. rotations, curvatures, couple stresses using the mean grain diameter as a characteristic length. This relation can reproduce the essential features of granular bodies during shear localisation. During FE-calculations, the attention was laid on the influence of boundary conditions and the distribution of imperfections in the granular specimen on the formation of patterns of shear zones.

Orthogonal Polarization Modes from PSR B0301+19 and B0355+54

We have analyzed the single pulse data of PSR B0301 + 19 and B0355+54 at 1.41 GHz taken from 100-m Effelsberg radio telescope of MPIfR on 22 and 30 August, 1996. The gray-scale maps are made for the polarization quantities to study the distribution of polarization modes at different pulse longitudes. Circular polarization flips the sign at the pulse center in the case PSR B0355+54 but in the case of PSR B0301 + 19 it is mostly positive throughout the pulse. We find the evidence for depolarization that most of the pulsar radiation depolarizes due to the superposition of orthogonal polarization modes.

Microwave backscattering by nonspherical ice particles at [formula omitted] using second-order perturbation series

Scattering of microwaves by an ensemble of nonspherical ice particles is studied using a scattering model based on a second-order perturbation series at 5.6 GHz (C-band). Particle shapes are defined using a Gaussian random sphere geometry. Particle inhomogeneity is taken into account using three different effective-medium approximations: Maxwell–Garnett, Bruggeman, and Coherent Potential mixing rules. By systematically varying particle size, liquid water content, Gaussian shape parameters, and internal structure, it is found that liquid water content is the most important factor for the co-polarized backscattering; the shape is relatively unimportant. For depolarized backscattering, the shape is of fundamental importance, although the other factors are significant too. Surprisingly, the type of nonsphericity is found to be important for depolarization even for scatterers that are in the Rayleigh region: elongated targets depolarize clearly stronger than more irregular shapes. This finding seems not to be strongly size dependent, at least for size parameters from 0.0059 to 0.47, and indicates that the accurate modeling of shape is important for polarization quantities even in the Rayleigh region.

Optical Interferometric Polarimetry. I. Foundation

The theoretical response of long-baseline optical interferometers and Fourier transform spectrometers, including polarization effects, is derived. The formalism, employing the Jones and Mueller calculi as well as the relationship between them, was adapted from previous work in radio interferometry and tailored specifically for optical wavelengths. Expressions for Jones and Mueller matrices corresponding to specific optical components and effects are stated. It was determined that the system squared visibility depends on the instrument, atmosphere, and normalized intrinsic polarization of sources under observation. A sample algebraic calculation was performed to highlight the typical functional form for the instrumental system squared visibility, demonstrating that reductions from unity can be determined directly from differential measurements of polarization quantities between the arms. Monte Carlo simulations were performed using two trains of identical mirrors with random relative orientation offsets, yielding results consistent with the algebraic example. Four mathematical appendices are provided for reference.

Shearing of a narrow granular layer with polar quantities

The paper deals with numerical investigations of the behaviour of granular bodies during shearing. Shearing of a narrow layer of sand between two very rough boundaries under constant vertical pressure is numerically modelled with a finite element method using a hypoplastic constitutive relation within a polar (Cosserat) continuum. The constitutive relation was obtained through an extension of a non-polar one by polar quantities, viz. rotations, curvatures, couple stresses using the mean grain diameter as a characteristic length. This relation can reproduce the essential features of granular bodies during shear localization. The material constants can be easily determined from element test results and can be estimated from granulometric properties. The attention is laid on the influence of the initial void ratio, pressure level, mean grain diameter and grain roughness on the thickness of shear zones. The results of shearing are also compared to solutions without the polar extensions. The FE-calculations demonstrate that polar effects manifested by the appearance of grain rotations and couple stresses are significant in the shear zone, and its thickness is sensitive to the initial void ratio, mean grain diameter and layer height. The effect of the pressure level is rather low within the considered range.

FE-studies on the influence of initial void ratio, pressure level and mean grain diameter on shear localization

The paper is concerned with shear localization in the form of a spontaneous shear zone inside a granular material during a plane strain compression test. The influence of an initial void ratio, pressure and a mean grain diameter on the thickness of a shear zone is investigated. A plane strain compression test with dry sand is numerically modelled with a finite element method taking into account a polar hypoplastic constitutive relation which was laid down within a polar (Cosserat) continuum. The relation was obtained through an extension of a non-polar hypoplastic constitutive law according to Gudehus and Bauer by polar quantities: rotations, curvatures, couple stresses and a characteristic length. It can reproduce the essential features of granular bodies during shear localization. The material constants can be easily calibrated. The FE-calculations demonstrate an increase in the thickness of the shear zone with increasing initial void ratio, pressure level and mean grain diameter. Polar effects manifested by the appearance of grain rotations and couple stresses are only significant in the shear zone. A comparison between numerical calculations and experimental results shows a satisfying agreement. Copyright © 1999 John Wiley & Sons, Ltd.

A “Class A” Prediction of the Bearing Capacity of Plane Strain Footings on Sand

The bearing capacity of plane strain model footings on sand is numerically investigated with a finite element method and a polar hypoplastic constitutive law. The constitutive law is obtained through an extension of a non-polar hypoplastic constitutive law by polar quantities : rotations, curvatures, couple stresses and a characteristic length. It can reproduce the salient features of granular bodies while taking into account shear localisation. The hypoplastic constants are calibrated with element test calculations on the basis of plane strain and triaxial compression tests. The FE-analyses are performed for both different mean grain diameters and initial densities of dry medium sand, and footing widths. The effect of material constants on the load-displacement curve is also investigated. The FE-results are compared with model tests. Advantages and limitations of a polar hypoplastic approach are outlined.

Identification of low-frequency kinetic wave modes in the Earth's ion foreshock

Abstract. In this work we use ion and magnetic field data from the AMPTE-UKS mission to study the characteristics of low frequency (ωr « Ωp) waves observed upstream of the Earth's bow shock. We test the application of various plasma-field correlations and magnetic ratios derived from linear Vlasov theory to identify the modes in this region. We evaluate (for a parameter space consistent with the ion foreshock) the Alfvén ratio, the parallel compressibility, the cross-helicity, the noncoplanar ratio, the magnetic compression and the polarization for the two kinetic instabilities that can be generated in the foreshock by the interaction of hot diffuse ions with the solar wind: the left-hand resonant and the right-hand resonant ion beam instabilities. Comparison of these quantities with the observed plasma-field correlations and various magnetic properties of the waves observed during 10 intervals on 30 October 1984, where the waves are associated with diffuse ions, allows us to identify regions with Alfvénic waves and regions where the predominant mode is the right-hand resonant instability. In all the cases the waves are transverse, propagating at angles ≤ 33° and are elliptically polarized. Our results suggest that while the observed Alfvén waves are generated locally by hot diffuse ions, the right-handed waves may result from the superposition of waves generated by two different types of beam distribution (i.e. cold beam and diffuse ions). Even when there was good agreement between the values of observed transport ratios and the values given by the theory, some discrepancies were found. This shows that the observed waves are different from the theoretical modes and that mode identification based only on polarization quantities does not give a complete picture of the waves' characteristics and can lead to mode identification of waves whose polarization may agree with theoretical predictions even when other properties can diverge from those of the theoretical modes.

Plane-wave scattering from a nonchiral object in a chiral environment

The problem of a nonchiral object in an isotropic medium is analyzed through wave-field decomposition and treatment of the chiral medium as a combination of two nonchiral media. Integral equations for the internal wave fields of the object are formed, suitable for numerical computation. For an object with small contrast, solutions are found through the Born approximation. As a special case, a spherical object is considered and expressions for the scattered far fields are found in explicit analytical form. As numerical examples, certain measurable polarization quantities are presented together with their interpretation. The theory is applicable, for example, to the analysis of data obtained from the measurement of the glucose content of blood in terms of light scattered from blood cells.

Study of three-photon resonance multiphoton ionization spectroscopy of 3p Rydberg states of m -dimethylbenzene within dye Rh560

In this paper, we studied experimentally the three-photon resonance four-photon ionization spectroscopy of m-dimethylbenzene within dye Rh560. We found several new 3p Rydberg vibronic states and measured their polarization characters. With the help of the measured polarization quantities, we gave the assignment results of these vibronic states: 9b01, A1; 1301, A1; 19a01, A1; 8a01, A1.

On the polarization of sea antiquarks in the proton

We give some predictions about the magnitude of the sea antiquarks polarization in the proton. In order to get the results we use the experimental data concerning β-decaygA coupling constants and magnetic moments of octet baryons. We also show the consistency between our calculations and those made in the MIT bag model with one-gluon-exchange correction taken into account. We also quote the numbers for the polarization quantities derived in two specific plausible models.

TR and TL tensor interactions in deuteron elastic scattering

For deuteron elastic scattering at intermediate energies, the tensor part of the scattering amplitude is approximately separated into the amplitude from the T R -type tensor interaction and that from the T L -type one. Numerical calculations justify this separation for the folding T R -type interaction and phenomenologically introduced T L-type ones. Some polarization quantities are shown to distinguish between these tensor interactions.

INCLUSIVE REACTIONS WITH THREE POLARIZED PARTICLES

In the reaction p+p→Λ+X with up to all three known particles polarized (which will be studied in Fermilab’s upcoming polarization facility) the relationship of the various polarization observables to the 20 three-in-three-out amplitudes is simply given by two 4-by-4 and 12 2-by-2 submatrices. The QCD predictions are said to be the firmest in the large momentum transfer region. There, in the lowest order perturbative calculations only two amplitudes are nonzero, thus yielding only six nonzero polarization quantities with four relations among them. For smaller momentum transfers, Regge model predictions for double correlation observables may be tested even though such models have failed to predict the large single Λ polarization which has been the subject of so much speculation in recent years. The three models which attempt to explain this large polarization can also be tested in these reactions with up to three polarized particles since they should yield small asymmetries for the incident particles. All in all, such polarization experiments will significantly strengthen the testing of the various proposed theoretical models.

Should we expect large polarization effects at high energies?

Abstract It is demonstrated that while in reactions at very high energies polarization quantities in which the polarization of only one particle is specified are likely to be small, due to dynamics-independent factors, for many of the kinematic configurations of interest (and particularly at small t values), this is in no way indicative of other polarization quantities many of which could very well be far from the trivial values of 0 and 1. An example illustrates the statement.

Structure of elastic p-p scattering at low and high energies.

It is observed that p-p elastic scattering at 90\ifmmode^\circ\else\textdegree\fi{} between 0.3 and 1.0 GeV is described by planar-transverse amplitude of which two are equal in magnitude and one is about three times larger in magnitude. This feature, extrapolated to much higher energies, is used to predict p-p polarization quantities, in part by itself, in part in combination with the extension of another, previously observed feature of planar-transverse amplitudes. Comparison with existing data is favorable. Predictions are then made for other, yet unmeasured but readily measurable polarization quantities for p-p elastic scattering.

Unambiguously Complete Characterization of Reactions

It is shown that in order to determine all reaction amplitudes for a reaction containing particles with arbitrary spins without even a discrete ambiguity (except for an overall phase factor), one must measure at least one observable with spin polarization along each of three noncoplanar directions. The result has an impact on experimental programs measuring polarization quantities in elementary particle, nuclear, atomic, and molecular physics.

Interpretation of Tests of Time-Reversal Invariance

Some of the most sensitive tests of time-reversal invariance in particle and nuclear physics involve the measurement of certain polarization quantities in elastic scattering which are thought to be exactly zero when time-reversal invariance holds. It is shown that a nonzero result for such quantities need not indicate a violation of time-reversal invariance, but can be the consequence of a dynamics which is time-reversal invariant but which violates rotation or Lorentz invariance. These two alternatives can be told apart by subsidiary measurements.

The differential cross section and polarization quantities in the 4He(d, p)n 4He and 2H(α, n)p 4He reactions

The differential cross section and the polarization quantities ( T 11, T 20, T 21, T 22, P γ' ) in the deuteron breakup reaction by an α-particle are calculated in the framework of the recently developed three-body model. All values are discussed under the incomplete kinematical condition. All polarization quantities are caused by the difference of the potential between p 3 2 and p 1 2 waves of the N-α interaction. Results of the calculation are compared with the available measurement of (i) the differential cross section and the deuteron vector analysing power in the 4He( d , p)n 4He reaction and (ii) the differential cross section and neutron polarization in the 2H(α, n )p 4He reaction. The agreement with experiment is very satisfactory in each case. Among the tensor analysing powers of the deuteron the absolute value of T 20 is very large. Observables at the FSI peak corresponding to 5He g.s. are discussed systematically in the energy region of 5.4–20 MeV of the incident deuteron in the 4He(d, p)n 4He reaction. Although the differential cross section is not sensitive to the energy of the three-body resonance, the polarization quantities T 11, T 20, P γ' are quite sensitive to it.

Absolute infrared intensities of methyl bromide and all deuterium derivatives

The integrated infrared intensities of all the fundamentals of CH3Br, CH2DBr, CHD2Br, and CD3Br are experimentally determined using nitrogen broadening pressures of 37 atm. The results are interpreted in terms of dipole moment derivatives with respect to the symmetry coordinates (∂μ/∂S) and in terms of bond charge parameters. These molecular polar quantities derived from the observed intensities are compared with the corresponding values from molecular orbital calculations.

Polarization transfer in deuteron elastic scattering and the deuteron-nucleus tensor interaction

Abstract It is shown that the angular distributions of the polarization transfer coefficients contain new complementary information on the tensor part of the deuteron-nucleus interaction which cannot be obtained solely from tensor analyzing power measurements. Using a formalism where the polarization quantities carry definite spin-flip quantum numbers we derive the linear combinations of observables expected to be more sensitive to tensor force effects. The way they can help to distinguish between different types of tensor potentials is briefly discussed.