Angular Plots Research Articles

Electromagnetic radiation in chiral matter: The Cherenkov case

Starting from the modified Maxwell equations in Carroll-Field-Jackiw electrodynamics we study the electromagnetic radiation in a chiral medium characterized by an axion coupling $\theta(x)=b_\mu x^\mu$, with $b_\mu= (0,\mathbf{b})$, which gives rise to the magnetoelectric effect. Employing the stationary phase approximation we construct the Green's matrix in the radiation zone which allows the calculation of the corresponding electromagnetic potentials and fields for arbitrary sources. We obtain a general expression for the angular distribution of the radiated energy per unit frequency. As an application we consider a charge moving at constant velocity parallel to $\mathbf{b}$ in the medium and discuss the resulting Cherenkov radiation. We recover the vacuum Cherenkov radiation. For the case of a material with refraction index $n > 1$ we find that zero, one or two Cherenkov cones can appear. The spectral distribution of the radiation together with the comparison of the radiation output of each cone are presented, as well as some angular plots showing the appearance of the cones.

Axon fiber orientation as the source of T1 relaxation anisotropy in white matter: A study on corpus callosum in vivo and ex vivo.

Recent studies indicate that T1 in white matter (WM) is influenced by fiber orientation in B0 . The purpose of the study was to investigate the interrelationships between axon fiber orientation in corpus callosum (CC) and T1 relaxation time in humans in vivo as well as in rat brain ex vivo. Volunteers were scanned for relaxometric and diffusion MRI at 3 T and 7 T. Angular T1 plots from WM were computed using fractional anisotropy and fiber-to-field-angle maps. T1 and fiber-to-field angle were measured in five sections of CC to estimate the effects of inherently varying fiber orientations on T1 within the same tracts in vivo. Ex vivo rat-brain preparation encompassing posterior CC was rotated in B0 and T1 , and diffusion MRI images acquired at 9.4 T. T1 angular plots were determined at several rotation angles in B0 . Angular T1 plots from global WM provided reference for estimated fiber orientation-linked T1 changes within CC. In anterior midbody of CC in vivo, where small axons are dominantly present, a shift in axon orientation is accompanied by a change in T1 , matching that estimated from WM T1 data. In CC, where large and giant axons are numerous, the measured T1 change is about 2-fold greater than the estimated one. Ex vivo rotation of the same midsagittal CC region of interest produced angular T1 plots at 9.4 T, matching those observed at 7 T in vivo. These data causally link axon fiber orientation in B0 to the T1 relaxation anisotropy in WM.

Microstructure, micromorphology, and fractal geometry of hard dental tissues: Evaluation of atomic force microscopy images.

Determining surface topography of different tissues of the molar tooth with novel analytical methods has opened new horizons in dental surface measurements which characterize tooth surface quality in dentistry. Studying surface topological measurements and comparing surface morphology of hard tissue of the molar tooth are the ultimate goals of the present study. Ten molar teeth have been chosen for investigating their surface characteristics through image processing techniques. The power spectral density (PSD) and fast Fourier transform algorithms of every molar tooth containing enamel, dentin, and cementum have determined that the characterization of surface profiles is possible. As can be seen, PSD along with fractal dimensions leads to good results for teeth surface topography. Moreover, PSD angular plot assures appropriate description of surface.

The Seasonality of Acute Attack of Primary Angle-Closure Glaucoma in Beijing, China

In this study, the seasonality of acute attack of primary angle-closure glaucoma (PACG) was analysed. This retrospective case series included 283 patients (200 women, 83 men; mean age, 68.2 ± 10.3 years; range, 37–96 years) with acute attack of PACG from a university-based clinic over 4 years. Patients’ age and sex, and the date and season of onset of PACG attack, were analysed. Descriptive analysis and von Mises distribution were used for statistical analysis. The highest incidence of acute attack of PACG was observed in those aged 60–69 years (34.6%). Descriptive analysis showed that the incidence was greater in June and July for men, November for women, and November for the entire sample. An angular plot (using von Mises distribution) of the individual dates of onset revealed the estimated peak onset on September 11, November 8, and October 28 for men, women, and both, respectively. Integration of the results from the two analyses revealed the incidence to be higher in the summer and winter for men, and in the winter for women and for the entire sample. More females than males were affected. Monthly and seasonal variations in onset were observed, which might be related to weather changes.

The devisable reflection-enhanced lumpy silver particle and its application in thin film amorphous silicon solar cell

A tailored large-size plasmonic core-protuberances silver particle with unique optical properties with promising applications in thin-film solar cells was numerically and experimentally studied. The designed particle possesses an extremely enhanced electromagnetic near-field excited by localized surface plasmons resonance and its far field angular plots of light scattering power indicated an enhanced back-scattering ability. When embedded the lumpy particles into the rear of thin-film amorphous silicon solar cells, light trapping in broad wavelength range and ideal short circuit density of the cells increased. A simple one-step reaction was established to acquire the structured particles. The strengthening backward scattering capacity in a broadband light region was also verified experimentally.

Wrist motion analysis in scaphoid nonunion.

The motion of human wrist is a complex and multidirectional process. The aim of this study was to develop a reliable and practicable method to measure motion impairment of the wrist in patients who incurred a scaphoid nonunion. A scaphoid nonunion in computed tomography as well as the consent in this study was required. A total of nine patients with unilateral scaphoid nonunion accomplished maximal circumferential wrist movements. The wrist movements were measured with an electrogoniometer (Biometrics Ltd.). To quantify maximal wrist motion we constructed the maximal boundaries of the wrist motion from angular plots in flexion-extension (FE) and radio-ulnar deviation (RUD). We calculated the area of the circumduction envelope, the ranges of motion in FE and RUD and the main axis in wrist motion (dart-throwin-motion). The collected data were reconstructed with a custom-made MatLab program. We compared the impaired with the unimpaired side of each patient and analyzed with student's t test. A scaphoid nonunion significantly reduced motion ranges in flexion/extension but not in ulnar and radial deviation. The overall mobility as quantified by the area of the circumduction envelope, decreased significantly. The circumduction boundaries of the wrists showed a kidney-shaped configuration with an oblique axis from radial/extension to ulnar/flexion. Our results demonstrate that scaphoid nonunion without pain has motion deficits and may be poorly quantified with conventional manual goniometers.

The phase diagram for coexisting d-wave superconductivity and charge-density waves: cuprates and beyond

Phase diagrams of d-wave superconductivity characterized by an order parameter Δ coexisting with charge-density waves (CDWs) characterized by an order parameter Σ were constructed for the two-dimensional Fermi surface (FS) appropriate to, e.g., cuprates. CDWs were considered as an origin of the pseudogap appearing at antinodal FS sections of the dx2−y2 superconductor. Two types of the Σ-reentrance were found: with the temperature, T, and with the opening of the CDW sector, 2α. The angular plots in the momentum space for the resulting gap profile over the FS (‘gap roses’) were obtained. The gap patterns are rather involved, giving insight into the difficulties of the interpretation of photoemission spectra. It was shown that the Σ–Δ coexistence region exists even for the complete dielectric gapping due to the distinction between the superconducting and CDW order parameter symmetries. The checkerboard and unidirectional CDW configurations were examined, and both the phase diagrams and the behavior with T and α of the order parameters were found to differ. A more general case with a non-zero mismatch angle β between the superconducting lobes and the CDW sectors was analyzed, the case β = π/4 corresponding to the dxy symmetry of the superconducting order parameter. The phase diagrams were found to be sensitive to β-variations, showing that internal strains and external pressure can drastically affect the behavior of Σ(T) and Δ(T).

Dynamic column formation in Na-FLHC clay particles: Wide angle X-ray scattering and rheological studies

The dynamic chain and column formation of 5wt.% clay particles suspended in silicone oil has been studied using synchrotron Wide Angle X-Ray Scattering (WAXS) technique and rheometry. The anisotropic arrangement of particles described by the global order parameter S has been investigated. The WAXS data have also allowed distinguishing between the chain and column formation processes by comparison of the change of WAXS angular plots maxima with the current density growth in function of time. The saturation time ts (after which there was no change in the system observed) was estimated. In addition, the rheological properties of the ERF have been measured including the static yield stress.

Wrist Circumduction Reduced by Finger Constraints

Assessment of wrist motion is important in diagnosing and treating motion impairment after injuries to the wrist. Little is known of how finger posture influences the movement of the wrist. The aim of this study was to investigate the effect of finger constraints on the maximum circumduction movement of the wrist. Fifteen male right-handed subjects performed maximal circumferential wrist movements under 4 finger conditions: unconstrained fingers, holding a large cylinder (50 mm diameter), holding a small cylinder (25 mm diameter), and closed fist position. The wrist motion was captured by a surface marker-based motion analysis system. To quantify wrist motion capability, we constructed the maximal boundaries of wrist motion (circumduction envelope) from angular plots in flexion-extension (FE) and radial-ulnar deviation (RUD). The ranges of motion in FE and RUD and the envelope area were calculated. Finger constraints significantly reduced motion ranges in flexion and ulnar deviation, but not in extension and radial deviation. In comparison to the unconstrained finger condition, the motion ranges in flexion decreased by 13%, 16%, and 27% for the large cylinder, small cylinder, and fist conditions, respectively. The range of ulnar deviation was reduced by 10% for the large and small cylinder conditions and by 11% for the fist condition. The overall mobility in FE and RUD, as quantified by the area of circumduction envelope, decreased by 15%, 15%, and 23% for the large cylinder, small cylinder, and fist conditions, respectively. Wrist mobility is facilitated by the synergistic motion of finger joints. Constraining fingers in static flexion posture reduces wrist flexion and ulnar deviation without decreasing extension and radial deviation. A clinical implication is that wrist motion should be assessed under standardized finger joint configuration.

Surface topography of the cylindrical gear tooth flanks after machining

The paper presents an analysis of three-dimensional surface topography of side and side out in tooth space flanks of cylindrical gear machined after hobbing and chiselling by Fellows method. The parameters and functions of surface topography as well as spectral analysis were used. Primary surface topography after extraction of involute tooth profile was analysed. It was found that contour maps of areal power spectral density and autocorrelation functions were very useful for the analysis of teeth flank surface topography. The angular plot of areal power spectral density function assures proper description of surface, background and defects directionalities. Surface texture parameter SPtr and isotropy index Spiso are useful for quantitative surface topography analysis. Good distribution functions of amplitudes and summit curvatures isolate surface roughness height and shape. It was proved using a kinematical–geometric digital model of machining simulation in 3D system, universal generalised model and experimental investigations that the roughness height and roughness spacing were smaller for the tooth point surface than for the root surface after hobbing and Fellows chiselling. Roughness height of tooth profile after machining by one-coil cutter with great axial feed and by modular gear-sharper cutter is smaller than roughness height of tooth line. Inverse dependencies take place after hobbing by three-coil cutter with small axial feed. It was also found that flank teeth surface topography, primary profile along teeth height and teeth line along its width were quasi-periodic. In all the analysed cases, teeth flank surfaces going to the machining have higher roughness height than surfaces going out from the machining. It was probably caused by direction of chips runout; chips damage surface going into the machining. The flank tooth surfaces of a gear made by hobbing and Fellows-chiselling method are anisotropic and strongly oriented along the helix. The orientation of the flank surfaces after hobbing is considerably lower than after Fellows chiselling.

Precise Investigation of Domain Pinning Energy in GaMnAs Using Planar Hall Effect and Magnetoresistance Measurements

The planar Hall effect (PHE) and magnetoresistance (MR) measurements have been carried out on a GaMnAs ferromagnetic semiconductor. The PHE and MR spectra exhibit interesting two-step magnetization switching behavior arising from the magnetic anisotropy properties of the system. By fitting the angle-dependent planar Hall resistance (PHR) data taken at 5 kG with the Stoner-Wohlfarth model, the cubic and uniaxial anisotropy constants were independently obtained. The anisotropy constants lead to the precise determination of easy axis direction, which turns out to be in good agreement with the easy axis determined from the angular plot of the switching field. The domain pinning energies were further obtained by fitting the angle dependence of the switching field, including the effect of uniaxial anisotropy

Three‐dimensional characterization of non‐gaussian water diffusion in humans using diffusion kurtosis imaging

Conventional diffusion tensor imaging (DTI) measures water diffusion parameters based on the assumption that the spin displacement distribution is a Gaussian function. However, water movement in biological tissue is often non-Gaussian and this non-Gaussian behavior may contain useful information related to tissue structure and pathophysiology. Here we propose an approach to directly measure the non-Gaussian property of water diffusion, characterized by a four-dimensional matrix referred to as the diffusion kurtosis tensor. This approach does not require the complete measurement of the displacement distribution function and, therefore, is more time efficient compared with the q-space imaging technique. A theoretical framework of the DK calculation is established, and experimental results are presented for humans obtained within a clinically feasible time of about 10 min. The resulting kurtosis maps are shown to be robust and reproducible. Directionally-averaged apparent kurtosis coefficients (AKC, a unitless parameter) are 0.74 +/- 0.03, 1.09 +/- 0.01 and 0.84 +/- 0.02 for gray matter, white matter and thalamus, respectively. The three-dimensional kurtosis angular plots show tissue-specific geometry for different brain regions and demonstrate the potential of identifying multiple fiber structures in a single voxel. Diffusion kurtosis imaging is a useful method to study non-Gaussian diffusion behavior and can provide complementary information to that of DTI.

Special issue: Physics of Organic Semiconductors

This special issue of physica status solidi (a) gives an overview of our present-day knowledge of the physics behind organic semiconductor devices, ranging from the growth of organic layers and crystals, their electronic properties at interfaces, their photophysics and electrical transport properties to the application in organic field-effect transistors, photovoltaic cells and organic light-emit-ting diodes. Guest Editor of the present issue is Wolfgang Brutting, professor at the University of Augsburg, where he leads a research group working on organic semiconductors, their physical and materials properties, and the understanding of the basic processes in these materials and devices. The cover picture is an angular plot of the anisotropy of the charge carrier mobility μ in the a–b plane of a rubrene single crystal, probed on an elastomeric rubber stamp field-effect transistor device. The black and red squares correspond to the values of μ extracted from the linear and saturation regimes of the transistor operation, respectively. More information can be found in the Review Article by R. W. I. de Boer et al. [1].

Chemometric techniques for exploring complex chromatograms: application of diode array detection high performance liquid chromatography electrospray ionisation mass spectrometry to chlorophyll a allomers

Triply coupled diode array detection high performance liquid chromatography mass spectroscopy is applied to a complex mixture of at least eight chlorophyll degradation products. Derivatives are employed to determine parts of the chromatogram of composition one. Mass selection is performed on the mass spectroscopic data. Principal components analysis is performed on both the raw and simultaneously normalised/standardised data; three dimensional projections of the data are obtained and compared to conventional two dimensional graphs. Angular plots between diode array loadings characteristic of individual compounds and scores of the diode array data are described. In mass spectra, angular plots between loadings characteristic of individual compounds and the remaining diagnostic masses reveal further mass spectral structure.

Numerical modelisation of the scattering of an acoustic wave from a wedge immersed in a fluid

In the present paper, we propose a numerical technique describing the scattering of an acoustic wave interacting with a sharp wedge immersed in water considered as homogeneous. The calculations are limited to the angular variations of the acoustic field scatttered in a plane perpendicular to the edge of the wedge. The theoretical angular plots which point out maxima in particular directions are compared with the experimental measurements. We notice a good agreement between the two determinations

Acoustic scattering by elastic spherical shells that have multiple massive internal components attached by compliant mounts

A study of the scattering of sound waves by a neutrally buoyant, submerged, spherical shell that has heavy masses internally mounted by springs to the shell is presented. The presence of the attached oscillating masses substantially changes the scattering cross section of the otherwise empty shell. Furthermore, if the compliance (i.e., the spring constants) of the mounts are varied—all else being the same—then the resulting cross section also varies substantially, often by more than an order of magnitude. It is seen that if the incident plane wave impinges upon the shell at its North pole, where the masses are mounted, then the effect of the spring-mass system on the scattering response is strongest. Away from the North pole, this effect weakens; when the incidence is from the South pole, it is weakest. In general, the cross-sectional distortion produced by the attached masses consists of a set of amplitude-modulated resonance features that are computed and displayed in a number of instances. These features seem to be confined around a frequency band containing the main resonances of the (coupled) oscillator formed by the masses. The shell motions are described by the bending theory and also by the exact elasticity theory. Comparing the two, it is possible to determine the limit of validity of the bending theory, which is seen to begin to fail just below the coincidence frequency for this shell. The ‘‘background’’ contribution is separated from the ‘‘resonance’’ contribution associated with the empty shell and also from that associated with the internal oscillator. This triple split, as emerging from a shell theory, does not seem to have been investigated in the past. (Bistatic) angular plots associated with peaks/dips in the backscattering cross section and some of the isolated and symmetric ‘‘rosettes’’ observable in selected cases are displayed. This analytic model is easily reproducible and does not require any special numerical code for evaluation.

Double photoionization of helium: Analysis of photoelectrons with respect to energies and angles.

The basic sixfold differential cross section ${\mathit{d}}^{6}$${\mathrm{\ensuremath{\sigma}}}^{2+}$/${\mathit{d}}^{3}$k${\mathit{d}}^{3}$k' (SDCS) of the double photoionization process is derived within a ``wave-function approach'' (WFA) using a highly correlated ground-state wave function and a double-continuum final state approximated by a symmetrized product of one-electron Coulomb waves with k and k' asymptotic momenta. Relevant integrations of the SDCS are shown to provide a complete description of the (\ensuremath{\gamma},2e) process. The theory is illustrated by calculations for helium targets: total cross sections, kinetic energy spectra, and angular plots of photoelectrons are presented. Considering the total cross section, it is found first that the agreement between the length and velocity result is worse than expected from the previous studies. In addition, the present model provides kinetic energy distributions of photoelectrons having the symmetry required by the Pauli principle. This is in contrast with earlier formulations of the WFA. For the SDCS, calculations have been done with final states where Coulomb waves were provided with either fixed charge (Z=2: unscreened nucleus) or variable effective charges. In the former case, it is found that the event where electrons escape with the same energy, along the polarization direction, has a significant probability. This deficiency is removed by use of angle-dependent effective charges since final-state correlation is partly accounted for in this way.

Interpretation of the three-dimensional sound fields scattered by submerged elastic shells and rigid spheroidal bodies

The direct scattering problem associated with submerged spheroidal targets at frequencies within their resonance regime is studied. The incident waves are plane and continuous, and the composition of the spheroid can be either impenetrable or penetrable. In the impenetrable case, the body is assumed rigid. In the penetrable case, the target is an elastic shell, whose motion is governed by the exact three-dimensional equations of linear elastodynamics. The aspect ratio of the spheroids takes on values from L/D=1.5–30. The method used in the calculations is the extended boundary condition (EBC) or T-matrix method. The target’s form function or scattering angular pattern in the farfield versus monostatic variable angles of incidence at fixed frequencies (i.e., monostatic angular plots), or versus frequency, at fixed directions of observation (i.e., backscattering responses), is displayed. The graphs exhibit the versatility of the EBC method, particularly in cases, such as for the elastic shell, in which analytic solutions are not possible. The case of an elastic shell is considerably more difficult than that of any impenetrable or solid elastic spheroid. The aspect ratio analyzed here for a shell is at the current upper limit of performance of the computational method used in our analysis. Various resonance effects in the displayed plots are studied, particularly the resonance isolation process present in the backscattering responses and the connection to combinations of Legendre functions observable in the angular plots. The relative values of the creeping-wave levels and those due to specular reflections are also compared. For very elongated spheroids, the creeping wave levels seem to be stronger(!). Calculated predictions are displayed, and an explanation of this interesting situation is offered.

Shape effects in the interaction between an edge dislocation and an elliptical inhomogeneity

The plane elasticity problem of the interaction between an edge dislocation and an elliptical inhomogeneity is solved, and the image glide-force on dislocation is computed. Contour plots of the force exterted by either an elliptic hole (crack) or a rigid elliptical inhomogeneity show that force is stronger for more elongated shapes, and that in some cases dislocation trapping effects undergo drastic changes even for slight shape variations. The general case is investigated by means of angular plots of force. They show increasing oscillatory angular depence on increasing both elongation and shear moduli difference.

Energy- and angular-dependent secondary-electron emission from a silicon (111) 7 × 7 surface. Emission from bulk states

Energy- and angular-dependent secondary-electron emission (EADSEE) spectra from a silicon (111) 7 \ifmmode\times\else\texttimes\fi{} 7 reconstructed surface are reported. Only spectra which consist of electrons that have emerged from bulk states are considered here. The spectra are interpreted in terms of the conventional three-step model, in which electrons are excited into high-lying conduction states, move to the surface, and emerge into the vacuum. Microscopic models are considered for the processes that contribute to each of the three steps. The processes which are important in determining the shape of these EADSEE spectra have been identified by comparing the predictions of the models with the observed spectra. The shape of the EADSEE spectra between 6 and 40 eV is determined mostly by the incoherent scattering that occurs as the electrons cross the reconstructed layer. This scattering obliterates the structure in the internal hot-electron distribution, structure which is observed in the spectra of electrons which emerge from a (111) 1 \ifmmode\times\else\texttimes\fi{} 1 unreconstructed surface. For emergence energies below 6 eV there is evidence for a number of processes. It is found that the spectral shape of the internal flux is dominated by structure in the density of conduction states, as first described by Kane. This shape is modified somewhat by energy-dependent transport losses. Most of the observed low-energy ( 6 eV) electrons have emerged coherently through the surface. The energy and angular structure in the low-energy secondary flux is affected in a number of ways in this emergence process. Evidence is seen for diffraction, refraction, and reflection of the emerging electrons. Diffraction at the surface causes peaks in the internal electron distribution to appear at angles of emergence not otherwise expected. Refraction of the outgoing waves leads to a cosine dependence of the angular plot of the secondary current for fixed energies. Reflection of the outgoing electrons at the surface barrier causes a decrease in the number of secondaries. With certain assumptions the reflection (transmission) coefficient of electrons at the barrier, and the wave-vector dependence of this coefficient, can be deduced from the data.