Angular Density Research Articles

The dynamics of the angular and radial density correlation scaling exponents in fractal to non-fractal morphodynamics

Abstract Fractal/non-fractal morphological transitions allow for the systematic study of the physics behind fractal morphogenesis in nature. In these systems, the fractal dimension is considered a non-thermal order parameter, commonly and equivalently computed from the scaling of the two-point radial- or angular-density correlations. However, these two quantities lead to discrepancies during the analysis of basic systems, such as in the diffusion-limited aggregation fractal. Hence, the corresponding clarification regarding the limits of the radial/angular scaling equivalence is needed. In this work, considering three fundamental fractal/non-fractal transitions in two dimensions, we show that the unavoidable emergence of growth anisotropies is responsible for the breaking-down of the radial/angular equivalence. Specifically, we show that the angular scaling behaves as a critical power-law, whereas the radial scaling as an exponential that, under the fractal dimension interpretation, resemble first- and second-order transitions, respectively. Remarkably, these and previous results can be unified under a single fractal dimensionality equation.

One-dimensional displacement of active matter on curved substrates

We analytically find the diffusion of overdamped active Brownian particles (ABPs) constrained to move along curved one-dimensional channels. The autonomous motion of these particles is achieved by a projection of their internal propulsion force along the channels' long section. In particular, the diffusion of ABPs moving on one-dimensional channels with a form of a circle, an ellipse, and a limacon of second order is analysed. To characterise the effect of substrate's geometry and self-propulsion on their diffusion, analytical expressions for the ABPs short- and long-time variances, as well as their steady angular probability density functions are offered. Curvature effects are found to reduce the time an ABP reaches its steady state. Our theoretical results are validated using Brownian dynamics simulations. This model may be relevant for experiments dealing with catalytic driven systems, bacteria, and tumour cell dispersion in one-dimensional channels.

Effect of equal-channel angular pressing (ECAP) and current density of cathodic hydrogen charging on hydrogen trapping in the low-alloy steel

Effect of equal-channel angular pressing (ECAP) and current density of cathodic hydrogen charging on hydrogen trapping in the low-alloy steel

High-brightness source of energetic He atoms

In atom beam lithography, a beam of kilo-electron-volt helium atoms illuminates a stencil mask and transmitted beamlets transfer the mask pattern to resist on a substrate. It shares the advantages of masked ion beam lithography but is immune to charging artifacts that limit resolution and pattern fidelity. This paper describes a high-brightness source of energetic He atoms, where He+ ions are extracted from a multicusp ion source, focused by two-stage accelerating optics, and neutralized by charge-transfer scattering in a differentially pumped, He-filled cell. Since scattering angles are extremely small, the straight line trajectories of scattered atoms are essentially tangent to the (possibly curved) trajectories of the parent ions. Space-charge repulsion prevents the ion beam crossing over; instead, it converges to a waist of minimum cross section before diverging further downstream. Atom trajectories produced by a cell placed in the region of intense space charge near the waist are strongly affected by the curvature of ion trajectories within the cell. The flaring of the ion beam due to space charge can be used to increase the width of the atom beam, although to the detriment of resolution. In this paper, the authors study a configuration where the cell is placed in the converging ion beam as far as practicable from the ion-beam waist. The atom beam then converges to a crossover, which becomes the virtual source seen by the mask. The source diameter and angular flux density initially increase with increasing cell pressure but saturate at higher pressures; the respective saturation values at 50 keV are 125 μm (2σ) and 8.7 × 1017 particles/s sr. Under these conditions, the beam diameter is ∼2.5 cm, 7 m from the source. A practical system for subnanometer printing is discussed with 0.2 nm (2σ) penumbral blur and 1.25 × 1013 particles/s cm2 flux density over a 1 cm circular field.

Renewal of Transient Spiral Modes in Disk Galaxies

Abstract Spiral structure in disk galaxies could arise from transient modes that create conditions conducive for their regeneration; this is the proposal of Sellwood and Carlberg, based on simulations of stellar disks. The linear response of an axisymmetric stellar disk, to an adiabatic nonaxisymmetric transient mode, gives a final distribution function (DF) that is equal to the initial DF everywhere in phase space, except at the Lindblad and corotation resonances where the final DF is singular. We use the nonlinear theory of adiabatic capture into resonance to resolve the singularities and calculate the finite changes in the DF. These take the form of axisymmetric “scars” concentrated around resonances, whose DFs have simple general forms. Global changes in the physical properties are explored for a cool Mestel disk: we calculate the DFs of scars and estimate the changes in the disk angular momentum, surface density, and orbital frequencies leading to shifts in resonances. Resonant torques between disk stars and any new linear nonaxisymmetric mode are suppressed within a scar, as is epicyclic heating. Because all resonances of a linear mode with the same angular wavenumber and pattern speed as its precursor lie inside the scars of the precursor, it suffers less damping. Hence, scars filter the spectrum of noise-generated modes, promoting the renewal of a few select modes. Relic scars sustained by a galaxy disk, due to past tidal interaction with a passing companion, may still be active enablers of nonaxisymmetric modes, such as the two-armed “grand design” spiral patterns.

Molecular dynamics studies the effects of the earth's surface depth on the heterogeneous kinetics of MgSiO3

This paper studies the shape of the earth's surface, the formation of layers and the influencing factors of the earth's surface: Depth (h), h = 0 km, 1820 km, 2912 km, 3640 km, 4550 km, 5460 km and h = 6371 km with MgSiO3 5000 atoms; atomic number (N), N = 3000 atoms, 4000 atoms, 5000 atoms, 6000 atoms at h = 2912 km; annealing time (t), t = 9.56 ps, 19.12 ps, 28.68 ps, 38.24 ps, 47.8 ps with MgSiO3 5000 atoms and h = 2912 km on the inhomogeneous kinetics of MgSiO3 material by means of Molecular Dynamics (MD) simulation with the Born-Mayer (BM) coupling potential, periodic boundary conditions. The inhomogeneous kinetic results of MgSiO3 material were analyzed through Radial Distribution Function (RDF), average Coordinate Number (CN), angular distribution, angular distribution density, size (l), the total energy of the system (Etot) and the length of the bonds Si-Si, Si-O, O-O, Si-Mg, O-Mg, Mg-Mg. The results show the effect of the depth of the earth's surface, the number of atoms, and the incubation time on the heterogeneous kinetics of MgSiO3 material. In addition, the results show that with the depth of the earth's surface from h = 0 km to h = 1820 km has the change of number of structural units SiO4, SiO5, SiO6, MgO3, MgO4, MgO5, MgO6, MgO7, MgO8, MgO9 are strongest, descending with 1820 km < h < 4550 km and unchanged with h > 4550 km and especially the disappearance of SiO4, SiO5, SiO6 structural units.

Analysis of aligning active local searchers orbiting around their common home position.

We discuss effects of pairwise aligning interactions in an ensemble of central place foragers or of searchers that are connected to a common home. In a wider sense, we also consider self-moving entities that are attracted to a central place such as, for instance, the zooplankton Daphnia being attracted to a beam of light. Single foragers move with constant speed due to some propulsive mechanism. They explore at random loops the space around and return rhytmically to their home. In the ensemble, the direction of the velocity of a searcher is aligned to the motion of its neighbors. At first, we perform simulations of this ensemble and find a cooperative behavior of the entities. Above an overcritical interaction strength the trajectories of the searcher qualitatively changes and searchers start to move along circles around the home position. Thereby, all searchers rotate either clockwise or anticlockwise around the central home position as it was reported for the zooplankton Daphnia. At second, the computational findings are analytically explained by the formulation of transport equations outgoing from the nonlinear mean field Fokker-Planck equation of the considered situation. In the asymptotic stationary limit, we find expressions for the critical interaction strength, the mean radial and orbital velocities of the searchers and their velocity variances. We also obtain the marginal spatial and angular densities in the undercritical regime where the foragers behave like individuals as well as in the overcritical regime where they rotate collectively around the considered home. We additionally elaborate the overdamped Smoluchowski-limit for the ensemble.

53.2: Invited Paper: Current IEC Standardization on Evaluating Image Resolution in VR/AR Displays

VR/AR eyewear displays are truly here in 2018, but the challenge remains. One of the potential benefits of VR/AR applications is the immersive experience with the virtual world that can suspend disbelief. However, the drawback is that the technology still needs improvement. Currently, most commercially available VR displays may only output 10‐20 ppd (pixel per degree) in angular resolution due to the limitation of the microdisplays. However, our human eye can dissolve the image details up over 60 ppd. Thus, the lack in image resolution can easily lose its capability of fooling the user. In order to improve the design such as the microdisplay panel or imaging optics, we need to evaluate the characteristics of the virtual images in the visual aspect. In conventional display measurement, pixel angular resolution is applied, but the pixel number is only a physical definition. Additionally, for a small pixel structure, it may have high spot luminance and low average image luminance which would cause an uncomfortable stimulus to the user.Therefore, what is a better way to define image resolution in VR/AR displays? In this work, we reviewed the current methods proposed in IEC TC110 on image quality. Then, some of the key factors that involve the image resolution measurement would be presented. We first reviewed the fundamental aspects of visual‐spatial perception and the mechanism of the human eye, and then we explained why such display limits the image quality of VR/AR display systems. In addition, we presented other measurement parameters including the newly proposed term ‐ pixel angular density, MTF (modulation transfer function) as well as the virtual image quality in static and moving picture conditions. These parameters were addressed in this work from introducing the definition to how and why they are necessary to test. An example of measurement in static picture resolution is shown in Figure1. The contrast modulation measurement is performed to determine static picture resolution. The test patterns and the calculation formula are critical in the measurement. The goal of this work is to provide some essential and fundamental guidelines to manufactures and engineers in the image resolution measurement of VR/AR systems.An example of contrast modulation measurementfigure

Atom-projected and angular momentum resolved density of states in the ONETEP code

Local and angular momentum projected densities of states (DOS) are invaluable sources of information that can be obtained from density functional theory calculations. In this work, we describe a theoretical framework within ONETEP’s linear-scaling DFT formalism that allows the calculation of local (atom-projected) and angular momentum projected density of states l-p-DOS. We describe four different bases that can be used for projecting the DOS with angular momentum resolution and perform a set of tests to compare them. We validate the results obtained with ONETEP’s l-p-DOS against the plane-wave DFT code CASTEP. Comparable results between ONETEP’s and CASTEP’s charge spilling parameters are observed when we use pseudo-atomic orbitals as the projection basis sets. In general, the charge spilling parameters show remarkably low values for projections using non-contracted spherical waves as the angular momentum resolved basis. We also calculate the d-band and d-band centres for Pt atoms in (1 1 1) facets of cuboctahedral Pt nanoparticles of increasing size, which is an example of l-p-DOS application commonly used as an electronic descriptor in heterogeneous catalysis. Interestingly, the different projection bases lead to similar conclusions, showing the reliability of the implemented method for such studies. The implementation of these methods in a linear-scaling framework such as ONETEP provides another tool for analysing the electronic structure of complex nanostructured materials.

Role of Columnar Defect Size in Angular Dependent Flux Pinning Properties of YBCO Thin Films

The effect of artificially produced BaHfO $_3$ , BaZrO $_3$ , and BaSnO $_3$ nanocolumns within the YBa $_2$ Cu $_3$ O $_{6+{\mathrm{x}}}$ (YBCO) lattice is investigated in terms of flux pinning and vortex dynamics by studying the properties of the angular dependent critical current density. Based on the differences in the growth mechanisms of discussed dopant species, the superconducting properties such as the critical current density, the accommodation field, and the effective pinning force have been observed to be greatly dependent on the size and the distribution of the nanocolumns. Therefore, the mechanisms of the collective individual and multivortex pinning have been observed being in a critical role when interpreting the in-field critical current anisotropy in YBCO films with artificial pinning centers.

Human foveal cone photoreceptor topography and its dependence on eye length

We provide the first measures of foveal cone density as a function of axial length in living eyes and discuss the physical and visual implications of our findings. We used a new generation Adaptive Optics Scanning Laser Ophthalmoscope to image cones at and near the fovea in 28 eyes of 16 subjects. Cone density and other metrics were computed in units of visual angle and linear retinal units. The foveal cone mosaic in longer eyes is expanded at the fovea, but not in proportion to eye length. Despite retinal stretching (decrease in cones/mm2), myopes generally have a higher angular sampling density (increase in cones/deg2) in and around the fovea compared to emmetropes, offering the potential for better visual acuity. Reports of deficits in best-corrected foveal vision in myopes compared to emmetropes cannot be explained by increased spacing between photoreceptors caused by retinal stretching during myopic progression.

Dynamics and density correlations in matter-wave jet emission of a driven condensate

Emission of matter wave jets has been recently observed in a Bose-Einstein condensate confined by a cylindrical box potential, induced by a periodically modulated inter-particle interaction (Nature {\bf 551}, 356 (2017)). In this paper we apply the time-dependent Bogoliubov theory to study the quantum dynamics and the correlation effects observed in this highly non-equilibrium phenomenon. Without any fitting parameter, our theoretical calculations on the number of ejected atoms and the angular density correlations are in excellent quantitative agreement with the experimental measurements. The exponential growth in time of the ejected atoms can be understood in terms of a dynamical instability associated with the modulation of the interaction. We interpret the angular density correlation of the jets as the Hanbury-Brown-Twiss effect between the excited quasi-particles with different angular momenta, and our theory explains the puzzling observation of the asymmetric density correlations between the jets with the same and opposite momenta. Our theory can also identify the main factors that control the height and width of the peaks in the density correlation function, which can be directly verified in future experiments.

3D Spatial Characteristics of C-V2X Communication Interference

In C-V2X (cellular vehicle-to-everything) communication networks, dense spatial reuse of the available radio spectrum is required to achieve efficient spectral usage. Spectrum reuse causes severe network interference where signals from many undesired transmitters are aggregated at a receiver. This paper investigates the 3D spatial characteristics of C-V2X communication interference in the angular domain. A 3D GIDM (Gaussian interference distribution model) is proposed, and the corresponding interference APD (angular power density) is given. Then, the closed-form expressions of some key spatial statistics of interference are derived based on the interference APD. Finally, the closed-form expressions of the probability density function and spatial correlation function of SIR (signal–to–interference ratio) are derived based on the 3D multipath APD model and spatial statistics of the Rice channel. Simulation analysis shows that 3D spatial angular directions have significant effect on these spatial statistics of interference and the spatial correlation function of SIR. The results provide useful insight on the analysis and design of the interference-limited networks.

Phase descriptions of a multidimensional Ornstein-Uhlenbeck process.

Stochastic oscillators play a prominent role in different fields of science. Their simplified description in terms of a phase has been advocated by different authors using distinct phase definitions in the stochastic case. One notion of phase that we put forward previously, the asymptotic phase of a stochastic oscillator, is based on the eigenfunction expansion of its probability density. More specifically, it is given by the complex argument of the eigenfunction of the backward operator corresponding to the least-negative eigenvalue. Formally, besides the "backward" phase, one can also define the "forward" phase as the complex argument of the eigenfunction of the forward Kolomogorov operator corresponding to the least-negative eigenvalue. Until now, the intuition about these phase descriptions has been limited. Here we study these definitions for a process that is analytically tractable, the two-dimensional Ornstein-Uhlenbeck process with complex eigenvalues. For this process, (i) we give explicit expressions for the two phases; (ii) we demonstrate that the isochrons are always the spokes of a wheel but that (iii) the spacing of these isochrons (their angular density) is different for backward and forward phases; (iv) we show that the isochrons of the backward phase are completely determined by the deterministic part of the vector field, whereas the forward phase also depends on the noise matrix; and (v) we demonstrate that the mean progression of the backward phase in time is always uniform, whereas this is not true for the forward phase except in the rotationally symmetric case. We illustrate our analytical results for a number of qualitatively different cases.

Identification of incident parameters of interference beams using angular power spectral density

Laser interference lithography is attracting increasing interest among researchers because of its high-efficiency and low-cost in fabrication of patterns. However, there are always operational errors in the setup of interference systems, which have a significant effect on the finally produced interference pattern. This paper has systematically investigated the influence of incident parameters including the incident angle, azimuth angle, and polarization angle on interference patterns. An algorithm has been proposed to extract interference fringes from complicated multibeam interference patterns using the angular power spectral density (APSD) function. The incident parameters were calculated based on the data extracted from the APSD images. Simulations were carried out to validate the effectiveness of the proposed algorithm. 3-D periodic patterns were fabricated on silicon wafers using three-beam interference lithography. The topographies of the samples were measured using an optical profiler. Based on the established model, incident parameters of the interference system setup were calculated. The computational results are in good agreement with the preset values. The results have demonstrated the validation of the developed algorithm for incident parameter identification of interference beams.

Estimation of Two-Dimensional Non-Symmetric Incoherently Distributed Source with L-Shape Arrays.

In the field of array signal processing, distributed sources can be regarded as an assembly of point sources within a spatial distribution. In this study, a two-dimensional (2D) non-symmetric incoherently distributed (ID) source model is proposed; we explore the estimation of a 2D non-symmetric ID source using L-shape arrays. The 2D non-symmetric ID source is established by modeling the angular power density function (APDF) as a Gaussian mixture model. Estimation of the non-symmetric distributed source is proposed based on the expectation maximization (EM) framework. The proposed EM iterative framework contains three steps in the process of each circle. Firstly, the nominal azimuth and nominal elevation of each Gaussian component are obtained from the phase parts of elements in sample covariance matrices. Then the angular spreads can be solved through a one-dimensional (1D) search by the original generalized Capon estimator. Finally, weights of each Gaussian component are obtained by solving the least-squares estimator. Simulations are conducted to verify the effectiveness of the estimation technique.

Three-Dimensional Optical Spin Angular Momentum Flux of a Vector Beam with Radially-Variant Polarization in Near Field

The near-field characteristics of a radially-variant vector beam (RVVB) are analyzed by using the vectorial angular spectrum method. The non-paraxial RVVB can be decomposed into the propagating wave and the evanescent wave in near field. The coherent superposition of the longitudinal and transverse components of the RVVB results in a three-dimensional (3D) profile of the spin angular momentum flux density (SAM-FD). The evanescent wave part dominates the near field of a highly non-paraxial RVVB. The longitudinal component has a large impact on the 3D shape of the optical SAM-FD. Therefore, the 3D SAM-FD configuration of the RVVB can be manipulated by choosing the initial states of polarization arrangement. In particular, the transverse SAM-FD with a spin axis orthogonal to the propagation direction offers a promising range of applications spanning from nanophotonics and plasmonics to biophotonics.

Regression‐type models for extremal dependence

AbstractWe propose a vector generalized additive modeling framework for taking into account the effect of covariates on angular density functions in a multivariate extreme value context. The proposed methods are tailored for settings where the dependence between extreme values may change according to covariates. We devise a maximum penalized log‐likelihood estimator, discuss details of the estimation procedure, and derive its consistency and asymptotic normality. The simulation study suggests that the proposed methods perform well in a wealth of simulation scenarios by accurately recovering the true covariate‐adjusted angular density. Our empirical analysis reveals relevant dynamics of the dependence between extreme air temperatures in two alpine resorts during the winter season.

Improving AoA Localization Accuracy in Wireless Acoustic Sensor Networks with Angular Probability Density Functions.

Advances in energy efficient electronic components create new opportunities for wireless acoustic sensor networks. Such sensors can be deployed to localize unwanted and unexpected sound events in surveillance applications, home assisted living, etc. This research focused on a wireless acoustic sensor network with low-profile low-power linear MEMS microphone arrays, enabling the retrieval of angular information of sound events. The angular information was wirelessly transmitted to a central server, which estimated the location of the sound event. Common angle-of-arrival localization approaches use triangulation, however this article presents a way of using angular probability density functions combined with a matching algorithm to localize sound events. First, two computationally efficient delay-based angle-of-arrival calculation methods were investigated. The matching algorithm is described and compared to a common triangulation approach. The two localization algorithms were experimentally evaluated in a m by m room, localizing white noise and vocal sounds. The results demonstrate the superior accuracy of the proposed matching algorithm over a common triangulation approach. When localizing a white noise source, an accuracy improvement of up to 114% was achieved.

Interpretation of the results of the experiment on generation of parametric X-radiation by relativistic electrons in a single-crystal target

The coherent X-ray radiation generated by a relativistic electron beam in a monocrystalline target of a limited thickness is investigated in the framework of two-wave approximation of the dynamical theory of diffraction in the conditions of asymmetric reflection of the radiation waves in relation to the target surface. The calculations of the radiation angular density for the conditions of the recent experiment on generation of parametric X-ray radiation (PXR) have been carried out. It has been shown, that adequate description of such experiments is possible only with use of the dynamical theory which takes into account the effects of asymmetric reflection of the radiation.