Non-spherical Model Research Articles

ROLE OF MODEL PARTICLE SHAPE IN DISCRETE ELEMENT MODELS OF BED STRUCTURE IN CONTAINERS

ABSTRACT A container comprising 5,000 particles was simulated to investigate the role of particle shape on the bed structure of particulate materials. The effect of particle shape on the packing structure of granular beds was investigated in terms of bed height, the distribution of solid fraction, coordination number and the force acting at the bottom of the container. The solid fraction of the beds, which ranged from 0.7–0.9 for spherical particles and 0.6–0.8 for elongated particles, shows a compacted structure for beds of spherical particles. The average bed's solid fraction was 0.825 and 0.750 for beds of spherical and elongated particles, respectively. The overall reduction in the average solid fraction was about 8% as aspect ratio of particles changed from 1 to 4. The solid fraction frequency distribution of the beds implied a wider variety of void shape and size for elongated particles. There was also a significant difference between the coordination number of spherical particles and nonspherical particles. The coordination number was 4.7 and 3.6 for spherical and elongated particles, respectively. However, the change in the magnitude of coordination number was greater (15.1%) in between beds of spherical and nonspherical particles (particles of aspect ratio 2), than in between beds with aspect ratio 2 and 4 (11.3%). The numerical results indicated that for a reliable prediction of real material behavior via discrete element models, the employed model should be capable of manipulating individual elements with shape as close as possible to the shape of real particles. PRACTICAL APPLICATIONSAs most of the agricultural materials comprise a system of individual nonspherical particles, a suitable discrete element (DE) model should be employed to gain realistic results. The DE models with spherical particles are very simple, which are less costly, while these models cannot predict the accurate behavior of systems comprising nonspherical particles. Hence, for such materials, using nonspherical models such as multisphere models is a must. Examples of such produce that need models with nonspherical or elongated elements are kernels and some fruits, whereas some other agricultural particles that are nearly spherical can be successfully simulated with DE models of spherical elements. The DE model employing the multisphere method (MSM) can be used for either case (spherical or nonspherical) to study the agricultural particulate materials processing operations on a particle scale (microscale), such as collision forces between individual grain and fruits that cannot easily be gained from experiments.

沙尘暴粒子的非球形模型及其对激光的多次散射特性研究

沙尘暴粒子的非球形模型及其对激光的多次散射特性研究

Simulation of filtration processes in deformable media

A Lagrangian solver to realistically model large, non-spherical dirt particles and their behaviour in the vicinity of deformable filtration fibres has been programmed. While this paper focuses on basic solver concepts as well as drag force implementations, a related article, concerning the realisation of interaction effects and result verification, is forthcoming, [3]. Within the framework of a digitally reconstructed, deformable filter fibre geometry, the solver traces the governing multi physics effects down to the occurrence of single force- and torque vectors. In order to go from an initial, spherical particle model [2], to a more sophisticated, non-spherical model, the capabilities of a Six Degrees of Freedom Solver have been included in the programming. A panel model and the concept of satellite help points are used to handle particles that encompass several fluid calculation cells. An innovative drag force implementation allows the consideration of rotational- and shear flow effects on particle motion. Results are evaluated and compared to an analytical formulation.

Utilizing Spaceborne Radars to Retrieve Dry Snowfall

Abstract A dataset consisting of one year of CloudSat Cloud Profiling Radar (CPR) near-surface radar reflectivity Z associated with dry snowfall is examined in this study. The CPR observations are converted to snowfall rates S using derived Ze–S relationships, which were created from backscatter cross sections of various nonspherical and spherical ice particle models. The CPR reflectivity histograms show that the dominant mode of global near-surface dry snowfall has extremely light reflectivity values (∼3–4 dBZe), and an estimated 94% of all CPR dry snowfall observations are less than 10 dBZe. The average conditional global snowfall rate is calculated to be about 0.28 mm h−1, but is regionally highly variable as well as strongly sensitive to the ice particle model chosen. Further, ground clutter contamination is found in regions of complex terrain even when a vertical reflectivity continuity threshold is utilized. The potential of future multifrequency spaceborne radars is evaluated using proxy 35–13.6-GHz reflectivities and sensor specifications of the proposed Global Precipitation Measurement dual-frequency precipitation radar (DPR). It is estimated that because of its higher detectability threshold, only about 7%–1% of the near-surface radar reflectivity values and about 17%–4% of the total accumulation associated with global dry snowfall would be detected by a DPR-like instrument, but these results are very sensitive to the chosen ice particle model. These potential detection shortcomings can be partially mitigated by using snowfall-rate distributions derived by the CPR or other similar high-frequency active sensors.

DENSITY PROFILES IN SEYFERT OUTFLOWS

For the past decade, ionized outflows of a few 100 km/s from nearby Seyfert galaxies have been studied in great detail using high resolution X-ray absorption spectra. A recurring feature of these outflows is their broad ionization distribution including essentially ions (e.g., of Fe) from neutral to fully ionized. The absorption measure distribution (AMD) is defined as the distribution of column density with ionization parameter |d N_H/d (log xi)|. AMDs of Seyfert outflows can span up to five orders of magnitude in xi. We present the AMD of five outflows and show that they are all rather flat, perhaps slightly rising towards high ionization. More quantitatively, a power-law fit for log AMD ~ (log xi)^a yields slopes of 0 < a < 0.4. These slopes tightly constrain the density profiles of the wind, which until now could be addressed only by theory. If the wind is distributed on large scales, the measured slopes imply a generic density radial profile of n ~ r^{-alpha} with 1 < alpha < 1.3. This scaling rules out a mass conserving radial flow of n ~ r^{-2}, or a constant density absorber, but is consistent with a non-spherical MHD outflow model in which n ~ r^{-1} along any given line of sight. On the other hand, if ionization variations are a result of local (delta r) density gradients, e.g. as in the turbulent interstellar medium (ISM), the AMD slopes imply density scaling of n ~ delta r^{-alpha} with 0.7 < alpha < 1.0, which is quite different from the scaling of approximately n ~ delta r^{0.4} found in the Milky Way ISM and typical of incompressible turbulence.

Dynamics of Black Holes in Rotating Cores

We study the dynamical interaction between stars surrounding black holes in self-gravitating galaxy cores by using realistic N-body techniques, calibrated by Fokker–Planck approximated models (Fiestas, Spurzem, &amp; Kim 2006). We study the evolution over the relaxation time (collisional nuclei) of non-spherical (triaxial) models as flattening of the system due to rotation is allowed. We follow the interplay between velocity diffusion due to relaxation and black hole star accretion and study accretion rates and cusp formation in spherically symmetric and axisymmetric models.

Model for light scattering in biological tissue and cells based on random rough nonspherical particles

A random nonspherical model for biological tissue and cells permits a better description of their optical properties. Rough surface nonspherical particles have been employed to model biological tissue and cells. The phase function, the anisotropy factor of scattering, and the reduced scattering coefficient are derived. The effect of different size distributions is also discussed. The theoretical results show good agreement with experimental data.

Fast Contact Detection Method for Discrete Element Method using Non-Spherical Particles

Discrete Element Method (DEM) is widely used to simulate behavior of powder material. It is well-known fact that interactions between particles affect this behavior. Especially, shape of the particle is the most important factor which governs these interactions. There have been reported some non-spherical models to simulate non-spherical powder particles. In the present paper, the author shows issues of these models and proposes a new model which can express arbitrary particle shapes. It is of great importance to develop a fast contact detection method for DEM simulation. A new method for the present particle model is developed and demonstrated in this paper.

The Construction of Nonspherical Models of Quasi‐Relaxed Stellar Systems

Spherical models of collisionless but quasi-relaxed stellar systems have long been studied as a natural framework for the description of globular clusters. Here we consider the construction of self-consistent models under the same physical conditions, but including explicitly the ingredients that lead to departures from spherical symmetry. In particular, we focus on the effects of the tidal field associated with the hosting galaxy. We then take a stellar system on a circular orbit inside a galaxy represented as a frozen external field. The equilibrium distribution function is obtained from the one describing the spherical case by replacing the energy integral with the relevant Jacobi integral in the presence of the external tidal field. Then the construction of the model requires the investigation of a singular perturbation problem for an elliptic partial differential equation with a free boundary, for which we provide a method of solution to any desired order, with explicit solutions to 2 orders. We outline the relevant parameter space, thus opening the way to a systematic study of the properties of a two-parameter family of physically justified nonspherical models of quasi-relaxed stellar systems. The general method developed here can also be used to construct models for which the nonspherical shape is due to internal rotation. Eventually, the models will be a useful tool to investigate whether the shapes of globular clusters are primarily determined by internal rotation, by external tides, or by pressure anisotropy.

Dust Envelopes around Massive Young Stellar Objects

We investigate the spectral energy distributions (SEDs) of Massive Young Stellar Objects (MYSOs) using the various infrared observational data including the Infrared Space Observatory (ISO) data. We model the dust envelopes around the stars using a radiative transfer model for spherically symmetric geometry. Comparing the model results with the observed SEDs of the two MYSOs (AFGL 4176 and AFGL 2591), we derive the relevant dust shell parameters including the dust opacity, the dust density distribution, and dust temperature distribution. We find that the spherical model can produce the SEDs roughly similar to the observations. We expect that the results would be helpful for making more realistic non-spherical dust envelope models for MYSOs.

An analytic model for non-spherical lenses in covariant MOdified Newtonian Dynamics

Strong gravitational lensing by galaxies in MOdified Newtonian Dynamics (MOND) has until now been restricted to spherically symmetric models. These models were able to account for the size of the Einstein ring of observed lenses, but were unable to account for double-imaged systems with collinear images, as well as four-image lenses. Non-spherical models are generally cumbersome to compute numerically in MOND, but we present here a class of analytic non-spherical models that can be applied to fit double-imaged and quadruple-imaged systems. We use them to obtain a reasonable MOND fit to ten double-imaged systems, as well as to the quadruple-imaged system Q2237+030 which is an isolated bulge-disc lens producing an Einstein cross. However, we also find five double-imaged systems and three quadruple-imaged systems for which no reasonable MOND fit can be obtained with our models. We argue that this is mostly due to the intrinsic limitation of the analytic models, even though the presence of small amounts of additional dark mass on galaxy scales in MOND is also plausible.

Numerical Study of Cavitation Inception Due to Vortex/Vortex Interaction in a Ducted Propulsor

Cavitation inception in a ducted propulsor was studied numerically using Navier-Stokes computations and bubble dynamics models. Experimental observations of the propulsor model and previous numerical computations using Reynolds-averaged Navier-Stokes (RANS) codes indicated that cavitation inception occurred in the region of interaction of the leakage and trailing tip vortices. The RANS simulations failed, however, to predict correctly both the cavitation inception index value and the inception location. To improve the numerical predictions, we complemented here the RANS computations with a direct Navier-Stokes simulation in a reduced computational domain including the region of interaction of the two vortices. Initial and boundary conditions in the reduced domain were provided by the RANS solution of the full ducted propulsor flow. Bubble nuclei were released in this flow field, and spherical and nonspherical bubble dynamics models were exercised to investigate cavitation inception. This resulted in a solution in much better agreement with the experimental measurements than the original RANS solution. Both the value of the cavitation inception index and the location of the cavitation inception were very well captured. The characteristics of the emitted acoustic signals and of the bubble shapes during a cavitation event were also computed.

A Non-Spherical Model for Bubble Formation with Chemical Reaction at a Submerged Orifice

Bubble formation with chemical reaction and mass transfer at a submerged orifice is analyzed theoretically. The phenomena of both hydrodynamics and mass transfer with chemical reaction are modeled successfully by the combination of the interfacial element approach and the penetration theory. Instantaneous bubble shapes, bubble volume and bubble growth rate simulated by the new model are in a good agreement with experimental data. Instantaneous liquid phase mass transfer coefficient, mass transfer rate from bubble surface, and gas–liquid contacting area are also predicted.

Impact of ice particle shape on short-wave radiative forcing: A case study for an arctic ice cloud

We used four different non-spherical particle models to compute optical properties of an arctic ice cloud and to simulate corresponding cloud radiative forcings and fluxes. One important finding is that differences in cloud forcing, downward flux at the surface, and absorbed flux in the atmosphere resulting from the use of the four different ice cloud particle models are comparable to differences in these quantities resulting from changing the surface albedo from 0.4 to 0.8, or by varying the ice water content (IWC) by a factor of 2. These findings show that the use of a suitable non-spherical ice cloud particle model is very important for a realistic assessment of the radiative impact of arctic ice clouds. The differences in radiative broadband fluxes predicted by the four different particle models were found to be caused mainly by differences in the optical depth and the asymmetry parameter. These two parameters were found to have nearly the same impact on the predicted cloud forcing. Computations were performed first by assuming a given vertical profile of the particle number density, then by assuming a given profile of the IWC. In both cases, the differences between the cloud radiative forcings computed with the four different non-spherical particle models were found to be of comparable magnitude. This finding shows that precise knowledge of ice particle number density or particle mass is not sufficient for accurate prediction of ice cloud radiative forcing. It is equally important to employ a non-spherical shape model that accurately reproduces the ice particle's dimension-to-volume ratio and its asymmetry parameter. The hexagonal column/plate model with air-bubble inclusions seems to offer the highest degree of flexibility.

A spherical model with directional interactions. I. Static properties

We introduce a simple spherical model whose structural properties are similar to the ones generated by models with directional interactions, by employing a binary mixture of large and small hard spheres, with a square-well attraction acting only between particles of different sizes. The small particles provide the bonds between the large ones. With a proper choice of the interaction parameters, as well as of the relative concentration of the two species, it is possible to control the effective valence. Here we focus on a specific choice of the parameters which favors tetrahedral ordering and study the equilibrium static properties of the system in a large window of densities and temperatures. Upon lowering the temperature we observe a progressive increase in local order, accompanied by the formation of a four-coordinated network of bonds. Three different density regions are observed: At low density the system phase separates into a gas and a liquid phase; at intermediate densities a network of fully bonded particles develops; at high densities--due to the competition between excluded volume and attractive interactions--the system forms a defective network. The very same behavior has been previously observed in numerical studies of nonspherical models for molecular liquids, such as water, and in models of patchy colloidal particles. Different from these models, theoretical treatments devised for spherical potentials, e.g., integral equations and ideal mode coupling theory for the glass transition, can be applied in the present case, opening the way for a deeper understanding of the thermodynamic and dynamic behavior of low valence molecules and particles.

Can MOND take a bullet? Analytical comparisons of three versions of MOND beyond spherical symmetry

A proper test of modified Newtonian dynamics (MOND) in systems of non-trivial geometries depends on modelling subtle differences in several versions of its postulated theories. This is especially true for lensing and dynamics of barely virialized galaxy clusters with typical gravity of scale a0. The original MOND formula, the classical single-field modification of the Poisson equation, and the multifield general relativistic theory of Bekenstein (tensor-vector-scalar, TeVeS) all lead to different predictions as we stray from spherical symmetry. In this paper, we study a class of analytical MONDian models for a system with a semi-Hernquist baryonic profile. After presenting the analytical distribution function of the baryons in spherical limits, we develop orbits and gravitational lensing of the models in non-spherical geometries. In particular, we can generate a multicentred baryonic system with a weak lensing signal resembling that of the merging galaxy cluster 1E 0657-56 with a bullet-like light distribution. We finally present analytical scale-free highly non-spherical models to show the subtle differences between the single-field classical MOND theory and the multifield TeVeS theory. © 2006 RAS.

Retrieval of aerosol optical and physical properties from ground-based spectral, multi-angular, and polarized sun-photometer measurements

An inversion algorithm to retrieve a complete set of aerosol optical and physical properties has been developed. The algorithm is based on sun-photometer measurements with emphasis on polarimetric observations. At present, these polarized sun-photometer observations are mainly provided by PHOTONS network included in AERONET worldwide network. With ground-based measurement of direct sun irradiance, as well as total and polarized sky radiance, most of key characteristics of atmospheric aerosols are retrieved, including spectral single-scattering albedo from UV to NIR wavelength, elements of scattering matrix F 11 and − F 12 (i.e. phase function and polarized phase function), complex refractive index, and size distribution. These parameters are fundamentally valuable in atmospheric physical and chemical studies. The theoretical accuracy is assessed based on three distinct bimodal log-normal aerosol models. The sensitivity studies to measurement uncertainties and to observing geometrical conditions are implemented to estimate the retrieval accuracy. Examples of typical retrievals when applying to real measurements are illustrated and compared with AERONET operational inversions. The particle shape-independent advantage of the retrieved single-scattering albedo, phase function, and polarized phase function is validated by considering a non-spherical aerosol model, which consisted of spheroid particles.

Fluorescent Monodisperse Silica Ellipsoids for Optical Rotational Diffusion Studies

We report on the preparation of monodisperse, fluorescent hematite-silica core-shell ellipsoids, with adjustable shapes ranging from spindles to nearly spheres, that are suitable for optical rotational diffusion studies. Hematite cores are grafted with poly(vinylpyrrolidone) which ensures colloidal stability during the silica coating provided by the base-catalyzed hydrolysis and polymerization of tetraethoxysilane. Using tetramethylammonium hydroxide as base instead of the volatile ammonia facilitates continuous seeded growth of silica to colloids with a desired aspect ratio. A convenient feature of the hematite-silica particles is the rapid dissolution of the iron oxide core by acid, producing hollow silica ellipsoids that can be optically matched to near transparency. The control of shape and size of the silica ellipsoids, their optical properties, and the fairly high yield in comparison to other preparation methods for nonspherical model colloids make the ellipsoids very suitable for quantitative studies. As a case in point, we have measured the rotational diffusion coefficient of fluorescent ellipsoids with rotational fluorescence recovery after photobleaching. Dye-labeled ellipsoids can be imaged with confocal microscopy.

Remote sensing of aerosols over the oceans using MSG/SEVIRI imagery

Abstract. The SEVIRI instrument on board Meteosat Second Generation (MSG) offers new capabilities to monitor aerosol transport over the Atlantic and the Mediterranean at high temporal and spatial resolutions, in particular, Saharan dust from North Africa, biomass-burning aerosols from subtropical Africa and pollution from Europe. An inversion technique was developed to estimate both aerosol optical thickness and Angström coefficients from SEVIRI measurements at 0.63 and 0.81 µm. This method relies on an optimized set of aerosol models to ensure a fast processing of full-resolution MSG images and to allow the processing of long time series. SEVIRI images for slots 45, 49 and 53 (11:15, 12:15, 13:15 UT) were processed for June 2003. The retrieved optical thicknesses and Angström coefficients are in good agreement with AERONET in-situ measurements in the Atlantic and in the Mediterranean. Monthly mean maps of both parameters are compared to that obtained with the polar orbiting sensor POLDER for June 2003. There is a good consistency between the two monthly means in terms of optical thickness, but the Angström coefficients show significant differences in the Atlantic zone which is affected by dust transport. These differences may be explained by the lack of specific non-spherical dust models within the inversion. The preliminary results presented in this paper demonstrate, nevertheless, the potential of MSG/SEVIRI for the monitoring of aerosol optical properties at high frequencies over the Atlantic and the Mediterranean.

Comparison of Moderate Resolution Imaging Spectroradiometer (MODIS) and Aerosol Robotic Network (AERONET) remote‐sensing retrievals of aerosol fine mode fraction over ocean

Aerosol particle size is one of the fundamental quantities needed to determine the role of aerosols in forcing climate, modifying the hydrological cycle, and affecting human health and to separate natural from man‐made aerosol components. Aerosol size information can be retrieved from remote‐sensing instruments including satellite sensors such as Moderate Resolution Imaging Spectroradiometer (MODIS) and ground‐based radiometers such as Aerosol Robotic Network (AERONET). Both satellite and ground‐based instruments measure the total column ambient aerosol characteristics. Aerosol size can be characterized by a variety of parameters. Here we compare remote‐sensing retrievals of aerosol fine mode fraction over ocean. AERONET retrieves fine mode fraction using two methods: the Dubovik inversion of sky radiances and the O'Neill inversion of spectral Sun measurements. Relative to the Dubovik inversion of AERONET sky measurements, MODIS slightly overestimates fine fraction for dust‐dominated aerosols and underestimates in smoke‐ and pollution‐dominated aerosol conditions. Both MODIS and the Dubovik inversion overestimate fine fraction for dust aerosols by 0.1–0.2 relative to the O'Neill method of inverting AERONET aerosol optical depth spectra. Differences between the two AERONET methods are principally the result of the different definitions of fine and coarse mode employed in their computational methodologies. These two methods should come into better agreement as a dynamic radius cutoff for fine and coarse mode is implemented for the Dubovik inversion. MODIS overestimation in dust‐dominated aerosol conditions should decrease significantly with the inclusion of a nonspherical model.