Self-Consistent Calculations on the Atomic Electron Affinity and Ionization Energy with Taking Effects of the Nonspherical Distribution of Electrons into Account

We perform the self-consistent calculations on the atomic electron affinity and ionization energy for the first-row atoms by means of our scheme. A striking feature of the present work is the variational method with taking into account effects of the nonspherical distribution of electrons explicitly. Comparing the present results with those of the conventional spherical approximation, the systematical improvement can be found. This means that effects of the nonspherical distribution of electrons may play an essential role on the description of the atomic structures.

Oblique impact breakage unification of nonspherical particles using discrete element method

Particle breakage commonly occurs during processing of particulate materials,but a mechanistic model of particle impact breakage is not fully established.This article presents oblique impact breakage characteristics of nonspherical particles using discrete element method(DEM)simulations.Three different particle shapes,i.e.spherical,cuboidal and cylindrical,are investigated.Constituent spheres are agglomerated with bridging bonds to model the breakage characteristics under impact conditions.The effect of agglomerate shapes on the breakage pattern,damage ratio,and fragment size distribution is fully investigated.By using a newly proposed oblique impact model,unified breakage master surfaces are theoretically constructed for all the particle shapes under oblique impact conditions.The developed approach can be applied to modelling particulate processes where nonspherical particles and oblique impact breakage are prevailing.

A New Nonspherical Oxidation Model of Metal Particles

This paper analyzes the oxidation law of metal particles and proposes a new oxidation reaction rate model,based on measurements of thermogravimetric-mass spectrometer(TG-MS),X-ray diffractometer(XRD)and scanning electron microscope(SEM).The model is named EBM(egg broken model)with a formula of exponential law.According to the model,the aluminum particles do not react in a spherical shape,but crack and the melted metal inside flows out to form a new nonspherical surface and the reaction rate is still determined by the surface area.The model is verified with heating rates of 5℃/min,10℃/min and 25℃/min,and with particle size of 1–2μm,8–9μm and 20–22μm.Many models are based on spherical hypothesis and the new model gives a different physical illustration to explain oxidation progress of metal particles.The new model gives an exponential law,which fits the experimental data well,and it may be useful to understand oxidation mechanism of metal particles.

Flow characteristics of nonspherical granular materials simulated with multi-superquadric elements

The superquadric equation is typically used to mathematically describe nonspherical particles and construct particle shapes with different surface sharpness and aspect ratios.However,nonspherical elements constructed using the superquadric equation are strictly convex,limiting their engineering application.In this study,a multi-superquadric model based on a superquadric equation is developed.The model combines several superquadric elements that can be used to construct concave and convex particle shapes.Four tests are performed to examine the applicability of the multi-superquadric approach.The first involves a comparison of theoretical results for a single spherocylinder impacting a flat wall.The second involves the formation of a nonspherical granular bed.The third investigates the effects of the particle shape on the hopper discharge and angle of repose.The final test evaluates the mixing behaviors of granular materials within a horizontally rotating drum.These tests demonstrate the applicability of the multi-superquadric approach to nonspherical granular systems.Furthermore,the effects of particle shape on the packing density,discharge rate,angle of repose,and Lacey mixing index are discussed.Results indicate that concave particles have a lower packing density,flow rate,and mixing rate and higher angles of repose than convex particles.Interlocking of elements becomes more pronounced for concave particles and results in local cluster structures,thereby enhancing the stability of granular systems and limiting sliding or rotation between nonspherical particles.

Analytic perturbation solutions to the Venusian orbiter due to the nonspherical gravitational potential

The analytic perturbation solutions to the motions of a planetary orbiter given in this paper are effective for 0e1, where e is the orbital eccentricity of the orbiter. In the solution, it is assumed that the rotation of the central body is slow, and its astronomical background is clear. Examples for such planets in the solar system are Venus and Mercury. The perturbation solution is tested numerically on two Venusian orbiters with eccentric orbits, PVO and Magellan, and found to be effective.

PREPARATION OF MICRON-SIZED NONSPHERICAL POLYSTYRENE/POLY(STYRENE-co-ETHYLENEGLYCOL DIMETHACRYLATE) PARTICLES BY SEEDED SOAP-FREE EMULSION POLYMERIZATION

Micron-sized nonspherical polymer particles having different morphologies were synthesized by seeded soap-free emulsion polymerization of styrene （St） and ethyleneglycol dimethacrylate （EGDMA, used as a crosslinker） on spherical, linear polystyrene （PS） seed particles. The morphology of the resulting PS/poly（St-co-EGDMA） particles was dependent on the crosslinker concentration and polymerization temperature.

Light-scattering model for aerosol particles with irregular shapes and inhomogeneous compositions using a parallelized pseudo-spectral time-domain technique

To improve the modeling accuracy of radiative transfer,the scattering properties of aerosol particles with irregular shapes and inhomogeneous compositions should be simulated accurately.To this end,a light-scattering model for nonspherical particles is established based on the pseudo-spectral time domain(PSTD)technique.In this model,the perfectly matched layer with auxiliary differential equation(ADE-PML),an excellent absorption boundary condition(ABC)in the finite difference time domain generalized for the PSTD,and the weighted total field/scattered field(TF/SF)technique is employed to introduce the incident light into 3 D computational domain.To improve computational efficiency,the model is further parallelized using the Open MP technique.The modeling accuracy of the PSTD scheme is validated against Lorenz–Mie,Aden–Kerker,T-matrix theory and DDA for spheres,inhomogeneous particles and nonspherical particles,and the influence of the spatial resolution and thickness of ADE-PML on the modeling accuracy is discussed as well.Finally,the parallel computational efficiency of the model is also analyzed.The results show that an excellent agreement is achieved between the results of PSTD and well-tested scattering models,where the simulation errors of extinction efficiencies are generally smaller than 1%,indicating the high accuracy of our model.Despite its low spatial resolution,reliable modeling precision can still be achieved by using the PSTD technique,especially for large particles.To suppress the electromagnetic wave reflected by the absorption layers,a six-layer ADE-PML should be set in the computational domain at least.

A Scheme for Calculating Atomic Structures beyond the Spherical Approximation

We present a scheme for calculating atomic single-particle wave functions and spectra with taking into ac-count the nonspherical effect explicitly. The actual calculation is also performed for the neutral carbon atom within the Hartree-Fock-Slater approximation. As compared with the conventional atomic structure of the spherical approximation, the degenerate energy levels are split partially. The ground state values of the total orbital and spin angular momenta are estimated to be both about unity, which corresponds to the term P3PP in the LS-multiplet theory. This means that the nonspherical effect may play an essential role on the description of the magnetization caused by the orbital polarization.

Bekenstein-Hawking Cosmological Entropy and Correction Term Corresponding Cosmological Horizon of Rotating and Charged Black String

Utilizing the quantum statistical method and applying the new state density equation motivated by generalized uncertainty principle in quantum gravitaty, we avoid the difficulty in solving wave equation and directly calculate the partition function of bosonic and fermionic field on the background of rotating and charged black string. Then near the cosmological horizon, entropies of bosonic and fermionic field are calculated on the background of black string. When constant A introduced in generalized uncertainty principle takes a proper value, we derive Bekenstein- Hawking entropy and the correction value corresponding cosmologicaJ horizon on the background of rotating and charged black string. Because we use the new state density equation, in our calculation there are not divergent term and small mass approximation in the original brick-wall method. From the view of quantum statistic mechanics, the correction value to Bekenstein-Hawking entropy of the black string is derived. It makes people deeply understand the correction value to the entropy of the black string cosmological horizon in non-spherical coordinate spacetime.

Entropy of a rotating and charged black string to all orders in the Planck length

By using the entanglement entropy method, this paper calculates the statistical entropy of the Bose and Fermi fields in thin films, and derives the Bekenstein-Hawking entropy and its correction term on the background of a rotating and charged black string. Here, the quantum field is entangled with quantum states in the black string and thin film to the event horizon from outside the rotating and charged black string. Taking into account the effect of the generalized uncertainty principle on quantum state density, it removes the difficulty of the divergence of state density near the event horizon in the brick-wall model. These calculations and discussions imply that high density quantum states near the event horizon of a black string are strongly correlated with the quantum states in a black string and that black string entropy is a quantum effect. The ultraviolet cut-off in the brick-wall model is not reasonable. The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon. From the viewpoint of quantum statistical mechanics, the correction value of Bekenstein-Hawking entropy is obtained. This allows the fundamental recognition of the correction value of black string entropy at nonspherical coordinates.

Simulation and evaluation study of atmospheric aerosol nonsphericity as a function of particle size

Aerosol nonsphericity causes great uncertainty in radiative forcing assessments and climate simulations.Although considerable studies have attempted to quantify this uncertainty,the relationship between aerosol nonsphericity and particle size is usually not considered,thus reducing the accuracy of the results.In this study,a coupled inversion algorithm combining an improved stochastic particle swarm optimization algorithm and angular light scattering is used for the nonparametric estimation of aerosol nonsphericity variation with particle size,and the optimal sample selection method is employed to screen the data.Based on the verification of inversion accuracy,the variation of aerosol aspect ratio with particle size based on the ellipsoidal model in global regions has been obtained from Aerosol Robotic Network(AERONET)data,and the effect of nonsphericity on radiative forcing and dry deposition has been studied.The results show that the aspect ratio increases with particle size in all regions,with the maximum ranging from 1.4 to 1.8 in the desert,reflecting the differences in aerosol composition at different particle sizes.In radiation calculations,considering aerosol nonsphericity makes the aerosol cooling effect weaker and surface radiative fluxes increase,but hardly changes the aerosol absorption,with maximum differences of 9.22%and 22.12%at the bottom and top of the atmosphere,respectively.Meanwhile,the differences in radiative forcing between aspect ratios as a function of particle size and not varying with particle size are not significant,averaging less than 2%.Besides,the aspect ratio not varying with particle size underestimates the deposition velocity of small particles and overestimates that of large particles compared to that as a function of particle size,with maximum differences of 7%and 4%,respectively.

Synthesis of submicron-sized peanut-shaped poly(methyl methacrylate)/polystyrene particles by seeded soap-free emulsion polymerization

Submicron-sized peanut-shaped poly（methyl methacrylate）/polystyrene （PMMA/PS） particles were successfully synthesized by seeded soap-free emulsion polymerization of styrene on the spherical crosslinked PMMA seed particles. The obtained peanut- shaped particles showed a novel internal morphology： PS phase formed one domain which linked to the other domain having PMMA core encased by PS shell.

Discrete element method modeling of corn-shaped particle flow in rectangular hopper

Discrete element method(DEM)was developed to simulate the corn-shaped particles flow in the hopper.The corn-shaped particle was described by four overlapping spheres.Contact force and gravity force were considered when establishing the model.In addition,flowing characteristic of particles in the hopper was studied.The effect of friction coefficient on the wall pressure,voidage and velocity distribution was analyzed.The results show that the discharge rate decreases with the friction coefficient increasing;and the"over-pressure"phenomenon occurs in the discharging process for two different friction coefficients.The voidage also increases as the friction coefficient increasing.And the velocity distribution is more uniformity and is closer to the mass flow with the friction coefficient deceasing.