Projection Operator and Feynman Propagator for a Free Massive Particle of Arbitrary Spin

Based on the solution to the Bargmann Wigner equations, a direct derivation of the projection operator and Feynman propagator for a free massive particle of arbitrary spin is worked out. The projection operator constructed by Behrends and Fronsdal is re-deduced and confirmed, and simplified in the case of half-integral spin, the general commutation rules and Feynman propagator with additional non-covariant terms for a free massive particle with any spin are derived, and explicit expressions for the propagators for spins 3/2, 2, 5/2, 3, 7/2, and 4 are provided.

Motion behavior of particles in air-solid magnetically stabilized fluidized beds for separation

In order to study the settling mechanism of particles in an air-solid magnetically stabilized fluidized bed(MSFB) for separation,we carried out free settling and quasi-zero settling tests on the tracing particles.The results show that the main resistance forces as the tracing particles settled in an air-solid MSFB were motion resistance force and yield force.The motion resistance and yield forces greatly hindered the free settling of the particles by greatly decreasing the acceleration for settling process of the particles.The acceleration decreased from 3022.62 cm/s 2 to zero in 0.1 s,and in the end,the particles stopped in the air-solid MSFB.The yield force on particles increased with increasing the magnetic field intensity,resulting in decrease of the quasi-zero settling displacement.However,the yield force on particles decreased with increasing the fluidized air velocity,leading to increase of the quasi-zero settling displacement.When the structure and operating parameters of the air-solid MSFB were set up,the yield stress on particles stopped in an air-solid MSFB was a function of diameter and density of particles.The settling displacements of equal diameter particles increased with increasing their densities,and the settling displacements of equal density particles increased with increasing their diameters.

Experimental study on influence of blade angle and particle size on particle mechanics on a batch-operated single floor of a multiple hearth furnace

In industry,multiple hearth furnaces are used for the thermal treatment of particulate material.The current contribution concentrates on the experimental analysis of particle mechanics for a batch-operated single floor of a multiple hearth furnace.The particles are agitated on the circular floor by a single,rotating rabble arm equipped with three flat rabble blades of 10 mm thickness.The blade angle,defined as the angle,which the blade is inclined against the tangential direction,is varied from 0°to 90°.A single layer of spherical polyoxymethylene(POM)particles with three different diameters(5,10 and 20 mm)is placed on the floor.To analyze the results,two parameters have been extracted from image analysis when the bed of particles is agitated,first,the area not covered by particles and second,the frequency distribution of the mean distance among the particles.The particle free surface area increases with the inclination of the blades.The evolution of the particle free surface area differs for the different particle diameters.In general,the maximum particle free area for all blade angles is the largest for the 5 mm particles followed by the 20 mm particles.For the 10 mm particles,the particle free surface area starts for a blade angle of 0°at larger values than for the 20 mm particles but the values fall below the values for the 20 mm particles for larger blade angles.The reason for this behavior is discussed in detail.The mean distance among the particles is a parameter characterizing the length scales dominating the effects on the floor.The frequency distribution of the mean distance among particles provides infor-mation about the morphology of the particle bulk,for example,whether the free surface area is inter-spersed with particles.

Acoustic radiation force on a rigid cylinder between two impedance boundaries in a viscous fluid

Acoustofluidic technology combines acoustic and microfluidic technologies to realize particle manipulation in microchannels driven by acoustic waves,and the acoustic radiation force(ARF)with boundaries is important for particle manipulation in an acoustofluidic device.In the work reported here,the ARF on a free cylinder immersed in a viscous fluid with an incident plane wave between two impedance boundaries is derived analytically and calculated numerically.The influence of multiple scattering between the particle and the impedance boundaries is described by means of image theory,the finite-series method,and the translational addition theorem,and multiple scattering is included partly in image theory.The ARF on a free rigid cylinder in a viscous fluid is analyzed by numerical calculation,with consideration given to the effects of the distances from cylinder edge to boundaries,fluid viscosity,cylinder size,and boundary reflectivity.The results show that the interaction between the two boundaries and the cylinder makes the ARF change more violently with different frequencies,while increasing the viscosity can reduce the amplitude of the ARF in boundary space.This study provides a theoretical basis for particle manipulation by the ARF in acoustofluidics.

Correlation analysis of three influencing factors and the dust production rate for a free-falling particle stream

The effects of three factors （i.e., drop height h, hopper outlet diameter do, and material temperature T] on the dust generation rate derived from a free falling particle stream were investigated via filll factorial experiments. The correlation between the three factors and dust generation rate was also analysed. Results show that Tand h affect the first fugitive dust rate largely, whereas the second fugitive dust rate is mainly dominated by h and do. Through analysing the first fugitive dust percentage data, it is found that h and T should be considered first for higher temperatures and lower flow rates, whereas h and do can be considered under contrasting conditions, and h should be controlled in the remaining two sets of conditions. Relationships between the influencing factors and total and first fugitive dust rates were developed via multiple regression to quantify the dust emission rates for different contact surfaces （rigid or water）.

Implementation of the moving particle semi-implicit method on GPU

The Moving Particle Semi-implicit (MPS) method performs well in simulating violent free surface flow and hence becomes popular in the area of fluid flow simulation. However, the implementations of searching neighbouring particles and solving the large sparse matrix equations (Poisson-type equation) are very time-consuming. In order to utilize the tremendous power of parallel computation of Graphics Processing Units (GPU), this study has developed a GPU-based MPS model employing the Compute Unified Device Architecture (CUDA) on NVIDIA GTX 280. The efficient neighbourhood particle searching is done through an indirect method and the Poisson-type pressure equation is solved by the Bi-Conjugate Gradient (BiCG) method. Four different optimization levels for the present general parallel GPU-based MPS model are demonstrated. In addition, the elaborate optimization of GPU code is also discussed. A benchmark problem of dam-breaking flow is simulated using both codes of the present GPU-based MPS and the original CPU-based MPS. The comparisons between them show that the GPU-based MPS model outperforms 26 times the traditional CPU model.

Improved Flight Conflict Detection Algorithm Based on Gauss-Hermite Particle Filter

In order to improve the accuracy of free flight conflict detection and reduce the false alarm rate, an improved flight conflict detection algorithm is proposed based on Gauss-Hermite particle filter（GHPF）. The algorithm improves the traditional flight conflict detection method in two aspects：（i） New observation data are integrated into system state transition probability, and Gauss-Hermite Filter（GHF） is used for generating the importance density function.（ii） GHPF is used for flight trajectory prediction and flight conflict probability calculation. The experimental results show that the accuracy of conflict detection and tracing with GHPF is better than that with standard particle filter. The detected conflict probability is more precise with GHPF, and GHPF is suitable for early free flight conflict detection.

Mechanism and inhibition of trisodium phosphate particle caking： Effect of particle shape and solubility

We investigated the influence of particle shape and solubility on the caking behavior of trisodium phosphate by considering the adhesion free energy and crystal bridge theory. Caking of trisodium phosphate during the drying process under static conditions is a two-step process： adhesion followed by crystal bridge formation between particles. The adhesion free energy plays an important role in adhesion. Trisodium phosphate particles cannot adhere to each other and cake when the adhesion free energy is greater than a critical value, which varies with particle shape. Compared with granular particles, cylindrical particles have larger contact area between particles, which results in more crystal bridges forming and a higher caking ratio. Thus, the critical value is about 100 mJ/m^2 for cylindrical particles, but 60 mJ/m^2 for granular particles at 25 ℃. Concerning the solubility, when particles are similar shapes and soluble in the rinsing liquid, the caking ratio has a linear relationship with adhesion free energy. However, if the particles are insoluble in the rinsing liquid, caking can be completely prevented regardless of adhesion free energy because no crystal bridges form during the growth process. Hence, caking of trisodium phosphate particles could be inhibited by screening rinsing liquids, and optimizing the particle shape and size distribution.

Classical mechanics in non-commutative phase space

In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space. The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity. First, new Poisson brackets have been defined in non-commutative phase space. They contain corrections due to the non-commutativity of coordinates and momenta. On the basis of this new Poisson brackets, a new modified second law of Newton has been obtained. For two cases, the free particle and the harmonic oscillator, the equations of motion are derived on basis of the modified second law of Newton and the linear transformation （Phys. Rev. D, 2005, 72： 025010）. The consistency between both methods is demonstrated. It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space, but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative.

Geometries with the Second Poincar Symmetry

The second Poincard kinematical group serves as one of new ones in addition to the known possible kinematics. The geometries with the second Poincard symmetry is presented and their properties are analyzed. On the geometries, the new mechanics based on the principle of relativity with two universal constants （c, l） can be established.

Aerodynamic design optimization of nacelle/pylon position on an aircraft

The arbitrary space-shape free form deformation （FFD） method developed in this paper is based on non-uniform rational B-splines （NURBS） basis function and used for the integral parameterization of nacelle-pylon geometry. The multi-block structured grid deformation technique is established by Delaunay graph mapping method. The optimization objects of aerodynamic characteristics are evaluated by solving NavierStokes equations on the basis of multi-block structured grid. The advanced particle swarm optimization （PSO） is utilized as search algorithm, which com-bines the Kriging model as surrogate model during optimization. The optimization system is used for optimizing the nacelle location of DLR-F6 wing-body-pylon-nacelle. The results indicate that the aerodynamic interference between the parts is significantly reduced. The optimization design system established in this paper has extensive applications and engineering value.