Simulation of Particle Motion Behavior in Fluidized Bed Opposed Jet Mill

In order to study the influence of the internal flow field of the fluidized bed opposed jet mill on the motion behavior of particles, Computational Fluid Dynamics (CFD) and Discrete Dlement Method (DEM) are used for coupling calculations. By adjusting the nozzle spacing and inlet pressure, Numerical simulation is carried out on the process of particles collisions with each other after accelerating under the high-speed jet produced by the nozzle. The trajectory of the particles in the flow field of the collision area and the change of the collision state of the particles are analyzed. Finally, the best parameters are selected based on the total collision energy. The results show that the particles will gradually shift and spread during the acceleration process. The reduction of the nozzle spacing is beneficial to increase the probability of particle collisions. However, if the spacing is too small, the particles cannot be fully accelerated; the increase in inlet pressure will increase the kinetic energy of the particles, and number of collisions is almost unaffected. By comparing the total collision energy, the best-simulated preparation conditions are selected as 110mm and 1.1MPa.

Total Collisions in the N-Body Shape Space

We discuss the total collision singularities of the gravitational N-body problem on shape space. Shape space is the relational configuration space of the system obtained by quotienting ordinary configuration space with respect to the similarity group of total translations, rotations, and scalings. For the zero-energy gravitating N-body system, the dynamics on shape space can be constructed explicitly and the points of total collision, which are the points of central configuration and zero shape momenta, can be analyzed in detail. It turns out that, even on shape space where scale is not part of the description, the equations of motion diverge at (and only at) the points of total collision. We construct and study the stratified total-collision manifold and show that, at the points of total collision on shape space, the singularity is essential. There is, thus, no way to evolve solutions through these points. This mirrors closely the big bang singularity of general relativity, where the homogeneous-but-not-isotropic cosmological model of Bianchi IX shows an essential singularity at the big bang. A simple modification of the general-relativistic model (the addition of a stiff matter field) changes the system into one whose shape-dynamical description allows for a deterministic evolution through the singularity. We suspect that, similarly, some modification of the dynamics would be required in order to regularize the total collision singularity of the N-body model.

Investigating Total Collisions of the Newtonian N-Body Problem on Shape Space

We analyze the points of total collision of the Newtonian gravitational system on shape space (the relational configuration space of the system). While the Newtonian equations of motion, formulated with respect to absolute space and time, are singular at the point of total collision due to the singularity of the Newton potential at that point, this need not be the case on shape space where absolute scale doesn’t exist. We investigate whether, adopting a relational description of the system, the shape degrees of freedom, which are merely angles and their conjugate momenta, can be evolved through the points of total collision. Unfortunately, this is not the case. Even without scale, the equations of motion are singular at the points of total collision (and only there). This follows from the special behavior of the shape momenta. While this behavior induces the singularity, it at the same time provides a purely shape-dynamical description of total collisions. By help of this, we are able to discern total-collision solutions from non-collision solutions on shape space, that is, without reference to (external) scale. We can further use the shape-dynamical description to show that total-collision solutions form a set of measure zero among all solutions.

Multi-layer kinematics and collision energy in a large-scale grinding mill-the largest semi-autogenous grinding mill in China

Using the largest semi-autogenous grinding mill in China as a model, collision energy was analyzed on the basis of the multi-layer kinematics of the steel balls. First, the kinematic equation of the steel balls was obtained by considering the multi-layer characteristics of the steel balls. Second, the collision energy of the inner-layer steel balls was addressed according to its kinematic characteristics. Finally, the total collision energy per unit time was obtained. Results show that the leaving angle decreases as the mill speed ratio increases and as the radius ratio increases, but the leaving velocity increases linearly. Moreover, a discontinuity point of the tangential collision velocity occurs at an angle factor β = 0, and the angle factor β is divided into two intervals: [−3, 0] and [0, 1.5]. The leaving angles corresponding to a tangential velocity equal to zero are calculated to be 1.185 and 0.7854 rad in the two intervals. In addition, the sum collision velocity increases when β is less than zero, but it decreases sharply above zero. The maximum total collision energy per unit time occurs at 84.2% of the mill speed corresponding to the optimal mill speed ratio.

Trki ptic v stekleno pročelje poslovne stavbe v Ljubljani (osrednja Slovenija) jeseni 2012/ Bird collisions with glass façade of a commercial building in Ljubljana (central Slovenia) in autumn 2012

From 28 Sep to 7 Oct 2012, bird collisions with the glass façade of a commercial building in the centre of Ljubljana were monitored. The observations lasted 45-60 minutes in the morning (7.00-10.00 hrs), around midday (11.00-14.00 hrs) and in the afternoon (15.00-18.00 hrs). Behaviour of all birds and scavengers, which could potentially be looking for bird carcasses in the vicinity of the building, was noted. In 27.25 hours of observation, 16 collisions (3 resulting in death, 13 cases with birds flying away seemingly unharmed) and 19 near collisions, when birds avoided the building at the last moment before collision, were recorded. The total collision rate was 0.59 collisions per hour of observation. All birds that collided with the building, except Feral Pigeon Columba livia f. domestica, were passerines, among which tits Paridae predominated (62.5% of birds that collided with the building). The glass façade functioned as a mirror, reflecting tree crowns from across the street. Data show that most collisions occurred in the middle part of the building during the morning. Among potential scavengers, domestic cat Felis domesticus and Hooded Crow Corvus cornix were observed. The latter regularly flew around the building during the observation period, possibly looking for bird carcasses.

Nonthermal effects on the elastic electron–atom collision in generalized Lorentzian semiclassical plasmas: Lorentzian renormalization shielding

The Lorentzian renormalization plasma shielding effects on the elastic electron–atom collision are investigated in generalized Lorentzian semiclassical plasmas. The eikonal analysis and the effective interaction potential are employed to obtain the eikonal scattering phase shift, differential eikonal collision cross section, and total eikonal collision cross section as functions of the collision energy, impact parameter, nonthermal renormalization parameter, and spectral index of the Lorentzian plasma. It is found that the influence of Lorentzian renormalization shielding suppresses the eikonal scattering phase shift and, however, enhances the eikonal collision cross section in Lorentzian semiclassical plasmas. Additionally, the energy dependence on the total collision cross section in nonthermal plasmas is found to be more significant than that in thermal plasmas.

EFFECTS OF INTER-PARTICLE INTERACTIONS AND HYDRODYNAMICS ON THE BROWNIAN COAGULATION RATE OF POLYDISPERSE NANOPARTICLES

The Brownian coagulation rate of polydisperse nanoparticles by considering the effects of inter-particle interactions and hydrodynamics is studied in the gas-slip regime. The collision efficiency before and after particle contact is calculated by considering the van der Waals force, electrical repulsion, electrostatic force and elastic deformation force, respectively. It is found that the total collision efficiency decreases with the increase of both particle diameter and particle size ratio. Based on the total collision efficiency, the coagulation rate of polydisperse nanoparticles with considering the effects of inter-particle interactions and hydrodynamics is calculated. The results show that the coagulation rate with considering such effects is closer to the experimental data and much smaller than that without considering the effects. The inter-particle interactions and hydrodynamics make particles more difficult to coagulate and cause the coagulation rate to become weaker when the Knudsen number increases. The particles with high polydispersity coagulate more easily.

PERIODIC ORBITS NEAR A HETEROCLINIC LOOP FORMED BY ONE-DIMENSIONAL ORBIT AND A TWO-DIMENSIONAL MANIFOLD: APPLICATION TO THE CHARGED COLLINEAR THREE-BODY PROBLEM

This paper is devoted to the study of a type of differential systems which appear usually in the study of the Hamiltonian systems with two degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near to the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear three-body problem.