The specific selection function effect on clinker grinding efficiency in a dry batch ball mill

Dry grinding experiments on cement clinker were carried out using a laboratory batch ball mill equipped with a torque measurement. The influence of the ball size distribution on the specific selection function can be approached by laboratory runs using mono-size balls. The breakage is more efficient with maximal specific selection functions at the initial size reduction stage. But, in terms of cement finish grinding all stages of grinding are determinant for the production of a required Blaine surface area (3500 cm2/g). So, the choice of ball size according to a maximal specific selection function leads to an increase of the energy consumption. In addition, investigations on the mono-sized fractions and on the crude material (size minus 2.8 mm) demonstrate that the energy efficiency factor can be optimized using ball size corresponding to relatively low specific selection function

Gauged Q ball in a piecewise parabolic potential

Q ball solutions are considered within the theory of a complex scalar field with a gauged U(1) symmetry and a parabolic-type potential. In the thin-walled limit, we show explicitly that there is a maximum size for these objects because of the repulsive Coulomb force. The size of Q ball will increase with the decrease of local minimum of the potential. And when the two minima degenerate, the energy stored within the surface of the Q ball becomes significant. Furthermore, we find an analytic expression for gauged Q ball, which is beyond the conventional thin-walled limit.Comment: 1 figure

Dynamics of Vesicle Formation from Lipid Droplet: Mechanism and Controllability

A coarse-grained model developed by Marrink et al. [J. Phys. Chem. B 111, 7812 (2007)] is applied to investigate vesiculation of lipid [dipalmitoylphosphatidylcholine (DPPC)] droplets in water. Three kinds of morphologies of micelles are found with increasing lipid droplet size. When the initial lipid droplet is smaller, the equilibrium structure of the droplet is a spherical micelle. When the initial lipid droplet is larger, the lipid ball starts to transform into a disk micelle or vesicle. The mechanism of vesicle formation from a lipid ball is analyzed from the self-assembly of DPPC on the molecular level, and the morphological transition from disk to vesicle with increasing droplet size is demonstrated. Importantly, we discover that the transition point is not very sharp, and for a fixed-size lipid ball, the disk and vesicle appear with certain probabilities. The splitting phenomenon, i.e., the formation of a disk/vesicle structure from a lipid droplet, is explained by applying a hybrid model of the Helfrich membrane theory. The elastic module of the DPPC bilayer and the smallest size of a lipid droplet for certain formation of a vesicle are successfully predicted.Comment: 22 pages, 11 figures Submitted to J. Chem. Phy

Interfacial reaction between SAC305 and SAC405 lead-free solders and electroless nickel/immersion silver (ENImAg) surface finish

The different surface finish and solder size on printed circuit board strongly affect the formation of intermetallic compounds (IMCs) and solder joint reliability. Among of various surface finish in the electronic industry, electroless nickel/immersion gold is the most popular at the moment. However, because their black pad issues, electroless nickel/immersion silver (ENImAg) was developed as an alternative surface finish. Therefore, the effect on an interfacial reaction between lead-free solder and ENImAg surface finish using different solder ball size (Ø300μm, Ø500μm and Ø700μm) was investigated. All samples were subjected to an aging process with different aging times. The characterizations of IMC formation were examined by image analyzer, scanning electron microscopy and energy dispersive x-ray. The results showed that ENImAg finish was free from the black pad nickel. Subsequently, the solder ball size has a significant effect on the IMC formation and fracture surface of as-reflowed and aged solder joint. The IMC thickness of larger solder balls was found to be thicker (1.74 μm) than smaller solder balls (1.32 μm) during soldering. In contrast to aged solder joints, the smaller solder ball produced thicker (3.51 μm) IMC compared to bigger solder balls (2.47 μm). Furthermore, the fracture surface of smaller solder ball size showed ductile mode for both reflowed and aged solder joints. In addition, the solder joint on ENImAg surface finish displayed a thinner layer and smaller grain sizes compared to solder joint on bare copper

Limits on Q-ball size due to gravity

Solitonic scalar field configurations are studied in a theory coupled to gravity. It is found that non-topological solitons, Q-balls, are present in the theory. Properties of gravitationally self coupled Q-balls are studied by analytical and numerical means. Analytical arguments show that, unlike in the typical flat space scenario, the size of Q-balls is ultimately limited by gravitational effects. Even though the largest Q-balls are very dense, their radii are still much larger than the corresponding Schwarzschild radii. Gravity can also act as a stabilising mechanism for otherwise energetically unstable Q-balls.Comment: 11 pages, 4 figure

Non-ergodic Convergence Analysis of Heavy-Ball Algorithms

In this paper, we revisit the convergence of the Heavy-ball method, and present improved convergence complexity results in the convex setting. We provide the first non-ergodic O(1/k) rate result of the Heavy-ball algorithm with constant step size for coercive objective functions. For objective functions satisfying a relaxed strongly convex condition, the linear convergence is established under weaker assumptions on the step size and inertial parameter than made in the existing literature. We extend our results to multi-block version of the algorithm with both the cyclic and stochastic update rules. In addition, our results can also be extended to decentralized optimization, where the ergodic analysis is not applicable

Relativistic Charged Balls

It is proven that the relativistic charged ball with its charge less than its mass (in natural units) cannot have a non-singular static configuration while its radius approaches its external horizon size. This conclusion does not depend on the details of charge distribution and the equation of state. The involved assumptions are (1) the ball is made of perfect fluid, (2) the energy density is everywhere non-negative.Comment: revtex, 11 page

Submicron metal powders produced by ball milling with grinding aids

In ball milling metal powders to submicron size, various salts are more effective as grinding aids than conventional surfactants. Absolute ethyl alcohol is used as the grinding liquid