Probability density function of bubble size based reagent dosage predictive control for copper roughing flotation

As an effective measurement indicator of bubble stability, bubble size structure is believed to be closely related to flotation performance in copper roughing flotation. Moreover, reagent dosage has a very important influence on bubble size structure. In this paper, a novel reagent dosage predictive control method based on probability density function (PDF) of bubble size is proposed to implement the indices of roughing circuit. Firstly, the froth images captured in the copper roughing are segmented by using a two-pass watershed algorithm. In order to characterize bubble size structure with non-Gaussian feature, an entropy based B-spline estimator is hence investigated to depict the PDF of the bubble size. Since the weights of B-spline are interrelated and related to the reagent dosage, a multi-output least square support vector machine (MLS-SVM) is applied to depict a dynamic relationship between the weights and the reagent dosage. Finally, an entropy based optimization algorithm is proposed to determine reagent dosage in order to implement tracking control for the PDF of the output bubble size. Experimental results can show the effectiveness of the proposed method

A hybrid multiobjective differential evolution algorithm and its application to the optimization of grinding and classification

The grinding-classification is the prerequisite process for full recovery of the nonrenewable minerals with both production quality and quantity objectives concerned. Its natural formulation is a constrained multiobjective optimization problem of complex expression since the process is composed of one grinding machine and two classification machines. In this paper, a hybrid differential evolution (DE) algorithm with multi-population is proposed. Some infeasible solutions with better performance are allowed to be saved, and they participate randomly in the evolution. In order to exploit the meaningful infeasible solutions, a functionally partitioned multi-population mechanism is designed to find an optimal solution from all possible directions. Meanwhile, a simplex method for local search is inserted into the evolution process to enhance the searching strategy in the optimization process. Simulation results from the test of some benchmark problems indicate that the proposed algorithm tends to converge quickly and effectively to the Pareto frontier with better distribution. Finally, the proposed algorithm is applied to solve a multiobjective optimization model of a grinding and classification process. Based on the technique for order performance by similarity to ideal solution (TOPSIS), the satisfactory solution is obtained by using a decision-making method for multiple attributes

On the line shape of the electrically detected ferromagnetic resonance

This work reviews and examines two particular issues related with the new technique of electrical detection of ferromagnetic resonance (FMR). This powerful technique has been broadly applied for studying magnetization and spin dynamics over the past few years. The first issue is the relation and distinction between different mechanisms that give rise to a photovoltage via FMR in composite magnetic structures, and the second is the proper analysis of the FMR line shape, which remains the "Achilles heel" in interpreting experimental results, especially for either studying the spin pumping effect or quantifying the spin Hall angles via the electrically detected FMR.Comment: 14 pages, 9 figure

Quantum mechanical path integrals and thermal radiation in static curved spacetimes

The propagator of a spinless particle is calculated from the quantum mechanical path integral formalism in static curved spacetimes endowed with event-horizons. A toy model, the Gui spacetime, and the 2D and 4D Schwarzschild black holes are considered. The role of the topology of the coordinates configuration space is emphasised in this framework. To cover entirely the above spacetimes with a single set of coordinates, tortoise coordinates are extended to complex values. It is shown that the homotopic properties of the complex tortoise configuration space imply the thermal behaviour of the propagator in these spacetimes. The propagator is calculated when end points are located in identical or distinct spacetime regions separated by one or several event-horizons. Quantum evolution through the event-horizons is shown to be unitary in the fifth variable.Comment: 22 pages, 10 figure

Symmetry of Traveling Wave Solutions to the Allen-Cahn Equation in \Er^2

In this paper, we prove even symmetry of monotone traveling wave solutions to the balanced Allen-Cahn equation in the entire plane. Related results for the unbalanced Allen-Cahn equation are also discussed

Topological phase transitions between chiral and helical spin textures in a lattice with spin-orbit coupling and a magnetic field

We consider the combined effects of large spin-orbit couplings and a perpendicular magnetic field in a 2D honeycomb fermionic lattice. This system provides an elegant setup to generate versatile spin textures propagating along the edge of a sample. The spin-orbit coupling is shown to induce topological phase transitions between a helical quantum spin Hall phase and a chiral spin-imbalanced quantum Hall state. Besides, we find that the spin orientation of a single topological edge state can be tuned by a Rashba spin-orbit coupling, opening an interesting route towards quantum spin manipulation. We discuss the possible realization of our results using cold atoms trapped in optical lattices, where large synthetic magnetic fields and spin-orbit couplings can be engineered and finely tuned. In particular, this system would lead to the observation of a time-reversal-symmetry-broken quantum spin Hall phase.Comment: 8 pages, 3 figures, Accepted in Europhys. Lett. (Dec 2011