Reduction Kinetics of Fine Hematite Ore Particles in Suspension

Suspension reduction kinetics of hematite ore particles at 1710 K to 1785 K was described by the Johnson-Mehl-Avrami-Kolmogorov model with Avrami exponent of 1.405. The apparent activation energy is 105.5 kJ mol−1 with the rate determining step of nucleation and growth. The reduction degree of the hematite at the endpoint is a linear function of temperature and the logarithmic oxygen potential of the reacting gas. A peak function of reaction rate constant with particle size has been verified in this work, and the maximum value of the reaction rate is located at around 85 µm particle size. The influence of heat transfer on the reaction process has been evaluated. The results suggest that the heating-up process for large particles, 244 µm particles, for instance, cannot be ignored. It can retard the reaction rate compared to small particles. Normally, the reaction rate constant decreases linearly with the increase of ln[p(O2)] of the reacting gas mixture. However, 95 vol pct CO2 in the reacting gas can accelerate the reaction rate of thermal decomposition of hematite due to the emissivity of CO2 gas. It results in a higher reaction rate of 110 µm particles in 95 vol pct CO2-containing gas than that in other less CO2-containing gases.

Rheological Behavior of Blends of Metallocene Catalyzed Long-Chain Branched Polyethylenes. Part I: Shear Rheological and Thermorheological Behavior

Long-chain branched metallocene-catalyzed high-density polyethylenes (LCB-mHDPE) were solution blended to obtain blends with varying degrees of branching. A high molecular LCB-mHDPE was mixed with low molecular LCB-mHDPE are varying concentrations, whose rheological behavior is similar but whose molar mass and molar mass distribution is significantly different. Those blends were characterized rheologically to study the effects of concentration, molar mass distribution, and long-chain branching level of the low molecular LCB-mHDPE. Owing to the ultra-long relaxation times of the high molecular LCB-mHDPE, the blends started behaving clearly more long-chain branched than the base materials. The thermorheological complexity showed an apparent increase in the activation energies Ea determined from G’, G”, and especially δ. Ea(δ), which for LCB-mHDPE is a peak function, turned out to produce even more pronounced peaks than observed for regular LCB-mPE and also LCB-mPE with broader molar mass distribution. Thus, it is possible to estimate the molar mass distribution from the details of the thermorheological complexity.

Rheological Behavior of Blends of Metallocene Catalyzed Long-Chain Branched Polyethylenes. Part I: Shear Rheological and Thermorheological Behavior

Long-chain branched metallocene-catalyzed high-density polyethylenes (LCB-mHDPE) were solution blended to obtain blends with varying degrees of branching. A high molecular LCB-mHDPE was mixed with low molecular LCB-mHDPE are varying concentrations, whose rheological behavior is similar but whose molar mass and molar mass distribution is significantly different. Those blends were characterized rheologically to study the effects of concentration, molar mass distribution, and long-chain branching level of the low molecular LCB-mHDPE. Owing to the ultra-long relaxation times of the high molecular LCB-mHDPE, the blends started behaving clearly more long-chain branched than the base materials. The thermorheological complexity showed an apparent increase in the activation energies Ea determined from G’, G”, and especially δ. Ea(δ), which for LCB-mHDPE is a peak function, turned out to produce even more pronounced peaks than observed for regular LCB-mPE and also LCB-mPE with broader molar mass distribution. Thus, it is possible to estimate the molar mass distribution from the details of the thermorheological complexity.

Baseline Water Temperature: Estimation of the Annual Cycle of Surface Water Temperature in Lakes in North-Central Poland over the 1951–1968 Period

Water temperature is an important ecological variable that affects the functioning of lakes. Unfortunately, for many lakes there are no long-term observations enabling the assessment of changes in water temperatures. This makes it difficult to include this aspect in research into the biology, ecology and chemistry of such lakes. This paper presents a literature review related to changes of surface water temperatures in lakes and in particular describing the response of water temperatures and stratification to changing climate in Polish lakes. On this basis, a model based on the available data on water temperature in 931 Polish lakes in the years 1951–1968 was proposed, which allows to estimate the baseline water temperature on any day of the year. This model is calculated using the complementary error peak function on the 0–3 m water temperature dataset, which provides the best reduction of diurnal temperature fluctuations. It can be an alternative to the average temperature of surface waters, which are calculated on the basis of systematically collected data. Based on the average water temperature data obtained from 56 thermal profiles in 10 lakes in 2010–2019, the equation was analogically calculated. The average monthly water temperatures in June, July, August and September and the change in water temperature (0.24–0.30 °C decade−1) in the period 1951–1968/2010–2019 were estimated then. Similar regional or single lake trends have been found in studies by other authors covering a similar or longer period of time. The proposed method, which is suitable for simulating temperatures, especially in summer, enables the determination of the value of changes in surface water temperature in Polish lakes when only thermal profiles data from different dates are available, which can be especially helpful when analyzing hydrobiological results.

A Self-Adaptive Step Glowworm Swarm Optimization Approach

When the basic glowworm swarm optimization (GSO) algorithm optimizes the multi-peak function, the solution accuracy is not high, the later convergence is slow. To solve these problems, the fluorescent factor is introduced to adaptively adjust the step length of the firefly, an adaptive step length firefly optimization algorithm is proposed, this algorithm is an improved self-adaptive step glowworm swarm optimization (ASGSO). In this algorithm, the behavior of glowworms are developed, the step size is dynamically adjusted by the fluorescent factor, the algorithm avoids falling into a local optimum and improves the optimization speed and accuracy. The simulation results show that the improved ASGSO can search for global optimization more quickly and precisely.

Niche Brain Storm Optimization Algorithm for Multi-Peak Function Optimization

Brain Storm Optimization (BSO) is a novel proposed swarm intelligence optimization algorithm which has a fast convergent speed. However, it is easy to trap into local optimal. In this paper, a new model based on niche technology, which is named Niche Brain Storm Optimization (NBSO), is proposed to overcome the shortcoming of BSO. Niche technology effectively prevents premature and maintains population diversity during the evolution process. NBSO shows excellent performance in searching global value and finding multiple global and local optimal solutions for the multi-peak problems. Several benchmark functions are introduced to evaluate its performance. Experimental results show that NBSO performs better than BSO in global searching ability and faster than Niche Genetic Algorithm (NGA) in finding peaks for multi-peak function.

An Improved Particle Swarm Optimization Algorithm

Niche is an important technique for multi-peak function optimization. When the particle swarm optimization (PSO) algorithm is used in multi-peak function optimization, there exist some problems, such as easily falling into prematurely, having slow convergence rate and so on. To solve above problems, an improved PSO algorithm based on niche technique is brought forward. PSO algorithm utilizes properties of swarm behavior to solve optimization problems rapidly. Niche techniques have the ability to locate multiple solutions in multimodal domains. The improved PSO algorithm not only has the efficient parallelism but also increases the diversity of population because of the niche technique. The simulation result shows that the new algorithm is prior to traditional PSO algorithm, having stronger adaptability and convergence, solving better the question on multi-peak function optimization.

ASYMPTOTIC APPROXIMATIONS AND A BOREL-TYPE RESULT FOR CR FUNCTIONS

We show that for any smooth CR manifold which has a peak function (in a weak sense) at some point p, formal power series at p can be approximated asymptotically by continuous CR functions. Furthermore, if the peak function satisfies a certain growth property, the asymptotic approximation is actually smooth. This in fact allows to invert, in a Borel-type theorem, the natural map taking a smooth CR function to its formal Taylor series.