Model reduction of multi-scale chemical Langevin equations

This paper addresses the model reduction problem for a class of stiff chemical Langevin equations that arise as models of biomolecular networks with fast and slow reactions and can be described as continuous Markov processes. Initially, a coordinate transformation is sought that allows the decoupling of fast and slow variables in the model equations. Necessary and sufficient conditions are derived for such a linear transformation to exist, along with an explicit change of variables which achieves the desired decoupling. For the systems for which this step is applicable, the method of adiabatic elimination is applied to determine a representation of the slow dynamics. Theoretical concepts and results are illustrated with simple examples.     

Solid-State Synthesis and Thermoelectric Properties of Sb-Doped Mg2Si Materials

Sb-doped magnesium silicide compounds have been prepared through ball milling and solid-state reaction. Materials produced were near-stoichiometric. The structural modifications have been studied with powder x-ray diffraction. Highly dense pellets of Mg₂Si_1?x Sb _x (0 ≤ x ≤ 0.04) were fabricated via hot pressing and studied in terms of Seebeck coefficient, electrical and thermal conductivity, and free carrier concentration as a function of Sb concentration. Their thermoelectric performance in the high temperature range is presented, and the maximum value of the dimensionless figure of merit was found to be 0.46 at 810 K, for the Mg₂Si_0.915Sb_0.015 member.     

PAH formation in one-dimensional premixed fuel-rich atmospheric pressure ethylbenzene and ethyl alcohol flames

This study addresses health-hazardous emissions from combustion of aromatic and oxygenated components of engine fuel blends. An investigation was conducted on the evolution of polycyclic aromatic hydrocarbons (PAH) and other pollutants (soot, CO, unburned light hydrocarbons) emitted from one-dimensional ethylbenzene and ethyl alcohol flames. The study of ethylbenzene combustion is also pertinent to that of waste polystyrene, as past work has indicated that ethylbenzene may be a surrogate for initial products of polystyrene pyrolysis. Both liquid fuels were prevaporized in nitrogen, mixed with oxygen and additional nitrogen, and upon ignition, premixed flat flames were stabilized over a burner. Temperature measurements and product sampling were conducted at various heights above the burner. Results showed that ethyl alcohol combustion generated small yields of PAH, even under the adverse fuel-rich conditions of this study (?=2.5). PAH mole fractions in the ethyl alcohol flame were 2-5 orders of magnitude lower than those in the ethylbenzene flame at the same location. PAH mole fractions often peaked in the postflame region and remained at relatively high levels thereafter. PAH mole fractions in premixed fuel-rich benzene, ethane, ethylene, and methane flames, published in the literature, were typically in between those found in the two flames of this study. Computations were conducted using a currently developed detailed kinetic model, allowing for the prediction of formation and depletion of major PAH and soot particles of different sizes. The computed chemical flame structures were compared to experimental data obtained in the present work. Predicted mole fractions were often close to the experimentally obtained values or, at worse, within the same order of magnitude for both fuels. Reaction pathways are discussed.     

Classical and alternative fuel mix optimization in cement production using mathematical programming

In this paper a systematic methodology is presented for the simultaneous optimal selection of raw materials, fossil fuels and alternative fuels in cement production. The aim is to offer a generic mathematical formulation that can be used as the basis for developing case specific mathematical formulations that can assist the strategic decision-making process. The mathematical model presented takes into consideration the essential elements of a cement plant operation. The final formulation is a mixed integer linear programming problem that aims at minimizing the overall operating cost. A realistic case study is presented which demonstrates the usefulness of the proposed mathematical programming methodology.     

Porous,Sintered Glass‐Ceramics from Inorganic Polymers Based on Fayalite Slag

The present paper deals with the synthesis of porous, sintered glass‐ceramics obtained at temperatures below 1150°C, originating from inorganic polymers based on fayalite slag. Firing led to the evaporation of water, dehydroxylation, and oxidation of Fe²⁺ above 345°C. For heating >700°C, the Si–O stretching band shifted from the 1160 and 750 cm^?1 to the 1255 and 830 cm^?1 region, due to a structural reorganization of the amorphous phase, whereas Fe–O bands appeared at 550 cm^?1. The final microstructure consisted predominantly of an amorphous phase, hematite, and franklinite. The open porosity and compressive strength decreased and increased, respectively, as the firing temperature increased. The final values suggest properties comparable to that of structural lightweight concrete, still, the materials synthesized herein, are lighter, and made primarily from secondary resources.     

Inorganic polymers made of fayalite slag: On the microstructure and behavior of Fe

The microstructure of inorganic polymers (IP) formed from fayalite slag was investigated as a function of the composition of different activating solutions. The starting slag was 80 wt% amorphous, and after activation using sodium silicate solutions with varying SiO₂/Na₂O molar ratios, the amorphous phase dissolved and a binder phase was formed. The morphology of this binder, including the population and size of remnant particles and pores, was dependent on the particular activating solution used, and became denser as the level of silicate rose. ⁵⁷Fe Mössbauer spectroscopy revealed that the IP synthesis reaction is combined with the oxidation of Fe²⁺ from the fayalite slag to Fe³⁺ in the inorganic polymer binder. The reaction extent varied and could be quantified using the absorption areas of these ions. Data corroborate that the Fe²⁺ ions in the amorphous part of the fayalite slag and the Fe³⁺ ions in the new binder phase had an average oxygen‐coordination number of 5.     

The fate of iron during the alkali‐activation of synthetic (CaO‐)FeOx‐SiO2 slags: An Fe K‐edge XANES study

Slags from the nonferrous metals industry have great potential to be used as feedstocks for the production of alkali‐activated materials. Until now, however, only very limited information has been available about the structural characteristics of these materials. In the work presented herein, synthetic slags in the CaO–FeO_x–SiO₂ system, representing typical compositions of Fe‐rich slags, and inorganic polymers (IPs) produced from the synthetic slags by activation with alkali silicate solutions have been studied by means of X‐ray absorption near‐edge structure (XANES) spectroscopy at the Fe K‐edge. The iron in the slags was largely Fe²⁺, with an average coordination number of approximately 5 for the iron in the amorphous fraction. The increase in average oxidation number after alkali‐activation was conceptualized as the consequence of slag dissolution and IP precipitation, and employed to calculate the degrees of reaction of the slags. The degree of reaction of the slags increased with increasing amorphous fraction. The iron in the IPs had an average coordination number of approximately 5; thus, IPs produced from the Fe‐rich slags studied here are not Fe‐analogs of aluminosilicate geopolymers, but differ significantly in terms of structure from the latter.     

Kinetics of pore formation and resulting properties of lightweight inorganic polymers

Inorganic polymer (IP) foams could be used as an alternative to commonly available cellular concretes. To do so, however, it is crucial to understand how the foaming kinetics and the final foam properties can be controlled and tailored to delivered the desired performance. The research reported in this article investigates the influence of the SiO₂/Na₂O ratio of the activating solution, addition time of foaming agent, and temperature, on the reaction kinetics and final properties of a porous IP. The IPs were formed by activating fayalite slag, a by-product of secondary copper production, with a sodium-silicate solution. Foaming was achieved by introducing metallic Al into the formulation, oxidizing it in the alkaline environment, liberating H₂ gas, and entrapping it. Reaction kinetics were assessed using isothermal calorimetry, rheology, and a dedicated setup to record the foaming. The mechanical and physical properties of the foam were assessed via compressive strength and water absorption measurements. Microstructural analysis was undertaken using electron microscopy and computed tomography. The results showed that by decreasing the SiO₂/Na₂O ratio and/or increasing the temperature, the reaction kinetics were accelerated. Regarding the properties, postponing the initiation of the foaming led to more uniform and smaller pores, resulting in an increased compressive strength-to-density ratio.     

Pressure- and Temperature-Driven Flow Through Triangular and Trapezoidal Microchannels

A detailed study of pressure- and temperature-driven flows through long channels of triangular and trapezoidal cross sections is carried out. Due to the imposed pressure and temperature gradients there is a combined gas flow consisting of a thermal creep flow from the cold toward the hot reservoir and a Poiseuille flow from the high- toward the low-pressure reservoir. The formulation is based on the linearized Shakhov model subject to Maxwell boundary conditions, and it is solved numerically using a finite-difference scheme in the physical space and the discrete velocity method in the molecular velocity space. The results are valid in the whole range of the Knudsen number. In addition to the dimensionless flow rates, a methodology is presented to estimate for a certain set of input data the mass flow rates and the pressure distribution along the channel. Finally, special attention is given to the case of zero net mass flow and to the computation of the coefficient of the thermomolecular pressure difference.     

Combustion behavior in air of single particles from three different coal ranks and from sugarcane bagasse

Comparative combustion studies were performed on particles of pulverized coal samples from three different ranks: a high-volatile bituminous coal, a sub-bituminous coal, and two lignite coals. The study was augmented to include observations on burning pulverized woody biomass residues, in the form of sugarcane bagasse. Fuel particles, in the range of 75–90 μm, were injected in a bench-scale, transparent drop-tube furnace, electrically-heated to 1400 K, where they experienced high-heating rates, ignited and burned. The combustion of individual particles in air was observed with three-color pyrometry and high-speed high-resolution cinematography to obtain temperature–time–size histories. Based on combined observations from these techniques, in conjunction to morphological examinations of particles, a comprehensive understanding of the combustion behaviors of these fuels was developed. Observed differences among the coals have been striking. Upon pyrolysis, the bituminous coal chars experienced the phenomena of softening, melting, swelling and formation of large blowholes through which volatile matter escaped. Combustion of the volatile matter was sooty and very luminous with large co-tails forming in the wake of the particle trajectories. Only after the volatile matter flames extinguished, the char combustion commenced and was also very luminous. In contrast, upon pyrolysis, lignite coals became fragile and experienced extensive fragmentation, immediately followed by ignition of the char fragments (numbering in the order of 10–100, depending on the origin of the lignite coal) spread apart into a relatively large volume. As no separate volatile matter combustion period was evident, it is likely that volatiles burned on the surface of the chars. The combustion of the sub-bituminous coal was also different. Most particles experienced limited fragmentation, upon pyrolysis, to several char fragments, with or without the presence of brief and low-luminosity volatile flames; other particles did not fragment and directly proceeded to char combustion. Finally combustion of bagasse was once again very distinctive. Upon pyrolysis, long-lasting, low-luminosity, nearly-transparent spherical flames formed around slowly-settling devolatilizing particles. They were followed by bright, short-lived combustion of the chars. Both volatiles and chars experienced shrinking core mode of burning. For all fuels, flame and char temperature profiles were deduced from pyrometric data and burnout times were measured. Combustion rates were calculated from luminous carbon disappearance measurements, and were compared with predictions based on published kinetic expressions.