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The purpose of this study is to present a newly proposed and developed sorting algorithm-based merging weighted fraction Monte Carlo (SAMWFMC) method for solving the population balance equation for the weighted fraction coagulation process in aerosol dynamics with high computational accuracy and efficiency.

In the new SAMWFMC method, the jump Markov process is constructed as the weighted fraction Monte Carlo (WFMC) method (Jiang and Chan, 2021) with a fraction function. Both adjustable and constant fraction functions are used to validate the computational accuracy and efficiency. A new merging scheme is also proposed to ensure a constant-number and constant-volume scheme.

The new SAMWFMC method is fully validated by comparing with existing analytical solutions for six benchmark test cases. The numerical results obtained from the SAMWFMC method with both adjustable and constant fraction functions show excellent agreement with the analytical solutions and low stochastic errors. Compared with the WFMC method (Jiang and Chan, 2021), the SAMWFMC method can significantly reduce the stochastic error in the total particle number concentration without increasing the stochastic errors in high-order moments of the particle size distribution at only slightly higher computational cost.

The WFMC method (Jiang and Chan, 2021) has a stringent restriction on the fraction functions, making few fraction functions applicable to the WFMC method except for several specifically selected adjustable fraction functions, while the stochastic error in the total particle number concentration is considerably large. The newly developed SAMWFMC method shows significant improvement and advantage in dealing with weighted fraction coagulation process in aerosol dynamics and provides an excellent potential to deal with various fraction functions with higher computational accuracy and efficiency.

The purpose of this study is to investigate the aerosol dynamics of the particle coagulation process using a newly developed weighted fraction Monte Carlo (WFMC) method.

The weighted numerical particles are adopted in a similar manner to the multi-Monte Carlo (MMC) method, with the addition of a new fraction function (α). Probabilistic removal is also introduced to maintain a constant number scheme.

Three typical cases with constant kernel, free-molecular coagulation kernel and different initial distributions for particle coagulation are simulated and validated. The results show an excellent agreement between the Monte Carlo (MC) method and the corresponding analytical solutions or sectional method results. Further numerical results show that the critical stochastic error in the newly proposed WFMC method is significantly reduced when compared with the traditional MMC method for higher-order moments with only a slight increase in computational cost. The particle size distribution is also found to extend for the larger size regime with the WFMC method, which is traditionally insufficient in the classical direct simulation MC and MMC methods. The effects of different fraction functions on the weight function are also investigated.

Stochastic error is inevitable in MC simulations of aerosol dynamics. To minimize this critical stochastic error, many algorithms, such as MMC method, have been proposed. However, the weight of the numerical particles is not adjustable. This newly developed algorithm with an adjustable weight of the numerical particles can provide improved stochastic error reduction.

The purpose of this paper is to study the complex aerosol dynamic processes by using this newly developed stochastically weighted operator splitting Monte Carlo (SWOSMC) method.

Stochastically weighted particle method and operator splitting method are coupled to formulate the SWOSMC method for the numerical simulation of particle-fluid systems undergoing the complex simultaneous processes.

This SWOSMC method is first validated by comparing its numerical simulation results of constant rate coagulation and linear rate condensation with the corresponding analytical solutions. Coagulation and nucleation cases are further studied whose results are compared with the sectional method in excellent agreement. This SWOSMC method has also demonstrated its high numerical simulation capability when used to deal with simultaneous aerosol dynamic processes including coagulation, nucleation and condensation.

There always exists conflict and tradeoffs between computational cost and accuracy for Monte Carlo-based methods for the numerical simulation of aerosol dynamics. The operator splitting method has been widely used in solving complex partial differential equations, while the stochastic-weighted particle method has been commonly used in numerical simulation of aerosol dynamics. However, the integration of these two methods has not been well investigated.

The purpose of this paper is to study nanoparticles diffusion and coagulation processes in a twin-jet.

Large eddy simulation (LES) and Taylor-series expansion moment method (TEMOM) are employed to deal with a nanoparticle-laden twin-jet flow.

The numerical results show that the interaction of the two jets and turbulence eddy structures rolling-up, paring and shedding in flow sharply affects particles number concentration. Particle diameter grows quickly at the interfaces of jets. Coagulation shows more obvious effect at initial stage than that in the subsequent period. Then diffusion makes the particle diameter distribution much more uniform.

In recent years a great number of attentions have been focussed on the issue of particulate dynamics processes including diffusion, coagulation and deposition, etc. However, up to now few works have been focus on the nanoparticles coagulation and dispersion in turbulent flows. The investigation on the diffusion and coagulation process of nanoparticles using TEMOM in a twin-jet flow has not been found.

The purpose of this paper is to study the evolution and growth of aerosol particles in a turbulent planar jet by using the newly developed large eddy simulation (LES)-differentially weighted operator splitting Monte Carlo (DWOSMC) method.

The DWOSMC method is coupled with LES for the numerical simulation of aerosol dynamics in turbulent flows.

Firstly, the newly developed and coupled LES-DWOSMC method is verified by the results obtained from a direct numerical simulation-sectional method (DNS-SM) for coagulation occurring in a turbulent planar jet from available literature. Then, the effects of jet temperature and Reynolds number on the evolution of time-averaged mean particle diameter, normalized particle number concentration and particle size distributions (PSDs) are studied numerically on both coagulation and condensation processes. The jet temperature and Reynolds number are shown to be two important parameters that can be used to control the evolution and pattern of PSD in an aerosol reactor.

The coupling between the Monte Carlo method and turbulent flow still encounters many technical difficulties. In addition, the relationship between turbulence, particle properties and collision kernels of aerosol dynamics is not yet well understood due to the theoretical limitations and experimental difficulties. In the present study, the developed and coupled LES-DWOSMC method is capable of solving the aerosol dynamics in turbulent flows.

The purpose of this paper is to study the soot formation and evolution by using this newly developed Lagrangian particle tracking with weighted fraction Monte Carlo (LPT-WFMC) method.

The weighted soot particles are used in this MC framework and is tracked using Lagrangian approach. A detailed soot model based on the LPT-WFMC method is used to study the soot formation and evolution in ethylene laminar premixed flames.

The LPT-WFMC method is validated by both experimental and numerical results of the direct simulation Monte Carlo (DSMC) and Multi-Monte Carlo (MMC) methods. Compared with DSMC and MMC methods, the stochastic error analysis shows this new LPT-WFMC method could further extend the particle size distributions (PSDs) and improve the accuracy for predicting soot PSDs at larger particle size regime.

Compared with conventional weighted particle schemes, the weight distributions in LPT-WFMC method are adjustable by adopting different fraction functions. As a result, the number of numerical soot particles in each size interval could be also adjustable. The stochastic error of PSDs in larger particle size regime can also be minimized by increasing the number of numerical soot particles at larger size interval.

The purpose of this paper is to provide a theoretical framework for predicting the next period financial behavior of bank mergers within a statistical-oriented setting.

Bank mergers are modeled combining a discrete variant of the Smoluchowski coagulation equation with a reverse engineering method. This new approach allows to compute the correct merging probability values via the construction and solution of a multi-variable matrix equation. The model is tested on real financial data relative to US banks collected from the National Information Centre.

Bank size distributions predicted by the proposed method are much more adherent to real data than those derived from the estimation method. The proposed method provides a valid alternative to estimation approaches while overcoming some of their typical drawbacks.

Bank mergers are interpreted as stochastic processes focusing on two main parameters, that is, number of banks and asset size. Future research could expand the model analyzing the micro-dynamic taking place behind bank mergers. Furthermore, bank demerging and partial bank merging could be considered in order to complete and strengthen the proposed approach.

The implementation of the proposed method assists managers in making informed decisions regarding future merging actions and marketing strategies so as to maximize the benefits of merging actions while reducing the associated potential risks from both a financial and marketing viewpoint.

To the best of the authors’ knowledge, this is the first study where bank merging is analyzed using a dynamic stochastic model and the merging probabilities are determined by a multi-variable matrix equation in place of an estimation procedure.

The purpose of this paper is to investigate the batch treatment of pulp and paper mill wastewater using electro-coagulation (EC).

Statistical experimental design was used to investigate the effect of initial pH, current density and temperature. Experiments were planned to obtain the maximum amount of information in the fewest number of runs. Minimum-maximum values of current density, initial pH, temperature of medium were selected as 9-25 mA/cm2, 5-9, 25-50°C, respectively. A total number of 20 experiments including eight factorial points, six axial points and six replicates in centre points were carried out and experimental data were collected. Optimum operating parameters were determined by evaluating experimental results in MATLAB 7.9®.

According to the results, the optimum values of current density, initial pH and temperature of medium are determined as 14.12 mA/cm2, 8.22 and 34.21°C, respectively.

Many researches about different techniques including physical, chemical and biological methods have been done on the subject of pulp and paper wastewater treatment. In physical and chemical processes low molecular weight compounds are not removed efficiently, also these methods are quite expensive. Electrochemical degradation has an advantage of removing even the smallest colloidal particles compared with traditional flocculation and coagulation.

Complete removal of pollutants, less sludge generation, simple process design and easy operation are standard features of the EC and it comes forward as one of the promising techniques.

The purpose of this study is to focus on Tunisian tannery sector that causes a considerable damage to the environment and consequently leads to serious health problems due to the untreated effluents generated from the various leather processing stages.

This paper discusses a voluntary initiative taken by the top managers of tannery enterprise to prevent pollution and disseminate the concept of eco-industrial activities between employees and stakeholders. In addition, this research assesses the performance of such treatment that characterizes the chemical parameters of generated pollutants. It also aims at optimizing the industrial process for cleaner production. Coagulation–flocculation process is investigated in this study. Moreover, oxidation phase by ozone is taking into account before and after coagulation–flocculation process to measure the effectiveness of the combined method for reducing the main pollutant concentrations.

The unhairing and chrome (Cr) tanning steps are considered the most polluting steps. Therefore, the application of various treatment techniques, including chemical and physicochemical processes, is realized to reduce the toxicity of the effluents. The correlation between experimental and modeling results, using artificial neural network (ANN) method, was investigated in this research. The results of the constructed ANN model are measured by the correlation of experimental and model results during coagulation–flocculation and oxidation stages. The validation of the elaborated model through the error calculation (MSE) and the correlation coefficient (R) confirm the reliability of ANN method.

Eventually, the establishment of ANN model for performance prediction of wastewater parameters is investigated due to different measurements of physical effluent outputs, such as: pH, turbidity, TSS, DS, COD, fat, TSS, S^2- and Cr. This study uses predictive modeling, a machine learning technique to tackle the problem of accurately predicting the behavior of unseen configuration.

This study aims to investigate the insights of soot formation such as rate of soot coagulation, rate of soot nucleation, rate of soot surface growth and soot surface oxidation in ethylene/hydrogen/nitrogen diffusion jet flame at standard atmospheric conditions, which is very challenging to capture even with highly sophisticated measuring systems such as Laser Induced Incandescence and Planar laser-induced fluorescence. The study also aims to investigate the volume of soot in the flame using soot volume fraction and to understand the global correlation effect in the formation of soot in ethylene/hydrogen/nitrogen diffusion jet flame.

A large eddy simulation (LES) was performed using box filtered subgrid-scale tensor. A filtered and residual component of the governing equations such as continuity, momentum, energy and species are resolved and modeled, respectively. All the filtered and residual components are numerically solved using the ILU method by considering PISO pressure–velocity solver. All the hyperbolic flux uses the QUICK algorithm, and an elliptic flux uses SOU to evaluate face values. In all the cases, Courant–Friedrichs–Lewy (CFL) conditions are maintained unity.

The findings are as follows: soot volume fraction (SVF) as a function of a flame-normalized length for three different Reynolds number configurations (Re = 15,000, Re = 8,000 and Re = 5,000) using LES; soot gas phase and particulate phase insights such as rate of soot nucleation, rate of soot coagulation, rate of soot surface growth and soot surface oxidation for three different Reynolds number configurations (Re = 15,000, Re = 8,000 and Re = 5,000); and soot global correction using total soot volume in the flame volume as a function of Reynolds number and Froude number.

The originality of this study includes the following: coupling LES turbulent model with chemical equilibrium diffusion combustion conjunction with semi-empirical Brookes Moss Hall (BMH) soot model by choosing C6H6 as a soot precursor kinetic pathway; insights of soot formations such as rate of soot nucleation, soot coagulation rate, soot surface growth rate and soot oxidation rate for ethylene/hydrogen/nitrogen co-flow flame; and SVF and its insights study for three inlet fuel port configurations having the three different Reynolds number (Re = 15,000, Re = 8,000 and Re = 5,000).