A new weighted fraction Monte Carlo method for particle coagulation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Xiao Jiang ◽  
Tat Leung Chan
Keyword(s):  
Monte Carlo ◽  
Design Methodology ◽  
Computational Cost ◽  
Particle Coagulation ◽  
Content Type ◽  
Aerosol Dynamics ◽  
Stochastic Error ◽  
Adjustable Weight ◽  
Initial Distributions ◽  
Coagulation Kernel

Purpose 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. Design/methodology/approach 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. Findings 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. Originality Value 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.

A stochastically weighted operator splitting Monte Carlo (SWOSMC) method for the numerical simulation of complex aerosol dynamic processes

2017 ◽  
Vol 27 (1) ◽  
pp. 263-278 ◽  
Author(s):  
Shuyuan Liu ◽  
Tat L. Chan
Keyword(s):  
Numerical Simulation ◽  
Monte Carlo ◽  
Operator Splitting ◽  
Splitting Method ◽  
Computational Cost ◽  
Particle Method ◽  
Dynamic Processes ◽  
Content Type ◽  
Aerosol Dynamics ◽  
Operator Splitting Method

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

Stageless evaluation for a vector Preisach model based on rotational operators

2017 ◽  
Vol 36 (5) ◽  
pp. 1501-1516
Author(s):  
Michael Nierla ◽  
Alexander Sutor ◽  
Stefan Johann Rupitsch ◽  
Manfred Kaltenbacher
Keyword(s):  
Design Methodology ◽  
Computational Cost ◽  
Direct Application ◽  
Preisach Model ◽  
Machine Precision ◽  
Content Type ◽  
Model Based ◽  
Evaluation Scheme ◽  
Computational Resources ◽  
Rotational Operator

Purpose This paper aims to present a novel stageless evaluation scheme for a vector Preisach model that exploits rotational operators for the description of vector hysteresis. It is meant to resolve the discretizational errors that arise during the application of the standard matrix-based implementation of Preisach-based models. Design/methodology/approach The newly developed evaluation uses a nested-list data structure. Together with an adapted form of the Everett function, it allows to represent both the additional rotational operator and the switching operator of the standard scalar Preisach model in a stageless fashion, i.e. without introducing discretization errors. Additionally, presented updating and simplification rules ensure the computational efficiency of the scheme. Findings A comparison between the stageless evaluation scheme and the commonly used matrix approach reveals not only an improvement in accuracy up to machine precision but, furthermore, a reduction of computational resources. Research limitations/implications The presented evaluation scheme is especially designed for a vector Preisach model, which is based on an additional rotational operator. A direct application to other vector Preisach models that do not rely on rotational operators is not intended. Nevertheless, the presented methodology allows an easy adaption to similar vector Preisach schemes that use modified setting rules for the rotational operator and/or the switching operator. Originality/value Prior to this contribution, the vector Preisach model based on rotational operators could only be evaluated using a matrix-based approach that works with discretized forms of rotational and switching operator. The presented evaluation scheme offers reduced computational cost at much higher accuracy. Therefore, it is of great interest for all users of the mentioned or similar vector Preisach models.

Lagrangian particle tracking with new weighted fraction Monte Carlo method for studying the soot particle size distributions in premixed flames

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Xiao Jiang ◽  
Tat Leung Chan
Keyword(s):  
Particle Size ◽  
Monte Carlo ◽  
Soot Formation ◽  
Particle Size Distributions ◽  
Lagrangian Particle ◽  
Content Type ◽  
Soot Particles ◽  
Stochastic Error ◽  
Formation And Evolution ◽  
Size Interval

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

Estimates and inferences in accounting panel data sets: comparing approaches

2017 ◽  
Vol 18 (3) ◽  
pp. 268-283
Author(s):  
Felix Canitz ◽  
Panagiotis Ballis-Papanastasiou ◽  
Christian Fieberg ◽  
Kerstin Lopatta ◽  
Armin Varmaz ◽  
...  
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Cross Section ◽  
Design Methodology ◽  
Estimation Methods ◽  
Standard Errors ◽  
Data Sets ◽  
Content Type ◽  
The Mean ◽  
Robust Standard Errors

Purpose The purpose of this paper is to review and evaluate the methods commonly used in accounting literature to correct for cointegrated data and data that are neither stationary nor cointegrated. Design/methodology/approach The authors conducted Monte Carlo simulations according to Baltagi et al. (2011), Petersen (2009) and Gow et al. (2010), to analyze how regression results are affected by the possible nonstationarity of the variables of interest. Findings The results of this study suggest that biases in regression estimates can be reduced and valid inferences can be obtained by using robust standard errors clustered by firm, clustered by firm and time or Fama–MacBeth t-statistics based on the mean and standard errors of the cross section of coefficients from time-series regressions. Originality/value The findings of this study are suited to guide future researchers regarding which estimation methods are the most reliable given the possible nonstationarity of the variables of interest.

Analysis of FE

2015 ◽  
Vol 34 (2) ◽  
pp. 596-603
Author(s):  
Peter Offermann ◽  
Kay Hameyer
Keyword(s):  
Design Methodology ◽  
Computational Cost ◽  
Element Model ◽  
Fast Method ◽  
Mesh Quality ◽  
Improved Method ◽  
Stochastic Variation ◽  
Cogging Torque ◽  
Content Type ◽  
Conventional Analysis

Purpose – The consideration of uncertainties in the numerical computation of electromagnetic fields has recently gained a lot of attention. Most publications focus on the creation of models for the uncertainty quantification, however, neglect the inaccuracy of the applied finite element model itself. Thus, the purpose of this paper is to analyze the influence of mesh quality on stochastic cogging torque calculations. Design/methodology/approach – The presented work consists of three steps. At first, a conventional analysis of the influence of mesh accuracy onto cogging torque is presented. Afterwards, the method is extended to stochastic calculations. Based on a comparison of the convergence behavior of both approaches, a method for more accurate cogging torque predictions with fewer necessary calculations is derived. Findings – An improved method to calculate probability predictions at minimum computational cost is presented and applied. Research limitations/implications – The presented approach requires the exact knowledge of the system’s stochastic variation boundaries. Originality/value – A fast method for more accurate stochastic cogging torque calculations is developed.

Adjusted reactive solutions for multiple power flow computations

2013 ◽  
Vol 33 (1/2) ◽  
pp. 581-593
Author(s):  
Camillo Genesi ◽  
Mario Montagna
Keyword(s):  
Monte Carlo ◽  
Design Methodology ◽  
Power Flow ◽  
Classical Method ◽  
Short Circuit ◽  
Content Type ◽  
Multiple Power ◽  
Speed And Accuracy ◽  
Node Type ◽  
Computation Speed

Purpose – The purpose of this work is that of showing some efficient techniques to perform PV-PQ node type switching in multiple power flow computations. Design/methodology/approach – Reactive generation limits of generation buses must be taken into account to obtain realistic power flow solutions. This may result computationally demanding when many power flow computations are required as in contingency screening or Monte Carlo simulations. In the present paper, the implementation of efficient PV-PQ node type switching is examined with particular emphasis on the efficiency of computation. Some different methods are proposed and compared on the basis of computation speed and accuracy. Findings – Tests show the efficiency of the proposed methods with reference to actual networks with up to 800 buses. Originality/value – The classical method of (partial) re-factorisation is not very efficient when many power flow solutions are to be evaluated. In the present work, a different approach is proposed; it is based on grounding each PV node by a fictitious short-circuit branch which is removed when the node type is changed to PQ. This operation is carried out by compensation of the solution and combined with the modifications required for contingency simulation.

Fast tolerance-aware design optimization of miniaturized microstrip couplers using variable-fidelity EM simulations and response features

2019 ◽  
Vol 36 (9) ◽  
pp. 2983-2995
Author(s):  
Slawomir Koziel ◽  
Adrian Bekasiewicz
Keyword(s):  
Monte Carlo ◽  
Statistical Analysis ◽  
Low Cost ◽  
Computational Cost ◽  
Data Driven ◽  
Yield Optimization ◽  
Content Type ◽  
Frequency Responses ◽  
Training Samples ◽  
Variable Fidelity

Purpose This paper aims to investigate the strategy for low-cost yield optimization of miniaturized microstrip couplers using variable-fidelity electromagnetic (EM) simulations. Design/methodology/approach Usefulness of data-driven models constructed from structure frequency responses formulated in the form of suitably defined characteristic points for statistical analysis is investigated. Reformulation of the characteristics leads to a less nonlinear functional landscape and reduces the number of training samples required for accurate modeling. Further reduction of the cost associated with construction of the data-driven model, is achieved using variable-fidelity methods. Numerical case study is provided demonstrating feasibility of the feature-based modeling for low cost statistical analysis and yield optimization. Findings It is possible, through reformulation of the structure frequency responses in the form of suitably defined feature points, to reduce the number of training samples required for its data-driven modeling. The approximation model can be used as an accurate evaluation engine for a low-cost Monte Carlo analysis. Yield optimization can be realized through minimization of yield within the data-driven model bounds and subsequent model re-set around the optimized design. Research limitations/implications The investigated technique exceeds capabilities of conventional Monte Carlo-based approaches for statistical analysis in terms of computational cost without compromising its accuracy with respect to the conventional EM-based Monte Carlo. Originality/value The proposed tolerance-aware design approach proved useful for rapid yield optimization of compact microstrip couplers represented using EM-simulation models, which is extremely challenging when using conventional approaches due to tremendous number of EM evaluations required for statistical analysis.

scholarly journals On Stochastic Error and Computational Efficiency of the Markov Chain Monte Carlo Method

2014 ◽  
Vol 16 (2) ◽  
pp. 467-490 ◽  
Author(s):  
Jun Li ◽  
Philippe Vignal ◽  
Shuyu Sun ◽  
Victor M. Calo
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Sample Size ◽  
Computational Cost ◽  
Sampling Interval ◽  
Ensemble Average ◽  
Cycle Number ◽  
Stochastic Error ◽  
General Rules

AbstractIn Markov Chain Monte Carlo (MCMC) simulations, thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated samples. These samples are selected in accordance with the probability distribution function, known from the partition function of equilibrium state. As the stochastic error of the simulation results is significant, it is desirable to understand the variance of the estimation by ensemble average, which depends on the sample size (i.e., the total number of samples in the set) and the sampling interval (i.e., cycle number between two consecutive samples). Although large sample sizes reduce the variance, they increase the computational cost of the simulation. For a given CPU time, the sample size can be reduced greatly by increasing the sampling interval, while having the corresponding increase in variance be negligible if the original sampling interval is very small. In this work, we report a few general rules that relate the variance with the sample size and the sampling interval. These results are observed and confirmed numerically. These variance rules are derived for the MCMC method but are also valid for the correlated samples obtained using other Monte Carlo methods. The main contribution of this work includes the theoretical proof of these numerical observations and the set of assumptions that lead to them.

A coupled LES-Monte Carlo method for simulating aerosol dynamics in a turbulent planar jet

2019 ◽  
Vol 30 (2) ◽  
pp. 855-881 ◽  
Author(s):  
Hongmei Liu ◽  
Tat Leung Chan
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Turbulent Flows ◽  
Operator Splitting ◽  
Particle Diameter ◽  
Content Type ◽  
Aerosol Dynamics ◽  
Planar Jet

Purpose 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. Design/methodology/approach The DWOSMC method is coupled with LES for the numerical simulation of aerosol dynamics in turbulent flows. Findings 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. Originality/value 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.

scholarly journals Vulnerable adults in police custody

2019 ◽  
Vol 22 (1) ◽  
pp. 5-8
Author(s):  
Ian Cummins
Keyword(s):  
Design Methodology ◽  
Research Literature ◽  
Police Custody ◽  
England And Wales ◽  
Content Type ◽  
Increased Risk ◽  
Vulnerable Adults

Purpose The purpose of this paper is to discuss the recent National Appropriate Adult Network (NAAN) report on the role of the appropriate adult. Design/methodology/approach This paper is based on the NAAN report and a review of relevant policy and research literature. Findings There to Help 2 highlights that there are still significant gaps in the provision of appropriate adult schemes across England and Wales. These gaps potentially place vulnerable adults at increased risk. Originality/value This paper is a review of recent research.

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