Method“Monte Carlo”in healthcare

In public health,simulation modeling stands as an invaluable asset,enabling the evaluation of new systems without their physical implementation,experimentation with existing systems without operational adjustments,and testing system limits without real-world repercussions.In simulation modeling,the Monte Carlo method emerges as a powerful yet underutilized tool.Although the Monte Carlo method has not yet gained widespread prominence in healthcare,its technological capabilities hold promise for substantial cost reduction and risk mitigation.In this review article,we aimed to explore the transformative potential of the Monte Carlo method in healthcare contexts.We underscore the significance of experiential insights derived from simulated experimentation,especially in resource-constrained scenarios where time,financial constraints,and limited resources necessitate innovative and efficient approaches.As public health faces increasing challenges,incorporating the Monte Carlo method presents an opportunity for enhanced system construction,analysis,and evaluation.

Statistical Modification Analysis of Helical Planetary Gears based on Response Surface Method and Monte Carlo Simulation

Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.

Monte Carlo Simulation of Fractures Using Isogeometric Boundary Element Methods Based on POD-RBF

This paper presents a novel framework for stochastic analysis of linear elastic fracture problems.Monte Carlo simulation(MCs)is adopted to address the multi-dimensional uncertainties,whose computation cost is reduced by combination of Proper Orthogonal Decomposition(POD)and the Radial Basis Function(RBF).In order to avoid re-meshing and retain the geometric exactness,isogeometric boundary element method(IGABEM)is employed for simulation,in which the Non-Uniform Rational B-splines(NURBS)are employed for representing the crack surfaces and discretizing dual boundary integral equations.The stress intensity factors(SIFs)are extracted by M integral method.The numerical examples simulate several cracked structures with various uncertain parameters such as load effects,materials,geometric dimensions,and the results are verified by comparison with the analytical solutions.

Verification of modified sum-peak method in Monte Carlo simulation of full energy peak and sum-peak efficiencies of a HPGe detector

The modified sum-peak method estimates radioactivity by using only the peak and the sum-peak count rates.To verify the modified sum-peak method,the dependence of the full energy peak efficiency on the source-to-detector distance in a high-purity germanium detector system was studied using a Geant4 Monte Carlo simulation.The effect of the deadlayer in the germanium crystal was estimated by reference to experiments on 241 Am and the relative efficiency of the detector.The peak efficiency dependence on the source-to-detector distance was compared between the simulation and measurements.The modified sum-peak method is discussed with respect to these peak efficiencies.

Security Simulation of Continuous-Variable Quantum Key Distribution over Air-to-Water Channel Using Monte Carlo Method

Considering the ocean water＇s optical attenuation and the roughness of the sea surface, we analyze the security of continuous-variable （CV） quantum key distribution （QKD） based Mr-to-water channel. The effects of the absorp- tion and scattering on the transmittance of underwater quantum channel and the maximum secure transmission distance are studied. Considering the roughness of the sea surface, we simulate the performance bounds of CV QKD with different wind speeds using the Monte Carlo method. The results show that even if the secret key rate gradually reduces as the wind speed increases, the maximum transmission distance will not be affected obviously. Compared to the works regarding short-distance underwater optical communication, our research represents a significant step towards establishing secure communication between air platform and submarine vehicle.

COMPUTERIZED SIMULATION OF THERMODYNAMICS FOR MOLTEN LiF-KF SOLUTION BY MONTE CARLO METHOD

The structure and behaviour of LiF-KF solution,as a typical common-anion system,has been simulated by Monte Carlo method.The calculation of partial radial distribution function of ions,heat of mixing and potential energy distribution shows that the average distance be- tween Li^+ and F^- ions will significantly narrow after mixing of molten LiF and KF.This is very similar to the lean-on-one-side effect in molten LiF-KCl solution.The calculated heat of mixing is in fair agreement with the measured one.The dominant source of the energy of mixing may be that the decrease of the repulsion energy between cations,the decrease of the attraction energy between cations and anions,and the decrease of the repulsion energy be- tween anions.

COMPUTER SIMULATION OF STRUCTURE OF MOLTEN DyF_3－BaF_2－LiF SYSTEM BY MONTE CARLO METHOD

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Seismic Inventory Simulation and Conformance Test Based on the Monte Carlo Method——A Case Study of the Fenhe-Weihe Belt

Artificial earthquake catalogue simulation is one of the ways to effectively improve the incompleteness of the existing earthquake catalogue,the scarcity of large earthquake records and the improvement of seismological research. Based on the Poisson distribution model of seismic activity and the Gutenberg-Richter magnitude-frequency relationship,the Monte Carlo method which can describe the characteristics of the stochastic nature and the physical experiment process is used. This paper simulates the future seismic catalogues of the Fenhe-Weihe seismic belt of different durations and conducts statistical tests on them.The analysis shows that the simulation catalogue meets the set seismic activity parameters and meets the Poisson distribution hypothesis,which can obtain a better simulated earthquake catalogues that meets the seismic activity characteristics. According to the simulated earthquake catalogues,future earthquake trends in this region are analyzed to provide reference for seismic hazard analysis.

Monte Carlo simulation based thinning and calculating method for noninvasive blood glucose sensing by near-infrared spectroscopy

Previous results show that the floating reference theory(FRT)is an effective tool to reduce the infuence of interference factors on noninvasive blood glucose sensing by near infrared spectros-copy(NIRS).It is the key to measure the floating reference point(FRP)precisely for the application of FRT.Monte Carlo(MC)simulation has been introduced to quantitatively in-vestigate the effects of positioning errors and light source drifts on measuring FRP.In this article,thinning and calculating method(TCM)is proposed to quantify the positioning error.Mean-while,the normalization process(NP)is developed to significantly reduce the error induced by light source drift.The results according to TCM show that 7 purm deviations in positioning can generate about 10.63%relative error in FRP.It is more noticeable that 1%fluctuation in light source intensity may lead to 12.21%relative errors.Gratifyingly,the proposed NP model can effectively reduce the error caused by light source drift.Therefore,the measurement system for FRPs must meet that the positioning error is less than 7 purm,and the light source drift is kept within 1%.Furthermore,an improvement for measurement system is proposed in order to take advantage of the NP model.

MONTE CARLO SIMULATION OF RADIATION FIELD OPTIMIZATION FOR MEDICAL LINAC

A method for designing an X-ray flatness filter for medical electron linac is developed. It is used in the optimization process in the electron beam radiation system. Monte Carlo simulation method is used and two examples of real radiation system optimization processes for China-made medical electron linac are provided： 15 MV X- ray system of BJ-20 linac, and 12 MeV electron system of BJ-14. Results are verified by using the traditional method.

ON THE MONTE CARLO SIMULATION OF NORMAL GRAIN GROWTH

The microstructures and their kinetics of normal grain growth are simulated using different Monte Carlo （MC） algorithms. Compared with the relative figures and the theoretical normal grain growth exponents of n =0.5, the effects of some factors of MC algorithm, i.e. the lattice types, the methods of selecting lattice sites, and the neighbors selection for energy calculations, on the simulation results of grain growth are studied. Two methods of regression were compared, and the three-parameter nonlinear regression is much more suitable for fitting the grain growth kinetics. A better model with appropriate factors included triangular lattice, the attempted site randomly selected, and the first and second nearest neighbors for energy calculations is obtained.

A MONTE CARLO SIMULATION OF THE CVD DIAMOND FILM

A Monte Carlo algorithm has been developed by the authors to simulate the chemical vapor deposition (CVD) processes of diamond films. The method considers both the diffusion and the incorporation of the growth radicals on the growing surface in simulating the evolution of the morphology and microstructure. The calculation of configuration energy is used to determine the orientation of adsorbed growth radicals. The effect of processing variables such as nucleation density and substrate temperature on the morphology and microstructure is discussed. It is found that competitive characteristic and coarsening effect exist in the simulation results, which agree with the experimental observations.

Monte Carlo Simulations of Density Profiles for Hard-Sphere Chain Fluids Confined Between Surfaces

Covering a wide range of bulk densities, density profiles for hard-sphere chain fluids (HSCFs) with chain length of 3,4,8,20,32 and 64 confined between two surfaces were obtained by Monte Carlo simulations using extended continuum configurational-bias (ECCB) method. It is shown that the enrichment of beads near surfaces is happened at high densities due to the bulk packing effect, on the contrary, the depletion is revealed at low densities owing to the configurational entropic contribution. Comparisons with those calculated by density functional theory presented by Cai et al. indicate that the agreement between simulations and predictions is good. Compressibility factors of bulk HSCFs calculated using volume fractions at surfaces were also used to test the reliability of various equations of state of HSCFs by different authors.

Monte Carlo simulation of sequential structure control of AN-MA-IA aqueous copolymerization by different operation modes

The regulation of polyacrylonitrile(PAN)copolymer composition and sequence structure is the precondition for producing high-quality carbon fiber high quality.In this work,the sequential structure control of acrylonitrile(AN),methyl acrylate(MA)and itaconic acid(IA)aqueous copolymerization was investigated by Monte Carlo(MC)simulation.The parameters used in Monte Carlo were optimized via machine learning(ML)and genetic algorithms(GA)using the experimental data from batch copolymerization.The results reveal that it is difficult to control the aqueous copolymerization to obtain PAN copolymer with uniform sequence structure by batch polymerization with one-time feeding.By contrary,it is found that the PAN copolymer with uniform composition and sequence structure can be obtained by adjusting IA feeding quantity in each reactor of a train of five CSTRs.Hopefully,the results obtained in this work can provide valuable information for the understanding and optimization of AN copolymerization process to obtain high-quality PAN copolymer precursor.

Monte-Carlo Simulation of Surface Crack Growth Rate for Offshore Structural Steel E36-Z35

The Monte- Carlo method is used to simulate the surface fatigue crack growth rate for offshore structural steel E36-Z35, and to determine the distributions and relevance of the parameters in the Paris equation. By this method, the time and cost of fatigue crack propagation testing can be reduced. The application of the method is demonstrated by use of four sets of fatigue crack propagation data for offshore structural steel E36-Z35. A comparison of the test data with the theoretical prediction for surface crack growth rate shows the application of the simulation method to the fatigue crack propagation tests is successful.

Implementation of 3D Lattice Monte Carlo Simulation on a Cluster of Symmetric Multiprocessors

This paper presents a new approach to parallelize 3D lattice Monte Carlo algorithms used in the numerical simulation of polymer on ZiQiang 2000 a cluster of symmetric multiprocessors (SMPs). The combined load for cell and energy calculations over the time step is balanced together to form a single spatial decomposition. Basic aspects and strategies of running Monte Carlo calculations on parallel computers are studied. Different steps involved in porting the software on a parallel architecture based on ZiQiang 2000 running under Linux and MPI are described briefly. It is found that parallelization becomes more advantageous when either the lattice is very large or the model contains many cells and chains.

Kinetic Monte Carlo simulation of physical vapor deposition of thin Cu film

A two-dimensional Kinetic Monte Carlo method has been developed for simulating the physical vapor deposition of thin Cu films on Cu substrate. An improved embedded atom method was used to calculate the interatomic potential and determine the diffusion barrier energy and residence time. Parameters, including incident angle,deposition rate and substrate temperature, were investigated and discussed in order to find their influences on the thin film morphology.

Reduced Expanding Load Method for Simulation-Based Structural System Reliability Analysis

The current situation and difficulties of the structural system reliability analysis are mentioned. Then on the basis of Monte Carlo method and computer simulation, a new analysis method reduced expanding load method (RELM) is presented, which can be used to solve structural reliability problems effectively and conveniently. In this method, the uncertainties of loads, structural material properties and dimensions can be fully considered. If the statistic parameters of stochastic variables are known, by using this method, the probability of failure can be estimated rather accurately. In contrast with traditional approaches,RELM method gives a much better understanding of structural failure frequency and its reliability index β is more meaningful.To illustrate this new idea, a specific example is given.

Quasi-Monte Carlo Simulation-Based SFEM for Slope Reliability Analysis

Considering the stochastic spatial variation of geotechnical parameters over the slope, a Stochastic Finite Element Method (SFEM) is established based on the combination of the Shear Strength Reduction (SSR) concept and quasi-Monte Carlo simulation. The shear strength reduction FEM is superior to the slice method based on the limit equilibrium theory in many ways, so it will be more powerful to assess the reliability of global slope stability when combined with probability theory. To illustrate the performance of the proposed method, it is applied to an example of simple slope. The results of simulation show that the proposed method is effective to perform the reliability analysis of global slope stability without presupposing a potential slip surface.

Research on Simulation of Langlie Method Test of Fuze Arming Distance

In mathematically statistical test methods that were used to get arming distance of fuze,Langlie method has been widely applied because it only use a few samples. Monte-Carlo method was used to simulate and calculate Langlie method test of fuze arming distance by using computer. The result shows that the larger error and scatter exist in the estimate of arming distance variance although 50% response level of arming distance can be estimated using a little sample; the correction coefficient of variance estimate can be got by simulating and calculating,but it is useless to a certain single test; this means that a larger error exists when Langlie method test is used to get the muzzle safety distance and the arming distance of fuze,and the maximum arming distance becomes shorter and the minimum one longer without correcting.