scholarly journals Monte Carlo Simulation of the Formation of Snowflakes

2005 ◽  
Vol 62 (5) ◽  
pp. 1529-1544 ◽  
Author(s):  
Ken-ichi Maruyama ◽  
Yasushi Fujiyoshi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Standard Deviation ◽  
Cross Section ◽  
Collision Cross Section ◽  
Initial Distribution ◽  
Sphere Model ◽  
Aggregate Model ◽  
Mean Diameter ◽  
The Mean

Abstract A stochastic microphysical model of snow aggregation that combines a simple aggregation model with a Monte Carlo method was developed. Explicit treatment of the shape of individual snowflakes in the new model facilitates examination of the structure of snowflakes and the relationships between the parameters of the generated snowflakes, such as mass versus diameter, in addition to comparisons with observations. In this study, complexities in the shape of snowflakes are successfully simulated, and the understanding of the evolution of their size distribution is advanced. The mean diameter of snow particles evolves more rapidly in the aggregate model than in the sphere model. However, growth rates of the aggregates greatly depend on the collision section of particles in aggregation. The mean mass of snowflakes in the aggregate model grows more slowly than the mass in the sphere model when the sum of the particle cross section is used as the collision cross section. The mean mass grows more quickly when a circle is used whose radius is the sum of the radii of two particles. Sensitivity experiments showed that aggregation also depends on the mean and standard deviation of the initial distribution, and on the density of constituent particles.

scholarly journals ANALISIS PENJADWALAN PROYEK GEDUNG BERTINGKAT DENGAN METODE PERT DAN M-PERT MENGGUNAKAN SIMULASI MONTE CARLO

2020 ◽  
Vol 3 (3) ◽  
pp. 533
Author(s):  
Josua Guntur Putra ◽  
Jane Sekarsari
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Standard Deviation ◽  
Research Method ◽  
Probabilistic Approach ◽  
Deterministic Scheduling ◽  
Work Duration ◽  
The Mean ◽  
Building Project ◽  
Story Building

One of the keys to success in construction execution is timeliness. In fact, construction is often late than originally planned. It’s caused by project scheduling uncertainty. Deterministic scheduling methods use data from previous projects to determine work duration. However, not every project has same work duration. The PERT method provides a probabilistic approach that can overcome these uncertainties, but it doesn’t account for the increase in duration due to parallel activities. In 2017, the PERT method was developed into the M-PERT method. The purpose of this study is to compare the mean duration and standard deviation of the overall project between PERT and M-PERT methods and compare them in Monte Carlo simulation. The research method used is to calculate the mean duration of the project with the PERT, M-PERT, and Monte Carlo simulation. The study was applied to a three-story building project. From the results of the study, the standard deviation obtained was 5.079 for the M-PERT method, 8.915 for the PERT method, and 5.25 for the Monte Carlo simulation. These results show the M-PERT method can provide closer results to computer simulation result than the PERT method. Small standard deviation value indicates the M-PERT method gives more accurate results.ABSTRAKSalah satu kunci keberhasilan dalam suatu pelaksanaan konstruksi adalah ketepatan waktu. Kenyataannya, pelaksanaan konstruksi sering mengalami keterlambatan waktu dari yang direncanakan. Hal ini disebabkan oleh ketidakpastian dalam merencanakan penjadwalan proyek. Metode penjadwalan yang bersifat deterministik menggunakan data dari proyek sebelumnya untuk menentukan durasi pekerjaan. Akan tetapi, tidak setiap proyek memiliki durasi pekerjaan yang sama. Metode PERT memberikan pendekatan probabilistik yang dapat mengatasi ketidakpastian tersebut, tetapi metode ini tidak memperhitungkan pertambahan durasi akibat adanya kegiatan yang berbentuk paralel. Pada tahun 2017, metode PERT dikembangkan menjadi metode M-PERT. Tujuan dari penelitian ini adalah membandingkan mean durasi dan standar deviasi proyek secara keseluruhan antara metode PERT dan M-PERT dan membandingkan kedua metode tersebut dalam simulasi Monte Carlo. Metode penelitian yang dilakukan adalah menghitung mean durasi proyek dengan metode PERT, M-PERT, dan simulasi Monte Carlo. Penelitian diterapkan pada proyek gedung bertingkat tiga. Dari hasil penelitian, nilai standar deviasi diperoleh sebesar 5,079 untuk metode M-PERT, 8,915 untuk metode PERT, dan 5,25 untuk simulasi Monte Carlo. Hasil ini menunjukan metode M-PERT dapat memberikan hasil yang lebih mendekati hasil simulasi komputer daripada metode PERT. Nilai standar deviasi yang kecil menunjukan metode M-PERT memberikan hasil yang lebih akurat.

Bearing-capacity prediction of spatially random c – ϕ soils

2003 ◽  
Vol 40 (1) ◽  
pp. 54-65 ◽  
Author(s):  
G A Fenton ◽  
D V Griffiths
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Standard Deviation ◽  
Bearing Capacity ◽  
Soil Surface ◽  
Element Analysis ◽  
Worst Case ◽  
Random Field Theory ◽  
Out Of Plane ◽  
The Mean

Soils with spatially varying shear strengths are modeled using random field theory and elasto-plastic finite element analysis to evaluate the extent to which spatial variability and cross-correlation in soil properties (c and ϕ) affect bearing capacity. The analysis is two dimensional, corresponding to a strip footing with infinite correlation length in the out-of-plane direction, and the soil is assumed to be weightless with footing placed on the soil surface. Theoretical predictions of the mean and standard deviation of bearing capacity, for the case where c and ϕ are independent, are derived using a geometric averaging model and then verified via Monte Carlo simulation. The standard deviation prediction is found to be quite accurate, while the mean prediction is found to require some additional semi-empirical adjustment to give accurate results for "worst case" correlation lengths. Combined, the theory can be used to estimate the probability of bearing-capacity failure, but also sheds light on the stochastic behaviour of foundation bearing failure.Key words: bearing capacity, probability, random fields, geometric averaging, c–ϕ soil, Monte Carlo simulation.

Estimating the excess bed days and economic burden of healthcare-associated infections in Singapore public acute-care hospitals

2021 ◽  
pp. 1-4
Author(s):  
Yiying Cai ◽  
Indumathi Venkatachalam ◽  
Andrea L. Kwa ◽  
Paul A. Tambyah ◽  
Li Yang Hsu ◽  
...  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Standard Deviation ◽  
Acute Care ◽  
Economic Burden ◽  
Healthcare Associated Infections ◽  
Healthcare Associated Infection ◽  
Bed Days ◽  
The Mean ◽  
Healthcare Associated

Abstract We estimated the annual bed days lost and economic burden of healthcare-associated infections to Singapore hospitals using Monte Carlo simulation. The mean (standard deviation) cost of a single healthcare-associated infection was S$1,809 (S$440) [or US$1,362 (US$331)]. This translated to annual lost bed days and economic burden of 55,978 (20,506) days and S$152.0 million (S$37.1 million) [or US$114.4 million (US$27.9 million)], respectively.

Rigorous time-domain analysis of statistically oriented graphene sheet fluctuations

2017 ◽  
Vol 36 (5) ◽  
pp. 1351-1363 ◽  
Author(s):  
Athanasios N. Papadimopoulos ◽  
Stamatios A. Amanatiadis ◽  
Nikolaos V. Kantartzis ◽  
Theodoros T. Zygiridis ◽  
Theodoros D. Tsiboukis
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Finite Difference ◽  
Surface Waves ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Mean Value ◽  
Content Type ◽  
The Mean ◽  
Difference Time

Purpose Important statistical variations are likely to appear in the propagation of surface plasmon polariton waves atop the surface of graphene sheets, degrading the expected performance of real-life THz applications. This paper aims to introduce an efficient numerical algorithm that is able to accurately and rapidly predict the influence of material-based uncertainties for diverse graphene configurations. Design/methodology/approach Initially, the surface conductivity of graphene is described at the far infrared spectrum and the uncertainties of its main parameters, namely, the chemical potential and the relaxation time, on the propagation properties of the surface waves are investigated, unveiling a considerable impact. Furthermore, the demanding two-dimensional material is numerically modeled as a surface boundary through a frequency-dependent finite-difference time-domain scheme, while a robust stochastic realization is accordingly developed. Findings The mean value and standard deviation of the propagating surface waves are extracted through a single-pass simulation in contrast to the laborious Monte Carlo technique, proving the accomplished high efficiency. Moreover, numerical results, including graphene’s surface current density and electric field distribution, indicate the notable precision, stability and convergence of the new graphene-based stochastic time-domain method in terms of the mean value and the order of magnitude of the standard deviation. Originality/value The combined uncertainties of the main parameters in graphene layers are modeled through a high-performance stochastic numerical algorithm, based on the finite-difference time-domain method. The significant accuracy of the numerical results, compared to the cumbersome Monte Carlo analysis, renders the featured technique a flexible computational tool that is able to enhance the design of graphene THz devices due to the uncertainty prediction.

Kinetic Monte Carlo Simulation of Impurity Effects on Nucleation and Growth of SiC Clusters on Si(100)

2013 ◽  
Vol 740-742 ◽  
pp. 393-396
Author(s):  
Maxim N. Lubov ◽  
Jörg Pezoldt ◽  
Yuri V. Trushin
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Cluster Size ◽  
Kinetic Monte Carlo ◽  
Nucleation And Growth ◽  
Nucleation Density ◽  
Nucleation Process ◽  
Impurity Effects ◽  
Kinetic Monte Carlo Simulations ◽  
The Mean

The influence of attractive and repulsive impurities on the nucleation process of the SiC clusters on Si(100) surface was investigated. Kinetic Monte Carlo simulations of the SiC clusters growth show that that increase of the impurity concentration (both attractive and repulsive) leads to decrease of the mean cluster size and rise of the nucleation density of the clusters.

scholarly journals Statistical Mechanics of Discrete Multicomponent Fragmentation

2020 ◽  
Vol 5 (4) ◽  
pp. 64
Author(s):  
Themis Matsoukas
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Closed Form ◽  
Fixed Number ◽  
Arbitrary Degree ◽  
Fragment Distribution ◽  
The Mean ◽  
Fragmentation Event

We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer multicomponent mass is broken into fixed number of fragments and calculate the combinatorial multiplicity of all distributions in the set. We define random fragmentation by the condition that the probability of distribution be proportional to its multiplicity, and obtain the partition function and the mean distribution in closed form. We then introduce a functional that biases the probability of distribution to produce in a systematic manner fragment distributions that deviate to any arbitrary degree from the random case. We corroborate the results of the theory by Monte Carlo simulation, and demonstrate examples in which components in sieve cuts of the fragment distribution undergo preferential mixing or segregation relative to the parent particle.

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.

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