Monte Carlo Statistical Method Research Articles

Ab-initio simulation of hydrogenated graphene properties

Ab-initio simulation of hydrogenated graphene properties was performed. At present, graphene is considered one of the most promising materials for the formation of new semiconductor devices with good characteristics. Graphene has been the subject of many recent investigations due to its peculiar transport, mechanical and others properties [1]. The chemical modification of graphene named as graphane has recently entered the investigation as a possible candidate to solve problems connected with the lack of a graphene bandgap. Graphane is a compound material consisting of two-dimensional graphene bonded by some atoms of hydrogen. The investigation shows that graphane has the three valley Г-М-K band structure with the Г valley, which has the smallest energy gap between the conductivity zone and the valence zone. The calculation of relative electron masses and non-parabolic coefficients in Г, М and K valleys was performed. Based on the obtained characteristics, it is possible to implement a statistical multi-particle Monte Carlo method to determine the characteristics of electron transfer in heterostructure semiconductor devices. A research on modified graphene structures is important for fundamental science and technological applications in high-speed transistor structures operating in the microwave and very high frequency ranges.

Viscoelasticity Modeling of Dielectric Elastomers by Kelvin Voigt-Generalized Maxwell Model.

Dielectric elastomers (DEs) are polymer materials consisting of a network of polymer chains connected by covalent cross-links. This type of structural feature allows DEs to generate large displacement outputs owing to the nonlinear electromechanical coupling and time-dependent viscoelastic behavior. The major challenge is to properly actuate the nonlinear soft materials in applications of robotic manipulations. To characterize the complex time-dependent viscoelasticity of the DEs, a nonlinear rheological model is proposed to describe the time-dependent viscoelastic behaviors of DEs by combining the advantages of the Kelvin–Voigt model and the generalized Maxwell model. We adopt a Monte Carlo statistical simulation method as an auxiliary method, to the best knowledge of the author which has never reportedly been used in this field, to improve the quantitative prediction ability of the generalized model. The proposed model can simultaneously describe the DE deformation processes under step voltage and alternating voltage excitation. Comparisons between the numerical simulation results and experimental data demonstrate the effectiveness of the proposed generalized rheological model with a maximum prediction error of 3.762% and root-mean-square prediction error of 9.03%. The results presented herein can provide theoretical guidance for the design of viscoelastic DE actuators and serve as a basis for manipulation control to suppress the viscoelastic creep and increase the speed response of the dielectric elastomer actuators (DEA).

Monte Carlo Analysis: An Application to Aircraft Design and Crash

The current study investigates the application of statistical methods to flight, which have been used in science over time to understand complex physical and mathematical systems by using randomly generated numbers as input into those systems to generate a range of solutions and, specifically, how mathematics is used to examine airplane design and crash frequency. In order to make very accurate predictions, one also requires an appropriate mathematical model. Using randomly selected numbers, the Monte Carlo statistical method is able to make very accurate predictions. With the Monte Carlo statistical method, by using significantly larger numbers of trials, the likelihood of the solutions can be determined very accurately. Currently, Monte Carlo methods are widely used and play a key part in various fields of science. Monte Carlo methods have vast uses in trials with limited observations that cannot be replicated many times. This paper adds new findings to the knowledge base on causes of crashes by airplane design. First, mathematical methods are used in this paper to investigate what the most likely casualty number and range are in the five years after the first flight based on 5000 simulations. Second, an investigation is performed to determine if certain casualty numbers are outliers of certain airplane designs based on the number of casualties reported using Monte Carlo analysis.

Evaluating and Assessing Radon Testing in Multifamily Housing.

To determine if radon mitigation is needed to protect occupants of multifamily housing, reliable testing procedures are needed. Yet, protocols on how many ground-contact housing units must be tested vary from 10% to 25% to 100%. To estimate the probability of failing to identify a building containing at least one unit with elevated radon level when all ground-contact units are not tested. Retrospective analysis of previously collected data from licensed (ie, certified) radon measurement professionals using hypergeometric and Monte Carlo statistical methods to estimate the confidence that there are no units with radon levels of 4 picoCuries/liter of air (pCi/L) or more based on various testing percentages. Testing data were obtained from 29 US states for 7892 ground-contact units in 687 multifamily buildings, primarily 5 to 20 units per building. Probability of failing to identify elevated radon levels in untested units. About 15% (n = 1163) of the units had radon levels of more than 4 pCi/L (the EPA action level); 59 units had more than 20 pCi/L (maximum of 96 pCi/L). For building sizes of 5 to 20 ground-contact units, the 2018 federal testing protocols that currently require testing of 10% and 25% of ground-contact units in each building failed to identify 47%-69% and 32%-46% of the units, respectively, depending on building size. Measurement of 90% of the ground-contact units in buildings with 5 to 20 ground-contact units results in up to 4% of the units with elevated radon levels being missed. To achieve 95% confidence that no units in the building have radon levels of 4 pCi/L or more in buildings up to 20 units, 100% sampling is required. For the vast majority of multifamily buildings, all ground-contact units in multifamily buildings should be tested for radon.

Вплив пропорцій орбітальних об’єктів простої форми на їхні аеродинамічні характеристики

When developing modern and promising aerospace technology models, the relevance of simulation of the flow around apparatuses (spacecraft) of various geometric shapes in a transitional mode corresponding to the flight in the region of the upper layers of the atmosphere and near space is growing. Solving the Boltzmann equation, which most adequately describes this process in the framework of kinetic theory, still remains a difficult task. To solve this equation, the Monte Carlo statistical methods are used quite successfully. An example of such a method is the direct statistical simulation, or, less common but also well-established in rarefied gas dynamics, the test particles method (TPM). The aim of this work is to study the effect of geometric proportions of simply-shaped orbiting objects during uncontrolled descent to dense layers of the atmosphere on their drag coefficients. Such objects may be elements of space debris or spacecraft of appropriate shapes and proportions. The studies were based on the results obtained by numerical simulation of TPMs on uniform rectangular grids. The shape of the orbital objects was set in the form of a circular cone, cylinder, rectangular parallelepiped of various elongations, and spheres. The calculations were carried out in a wide range of attack angles. The characteristic dimensions of the body class in question varied from 2 to 12 meters. According to the standard atmosphere for such characteristic dimensions, the transitional flow regime is realized at altitudes from 90 km to 180 km. It was found that the calculated values of the drag coefficients in the transition regime are in satisfactory agreement with the experimental data and calculations on the theory of local interaction, and at an altitude of 300 km, they correspond to the control free molecular values obtained by analytical formulas. The dependence of the drag coefficients of the bodies of the considered shapes on the angle of attack and flight altitude was studied. The influence of the choice of the characteristic area on the range of values of the calculation results is shown. The drag coefficient of the considered class of bodies at the entrance to the dense layers of the atmosphere using the TPM was calculated for the first time. Satisfactory agreement of the obtained results with the available experimental and calculated data confirms the effectiveness of the applied method in transition mode. This makes it possible to use it in practical calculations of the parameters of the external environment effect on the spacecraft in the most difficult to study altitude ranges corresponding to the transitional flow regime.

A Sea-Surface Temperature Homogenization Blend for the Northwest Atlantic

As part of the Atlantic Zone Monitoring Program two different methods were applied to merge three Level-3 AVHRR SST products into a homogenized blend covering the time period from 1982 to present over the Northwest Atlantic, providing a regionally-tuned climatological base on which to assess whether current observations are below, near or above normal. Weekly and monthly SST composites were constructed by averaging daily anomalies within each time period and adding the result to the climatological mean for the period. This approach reduces biases introduced from missing data during a strong warming/cooling seasonal period. Since AVHRR SST data have many spatial and temporal gaps, a common difficulty is establishing how much data are sufficient to yield useful estimations of temperature anomalies. A statistical Monte Carlo method showed that monthly and weekly regional averages composed respectively of as little as 7% and 10% of possible data still yield useful results. A test case shows the increased usefulness of the blend for State of the Ocean reporting. Application of the data set confirmed the use of coastal air temperature as a useful proxy for SST allowing hindcasting past changes or forecasting future changes associated with global warming over Eastern Canadian waters.

Analysis of the applicability of the classical probabilistic parameters of the Monte Carlo algorithm for problems of light transport in turbid biological media with continuous absorption and discrete scattering

Simulation of light propagation by the statistical Monte Carlo (MC) method is widely used in many fields, especially in astrophysics, atmospheric optics, ocean optics, and nuclear medicine. In the optics of biological tissues, the MC method is used to simulate the luminous flux, which is formed during various medical therapeutic or diagnostic procedures inside a biological tissue and on its surface. In such calculations, the MC method is commonly considered as a reference one, which ensures an arbitrarily high accuracy with an increase in the number of ‘photons’. However, it can be shown that this is not always the case. In this paper, in the methodological aspect, the idealised one-dimensional problems of the transport theory for a turbid medium with continuous absorption and scattering and a turbid medium with discrete scatterers inside a continuously absorbing medium are considered. Their exact analytical solutions are presented and compared with the results of statistical modelling by the MC method. It is found that the use of classical probabilistic parameters for a medium with continuous absorption and scattering in the MC algorithm leads to a systematic method error in determining the values of radiation fluxes for biological media with discrete scattering, up to 10% for fluxes at the boundary in some cases. The causes of the error are discussed and it is shown how to modify the probabilistic parameters of the MC algorithm to eliminate it.

Performance analysis of Otsu thresholding for sign language segmentation

Sign language recognition system generally consists of three main processes, which are segmentation, modelling, and classification. Image segmentation plays a crucial role as the initial step in sign language recognition. Despite the many sign language recognition system algorithms proposed in the literature and their well-understood usage, their performance analyses are relatively limited. As such, the main motivation of this paper is to critically analyse the feasibility of successful sign language segmentation under variation of dynamic scene parameters such as noise, hand size, and intensity difference between hand and background. The focus is on image thresholding using Otsu technique, since it is the most commonly used in initial process of sign language segmentation. The analysis of this work was developed based on Monte Carlo statistical method, which showed that the success of sign language segmentation depends on hand size, hand background intensity difference, and noise measurement. The result showed that the sign alphabets with handheld shape like A, E, I, M, N, S, and T is easier to segment, while sign alphabets with finger-extend shape like C, D, F, G, H, K, L, P, R, U, V, W, and Y is harder to segment. Experiment using real images demonstrate the capability of the conditions to correctly predict the outcome of sign language segmentation using Otsu technique. In conclusion, the success of sign language segmentation could be predicted beforehand with obtainable scene parameters.

The comparison of five proton linac beams in order to set up a thermal neutron radiography installation

Radiography without doubt is maybe the most famous non-destructive technique with many applications in a number of scientific fields. In the present study, the performance of five photo-neutrons which delivered by proton linear accelerators with energy equal with 8, 12, 16, 20 and 24 MeV for a thermal neutron radiography unit has been designed and simulated with the help of the MCNPX 2.5.0 software which based on the Monte Carlo statistical method. The geometrical arrangement of the unit has been simulated with primary goal to provide the highest thermal neutron flux in the location of the examined item. For every energy of the proton beam all the significant parameters with the thermal neutron radiography theory like the flux of the thermals neutrons, the (collimator length)/(aperture diameter) ratio and the percentage of the thermal neutron within the neutron beam simulated for a wide series of values. Owing to the fact that the there are many fast neutrons inside the beam, it is obligatory to decrease the quantity of the fast neutrons. For this reason, the addition of a single sapphire for fast neutron filtering has as a consequence a neutron beam with better quality. According to the simulations, the presence of the filter improves the % presence of the thermal neutrons with no substantial abatement in the flux of the slow neutrons.

Artificial neural network in the diagnostic problem of structural defects of printed components in electronic means

Problem statement. Modern radio-electronic means (RES) are complex technical systems that have found application in almost all industries and spheres of human activity. The wide functionality of RES often leads to a complication of their constructive implementation, and, as a result, to the complexity and ambiguity of diagnostic procedures performed during production and operation. In this regard, the issue of improving existing methods of technical control and developing new approaches to the diagnosis of RES in order to identify their hidden defects and increase the reliability of research results is quite acute. Goal. Improving the efficiency of diagnosing printed circuit assemblies of electronic devices in the process of their production, final inspection, testing and intended use. Research methods. At the initial stage of the study, a computer model of the printing unit under study was developed, containing detailed information about the device design. Then we analyzed the most common types of defects in printed components that occur during the production and operation of electronic devices. Seven characteristic defects were identified. Since each defect changed the type of dynamic response characteristics of the object under study, the amplitude-time characteristics of the printing unit were formed for the correct state of the device and for States with defects. Using the Monte Carlo method, a series of samples with acceptable ranges of parameter values was created for each defect. From the obtained samples (sets of amplitude characteristics of the investigated node), a fault database was formed, which was used as a comparison with the sample in diagnostic procedures. Next, a 3-layer artificial neural network (ins) was created, which was trained and tested on samples from the fault database. The results of training the ins based on activation functions allowed us to conclude that it has achieved the required level of pattern recognition and the specified reliability of the results obtained. Results. In the course of the study, a database of characteristic electronic failures was developed, for which, along with a physical experiment, mathematical modeling methods and the Monte Carlo statistical test method were used. In addition, an artificial neural network was created, which became the main tool for diagnostic research in order to detect defects in the electronic node and significantly increased the reliability of the results in comparison with existing diagnostic methods. Practical significance. To test the developed method, a series of computational experiments was performed. The type of test impact in the form of a sawtooth pulse with a linearly increasing leading edge was justified, and the parameters of this pulse were selected by calculation. The artificial neural network training technology allowed us to obtain reliable diagnostic results with a probability of P=0.99. The computational experiment was confirmed by physical tests of the radio-electronic unit on a vibration shock installation.

Output Characteristics of Graphene Field Effect Transistors

The use of graphene, which has high mobility of charge carriers, high thermal conductivity and a number of other positive properties, is promising for the creation of new semiconductor devices with good output characteristics. The aim was to simulate the output characteristics of field effect transistors containing graphene using the Monte-Carlo method and the Poisson equation.Two semiconductor structures in which a single layer (or monolayer) of graphene is placed on a substrate formed from 6H-SiC silicon carbide material are considered. The peculiarity of the first of them is that the contact areas of drain and source were completely located on the graphene layer, the length of which along the longitudinal coordinate was equal to the length of the substrate. The second structure differed in that the length of the graphene layer was shortened and the drain and source areas were partly located on the graphene layer and partly on the substrate.The main output characteristics of field-effect transistors based on the two semiconductor structures considered were obtained by modeling. The modeling was performed using the statistical Monte Carlo method. To perform the simulation, a computational algorithm was developed and a program of numerical simulation using the Monte-Carlo method in three-dimensional space using the Poisson equation was compiled and debugged.The results of the studies show that the development of field-effect transistors using graphene layers can improve the output characteristics – to increase the output current and transconductance, as well as the limit frequency of semiconductor structures in high frequency ranges.

Secondary structure specified polarizabilities of residues for an evaluation of circular dichroism spectra of proteins.

We present a model of circular dichroism for proteins that is based on the classical electromagnetic theory for optical activity. The two additional constituents of the model are as follows: an appropriate characterization of the secondary structure of the protein residues and the assignment of an effective polarizability to each type of classified residue. The set of effective polarizabilities is obtained by means of a Monte Carlo statistical method, which is used to analyze a series of synchrotron radiation circular dichroism spectra together with their corresponding crystallographic structures. As a result, the predicted spectra from our model are in good accord with experimental data, as well as with the results of some other theoretical approaches.

The fidelity of DSMC method to analyze the aerothermodynamics of the pure continuum flow regime

Abstract The statistical probabilistic Direct Simulation Monte Carlo (DSMC) method was developed to interrogate the flow regime, in which thermal non-equilibrium exists and flow properties are non-continuous. Unfortunately, the DSMC method had not been preferred for the pure continuum flow regime ascribed to the computational burden arises with the computation of a large number of simulated molecule trajectories. However, this study showed that the DSMC method can handle the number density of real molecules of the pure continuum flow regime. The DSMC predictions were in close proximity to the experimental measurements taken on an Orion aeroshell model at Mach 11.4, 12.4, and 12.5 of reacting air in an expansion tunnel facility. The measurements corresponded to laminar boundary layer conditions, whereby Schlieren images were taken to assess the shockwave encapsulating the Orion aeroshell. The DSMC model predicted no isolated bump of the stagnation point heat flux, which was in line with the experiments. At a 20° angle of attack of the aeroshell, the model could capture the non-axisymmetric flow-field, in which the shear layer was attached at the windward side aftbody and detached at the leeward side aftbody. Thinning of the shockwave with the increase of flow-field temperature and molecular dissociation was also visibly distinct. The outcomes suggest the fidelity of the DSMC method in capturing the molecular interactions and the associated reaction kinetics in regimes varying from continuum to a rarefied gas without any substantial compromise of accuracy.

The Convolutional Multiple Whole Profile (CMWP) Fitting Method, a Global Optimization Procedure for Microstructure Determination

The analysis of line broadening in X-ray and neutron diffraction patterns using profile functions constructed on the basis of well-established physical principles and TEM observations of lattice defects has proven to be a powerful tool for characterizing microstructures in crystalline materials. These principles are applied in the convolutional multiple-whole-profile (CMWP) procedure to determine dislocation densities, crystallite size, stacking fault and twin boundary densities, and intergranular strains. The different lattice defect contributions to line broadening are separated by considering the hkl dependence of strain anisotropy, planar defect broadening and peak shifts, and the defect dependent profile shapes. The Levenberg–Marquardt (LM) peak fitting procedure can be used successfully to determine crystal defect types and densities as long as the diffraction patterns are relatively simple. However, in more complicated cases like hexagonal materials or multiple-phase patterns, using the LM procedure alone may cause uncertainties. Here, we extended the CMWP procedure by including a Monte Carlo statistical method where the LM and a Monte Carlo algorithm were combined in an alternating manner. The updated CMWP procedure eliminated uncertainties and provided global optimized parameters of the microstructure in good correlation with electron microscopy methods.

Cosmological constrains on new generalized Chaplygin gas model

We use different combinations of data samples to investigate the new generalized Chaplygin gas (NGCG) model in the context of dark energy (DE) cosmology. Using the available cosmological data, we put constraints on the the free parameters of NGCG model based on the statistical Markov chain Monte Carlo method. We then find the best fit values of cosmological parameters and those confidence regions in NGCG cosmology. Our result for the matter density parameter calculated in NGCG model is in excellent agreement with that of the standard $$\Lambda $$ CDM cosmology. We also find that the equation of state of DE of the model slightly favors the phantom regime. We show that the big tension between the low- and high-redshift observations appearing in $$\Lambda $$ CDM universe to predict the Hubble constant $$H_0$$ can be alleviated in NGCG model. However, from the statistical point of view, our results show that the standard $$\Lambda $$ CDM model fits the observations better than the NGCG cosmology.

МАТЕМАТИЧЕСКАЯ МОДЕЛЬ ИЗМЕРЕНИЯ ШЕРОХОВАТОСТИ СФЕРИЧЕСКИМ ЩУПОМ

A measurement of surface roughness is commonly carried out with the aid of profilometers, but when measuring the roughness of a curved surface arise difficulties. A technical problem consists in a probe feed along the normal to a nominal surface and filtration followed to exclude a low-frequency constituent of a profile. That is why it is purposeful to use coordinate measuring machines which have a probe with a spherical tip. For the first time there is presented a simulator of a spherical probe flat contact and surface roughness. A contact model developed is based on the regulations of analytical geometry. With the use of a numerical algorithm one finds a contact point and the center of a probe circle. On the basis of the simulator there is carried out an investigation of the impact of a probe radius upon roughness parameters Ra, Rmax, Rq. As initial data were used measurement results of the profilometer and profiles modeled with the aid of Monte-Carlo statistical method. It is defined that with the increase of the radius of the spherical probe its penetrating capacity decreases. That is why height parameters of roughness are distorted. The application of the spherical probe with the radius of 5-50 mkm ensures satisfactory results.

Analyzing Markov chain Monte Carlo output

AbstractMarkov chain Monte Carlo (MCMC) is a sampling‐based method for estimating features of probability distributions. MCMC methods produce a serially correlated, yet representative, sample from the desired distribution. As such it can be difficult to assess when the MCMC method is producing reliable results. We present some fundamental methods for ensuring a reliable simulation experiment. In particular, we present a workflow for output analysis in MCMC providing estimators, approximate sampling distributions, stopping rules, and visualization tools.This article is categorized under: Statistical Models > Bayesian Models Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC) Statistical and Graphical Methods of Data Analysis > Monte Carlo Methods

Tristichopterids (Sarcopterygii, Tetrapodomorpha) from the Upper Devonian tetrapod-bearing locality of Strud (Belgium, upper Famennian), with phylogenetic and paleobiogeographic considerations

ABSTRACT We describe new material of the tristichopterids cf. Langlieria socqueti and cf. Eusthenodon wangsjoi and other unassignable tetrapodomorph remains from the upper Famennian locality of Strud, Belgium. Because of recent improvements in our tristichopterid knowledge, a new phylogenetic analysis is presented in addition to a paleobiogeographic analysis using the Bayesian binary Markov chain Monte Carlo (MCMC) statistical method. The origin of the whole tristichopterid clade is reconstructed with a very likely western European origin. Much of the early tristichopterid history took place in Euramerica. During the Late Devonian, tristichopterids most probably spread from Euramerica into Gondwana. The highly nested tristichopterid clade formed by Cabonnichthys burnsi, Mandageria fairfaxi, E. wangsjoi, Edenopteron keithcrooki, and Hyneria lindae most likely differentiated in Australia. Then dispersal events occurred from Australia to Euramerica with Hyneria lindae (to eastern North America) and E. wangsjoi (to Greenland/western Europe). The latter dispersal events, during the Famennian, are in agreement with the Great Devonian Interchange, which predicts dispersal events between Gondwana and Euramerica at this time.

Sensitivity investigation of a subsonic cascade performance to geometric deviations based on statistical method

This paper has established an evaluation system for the sensitivity analysis of cascade/compressor aerodynamic performance to geometric deviations. The system includes blade profile parameterization with non-uniform rational B-spline (NURBS), uniform Latin hypercube sampling in association with Monte Carlo algorithm and statistical investigation methods. The sensitivity of a subsonic cascade performance to its geometric deviations is investigated under different typical inflow conditions. Results show that there is an approximately linear relationship between the geometric deviations and the aerodynamic parameters. The total pressure loss coefficient is the most sensitive to the leading edge profile deviation at i=2°. However the suction profile deviation and the leading edge profile deviation dominate the total pressure loss when the incidences are i = −4° and i = −8°. The blocking effect of the increased leading edge profile moves forward the separation point of the boundary layer. Therefore the scale of the separation vortex is enlarged, the total pressure loss is increased at i = 2° condition. Regarding i = −8°, the enlarged suction profile deviation reduces the circumferential static pressure gradient, resulting in an increase of the scale of separation vortex on the pressure side. The work is helpful to robust design of compressor blade profile and manufacturing & maintenance techniques of compressor blades.

Dependence of the reliable graph failure probability on the topological indicators of its elements

An analysis is made of the dependence of the probability of network failure, presented in the form of reliability graphs, on the topological indicators of its elements, in particular, the variety of centrality proposed in the article in mediation. In connection with the study of the reliability of large networks (networks containing millions of elements), it became necessary to find critical groups of elements that have the greatest impact on the reliability of the system. The article solves the problem of quickly finding such elements without laborious analytical calculation. Monte Carlo analytical and statistical methods are used as methods in the article. As a result of the study, a method is obtained that allows one to find such groups of elements with a certain accuracy. As a confirmation of the great influence on the reliability of the system of the found group of elements, a repeated calculation of reliability was made with an increased probability of failure of the most influential nodes. The results obtained can effectively distribute resources to the most significant system nodes, and, accordingly, increase the reliability of these systems. The absence of a laborious calculation in the method makes it effective when working with large networks.