Monte Carlo Simulations Research Articles

A statistical learning framework for mapping indirect measurements of ergodic systems to emergent properties

The discovery of novel experimental techniques often lags behind contemporary theoretical understanding. In particular, it can be difficult to establish appropriate measurement protocols without analytic descriptions of the underlying system-of-interest. Here we propose a statistical learning framework that avoids the need for such descriptions for ergodic systems. We validate this framework by using Monte Carlo simulation and deep neural networks to learn a mapping between nuclear magnetic resonance spectra acquired on a novel low-field instrument and proton exchange rates in ethanol-water mixtures. We found that trained networks exhibited normalized-root-mean-square errors of less than 1% for exchange rates under 150 s−1 but performed poorly for rates above this range. This differential performance occurred because low-field measurements are indistinguishable from one another at fast exchange. Nonetheless, where a discoverable relationship between indirect measurements and emergent dynamics exists, we demonstrate the possibility of approximating it in an efficient, data-driven manner.

Outage Performance of Underlay CR-NOMA-based D2D Communications under Imperfect CSI and SIC

Background: Non-orthogonal multiple access (NOMA) is a promising technique for improving wireless communication performance in the future. In addition to NOMA, cognitive radio (CR) is another technology that can address the issue of limited spectrum availability and meet the increasing demands for wireless connectivity. Methods: This paper focuses on investigating underlay CR-NOMA-based D2D communications. The study assumes a decode-and-forward (DF) mode used in the system, where nearby users (D1, D2) act as helper users to assist distant users (D3, D4). The paper derives the closed-form expressions for outage probability (OP) and throughput at the far users in three scenarios: (1) Perfect successive interference cancellation (SIC) and perfect channel state information (CSI), (2) Imperfect CSI, and (3) Imperfect SIC. Results: In CR-NOMA mode, the results indicate that the performance of user D4 was better than user D3. Additionally, the OP performance of distant users employing CR-NOMA mode surpasses that of users using CR-OMA mode. The optimal power allocation (PA) values are investigated. Conclusion: The presence of imperfect CSI and SIC has an unfavorable influence on the outage performance. Monte Carlo simulations are used to validate the derived analytical expressions.

Surface accuracy prediction method for mesh reflector antenna considering uncertainty factors in manufacturing process

The cable-net structure of mesh reflector antenna meets the requirement of surface accuracy by optimizing the shape and tension. However, in the process of manufacturing and assembly, there are inevitable random errors and structure gravity, which lead to the displacement of the nodes in surface, the surface accuracy of the antenna decreases after fabrication eventually. It is challenging to analyze the uncertainty factors and the effects on the surface accuracy. Therefore, this paper analyzes the uncertainty factors of the antenna during fabrication and proposes a method to predict the surface accuracy of the antenna after manufacturing and assembly. Firstly, based on the equilibrium equation of the cable-net structure, the mechanism of node displacement induced by uncertainty factors leading to the reduction of surface accuracy is analyzed. Secondly, based on the structure characteristics and manufacturing conditions of the antenna, the uncertainty factors including cable-net manufacturing and assembly errors, cable-truss assembly errors and gravity are analyzed qualitatively and quantitatively, the distributions of the uncertainty factors are given. Thirdly, based on Monte Carlo method, the mean and interval of the surface accuracy of different dimension parameters are predicted, the empirical prediction formulas of the surface accuracy mean and interval are fitted. Finally, the accuracy and effectiveness of the proposed formulas are verified by several numerical simulations and surface accuracy measurement experiments. The prediction method can effectively guide the design and craft of large-aperture mesh reflector antenna.

Overbounding Ifree errors based on bayesian Gaussian mixture model for ground-based augmentation system

A dual-frequency measurement is employed in conjunction with an innovative Ifree filtering technique for mitigating the primary sources of Ifree influence on ground-based augmentation systems (GBAS) to safeguard the reliability of GBAS. The protective level achieved through the conventional Gaussian overbounding approach that are considered as much conventional technique. This adherence to tradition results in decreased reliability and a higher likelihood of false alarms. In contrast, the utilization of the Ifree algorithm contributes to reducing errors associated with dual-frequency measurements. This paper proposes the overbounding process according to Bayesian Gaussian mixture model (GMM) for maintaining Ifree-based GBAS range error. The Bayesian GMM is utilized for single-frequency model errors to examine the ambiguity estimations. The Monte Carlo (MC) simulation is established for defining estimated GMM assurance level accuracy which is attained through the general estimation method. Then, the last Bayesian GMM which is utilized for overbounding Ifree error distribution is investigated. According to the property of convolution invariance, the vertical protection in position field is determined without presenting difficult numerical calculations.

A framework for the in silico assessment of the robustness of an MPC in a CDC line in function of process variability

The shift from batch manufacturing towards continuous manufacturing for the production of oral solid dosages requires the development and implementation of process models and process control. Previous work focused mainly on developing deterministic models for the investigated system. Furthermore, the in silico tuning and analysis of a control strategy are mostly done based on deterministic models. This deterministic approach could lead to wrong actions in diversion strategies and poor transferability of the controller performance if the system behaves differently than the deterministic model. This work introduces a framework that explicitly includes the process variability which is characteristic of powder handling processes and tests it on a novel continuous feeding-blending unit (i.e., the FE continuous processing system (CPS)), followed by a tablet press (i.e., the FE 55). It employs a stochastic model by allowing the model parameters to have a probability distribution. The performance of a model predictive control (MPC), steering the feed rate of the main excipient feeder to compensate for the feed rate deviations of the active pharmaceutical ingredient (API) feeder to keep the API concentration close to the desired value, is evaluated and the impact of process variability is assessed in a Monte Carlo (MC) analysis. Next to the process variability, a model for the prediction error of the chemometric model and realistic feed rate disturbances were included to increase the transferability of the results to the real system. The obtained results show that process variability is inherently present and that wrong conclusions can be drawn if it is not taken into account in the in silico analysis.

Exploring the dynamic evolutionary trajectories for urban residential building carbon emissions toward 2060: Evidence from the HSCW zone in China

Revealing the long-term development trajectory and peak scenarios of the urban residential building sector is crucial for formulating targeted emission reduction strategies and contributing to achieving the “Dual carbon” target. Given that, significant variables affecting carbon emissions from urban residential buildings (URBCE) at both macro and end-use building levels are identified in this study. Furthermore, an innovative dynamic simulation model is developed by integrating the Monte Carlo simulation model with the Kaya identity model, taking into account the uncertainties of the variables. Subsequently, the long-term evolution trajectories, potential emission peaks, and peak time of the URBCE close to 2060 in China’s hot summer and cold winter (HSCW) zone are simulated. Results indicate that URBCE is expected to reach its peak of 272.43 Mt CO2 in 2040 under the baseline scenario. Through the dynamic simulation, the probable peak time of energy consumption in the HSCW zone is 2044 (±1.85), with a peak of 145.42 (±6.91) Mtce, and the possible peak time of carbon emissions is probably 2039 (±1.60), with a peak of 271.93 (±13.40) Mt CO2. According to dynamic sensitivity analysis, carbon emission factor, per capita residential space, and heating energy intensity can promote the peak size and timing. These findings lay a robust foundation for the formulation of regionally specific carbon reduction targets and initiatives.

Posterior Representations for Bayesian Context Trees: Sampling, Estimation and Convergence

We revisit the Bayesian Context Trees (BCT) modelling framework for discrete time series, which was recently found to be very effective in numerous tasks including model selection, estimation and prediction. A novel representation of the induced posterior distribution on model space is derived in terms of a simple branching process, and several consequences of this are explored in theory and in practice. First, it is shown that the branching process representation leads to a simple variable-dimensional Monte Carlo sampler for the joint posterior distribution on models and parameters, which can efficiently produce independent samples. This sampler is found to be more efficient than earlier MCMC samplers for the same tasks. Then, the branching process representation is used to establish the asymptotic consistency of the BCT posterior, including the derivation of an almost-sure convergence rate. Finally, an extensive study is carried out on the performance of the induced Bayesian entropy estimator. Its utility is illustrated through both simulation experiments and real-world applications, where it is found to outperform several state-of-the-art methods.

Security analysis and prediction of multi-relay networks over Fisher–Snedecor [formula omitted] fading channels

This paper investigates the physical layer security (PLS) of multi-relay networks over Fisher-Snedecor F fading channels. Precise expressions for outage probability (OP), intercept probability (IP), secure outage probability (SOP), and probability of strictly positive secrecy capacity (SPSC) are derived based on this considered model, which the SOP and SPSC are provided in a unified manner using Meijer’s G-function. Moreover, simulation consequences of Monte Carlo experiments validate derived mathematical expressions. Through theoretical analysis and simulation results, the interesting results are that larger msRD, smaller mRD, μRE and msRE the better secrecy performance of this system. Because deep learning has characteristics of low latency, strong learning ability, and adaptability, in order to pursue lower latency and universal applicability, we combine deep learning and wireless communication. On the basis of constructing a data set with exact closed-form expressions, the secrecy performance is predicted by utilizing a multi-layer perceptron (MLP) deep learning model. Moreover, by comparing the three algorithms of convolutional neural network (CNN), deep neural network (DNN), and two-layer long short-term memory network (LSTM), the MLP has the advantages of higher performance and lower complexity. Experimentations exhibit that the presented algorithm enhances the precision by 75.69% with LSTM for comparison and reduces the time complexity by 80.05% compared with DNN.

Probing the universe's expansion dynamics: The linear correction scenario perspective on dark energy

In this study, we investigate the cosmological evolution of the universe, focusing on the KMMS models in a model-independent approach, particularly the scenario involving linear correction, given by E2(z)=A(z)+β(1+γB(z)), where A(z)=Ωm0(1+z)3 and B(z)=z. By analyzing recent Cosmic Chronometers (CC) and the Pantheon+ samples, we determine the best-fit values of model parameters using a Markov chain Monte Carlo analysis. Our models exhibit unique dynamics, transitioning from super-exponential to exponential expansion, with a significant shift at redshift zt=0.83−0.10+0.11 and present deceleration parameter q0=−0.69−0.17+0.17. The jerk parameter exceeds 1, indicating a faster change in acceleration than predicted by ΛCDM. The energy density parameter is consistent with Planck observations, and the dark sector evolution follows the expected thermal history. The EoS parameter approaches ωde=−1 over time, with a current value of ωde0=−1.06±0.12, aligning with the phantom phase. Our model presents a new dark energy alternative, emphasizing the importance of considering models like KMMS in understanding cosmic evolution.

Floating solar power plant planning based on electricity price fluctuations in Towuti, south Sulawesi

A company located in South Sulawesi, intends to mitigate emissions from the Power Plant by constructing an environmentally friendly alternative, namely the Floating Solar Power Plant (FSPP), in Towuti. The development plan involves a feasibility analysis for each configuration of the FSPP, considering technological, economic, and environmental criteria. The selection of the preferred configuration is determined using the Analytical Hierarchy Process (AHP) method, based on input from experts. According to this method, the chosen configuration is the on-grid non-battery Floating Solar Power Plant, with a Net Present Value of Rp. 1,431,159,245,752, an Internal Rate of Return of 9.46%, a Payback Period of 8.916 years, a Profitability Ind ex of 1.299, a system efficiency of 21.56%, a carbon footprint of 35,003 kg CO2, and an emission reduction of 9,136,808,273 kg CO2. Decision analysis, involving open and abandonment scenarios based on fluctuations in industrial electricity prices, was conducted using Monte Carlo simulation, yielding a volatility value of 31.2%. The real options analysis recommends abandonment in the twentieth year, with a decision success potential of 38%, based on the results.

Using Monte Carlo method to Upgrade Zhentong Gao method

In recent decades, it has been found that the three-parament Weibull distribution plays an increasingly important role in the fields such as structural fatigue and reliability. However, the complexity of estimating these three parameters greatly affects the application of the Weibull distribution. In the past three years, the author has successively proposed the Zhentong Gao Method and the Generalized Zhentong Gao Method, which have effectively solved this problem. However, it has also been found that there is room for improvement in these two methods. That's what this paper is about, how to use the characteristics of the Monte Carlo and Metropolis-Hastings methods to upgrade the Zhentong Gao method and the Generalized Zhentong Gao method, so that these two upgraded methods can not only efficiently estimate the three parameters of the Weibull distribution, but also provide their confidence intervals, and can be used in more fields.

Seismic fragility analysis of simply supported bridges considering uncertainty in scour condition

Bridges are vital infrastructures but face compounding risks from scouring and seismic events. Although recent studies have explored these individual and overlapping hazards, they often utilize deterministic approaches and focus on specific bridge types in limited geographical areas. This study addresses these gaps by introducing a probabilistic framework for assessing the seismic performance of multi-span reinforced concrete (RC) highway bridges in the presence of scour-related uncertainties. A time-dependent scour model, informed by a Bayesian approach and literature-based uncertainties, is integrated into the framework. Probabilistic Seismic Hazard Analysis (PSHA) and record selection strategies are employed to define the seismic demand probabilistically. Monte Carlo simulation (MCS) is utilized to propagate combined uncertainties during the analysis, considering different scour scenarios defined according to the discharge peak condition of the flood event at the specific location of the bridge. In the last step of the probabilistic framework, fragility analyses are conducted on individual components and the entire system by means of nonlinear dynamic models and multiple stripe analysis (MSA). An actual five-span bridge with simply supported prestressed concrete girders, located in Chile, is used as application example of the proposed approach, considering measured hydrological data and seismic hazard of the real location of the bridge. The study identifies distinct vulnerabilities across various bridge components under scour conditions. Elastomeric bearings are particularly susceptible in scenarios characterized by low scour depths (low discharge peak condition). Conversely, abutments display heightened vulnerabilities as scour depth increases (medium discharge peak condition). Piles also exhibit notable vulnerability, escalating in scenarios with great scour depth (medium discharge peak condition). Notably, piles tend to be more susceptible than columns to scour effects, especially in bents featuring shorter columns. These disparities in vulnerability are influenced by the bridge design philosophy, as well as the synergistic effects of seismic forces and varying scour depths. System fragility curves further elucidate that the likelihood of exceeding specific damage thresholds varies according to different scour scenarios, with the deeper scour depth scenario, displaying the higher vulnerabilities.

Groundwater suitability assessment for irrigation and drinking purposes by integrating spatial analysis, machine learning, water quality index, and health risk model.

An in-depth understanding of nitrate-contaminated surface water and groundwater quality and associated risks is important for groundwater management. Hydrochemical characteristics and driving forces of groundwater quality and non-carcinogenic risks of nitrate were revealed by the integrated approaches of self-organizing map analysis, spatial visualization by geography information system, entropy and irrigation water quality indices, and human health risk model. Groundwater samples were categorized into two clusters by SOM analysis. Cluster I including three samples were Ca-SO4 type and cluster II of remaining 136 samples were Ca-HCO3 type. Hydrochemical compositions of two cluster samples were dominated by water-rock interaction: (1) calcite and gypsum dissolution for cluster I samples and (2) calcite dissolution, silicate weathering, and positive cation exchange for cluster II samples. Nitrate contamination occurred in both cluster I and II samples, primarily induced by agricultural nitrogen fertilizer. The EWQI results showed that 90.97% in total groundwater samples were suitable for drinking purpose, while the IWQI results demonstrated that 65.03% in total groundwater samples were appropriate for irrigation purpose. The HHR model and Monte Carlo simulation indicated that the non-carcinogenic nitrated risk was highest in children. Exposure frequency was the most sensitive factor (86.33% in total) influencing the total non-carcinogenic risk, indicated by sensitivity analysis. Compared with the two clusters of groundwater, surface water has a shorter circulation cycle and lower ion concentrations resulting in better water quality. This study can provide scientific basis for groundwater quality evaluation in other parts of the world.

Taillefer—A Tool for Sensitivity Analysis and Uncertainty Propagation Studies for Steady-State Thermal-Hydraulic Simulations of Involute Fuel Element Research Reactors

Taillefer is a versatile Python tool for carrying out Sensitivity Analysis (SA) and uncertainty propagation (UP) studies based on Monte Carlo sampling. Developed with the primary goal of investigating sensitivities and uncertainties of steady-state thermal-hydraulic (SSTH) safety parameters of the high-performance research reactors Forschungs Neutronenquelle Heinz Maier-Leibnitz (FRM II) in Garching, Germany, and the Réacteur à Haut Flux (RHF) in Grenoble, France, it can also be used for a large variety of other modeling problems. The work presented here aims to explain the underlying mathematical background of SA and UP studies with Taillefer and to show some steps to verify these routines. Furthermore, a real-life application example is provided that demonstrates Taillefer’s use in SSTH analysis of the RHF. For this purpose, Taillefer is coupled to the external thermal-hydraulic software PLTEMP/ANL, which is one of the codes used at FRM II and RHF to access SSTH performance and safety parameters. Determining these crucial quantities is part of identifying possible low-enriched uranium (LEU) core designs that are suitable to replace the currently used highly enriched uranium fuels of the two reactors, supporting global nonproliferation efforts. Taillefer is a powerful tool in these conversion studies, as it increases the reliability of the LEU safety parameters by providing information about sensitivities and uncertainties in addition to the nominal values predicted by the thermal-hydraulic software.

Determination of kilovoltage x-ray therapy depth doses with open-ended applicators.

The purpose of this work was to determine percentage depth dose (PDD) curves for kilovoltage x-rays from the WOmed-T105 unit, with open-ended steel applicators and beam qualities ranging from 0.5 to 4.2mm Al. Measurements were made with parallel plate chambers in a water phantom, with extrapolation based on a fifth order polynomial used to estimate the surface dose. Measurements were also made with parallel plate chambers in a plastic water phantom, with thin plastic sheets used to obtain detailed measurements at shallow depths (less than 1mm). Monte Carlo simulations were performed using the EGSnrc package, with two different sources as input: a SpekPy simulation of the x-ray beam and a full simulation of the x-ray tube, treatment head and applicators. Results showed that all four methods (two measurements and two simulations) agreed within the measurement uncertainty at depths greater than 2mm. At shallow depths, significant differences were noted. At depths less than 0.1mm, the full Monte Carlo simulation and the solid water measurements showed a sharp spike in surface dose which is attributed to electron contamination, which was not seen in the SpekPy Monte Carlo simulation or the extrapolated water measurements. At depths between 0.1mm and 2mm, beyond the range of contaminant electrons, the extrapolated water measurements underestimate the dose by up to 13% compared to the full Monte Carlo simulation and the solid water measurements, attributed to fluorescent photons generated in the applicators. This work demonstrates that for open-ended applicators, measurement of depth doses in water with extrapolation of surface dose has the potential to significantly underestimate the dose at shallow depths between the surface and 2mm, even after eliminating electron contamination from the beam.

On a conjecture concerning the Fisher–Widom line and the line of vanishing excess isothermal compressibility in simple fluids

In the statistical mechanics approach to liquid-state theory, understanding the role of the intermolecular potential in determining thermodynamic and structural properties is crucial. The Fisher–Widom (FW) line, which separates regions in the temperature vs density plane where the decay of the total correlation function is monotonic or oscillatory, provides insights into the dominance of the attractive or repulsive part of the interactions. Stopper et al. have recently conjectured [J. Chem. Phys. 151, 014501 (2019)] that the line of vanishing excess isothermal compressibility approximates the FW line in simple fluids. Here, we investigate this conjecture using the Jagla potential and also explore the line of vanishing excess pressure. We employ theoretical approximations and Monte Carlo simulations to study one-dimensional and three-dimensional systems. While exact results for the one-dimensional case do not support the conjecture, our Monte Carlo simulations for the three-dimensional fluid validate it. Our findings not only contribute to the understanding of the relationship between the three transition lines but also provide valuable insights into the thermodynamic and structural behaviour of simple fluids.

An extended Monte Carlo simulation code for modeling gas chromatography experiments with superheavy elements and their homologs

AbstractMonte Carlo simulations are commonly used to model the behavior of chemical species of the heaviest elements and their homologs in gas chromatography experiments. In this paper, we present an extension of the fundamental Monte Carlo simulation proposed by Zvara in 1985. While preserving the core functionality, our code features two enhancements: first, it allows simulating experiments in which a primary radioisotope decays into a daughter isotope belonging to a different element, hence exhibiting different chemical properties. Second, it allows modeling scenarios where conversion of an initial chemical species to a different one can occur at temperatures high enough to overcome an activation barrier, facilitating simulations of related physisorption and chemisorption processes. This Monte Carlo code is applicable to open tubular and rectangular chromatography columns.

A numerical investigation on the vibration of a two-deck Euler–Bernoulli beam flooded by a potential flow

Abstract This work concerns the structural vibration of a bladeless wind turbine, modelled by a two-deck Euler–Bernoulli beam, due to a surrounding potential flow. The deflection is governed by the Euler–Bernoulli equation which is studied first by a linear theory and then computed numerically by a finite difference method in space with a collocation method over the arc length, and an implicit Euler method in time. The fluid motion in the presence of gravity is governed by the full Euler equations and solved by the time-dependent conformal mapping technique together with a pseudo-spectral method. Numerical experiments of excitation by a moving disturbance on the fluid surface with/without a stochastic noise are carried out. The random process involved in generating the noise on the water surface is driven by a Wiener Process. A Monte Carlo method is used for stochastic computations. The generated surface waves impinge on the beam causing structural vibration which is presented and discussed in detail. By elementary statistical analysis, the structural response subject to the stochastic hydrodynamic disturbance caused by white noise is found to be Gaussian.

Investigation and comparison on the interaction of laser and bio-tissue based on two classical models, the beam broaden model and diffusion approximation equation model, theoretically and experimentally

Three methods are used for a numerical solution, the Monte Carlo method, diffusion approximation equation model, and beam broaden model based on Beer–Lambert’s law equation. The comparison between the first two methods is reported theoretically, and the latter is a better choice in the high-density tissue. However, the comparison between the third method and the first or the second method is rarely reported. Two classical theoretical models describing the interaction between the laser and the bio-tissue are analyzed and compared to determine which is more suitable for analyzing the interaction, the beam broaden model or diffusion approximation equation model. Intensity distribution is simulated and compared for the two models. Temperature distribution and thermal damage are investigated theoretically and experimentally for both models. The differences and the reasons are analyzed. The diffusion approximation equation model is more suitable for analyzing the mechanism between the laser and the bio-tissue based on the degree of fitting between the simulated and experimental data. Theoretical analyses for the two models are carried out in detail. The comparison between the two models is rarely reported, and it is reported in this article for the first time, theoretically and experimentally. This report provides a better choice for quickly analyzing the interaction mechanism between the laser and the bio-tissue.

Electron-induced hydrogen desorption from selected polymers (polyacetylene, polyethylene, polystyrene, and polymethyl-methacrylate)

Elastic Peak Electron Spectroscopy, abbreviated as EPES, involves the analysis of the line shape found in the elastic peak. The reduction in the energy of electrons within the elastic peak is a result of energy being transferred to the target atoms, a phenomenon referred to as recoil energy. EPES distinguishes itself among electron spectroscopies by its unique ability to identify hydrogen in polymers and hydrogenated carbon-based materials. This distinctiveness is particularly notable because lighter elements demonstrate more pronounced energy shifts. The detection of hydrogen in polymers entails measuring the energy difference between the positions of the carbon (or carbon+oxygen) elastic peak and the hydrogen elastic peak. This difference tends to increase as the kinetic energy of the incident electrons rises. Concerning hydrogen peak intensity, electron beam-induced damage represents a critical aspect of EPES, as hydrogen desorbs under electron irradiation. In this study, the Monte Carlo method was employed to simulate EPES spectra involving electrons interacting with polyacetylene (C2H2), polyethylene (C2H4), polystyrene (C8H8), and polymethyl-methacrylate (C5H8O2) and to evaluate electron-induced hydrogen desorption from these polymers.