Monte Carlo Simulations Research Articles

General estimation results for tdVARMA array models

The article will focus on vector autoregressive‐moving average (VARMA) models with time‐dependent coefficients (td) to represent general nonstationary time series, not necessarily Gaussian. The coefficients depend on time, possibly on the length of the series , hence the name tdVARMA for the models, but not necessarily on the rescaled time . As a consequence of the dependency on of the model, we need to consider array processes instead of stochastic processes. Under appropriate assumptions, it is shown that a Gaussian quasi‐maximum likelihood estimator is consistent in probability and asymptotically normal. The theoretical results are illustrated using three examples of bivariate processes, the first two with marginal heteroscedasticity. The first example is a tdVAR(1) process while the second example is a tdVMA(1) process. In these two cases, the finite‐sample behavior is checked via a Monte Carlo simulation study. The results are compatible with the asymptotic properties even for small . A third example shows the application of the tdVARMA models for a real time series.

A model for the lattice thermal conductivity of nanocrystalline materials with arbitrary grain size distribution

Nanocrystalline materials are a popular metamaterial used to control heat transport in semiconductor industrial applications. An accurate and reliable theoretical model is urgently needed but challenging for elucidating detailed microscopic heat transfer phenomena. In this study, we develop a mathematical model to predict the lattice thermal conductivity of nanocrystalline materials with arbitrary grain size distribution. The model first obtains the effective scattering rate of grain boundaries in single-grain-size materials, and then integrates the Landauer’s system transmission concept and series transmission concept to become applicable to multiple grain sizes. It takes into account not only intrinsic and grain boundary scattering effects, but also the effects of finite system size and grain size distribution. Numerical samples of silicon nanocrystals with single grain size, dual size, constant grain size distribution, and logarithmic normal grain size distribution are constructed and full-spectrum Monte Carlo simulations are performed for comparison. The excellent agreement observed between model predictions and simulation results validates the accuracy of the proposed theoretical model. This model will be very helpful in designing micron-scale thermal manipulation systems using nanostructures.

Extension of the lattice-based aggregation-volume-bias Monte Carlo approach to molecular crystals: Quantitative calculations on the thermodynamic stability of the urea polymorphs.

Motivated by the recent success in using a latticed-based version of the aggregation-volume-bias Monte Carlo method to determine the thermodynamic stabilities of both bcc and fcc clusters formed by Lennard-Jones particles, this approach is extended to the calculation of the nucleation-free energies of solid clusters formed by urea at 300K in two different polymorphs, i.e., form I and form IV. In addition to the lattice confinement, the constraint on the molecular orientation was found necessary to ensure that the clusters sampled in these simulations are in the corresponding form. A model that can reproduce the experimental properties such as density and lattice parameters of form I at ambient conditions is used in this study. From the size dependencies of the free energies obtained for a finite set of clusters studied, the free energies of clusters at other sizes, including an infinitely large cluster, were extrapolated. At the infinite size, equivalent to a bulk solid, form I was found to be more stable than form IV, which agrees with the experimental results. In addition, form I was found to be thermodynamically stable throughout the entire cluster size range investigated here, which contradicts the previous finding that small form I clusters are unstable from the crystal nucleation simulation studies.

Pricing for perpetual American strangle options under stochastic volatility with fast mean reversion

A perpetual American strangle option refers to an investment strategy combining the features of both call and put options on a single underlying asset, with an infinite time horizon. Investors are known to use this trading strategy when they expect the stock price to fluctuate significantly but cannot predict whether it will rise or fall. In this study, we consider the perpetual American strangle options under a stochastic volatility model and investigate the corrected option values and free boundaries using an asymptotic analysis technique. Further, we examine the pricing accuracy of the approximated formulas for perpetual American strangle options under stochastic volatility by comparing our solutions with the prices that are obtained from Monte Carlo simulations. We also investigate the sensitivities of the option values and free boundaries with respect to several model parameters.

The model and characteristics of polarized light transmission applicable to polydispersity particle underwater environment

The information about the polarization of underwater objects can be affected by the absorption and scattering of water particles, making it challenging to detect underwater targets accurately. Therefore, it is essential to analyze the characteristics of polarization transmission in water. Traditional Monte Carlo simulations have yet to effectively treat particle size in water, which is unsuitable for the underwater environment of polydispersity particles with significant particle size differences. In this paper, a new simulation model using a Monte Carlo method with random sampling fitting phase functions is proposed, which makes the transmission characteristics of water particles more in line with the actual probability model of complex water bodies. The experimental results demonstrate that the proposed Monte Carlo method produces polarization closer to experimental results. The larger the particle size of water suspensions, the greater change of the polarization degree of polarized light. The polarization-maintaining characteristics of circularly polarized light are better than those of linearly polarized light, providing data support for the transmission and detection of underwater light.

Remote Blood Pressure Management for Postpartum Hypertension: A Cost-Effectiveness Analysis

Recognizing the importance of close follow-up after hypertensive disorders of pregnancy (HDP), many centers have initiated programs to support postpartum remote blood pressure management (RBPM). We aim to evaluate the cost-effectiveness of RBPM to inform scalability of these programmatic interventions. We conducted a cost-effectiveness analysis of utilizing RBPM to manage postpartum hypertension versus usual care. The modeled RBPM included provision of a home blood pressure (BP) monitor, guidance on warning symptoms, instructions on BP self-monitoring twice daily, and clinical staff to manage population-level BPs as appropriate. Usual care was defined as guidance on warning symptoms and recommendation for one outpatient visit for BP monitoring within a week of discharge. We designed a Markov model that ran over 14 one-day cycles to reflect the initial two weeks after delivery when most ED visits and readmissions occur and RBPM is clinically anticipated to be most impactful. Parameter values for base case scenario were derived from both internal data and literature review. QALYs were calculated over the first year postpartum and reflected the short-term morbidities associated with HDP that, for most birthing people, resolve by two weeks postpartum. Sensitivity analyses were performed to assess strength and validity of the model. Primary outcome was incremental cost effectiveness ratio (ICER) defined as cost needed to gain one quality adjusted life year (QALY). Secondary outcome was incremental cost per readmission averted. Analyses were performed from a societal perspective. In the base case scenario, utilizing RBPM was the dominant strategy (i.e., cost less, higher QALYs). In univariate sensitivity analyses, the most cost-effective strategy shifted to usual care when cost of readmission fell below $2,987.92 and rate of reported severe range BP with a response in RBPM was less than 1%. Assuming a willingness-to-pay of $100,000 per QALY, utilizing RBPM was cost-effective in 99.28% of simulations in a Monte Carlo analysis. Using readmissions averted as a secondary effectiveness outcome, the incremental cost per readmission averted was $145.00. Remote blood pressure management of postpartum hypertension is cost saving with better outcomes compared to usual care. These data can be used to inform future dissemination of and support funding for RBPM programs.

A Geant4 monte carlo toolkit-based radiative transfer model for studying the impact of aerosols

Radiative transfer models are of prime importance in quantifying the earth-atmosphere energy budget. A radiative transfer model based on the Geant4 Monte Carlo toolkit was developed. This model is able to perform calculations of the spectral atmospheric transmittance, surface solar irradiance, as well as the Top of the Atmosphere TOA reflected irradiance over the spectral range from 280 nm to 3000 nm.Through this study, the Geant4 toolkit was used to study the effect of rural aerosols concentration on different radiative characteristics. Geant4 radiative calculations in the presence and absence of aerosols were compared to that of DISORT code. For both surface and Top of the atmosphere simulations, good agreement was observed between the two models. Specifically, under atmospheric visibility conditions of 23 km, the mean relative difference between Geant4 and DISORT code was found to be less than 2.46 % for Global irradiance calculations and less than 7.9 % for TOA reflected irradiance. A comparative analysis between the measured total global irradiance in Adrar city and the irradiance estimated by Geant4 demonstrated the general effectiveness of Geant4, with a coefficient of determination of 0.991 and a Mean Absolute Percentage Error (MAPE) of 5.851 %.

Solar–Hydrogen-Storage Integrated Electric Vehicle Charging Stations with Demand-Side Management and Social Welfare Maximization

The reliable operation of a power system requires a real-time balance between supply and demand. However, it is difficult to achieve this balance solely by relying on supply-side regulation. Therefore, it is necessary to cooperate with effective demand-side management, which is a key strategy within smart grid systems, encouraging end-users to actively engage and optimize their electricity usage. This paper proposes a novel bi-level optimization model for integrating solar, hydrogen, and battery storage systems with charging stations (SHS-EVCSs) to maximize social welfare. The first level employs a non-cooperative game theory model for each individual EVCS to minimize capital and operational costs. The second level uses a cooperative game framework with an internal management system to optimize energy transactions among multiple EVCSs while considering EV owners’ economic interests. A Markov decision process models uncertainties in EV charging times, and Monte Carlo simulations predict charging demand. Real-time electricity pricing based on the dual theory enables demand-side management strategies like peak shaving and valley filling. Case studies demonstrate the model’s effectiveness in reducing peak loads, balancing energy utilization, and enhancing overall system efficiency and sustainability through optimized renewable integration, energy storage, EV charging coordination, social welfare maximization, and cost minimization. The proposed approach offers a promising pathway toward sustainable energy infrastructure by harmonizing renewable sources, storage technologies, EV charging demands, and societal benefits.

Study of the out-of-field dose from an accelerator-based neutron source for boron neutron capture therapy

One important issue in Boron Neutron Capture Therapy is the delivered dose to the tissues outside the tumor. An international standard for light ion beam systems sets two recommended limits for out-of-field dose based on distance from the field edge: maximum absorbed dose from all radiation types shall not exceed 0.5 % of the maximum dose at distances 15 cm to 50 cm from the field edge. At distances >50 cm from the field edge, the maximum absorbed dose shall not exceed 0.1 %. This paper is a continuation of our previous works focused on the design of an accelerator-based neutron source for BNCT. We already designed a novel Beam Shape Assembly which meets the IAEA criteria for BNCT treatments. Using this BSA, in the present work, we characterize by Monte Carlo simulations the dose outside the neutron field. The out-of-field dose has been assessed via estimates using the ambient and equivalent dose. Also the boron uptake in healthy tissues has been analyzed for the equivalent dose computation. It is concluded that our design for a future accelerator-based source for BNCT meets reasonably well the criteria defined from other forms of radiotherapy on both equivalent and effective dose outside the field.

Adsorption capability and regenerability of carbon slit micropores for CO2 capture

To date, the exceptional performance of microporous carbon in CO2 capture has been widely acknowledged as a crucial step towards achieving global zero carbon emissions. In this molecular simulation study, we employ grand canonical Monte Carlo simulation (GCMC) to shed light on the significant influence of micropores on CO2 adsorption capability and regenerability, emphasizing the need for a rigorous selection of the swing adsorption process based on pore size. Our findings corroborate numerous experimental and numerical studies that the ultramicropore (pore size < 7 Å) is the appropriate range for CO2 capture, as it facilitates the formation of a horizontal monolayer of CO2 molecules. Furthermore, we highlight the importance of designing porous carbon materials with a large pore volume at the optimal ultramicropore sizes (approximately 5.8-6.4 Å depending on adsorption and desorption conditions) for obtaining high CO2 capture capacity and effective adsorbent regeneration. For the first time, taking into account the operational parameters of practical swing adsorption processes, our simulation study provides valuable guidance for selecting the most appropriate technology tailored to each specific range of micropore size in porous carbon. For porous carbon materials with an abundant volume of ultramicropores, pressure swing adsorption (PSA) and pressure-temperature swing adsorption (PTSA), as conventional and hybrid swing adsorption processes respectively, are the most effective practices, achieving high CO2 working capacity and regenerability exceeding 80%.

Evaluation of groundwater quality with multi-source pollution based on source identification and health risks

Groundwater is a crucial water supply source in Chengdu City, western China, a region experiencing significant water scarcity. The sources of inorganic pollutants in groundwater and their potential health risks are of great concern. In this study, based on 156 groundwater samples collected in 2021 in the study area were analyzed for hydrochemical characterization and controlling factors. The Positive Matrix Factorization (PMF) model was used for contaminant source analysis, and Monte Carlo Simulation (MCS) combined with the Health Risk Evaluation Model (HREM) was used to quantify the health risks. The results indicate that the groundwater in the study area is predominantly of the Ca·Na-SO4·HCO3, Ca·Na-HCO3·SO4 and Ca-HCO3·SO4 types, mainly influenced by the combination of evaporation-concentration-crystallization and rock leaching-weathering. K+, Na+, and Cl− mainly originate from the weathering and dissolution of potassium feldspar and rock salt, while Ca2+, Mg2+, HCO3−, and SO42− primarily come from the weathering and dissolution of sulfate minerals. The main sources of groundwater pollution and their contributions are as follows: domestic pollution (25.6 %), dissolution-filtration-evaporation-concentration action (22.8 %), hydrogeochemical evolution (15.8 %), water-rock interactions (12.8 %), primary geologic context (12.1 %), and agricultural non-point source pollution (11.0 %). Cl− and As are the primary contributors to non-carcinogenic and carcinogenic risks, respectively. Non-carcinogenic risks are below USEPA standards, while the average carcinogenic risk for arsenic exceeded the maximum acceptable risk level thresholds by 23 and 109 times for adults and children, respectively. Non-carcinogenic and carcinogenic health risks were mainly influenced by pollutant concentrations. The primary geological background and domestic pollution contributed the most to the non-carcinogenic risk for adults (50.3 %) and children (77.1 %), and 38.2 % and 10.3 %, respectively. This study highlights the necessity of establishing a comprehensive groundwater pollution monitoring system, enhancing industrial waste management practices, and raising public awareness to mitigate contamination and ensure the sustainable use of groundwater resources in Chengdu City.

Closed-form solution of the peak factor of hardening non-Gaussian cross-wind response with limited time history samples

The cross-wind response generally follows an un-skewed hardening non-Gaussian distribution around vortex-resonance wind speed, a great amount of samples are required to ensure the accuracy of the peak factor. This study aims to propose a robust methodology for estimating the peak factor, even when dealing with limited samples. The accurate description of the probability distribution for cross-wind response is essential to achieve a reliable peak factor. Since both the harmonic self-excited and Gaussian buffeting components contribute to the non-Gaussianity of the cross-wind response, this study explicates the probability density function (PDF) of the composite process combining the harmonic and Gaussian elements. Subsequently, the PDF of displacement is ascertained by the energy ratio between self-excited vibration and random buffeting, also a kurtosis-based function that can be derived from limited samples. Then the cumulative distribution function (CDF) of the extreme is derived based on the displacement PDF, and a closed-form solution determined by kurtosis for peak factor is derived. Finally, the validity of the proposed method is verified through both Monte Carlo simulations and field measurements. This method offers a practical mean to estimate the extreme values of hardening non-Gaussian responses in highly flexible structures using a limited number of samples.

Uncertainty of the initial phase estimation of a sinewave in the presence of phase noise, additive noise or jitter

This paper presents the derivation of a simple analytical expression for the precision of the initial phase estimates obtained through a least-squares procedure. That expression depends on number of samples, phase noise standard deviation and additive noise standard deviation. This study is applicable to the estimates obtained through the sine fitting algorithm with known frequency and to the Discrete Fourier Transform algorithm. The analytical expression supplied was verified using a Monte Carlo simulation with numerically created data. The non-ideal phenomena treated in this work is the presence of jitter in the sampling instant, phase noise in the oscillator and additive noise in the system both of which must be normally distributed with a known value of standard deviation. It is useful information for an engineer in order to choose the proper number of samples to acquire to achieve a desired level of precision on the estimates made and thus carry out an efficient data acquisition with no unnecessary samples thus optimizing the test duration.

Computational Optimization of 133m Xe Production in the Washington State University TRIGA Reactor

Here we present a new method of irradiating 132Xe capsules with neutrons to produce 133mXe gas standards that are used for radiation detector calibration at radioxenon measurement laboratories in support of the Comprehensive Test Ban Treaty (CTBT). This method is designed to maximize the production of 133mXe compared to 133Xe, both of which are competing products from the 132Xe(n, g) reaction. The 133mXe is produced at a much higher fraction for high-energy neutron absorptions in 132Xe (~50% for fast neutrons versus ~11% for thermal neutrons). We performed “spectral tuning” of the Washington State University (WSU) TRIGA reactor neutron spectrum inside the 132Xe ampules to maximize the number of fast neutrons and minimize the number of thermal neutrons available for 132Xe absorption. Spectral tuning analysis, done with Monte Carlo simulations, provided valuable insights into a future final design for a 132Xe irradiation capsule. With no spectral tuning, the fractional yield of 133mXe in the WSU reactor was ~11.7%. By surrounding the 132Xe capsule with a 0.5-cm-thick layer of tungsten and a 2.83-cm layer of europium (III) oxide and placing it in the reactor’s cadmium rotator tube next to the fuel elements, the fractional yield of 133mXe can be increased to 24.6%, a 111% increase in yield. Thus, by improving the fractional yield of 133mXe through spectral tuning, the CTBT will have better quality gas standards to use for radioxenon detector calibration to assist in the CTBT’s mission.

Vertical Distribution Characteristics and Ecological Risk Assessment of Mercury and Arsenic in Ice, Water, and Sediment at a Cold-Arid Lake

Mercury and arsenic are two highly toxic pollutants, and many researchers have explored the effects of the two substances on the environment. However, the research content of toxic substances in frozen periods is relatively small. To explore the spatial and vertical distribution of mercury and arsenic in the ice, water, and sediments of Wuliangsuhai Lake under ice conditions, and to assess the harm degree of the two toxic substances to human beings. We collected the ice, water, and sediments of the lake in December 2020, and tested the contents of Hg and As. The single-factor pollution index method, the local cumulative index method, and the ecological risk coding method were used to assess the pollution status in these three environmental media, and the Monte Carlo simulation combined with the quantitative model recommended by USEPA was used to assess the population health risk. The results showed that (1) The average single-factor pollution values of Hg and As in water were 0.367 and 0.114, both pollutants were at clean levels during the frozen period. (2) The mean Igeo values of Hg and As were 0.657 and −0.948. The bioavailability of Hg in the sediments of Wuliangsuhai Lake during the frozen period was high, and its average value was 7.8%, which belonged to the low-risk grade. The bioavailability of As ranged from 0.2% to 3.7%, with an average value of 1.3%. (3) Monte Carlo simulation results indicate acceptable levels of health risks in both water and ice. This study preliminarily investigated the distribution characteristics of toxic substances and their potential effects on human health in lakes in cold and arid regions during the frozen period. It not only clarified the pollution characteristics of lakes in cold and arid regions during the frozen period, but also provided beneficial supplements for the ecological protection of lake basins. This study lays a foundation for further environmental science research in the region in the future.

The role of Markov chain in Monte Carlo simulation

The Markov Chain Monte Carlo method has been applied in several fields and has thrived in academic research over the past few decades. The method is utilized to estimate the interest parameters posterior distribution through random sampling in the probability space. Monte Carlo method alone can accomplish random simulations for some complicated continuous integrals or discrete summations. However, the method requires the sample set corresponding to the distribution, which demands the application of Markov chain. Nevertheless, problems occur when the probability function of the samples remain unknown, under which circumstance the Markov Chain Monte Carlo method is no longer available. Therefore, the article introduced Metropolis-Hastings Algorithm as a resolution. The paper is intended to provide specific insights about Metropolis-Hastings Algorithm for Markov Chain Monte Carlo and the corresponding interdisciplinary applications. Specifically, the paper will discuss about using the theory mentioned above to check the relationships among species in a common ecosystem. The paper will cover several prepositive theories, including the Law of Large Numbers for Markov Chains, binary sequences, and Metropolis-Hastings Algorithm. Overall, specific cases and the way to draw correct conclusions will be most concerned.

Mesoscale modeling of new-to-old concrete interface under combined shear and compressive loads

A mesoscale model of new-to-old concrete interface under combined shear and compressive loads is established, and a parameter study is conducted to evaluate the influence of interface roughness, bond strength, and fracture energy. The mesoscale model is numerically generated using a random aggregate technique, in which the number of aggregates is calculated using the Fuller grading curve and Walraven formula and the aggregates are randomly placed using the Monte Carlo simulation. The concrete damaged plasticity model is employed to simulate the mechanical behaviors of new and old mortars, as well as the interfacial transition zone between the mortar and aggregate. The linear elastic model is utilized to simulate the behavior of aggregates, while the cohesive-friction model is employed to represent the behavior of new-to-old concrete interface. The effect of interface roughness, bond strength, and fracture energy on the interface shear strength and post-peak shear strength using the double-shear test specimens is investigated. The results indicate that increasing the roughness of old concrete surface leads to significant increases in both the interface shear strength and post-peak shear strength, but the larger interface roughness is not necessarily better. As the interface bond strength increases, the interface shear strength remains the same, whereas the post-peak shear strength shows a large increase with the lower interface roughness. Moreover, the interface fracture energy imparts the minimal influence on the interface shear strength and post-peak shear strength, but the higher interface fracture energy can improve the overall constitutive behavior of new-to-old concrete interface if the roughness of old concrete surface is low. The numerical mesoscale model presented can provide the theoretical guidance and technical support for effective design and construction of new-to-old concrete interface and structures.

Transfer functions for QA /QB international regulatory limits for the safe transport of radioactive materials

This paper presents a proposed revision of the International Atomic Energy Agency transport regulations, related to the A 1 and A 2 limit values used to determine the radioactive transport classification. Based on the ‘Q system’, a novel methodology was introduced to derive QA and QB values related to scenarios involving external exposure from a distant source. These values are key parameters that respectively represent the total effective dose and total equivalent dose to the skin, from all primary and secondary particles contributing to radiation exposure. The International Working Group (WG A 1/A 2) is established and associated with the TRANSSC Technical Expert Group on Radiation Protection. A review of the A 1 and A 2 values is performed in response to identified limitations within the existing Q system. The followed approach is based on Monte Carlo simulations that enabled the development of transfer functions aimed at reducing computational time and increasing the flexibility of dose evaluations for any radionuclide with known particle emission spectra. This method allows updating the QA and QB values to account for future data evolutions (decay data, fluence-to-dose conversion coefficients) and standardizing the calculation of regulation limits across all referenced radionuclides and scenarios related to external exposure. The transfer functions are established using three Monte Carlo simulation codes—FLUKA, Geant4, and MCNP—and address the previous limitations of the ‘Q system’, reflecting the latest International Commission for Radiation Protection recommendations and improvements in calculation techniques. The results of the WG show consistent agreement across the codes, with minor discrepancies observed at low primary energies due to statistical uncertainties and different handling of stopping power for electrons/positrons in the codes. This revised approach aligns with current standards and recommendations, ensuring that the radiological consequences of transport accidents are acceptable for the new A 1 and A 2 limits from a radiological protection perspective.

Enhancing Reconfigurable Intelligent Surface-Enabled Cognitive Radio Networks for Sixth Generation and Beyond: Performance Analysis and Parameter Optimization

In this paper, we propose a novel system integrating reconfigurable intelligent surfaces (RISs) with cognitive radio (CR) technology, presenting a forward-looking solution aligned with the evolving standards of 6G and beyond networks. The proposed RIS-assisted CR networks operate with a base station (BS) transmitting signals to two users, the primary user (PU) and secondary user (SU), through direct and reflected signal paths, respectively. Our mathematical analysis focuses on deriving expressions for SU in the RIS-assisted CR system, validated through Monte Carlo simulations. The investigation covers diverse aspects, including the impact of the signal-to-noise ratio (SNR), power allocations, the number of reflected surfaces, and blocklength variations. The results provide nuanced insights into RIS-assisted CR system performance, highlighting its sensitivity to factors like the number of reflectors, fading severity, and correlation coefficient. Careful parameter selection, such as optimizing the configuration of reflectors, is shown to prevent a complete outage, showcasing the system’s robustness. Additionally, the work suggests that the optimization of reflectors configuration can significantly enhance overall system performance, and RIS-assisted CR systems outperform reference schemes. This work contributes a thorough analysis of the proposed system, offering valuable insights for efficient performance evaluation and parameter optimization in RIS-assisted CR networks.

Study of the magnetic properties of a core/shell cylindrical structure with RKKY interaction using the Monte Carlo method

In this paper, we use Monte Carlo simulations to study the influence of physical parameters on the magnetic properties of a cylindrical core/shell structure separated by nonmagnetic cylindrical surfaces. The coupling between the two cylinders includes the spins σ=3/2 and S = 2 belonging to the core and shell, respectively. This study is based on the RKKY (Ruderman-Kittel-Kasuya-Yoshida) type of interaction. In order to complete this study, we carry out the hysteresis cycles of the system under study for a different number of non-magnetic surfaces.