Monte Carlo Simulations Research Articles

Performance evaluation of wireless node positioning over α − η − μ fading channel

Abstract The increasing demand for diverse services, ubiquitous coverage, and device-oriented point-to-point communications necessitates a focus on user mobility in characterizing the wireless channel environment. This study addresses the random waypoint mobility (RWP) model, where users follow a zigzag path between waypoints, causing significant fluctuations in perceived signal power. Recognizing the critical role of mobility-driven channel modelling in optimizing network infrastructure, this paper evaluates user mobility in non-linear and non-line-of-sight (NLOS) scenarios, leveraging the α-η-μ fading distribution. We derive a closed-form expression for the probability distribution function (PDF) by integrating the RWP mobility model with the α-η-μ fading channel. The study explores path loss exponent variations under different node positioning dimensions (1D, 2D, and 3D). The novel RWP-modelled α-η-μ composite fading channel PDF is then used to quantify performance metrics, including outage performance and bit error rate (BER) in communication systems, particularly in the context of evolving to 5 G networks. Additionally, this work considers dynamic node mobility in various distributions such as one-sided Gaussian, exponential, Nakagami-m (with its discrete version Chi), Rayleigh, and Weibull. The obtained results from the derived expressions are rigorously validated through Monte Carlo simulations.

Benchmark Paraffin Adsorption in a Super-Hydrophobic Porous Coordination Polymer with Blade-Like Circular Phenyl Nanotraps.

Selective capture of paraffin from olefin that permits one-step purification of olefin is significantly important, yet developing adsorbents with high selectivity and hydrophobicity remains a daunting challenge. Although aromatic environments can enhance paraffin affinity and hydrophobicity through nonpolar interactions, water adsorption still occurs in regions distant from the aromatic rings, as well as in secondary pores that are always overlooked. Herein, we reported an ultramicroporous porous coordination polymer (ZnFPCP) featuring blade-like circular phenyl paraffin nanotraps. As further validated by density functional tight binding (DFTB) calculations, grand canonical Monte Carlo (GCMC) simulations, and in situ Fourier-tansform infrared absorption (FT-IR) analysis, these ultramicroporous paraffin nanotraps created by surrounding benzene rings enhance the paraffin-selective adsorption, and the segmented spaces between adjacent nanotraps in the blade-like structure, combined with hydrophobic petal-like secondary pore channels enclosed by fluorinated functional groups, further mitigate the water co-adsorption. Remarkably, ZnFPCP exhibited outstanding ideal adsorption solution theory (IAST) selectivity (C3H8/C3H6: 2.08, C2H6/C2H4: 2.93) under ambient conditions and record-breaking C3H8/C2H6 uptake at low pressures. Breakthrough experiments demonstrated the excellent performance of ZnFPCP in olefin purification, affording the exceptional productivity of ultra-high purity (99.99%) for C3H6 and C2H4. Robust stability and super hydrophobicity highlight its potential in harsh industrial application scenarios.

Role of neutral impurities and non-parabolic dispersive electrons in HgCdTe avalanche photodiodes.

HgCdTe avalanche photodiodes (APDs) exhibit unique gain stability, making them advantageous for weak signal detection. However, research on neutral impurities (NIs) scattering in HgCdTe remains limited, and the non-parabolic electron dynamics pose significant error in current device scale models. These limitations hinder the theoretical and the industrial development of HgCdTe APD. Here, we designed Si-substrate devices and CdZnTe-substrate devices with high and low NI density, respectively, to clarify the role of NIs. Combining first-principle calculations with Monte Carlo transport simulations, we find that the avalanching electrons could be categorized into four types (I-IV below) with distinct behavior. Furthermore, we proposed a step-solving Monte Carlo (SSMC) simulation framework to resolve accurately electron trajectories with non-parabolic dispersion. We then clarify different contemporary models of impact ionization and polar optical phonon scattering with SSMC and experimental results. Notably, our findings also show that Si-substrate HgCdTe APDs show nearly the same avalanche performance as the classical CdZnTe ones, suggesting that they could play a pivotal role in high-performance infrared detection in the future.

Design of a Linear Floating Active Resistor with Low Temperature Coefficient

This paper presents the design and implementation of a linear, stable, low-power and PVT insensitive floating active resistor, which is realized using TSMC 40 nm CMOS process technology. By incorporating the automatic tuning circuit, this work has achieved improved performance metrics, which include low process sensitivity, reduced temperature coefficient, and good linearity. Monte Carlo (MC) simulations are conducted to evaluate the active resistor’s performance under variations in temperature, process, and supply voltage. The proposed design has demonstrated an average resistance process sensitivity of 0.64%, a temperature coefficient (T.C.) of 57 ppm/°C across −25 °C to 85 °C, and a linearity figure of merit (FOM) of 2.4 × 10−2 V−1 with a resistance close to MΩ level. It can achieve a linear resistance tuning range of 430.5 kΩ to 1.714 MΩ. The typical power consumption of a single active resistor is 0.25 µW at 2.1 V bootstrapped supply voltage through a Dickson charge pump (DCP) circuit using a DC input of 1 V. These results have confirmed that the proposed active resistor can function as a robust and efficient resistor for low-voltage integrated circuits and systems.

Leveraging initial conditions memory for modelling Rayleigh–Taylor turbulence

In this study, we tackle the challenge of inferring the initial conditions of a Rayleigh–Taylor mixing zone for modelling purposes by analysing zero-dimensional (0-D) turbulent quantities measured at an unspecified time. This approach assesses the extent to which 0-D observations retain the memory of the flow, evaluating their effectiveness in determining initial conditions and, consequently, in predicting the flow’s evolution. To this end, we generated a comprehensive dataset of direct numerical simulations, focusing on miscible fluids with low density contrasts. The initial interface deformations in these simulations are characterised by an annular spectrum parametrised by four non-dimensional numbers. To study the sensitivity of 0-D turbulent quantities to initial perturbation distributions, we developed a surrogate model using a physics-informed neural network (PINN). This model enables computation of the Sobol indices for the turbulent quantities, disentangling the effects of the initial parameters on the growth of the mixing layer. Within a Bayesian framework, we employ a Markov chain Monte Carlo (MCMC) method to determine the posterior distributions of initial conditions and time, given various state variables. This analysis sheds light on inertial and diffusive trajectories, as well as the progressive loss of initial conditions memory during the transition to turbulence. Furthermore, it identifies which turbulent quantities serve as better predictors of Rayleigh–Taylor mixing zone dynamics by more effectively retaining the memory of the flow. By inferring initial conditions and forward propagating the maximum a posteriori (MAP) estimate, we propose a strategy for modelling the Rayleigh–Taylor transition to turbulence.

Universal finite-size scaling in the extraordinary-log boundary phase of three-dimensional O(N) model

Recent advances in boundary critical phenomena have led to the discovery of a new surface universality class in the three-dimensional O(N) model. The newly found “extraordinary-log” phase can be realized on a two-dimensional surface for N<Nc, with Nc>3, and on a plane defect embedded into a three-dimensional system, for any N. One of the key features of the extraordinary-log phase is the presence of logarithmic violations of standard finite-size scaling. In this work we study finite-size scaling in the extraordinary-log universality class by means of Monte Carlo simulations of an improved lattice model. We simulate the model with open boundary conditions, realizing the extraordinary-log phase on the surface for N=2,3, as well as with fully periodic boundary conditions and in the presence of a plane defect for N=2,3,4. In line with theory predictions, renormalization-group invariant observables studied here exhibit a logarithmic dependence on the size of the system. We numerically access not only the leading term in the β function governing these logarithmic violations, but also the subleading term, which controls the evolution of the boundary phase diagram as a function of N. Published by the American Physical Society 2025

Measuring cosmic growth rate with CSST spectroscopic survey and fast radio burst

The cosmic growth rate, which is related to peculiar velocity and is a primary scientific objective of galaxy spectroscopic surveys, can be inferred from the Redshift Space Distortion effect and the kinetic Sunyaev–Zel’dovich (kSZ) effect. However, the reconstruction noise power spectrum of the radial velocity field in kSZ is significantly dependent on the measurement of the small-scale galaxy-electron power spectrum Pge. In this study, we thoroughly discuss the enhancement of cosmic growth rate measurements facilitated by Fast Radio Bursts (FRBs), which probe the electron density of the universe along their propagation paths to provide crucial additional information on Pge. Subsequently, we utilize future spectroscopic surveys from the Chinese Space Station Telescope and the CMB-S4 experiment, combined with FRB dispersion measures, to achieve precise measurements of the cosmic growth rate at redshifts zg=0.15,0.45,0.75. Employing Fisher matrix forecasting analysis, we anticipate that constraints on fσ8 will reach a precision of 0.1% with a sample size of 106 FRBs. Furthermore, we perform a global analysis using Markov Chain Monte Carlo methods to constrain key parameters of three distinct dark energy models and a modified gravity model based on cosmic growth rate measurements. The results demonstrate that these refined fσ8 measurements considerably enhance the constraints on relevant cosmological parameters compared to those obtained from Planck CMB data. As the number of observed FRBs increases, alongside more precise galaxy surveys and next-generation CMB observations, new opportunities will arise for constraining cosmological models using the kSZ effect and for developing novel cosmological applications of FRBs.

Effective dimensional reduction of complex systems based on tensor networks

Abstract The exact treatment of Markovian models of complex systems requires knowledge of probability distributions exponentially large in the number of components n. Mean-field approximations provide an effective reduction in complexity of the models, requiring only a number of phase space variables polynomial in system size. However, this comes at the cost of losing accuracy close to critical points in the systems dynamics and an inability to capture correlations in the system. In this work, we introduce a tunable approximation scheme for Markovian spreading models on networks based on matrix product states (MPSs). By controlling the bond dimensions of the MPS, we can investigate the effective dimensionality needed to accurately represent the exact 2 n dimensional steady-state distribution. We introduce the entanglement entropy as a measure of the compressibility of the system and find that it peaks just after the phase transition on the disordered side, in line with the intuition that more complex states are at the ‘edge of chaos’. We compare the accuracy of the MPS with exact methods on different types of small random networks and with Markov chain Monte Carlo methods for a simplified version of the railway network of the Netherlands with 55 nodes. The MPS provides a systematic way to tune the accuracy of the approximation by reducing the dimensionality of the systems state vector, leading to an improvement over second-order mean-field approximations for sufficiently large bond dimensions.

High frequency stimulation activates hot spots of spontaneous synaptic transmission

Neuronal transmitters are released at the morphological specializations known as active zones (AZs). Transmitters can be released either in response to a stimulus or spontaneously, and spontaneous transmission is a vital component of neuronal communication. Employing postsynaptically tethered calcium sensor GCaMP, we investigated how nerve stimulation affects spontaneous transmission at individual AZs at the Drosophila neuromuscular synapse. Optical monitoring of spontaneous transmission at individual AZs revealed that prolonged high-frequency stimulation (HFS, 30 Hz for 1 min) selectively activates the hot spots of spontaneous transmission, including the individual AZs with elevated activities as well as AZ clusters. In contrast, a brief tetanus (2 s) activated numerous low-activity AZs. We employed Monte-Carlo simulations of spontaneous transmission based on a three-state model of AZ preparedness, which incorporated longer-lasting (minutes) and shorter-lasting (sub-seconds to seconds) high-activity states of AZs. The simulations produced an accurate quantitative description of the variability and time-course of spontaneous transmission at individual AZs before and after the stimulation and suggested that HFS activates both longer-lasting and shorter-lasting states of AZ preparedness.

Cost-utility analysis of olaparib assisted targeted therapy for BRCA mutation HER2-negative early breast cancer in China and in the United States

BackgroundOlaparib, an inhibitor of poly (ADP-ribose) polymerase (PARP), has demonstrated promising outcomes in treating HER2-negative early-stage breast cancer with BRCA mutations. However, a comprehensive evaluation of its cost-effectiveness in the context of the United States and China has yet to be undertaken. This study seeks to fill this research void by performing a thorough cost-utility analysis.MethodsThis investigation takes as its foundation the findings from the OlympiA trial. We obtained survival curves from this trial and used the Weibull distribution function to calculate transition probabilities. Relevant literature provided the necessary data on costs, utility values, and discount rates applicable to both the United States and China. We utilized TreeAge software to construct Markov models for each country, simulating the progression of early-stage breast cancer. These models underwent extensive examination through multi-way analysis, cost-utility analysis, Monte Carlo simulations, one-way and two-way sensitivity analyses, as well as probabilistic sensitivity analysis.ResultsThe cost-utility analysis of the Chinese Markov model revealed that the total expenditure for the Olaparib cohort amounted to 384,274.75 RMB, generating 6.41 QALYs. Conversely, the placebo group incurred a total cost of 60,264.10 RMB, resulting in 6.34 QALYs. The Incremental Cost-Utility Ratio (ICUR) between the two cohorts stood at 5,007,332.36 RMB/QALY, which is significantly higher than thrice the Gross Domestic Product (GDP) per capita of China in 2022, set at 257,094 RMB. As for the U.S. model, the Olaparib group had a total expenditure of 245,604.01 USD, yielding 7.53 QALYs, while the placebo cohort had a total cost of 93,019.92 USD, generating 7.45 QALYs. The ICUR for the two groups was calculated at 1,891,974.19 USD/QALY, substantially surpassing the U.S. Willingness-To-Pay (WTP) threshold of 150,000 USD/QALY.ConclusionsWhen evaluated in the context of healthcare economics in both China and the United States, the implementation of an Olaparib-based treatment strategy for early-stage HER2-negative breast cancer with BRCA mutations does not present a cost-effective solution in either nation.

Assessment of Modeling Decisions for Depletion Multiphysics Studies of AHTR

The Advanced High Temperature Reactor (AHTR) is a prismatic Fluoride salt cooled High temperature Reactor (FHR) fueled by TRISO particles with a relatively large power of 3400 MW(thermal). Because of its double heterogeneity in fuel element geometry and complexity to model it, transport simulations of AHTR have mostly focused on using Monte Carlo methods. Detailed depletion studies with elements of multiphysics have not been done previously on AHTR, which created the need for a new tool to do so. A C++ script was created to enable such analyses of AHTR, including temperature feedback, thermal expansion, material property changes, and criticality search on control rod position. This paper begins with a brief summary of modeling capabilities and methodologies. Then, attention turns to depletion analysis of AHTR. In this work, five depletion cases of varying degrees of resolution and features are considered with results and comparisons presented. Three-dimensional depletion cases include single material tracking (core average), fine spatial tracking (4032 zones), thermal-hydraulic feedback substeps between burnup steps, criticality iteration substeps via control rod movement between burnup steps, and use of both criticality and thermal-hydraulic iteration substeps between burnup steps. The final case illustrates the full functionality to run detailed depletion studies in an automated fashion with elements of multiphysics. Although only applicable to AHTR, the script enables analyses not previously possible with existing tools and advances the state of the art for AHTR core design.

Reliability analysis of competing failure systems considering multiple-damage self-recovery and aggravation evolution mechanisms

ABSTRACT This paper proposes a competing failure system considering special damage evolution mechanisms, which can explain the self-adaptability of the system more comprehensively. In the process of operation, the system will be affected by external shocks and internal degradation. However, when subject to various shocks, the system exhibits distinct stress responses, mainly manifested as the amount of damage. Specifically, for different shock magnitudes, the system shows three diverse damage evolution mechanisms: solely self-recovery, solely aggravation, and a combination of both. In this paper, first, a mixed shock model based on cumulative and δ -shock model is used to construct the sudden failure process of the system. The above damage evolution mechanisms are first introduced into the modeling of cumulative shock model to make the mixed shock model more sufficient. Next, we describe the natural degradation path of the system as a linear degradation process. Furthermore, the reliability model of the competing failure system with internal degradation and external shocks is established, and the system reliability functions under the mixed shock model are calculated. Finally, based on a micro-electro-mechanical system (MEMS) engineering example, Monte Carlo simulation method is used to verify the feasibility of the reliability model.

Stochastic probabilistic robust control for discrete-time system with parametric uncertainties

This paper presents a novel robust controller design method for discrete linear systems with stochastic uncertainties. Traditional probabilistic robust control methods rely on extensive sampling, leading to high computational complexity. To address this issue, Lyapunov stability theory is applied to establish an approximate functional relationship between the system's robust performance indices and control parameters. This innovative approach enables efficient evaluation of system robustness and transforms the control problem into a standard convex optimisation problem. Monte Carlo simulations were used to validate the proposed method's performance under varying system parameters. The results show that the method meets control performance index requirements with high probability and outperforms traditional LMI and LQR control approaches in terms of probabilistic robustness. By achieving a favourable balance between control efficacy and computational efficiency, this approach shows considerable potential for applications requiring stringent control requirements.

Design and Implementation of an EWMA Control Chart for Zero‐Inflated Count Data in High‐Quality Processes

ABSTRACTThe Poisson distribution is often employed to model count data, but it may not accurately represent a dataset with frequent occurrences of zero counts. This limitation often arises in high‐quality processes where the production of nonconforming items is minimal. To address this issue, modified forms of existing distributions such as the zero‐inflated geometric (ZIG) distributions, zero‐inflated Poisson (ZIP), and zero‐inflated negative binomial (ZINB) have been developed to more accurately capture the zero‐inflated (ZI) count data. Control charts under ZIP distribution are effective for monitoring processes with zero defects. However, determining whether the data exhibit over‐dispersion or under‐dispersion is often challenging. To address this challenge and accommodate various dispersion patterns in zero‐defect datasets, a flexible distribution called the ZI Conway–Maxwell–Poisson (ZICOMP) distribution is developed in the literature. This distribution is capable of modeling datasets that are over‐dispersed, under‐dispersed, or equi‐dispersed. In this study, the ZICOMP distribution is integrated with the exponentially weighted moving average (EWMA) control charting structure to efficiently monitor the processes involving ZI count data, regardless of the dispersion level. Extensive Monte Carlo simulations are performed to evaluate the performance of the proposed chart under different parameter settings. Additionally, two real‐life applications are provided to demonstrate the practical implementation and effectiveness of the proposed chart for both over‐dispersion and under‐dispersion scenarios.

Quantifying the Effect of Posaconazole on Venetoclax Metabolism in Chinese Patients with Hematologic Diseases.

Venetoclax (Ven) and posaconazole (PSZ) are commonly co-administered in patients with hematological diseases, including acute myeloid leukemia, chronic lymphocytic leukemia, and other related conditions. Due to CYP3A inhibition by PSZ, Ven plasma concentrations (ConcVen) are elevated, necessitating dose adjustments. This study aimed to quantitatively characterize the relationship between PSZ exposure and Ven pharmacokinetics through retrospective analysis of data from hematological patients receiving concurrent therapy. We examined correlations between ConcVen (both absolute and normalized by daily dose [ConcVen/DD]) and PSZ exposure metrics (daily dose and plasma concentrations [ConcPSZ]) using Spearman's analysis. A population pharmacokinetic model incorporating an innovative rectified linear unit-like function was developed to quantify the nonlinear interaction between these drugs and characterize Ven disposition, providing a more precise mathematical description of their relationship. This was followed by Monte Carlo simulations to predict steady-state peak concentrations across various dosing scenarios and PSZ exposure concentrations. The analysis included 461 paired Ven-PSZ concentration measurements from 282 patients. Significant correlations were observed between both ConcVen and ConcVen/DD versus ConcPSZ (P <.01). Ven pharmacokinetics was best described by a two-compartment model, with clearance showing significant concentration-dependent reduction with increasing ConcPSZ. Simulations demonstrated that Ven doses of 70 and 100 mg daily maintained therapeutic steady-state concentrations. However, careful monitoring of Ven concentrations is warranted when ConcPSZ exceeds 2.5 µg/mL. Based on these findings, we recommend that Ven dose adjustments during concurrent PSZ therapy be guided by therapeutic drug monitoring of both agents, with dosing decisions informed by our population pharmacokinetic model incorporating measured ConcPSZ.

Exploration of Dual-Carbon Target Pathways Based on Machine Learning Stacking Model and Policy Simulation—A Case Study in Northeast China

Northeast China, a traditional heavy industrial base, faces significant carbon emissions challenges. This study analyzes the drivers of carbon emissions in 35 cities from 2000–2022, utilizing a machine-learning approach based on a stacking model. A stacking model, integrating random forest and eXtreme Gradient Boosting (XGBoost) as base learners and a support vector machine (SVM) as the meta-model, outperformed individual algorithms, achieving a coefficient of determination (R2) of 0.82. Compared to traditional methods, the stacking model significantly improves prediction accuracy and stability by combining the strengths of multiple algorithms. The Shapley additive explanations (SHAP) analysis identified key drivers: total energy consumption, urbanization rate, electricity consumption, and population positively influenced emissions, while sulfur dioxide (SO2) emissions, smoke dust emissions, average temperature, and average humidity showed negative correlations. Notably, green coverage exhibited a complex, slightly positive relationship with emissions. Monte Carlo simulations of three scenarios (Baseline Scenario (BS), Aggressive De-coal Scenario (ADS), and Climate Resilience Scenario (CRS)) the projected carbon peak by 2030 under the ADS, with the lowest emissions fluctuation (standard deviation of 5) and the largest carbon emissions reduction (17.5–24.6%). The Baseline and Climate Resilience scenarios indicated a peak around 2039–2040. These findings suggest the important role of de-coalization. Targeted policy recommendations emphasize accelerating energy transition, promoting low-carbon industrial transformation, fostering green urbanization, and enhancing carbon sequestration to support Northeast China’s sustainable development and the achievement of dual-carbon goals.

Framework of an Implementation Strategy for a Modular Construction Toolkit Design in Construction Companies

This paper presents a production flow-oriented framework for measuring and enhancing productivity in construction projects. Departing from traditional resource-based approaches, the proposed framework integrates value stream mapping with advanced simulation techniques and real-world data acquisition to comprehensively assess process performance. The simulation model employs a Monte Carlo method, incorporating lognormal distributions to generate realistic process durations for key construction activities. This approach effectively captures both central tendencies and variability while preventing the occurrence of unrealistically short process times. Data were collected from an actual construction site in Munich, where piles were constructed using Kelly drilling machines with a diameter of 50 cm and a depth of 12 m, followed by reinforcing and concreting. On-site measurements were obtained via manual recording and automated sensor technologies, including camera-based monitoring and data from construction equipment. The simulated and measured process times were compared using density graphs and statistical indicators. This showed that some of the processes are very similar to the reference processes but that there are also significant differences in variability and durations. These findings highlight the necessity for process-specific productivity benchmarks and underscore the importance of a flexible, production flow-oriented approach that can be adopted to the unique operational requirements of individual companies. The framework provides a robust tool for productivity assessment and offers practical insights for optimizing construction processes and reducing schedule variability.

Achieving high polarization of photons emitted by unpolarized electrons in ultrastrong laser fields

Nonlinear Compton scattering driven by ultraintense lasers presents a promising avenue for enhancing the photon energy, brilliance, and setup compactness of γ-ray sources. However, a significant challenge lies in achieving a high polarization degree with commonly generated unpolarized electrons, thus addressing a longstanding puzzle in the field. Here, we investigate the polarization dynamics of photons emitted by an unpolarized electron beam interacting with a counter-propagating ultraintense laser pulse numerically and propose a method to generate highly polarized γ rays via nonlinear Compton scattering with the aid of vacuum dichroism effect. Our simulations reveal that high-brilliance γ rays with polarization beyond 90% are feasible in a single-shot interaction, rivaling the highest achieved by any γ-ray sources to date, based on a developed Monte Carlo method incorporating polarization-resolved tree processes of nonlinear Compton scattering and Breit-Wheeler pair production and one-loop vacuum polarization. This generation method showcases an extraordinary ultra-high polarization degree and a user-friendly all-optical experimental setup while harnessing the high photon energy and brilliance characteristic of nonlinear Compton scattering sources, thus making it of great potential for experimental applications.

Bayesian method for comparing F1 scores in the absence of a gold standard

ABSTRACT In the field of medicine, evaluating the diagnostic performance of new diagnostic methods can be challenging, especially in the absence of a gold standard. This study proposes a methodology for assessing the performance of diagnostic tests by estimating the posterior distribution of the F 1 score using latent class analysis, without relying on a gold standard. The proposed method utilizes Markov Chain Monte Carlo sampling to estimate the posterior distribution of the F 1 score, enabling a comprehensive evaluation of diagnostic test methods. By applying this method to internet addiction, we demonstrate how latent class analysis can be effectively used to assess diagnostic performance, offering a practical solution for situations where no gold standard is available. The effectiveness of the proposed approach was evaluated through simulation studies by examining the coverage probability of the 95% highest density interval of the estimated posterior distributions.

Security-Reliability Analysis of NOMA-Assisted Hybrid Satellite-Terrestrial Relay Multi-Cast Transmission Networks Using Fountain Codes and Partial Relay Selection with Presence of Multiple Eavesdroppers

This article proposes a hybrid satellite-terrestrial relaying network (HSTRN) that integrates physical-layer security (PLS), Fountain codes (FCs), non-orthogonal multiple access (NOMA), and partial relay selection (PRS) to enhance system performance in terms of reliability, data rate, and security. In the proposed system, a satellite uses NOMA to simultaneously transmit Fountain packets to two clusters of terrestrial users. Data transmission is assisted by one of the terrestrial relay stations, selected by the PRS algorithm. We derive exact expressions for outage probability (OP) and system outage probability (SOP) at the legitimate users, as well as intercept probability (IP) and system intercept probability (SIP) at eavesdroppers. Monte Carlo simulations are realized to validate the accuracy of the analytical results, illustrate performance trends, and analyze the impact of key parameters on the considered performance.