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The article is an editorial introducing a special issue of the scientific journal Axioms titled "Mathematical Models and Simulations." The issue contains 13 papers that cover various mathematical models and simulations in fields such as physics, biology, finance, and engineering. The papers explore different types of mathematical models, including deterministic and stochastic models, and discuss their applications and numerical simulations. The authors provide a brief overview of each paper, highlighting their main findings and methodologies. The article aims to provide library patrons with a concise summary of the special issue, allowing them to decide if they want to explore the individual papers further. [Extracted from the article]

With the introduction of new technologies, the scope of miniaturization has broadened. The conditions under which complicated products are designed, manufactured, and assembled ultimately influence how well they perform. The intricacy and crucial functionality of products are frequently only fulfilled through the use of high-precision components such as micro gears. In power transmission systems, gears are used in a variety of industries. Micro gears or gears with micro features, with tolerances of less than 5 μm, are pushing manufacturing processes to their technological limits. Monte-Carlo simulation methods enable an accurate forecast of inaccuracies in compliance. The complexity of the micro gear's design, on the other hand, increases the simulation computation and runtime. An alternative method for simulation is to create a surrogate model to predict the behavior. This paper proposes a statistical surrogate model to predict the conformity of a pair of micro gears. Afterward, the advantage of the surrogate model enables the optimal tolerance assignment while taking gear functionality and production cost into account. [ABSTRACT FROM AUTHOR]

• Local and global reliability sensitivity analyses are conducted for robotic manipulators. • A novel analytical framework is proposed for computing Local and global reliability sensitivity. • Uncertainty propagation formula on motion groups is introduced to determine distribution parameters of the pose error. • Chi-square approximation and expectation propagation technique are explored to compute system kinematic reliabilities. • The proposed framework is highly efficient and accurate. This paper develops a novel analytical framework for system kinematic reliability sensitivity analysis of robotic manipulators, which can provide the analytical results of local and global reliability sensitivity defined on the pose and position errors. First, uncertainty analysis of the pose error of the end-effector is accomplished by virtue of the second-order closed-form error propagation formula on motion groups. Then, the system kinematic reliability, namely the probability of the system kinematic error located within the prescribed safe boundary, is analytically calculated. Specifically, the non-central chi-square approximation and expectation propagation technique are employed to compute the system kinematic reliability defined on the position and pose errors, respectively. On this basis, the local and global system kinematic reliability sensitivity of robotic manipulators are analytically obtained. Finally, the effectiveness of the proposed method is validated by comparison with the Monte Carlo simulation and Kriging modeling method. The results indicate the proposed method has good efficacy and efficiency in system kinematic reliability sensitivity analysis for robotic manipulators. [ABSTRACT FROM AUTHOR]

Orthogonal frequency division multiplexing (OFDM) has been widely used in wireless communication systems due to its robustness against the frequency selectivity of fading channels. It provides optimal performance and it also meets the requirements of the next generation communication systems. Although OFDM has these advantages, its spectrum efficiency is usually degraded significantly due to the use of cyclic prefix (CP). In this paper, motivated to deal with this issue, the combined structure of Fast Walsh‐Hadamard Transform (FWHT) and Time Domain Equalizer (TDE) is proposed to use in CP‐free OFDM systems. The results validated by Monte Carlo simulations decipher the improved performances in terms of spectral efficiencies, bit error rate, peak to average power ratio and out of band emission for using this structure over frequency selective multipath fading channels in CP‐free OFDM systems. The acquired simulation results have illustrated that the proposed method provides 20% spectral efficiency without compromising the BER performance. [ABSTRACT FROM AUTHOR]

Background: In many clinical applications, evolution of a longitudinal marker is censored by an event occurrence, and, symmetrically, event occurrence can be influenced by the longitudinal marker evolution. In such frameworks joint modeling is of high interest. The Joint Latent Class Model (JLCM) allows to stratify the population into groups (classes) of patients that are homogeneous both with respect to the evolution of a longitudinal marker and to the occurrence of an event; this model is widely employed in real-life applications. However, the finite sample-size properties of this model remain poorly explored.Methods: In the present paper, a simulation study is carried out to assess the impact of the number of individuals, of the censoring rate and of the degree of class separation on the finite sample size properties of the JLCM. A real-life application from the neurology domain is also presented. This study assesses the precision of class membership prediction and the impact of covariates omission on the model parameter estimates.Results: Simulation study reveals some departures from normality of the model for survival sub-model parameters. The censoring rate and the number of individuals impact the relative bias of parameters, especially when the classes are weakly distinguished. In real-data application the observed heterogeneity on individual profiles in terms of a longitudinal marker evolution and of the event occurrence remains after adjusting to clinically relevant and available covariates; CONCLUSION: The JLCM properties have been evaluated. We have illustrated the discovery in practice and highlights the usefulness of the joint models with latent classes in this kind of data even with pre-specified factors. We made some recommendations for the use of this model and for future research. [ABSTRACT FROM AUTHOR]

• Sensitivity Analysis (SA) for traffic simulation models. • New sampling-based approach for the SA of correlated parameters. • Gaussian copula linking marginal distributions of individual parameters with their global distributions and correlations. • Use of extended Sobol' formula to estimate the variance-based sensitivity indexes in a Monte Carlo framework. • Examples using two different car-following models. Analyzing the impacts of model parameters on model outputs is an important but challenging topic for scientific research involving simulation models. Global Sensitivity Analysis (SA) has been recently employed by many transportation researchers for such task, but a proper SA is still not a common practice. In particular, many modelers simply assume that all parameters are uncorrelated in the SA. However, this assumption is often unrealistic for traffic simulation models, in which many parameters are actually correlated, leading to wrong conclusions. In this paper, a sampling-based approach is provided for the SA of correlated parameters. It uses Gaussian copula to link the marginal distributions of individual parameters with their global distributions and correlations, and utilizes the extended Sobol' formula to estimate the variance-based sensitivity indexes in a Monte Carlo framework. Its application is illustrated using two different car-following models: the Intelligent Driver Model (IDM) and the Wiedemann-74 (W74) model. Results show that this method is able to accurately quantify the sensitivity of all model parameters. As a general method, this approach can be transferred like a standard quantitative SA tool to any traffic model or complex model in the wider scientific community, especially when correlated parameters exist. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of powered descent control of a lunar lander during its final landing phase, where soft and precise landing at the target cite is required. In the literature, this problem has been solved considering a fully actuated lunar lander. Recently, landers are designed as complex systems with several onboard payloads and subsystems for completing demanding mission tasks. There are increasing constraints on mass budget and space availability onboard a lander. In order to meet these requirements, a novel controller using a single thruster is proposed. The proposed controller has three control inputs (thrust and two gimbaled angles) to control the six degrees of motion of a lander; these control inputs are non-affine. The proposed controller is designed based on variable structure control technique augmented with a high order filter, an immersion and invariance-based mass estimator and a sliding mode angular velocity observer. The stability analysis using Lyapunov theory and the results of the numerical simulations along with Monte Carlo simulations of the system show that the precise landing of the lunar lander using a single thruster is feasible. • The position and attitude control of a lunar lander using a single thruster is examined. • A novel controller along with lander mass and angular velocity observers are designed. • The proposed controller is based on variable structure control technique. • The Lyapunov theory is applied to prove the stability of the proposed control scheme. • Results of numerical simulations show the feasibility of the proposed control scheme. [ABSTRACT FROM AUTHOR]

• Full-band phonon Monte Carlo simulation is conducted to study thermal spreading resistance in GaN HEMTs. • Different simulation approaches for simulation phonon transport in GaN HEMTs are thoroughly compared. • Incorporating first-principle-calculated phonon properties in device thermal simulations is essential. Accurate thermal simulation is essential for the near-junction thermal management and electro-thermal co-design of GaN HEMTs. While various methods have been employed to simulate phonon thermal transport in GaN, a comprehensive evaluation of their performance and reliability has yet to be conducted. In this work, first-principle-based steady-state full-band phonon tracing Monte Carlo (MC) simulations are conducted to study the thermal spreading resistance in GaN HEMTs. The results of full-band MC serve as a standard against which the applicability, accuracy, and computational efficiency of three widely-used approaches to simulate the near-junction phonon transport in GaN are thoroughly examined. The simulation techniques compared in this study include MC simulations with empirical isotropic phonon dispersion (isotropic MC), MC simulations with gray-medium approximation (gray MC), and finite-element methods (FEM) with effective thermal conductivities (FEM with k eff). It is found that isotropic MC largely overestimates the thermal resistance due to the empirical model's overestimation of phonon mean free path (MFP) distributions. By selecting an appropriate average MFP, gray MC can approximate the full-band results well, but due to its inability to reflect the contributions of different phonon modes, discrepancies are inevitable for some geometric parameters. For FEM-based analysis, although the diffusive nature of Fourier's law precludes the reproduction of channel temperature distributions, the influence of phonon ballistic effects on the junction temperature can be accurately reflected in the well-chosen effective thermal conductivities. The comparison highlights the importance of directly incorporating first-principles-calculated phonon properties into device thermal simulations, and the paper can provide a clearer understanding of near-junction thermal transport in GaN and can be useful for thermal simulations of GaN-based devices. [ABSTRACT FROM AUTHOR]