Search Results (969)

The mechanical properties of cellular materials are critical to their performance and must be accurately determined through both analytical and numerical methods. These approaches are essential not only for understanding material behavior but also for evaluating the effects of parametric variations within the unit cell structure. This study focuses on the in-plane comparison of analytical and numerical evaluations of key mechanical properties, including Young’s modulus, yield strength, and Poisson’s ratio of a 2D hexagonal unit cell subjected to systematic geometric and material variations. Analytically, the mechanical properties were derived based on the geometric configuration of the hexagonal unit cell. Numerically, the finite element method (FEM) simulations employed three different meshing methods: quadrilateral, quad-dominated, and triangular elements, to ensure precision and consistency in the results. The elastic response (Young’s modulus) was examined through a parametric sweep involving segmental length variations (4.41 to 4.71 mm) and material modulus (66.5 to 71.5 GPa), revealing percentage differences between analytical and numerical results ranging from −8.28% to 10.87% and −10.58% to 11.95%, respectively. Similarly, yield strength was evaluated with respect to variations in segmental length (4.41 to 4.71 mm) and wall thickness (1.08 to 1.11 mm), showing discrepancies between −2.86% to −5.53% for segmental length and 7.76% to 10.57% for thickness. For Poisson’s ratio, variations in the same parameters led to differences ranging from −7.05% to −12.48% and −9.11% to −12.64%, respectively. Additionally, uncertainty was assessed through relative entropy measures—Bhattacharyya, Kullback–Leibler, Hellinger, and Jeffreys—to evaluate the sensitivity of homogenized properties to input variability. These entropy measures quantify the probabilistic distance between core material distributions and their effective counterparts, reinforcing the importance of precise modeling in the design and optimization of cellular structures. Full article

Stochastic geometry provides a powerful analytical framework for evaluating interference-limited cellular networks with randomly deployed base stations (BSs). While prior studies have examined limited channel state information at the transmitter (CSIT) and low-resolution analog-to-digital converters (ADCs) separately, their joint impact in multi-user multiple-input multiple-output (MIMO) systems remains largely unexplored. This paper investigates a downlink cellular network in which BSs are distributed according to a homogeneous Poisson point process (PPP), employing zero-forcing beamforming (ZFBF) with limited feedback, and receivers are equipped with one-bit ADCs. We derive a tractable approximation for the achievable spectral efficiency that explicitly accounts for both the quantization error from limited feedback and the receiver distortion caused by coarse ADCs. Based on this approximation, we determine the optimal feedback rate that maximizes the net spectral efficiency. Our analysis reveals that the optimal number of feedback bits scales logarithmically with the channel coherence time but its absolute value decreases due to coarse quantization. Simulation results validate the accuracy of the proposed approximation and confirm the predicted scaling behavior, demonstrating its effectiveness for interference-limited multi-user MIMO networks. Full article

In the shale oil reservoirs, sandstone and shale often overlie each other. This significantly affects the vertical propagation of hydraulic fractures (HFs); however, the underlying mechanisms still remain unclear. This study employs Xsite software to investigate the influence of rock fracture toughness, tensile strength, elastic modulus, Poisson’s ratio, interlayer stress contrast, and the flow rate and viscosity of fracturing fluid on the propagation behaviour of HFs in sandstone–shale interbeds. As the type-I fracture toughness of the shale layer increases, the area of the vertical HF decreases and the average HF width becomes smaller. As the tensile strength of the sandstone layer increases, the distribution range of fluid pressure at the interface expands. The HF prefers to propagate in the softer rock rather than the harder one. A relatively narrower HF width is created in the layer with a higher elastic modulus resulting in a higher flow resistance to fracturing fluid. A shale layer with a high Poisson’s ratio is more likely to undergo a lateral expansion, causing stress at the fracture tip to be dispersed. When the effect of lithological interfaces is considered, an increasing interlayer stress contrast causes HFs to gradually transition from penetrating the interfaces to becoming confined between the two interfaces. When the influence of the lithological interface is not considered, an increasing interlayer stress contrast causes the HF to gradually transition from a penny-shaped fracture to a blade-shaped fracture. The HF penetrates the interfaces more easily at a higher injection rate and fluid viscosity, because most of the injected energy is used to create new fractures rather than leakoff into the interfaces. Understanding the influence of these factors on the HF propagation behaviour is of great significance for optimising hydraulic fracturing design. Full article

Accurate determination of elastic properties, especially Poisson’s ratio, is crucial for the design and modeling of composite materials. Traditional methods often struggle with low strain measurements and non-uniform strain distributions inherent in these anisotropic materials. This research work introduces a novel methodology that integrates Digital Image Correlation (DIC) with frequency analysis techniques to improve the precision of Poisson’s ratio determination during tensile tests, particularly at low strain ranges. The focus is on the evaluation of two distinct frequency-based approaches: Phase-Based Motion Magnification (PBMM) and Lock-in filtering. DIC + PBMM, while promising for motion amplification, encountered specific challenges in this application, particularly at very low strain amplitudes, leading to increased variability and computational demands. In contrast, the DIC + Lock-in filtering method proved highly effective. It provided stable, filtered strain distributions, significantly reducing measurement uncertainty compared to traditional DIC and other conventional methods like strain gauges and Video Extensometers. This study demonstrates the robust potential of Lock-in filtering for characterizing subtle periodic mechanical behaviors leading to a reduction of approximately 70% in the standard deviation of the measurement. This work lays a strong foundation for more precise and reliable material characterization, crucial for advancing composite design and engineering applications. Full article

The Bell regression model (BRM) is a statistical model that is often used in the analysis of count data that exhibits overdispersion. In this study, we propose a Bayesian analysis of the BRM and offer a new perspective on its application. Specifically, we introduce a G-prior distribution for Bayesian inference in BRM, in addition to a flat-normal prior distribution. To compare the performance of the proposed prior distributions, we conduct a simulation study and demonstrate that the G-prior distribution provides superior estimation results for the BRM. Furthermore, we apply the methodology to real data and compare the BRM to the Poisson and negative binomial regression model using various model selection criteria. Our results provide valuable insights into the use of Bayesian methods for estimation and inference of the BRM and highlight the importance of considering the choice of prior distribution in the analysis of count data. Full article

Practical problems often drive the development of new statistical methods by presenting real-world challenges. Testing the homogeneity of n independent Poisson means when only one observation per population is available is considered in this paper. This scenario is common in fields where limited data from multiple sources must be analyzed to determine whether different groups share the same underlying event rate or mean. These settings often exhibit underlying structural or spatial symmetries that influence statistical behavior. Traditional methods that rely on large sample sizes are not applicable. Hence, it is crucial to develop techniques tailored to the constraints of single observations. Under the null hypothesis, with large n and a fixed common mean $\lambda$, the likelihood ratio test statistic (LRTS) is shown to be asymptotically normally distributed, with the mean and variance being approximated by a truncation method and a parametric bootstrap method. Moreover, with fixed n and large $\lambda$, under the null hypothesis, the LRTS is shown to be asymptotically distributed as a chi-square with $n-1$ degrees of freedom. The Bartlett correction method is applied to improve the accuracy of the asymptotic distribution of the LRTS. We highlight the practical relevance of the proposed method through applications to wildfire and radioactive event data, where correlated observations and sparse sampling are common. Simulation studies further demonstrate the accuracy and robustness of the test under various scenarios, making it well-suited for modern applications in environmental science and risk assessment. Full article

In Bayesian statistics, the prior distributions play a key role in the inference, and there are procedures for finding prior distributions. An important problem is that these procedures often lead to improper prior distributions that cannot be normalized to probability measures. Such improper prior distributions lead to technical problems, in that certain calculations are only fully justified in the literature for probability measures or perhaps for finite measures. Recently, expectation measures were introduced as an alternative to probability measures as a foundation for a theory of uncertainty. Using expectation theory and point processes, it is possible to give a probabilistic interpretation of an improper prior distribution. This will provide us with a rigid formalism for calculating posterior distributions in cases where the prior distributions are not proper without relying on approximation arguments. Full article

The durations of wars fought between 1480 and 1941 A.D. were found to be well represented by random numbers chosen from a single-event Poisson distribution with a half-life of (1.25 ± 0.1) years. This result complements the work of L.F. Richardson who found that the frequency of outbreaks of wars can be described as a Poisson process. This result suggests that a quick return on investment requires a distillation of the many stressors of the day, each one of which has a small probability of being included in a convincing well-orchestrated simple call-to-arms. The half-life is a measure of how this call wanes with time. Full article

This paper considers a heterogeneous queuing system with an unlimited number of servers, where the parameters are determined by a random environment. A distinctive feature is that the parameters of the exponential distribution of the request processing time do not change their values until the end of service. Thus, the devices in the system under consideration are heterogeneous. For the study, a method of asymptotic analysis is proposed under the condition of extremely rare changes in the states of the random environment. We consider the following problem. Cloud node accepts requests of one type that have a similar intensity of arrival and duration of processing. Sometimes an input scheduler switches to accept requests of another type with other intensity and duration of processing. We model the system as an infinite-server queue in a random environment, which influences the arrival intensity and service time of new requests. The random environment is modeled by a Markov chain with a finite number of states. Arrivals are modeled as a Poisson process with intensity dependent on the state of the random environment. Service times are exponentially distributed with rates also dependent on the state of the random environment at the time moment when the request arrived. When the environment changes its state, requests that are already in the system do not change their service times. So, we have requests of different types (serviced with different rates) present in the system at the same time. For the study, we consider a situation where changes of the random environment are made rarely. The method of asymptotic analysis is used for the study. The asymptotic condition of a rarely changing random environment (entries of the generator of the corresponding Markov chain tend to zero) is used. A multi-dimensional joint steady-state probability distribution of the number of requests of different types present in the system is obtained. Several numerical examples illustrate the comparisons of asymptotic results to simulations. Full article

This study investigates the mechanical behavior of Nylon 12 Carbon Fiber specimens manufactured through fused filament fabrication (FFF) for potential integration into light water well drilling rigs. Fifteen tensile test samples were 3D-printed on a MakerBot Method X printer in three orientations: horizontal, vertical, and lateral. Each specimen was printed with a soluble SR-30 support material, which was subsequently dissolved in an SCA 1200-HT wash station using heated alkaline solution. Following support removal, all samples underwent thermal annealing at 80 °C for 5 h in the printer’s controlled chamber to eliminate residual moisture and improve structural integrity. The annealed specimens were subjected to uniaxial tensile testing using an Instron 8875 electrohydraulic machine, with strain measured by digital image correlation (DIC) on a speckle-patterned gauge section. Key mechanical properties, including Young’s modulus, Poisson’s ratio, yield strength, and ultimate tensile strength, were determined. Finally, a finite element analysis (FEA) was performed using MSC Visual Nastran for Windows to simulate the tensile loading conditions and assess internal stress distributions for each print orientation. The combined experimental and numerical results confirm the feasibility of using additively manufactured parts in demanding engineering applications. Full article

In this paper we present an exact numerical model for the evaluation of a three-echelon supply chain with multiple retailers. Poisson demand, exponentially distributed transportation times and lost sales at the retailers are assumed. The system is modeled as a continuous time Markov chain, and the analysis is based on matrix analytic methods. We analyze the infinitesimal generator matrix of the process and develop an algorithm for its construction. Performance measures for the system are calculated algorithmically from the stationary probabilities vector. The algorithm is used for an extensive numerical investigation of the system so that conclusions of managerial importance may be drawn. Full article

While it is undisputed that Poisson GLMs represent the gold standard for counting COVID-19 deaths, recent studies have analyzed the seasonal growth and decline trends of these deaths in Italy using a simple segmented linear regression. They found that, despite an overall decreasing trend throughout the entire period analyzed (2021–2025), rising mortality trends from COVID-19 emerged in all summers and winters of the period, though they were more pronounced in winter. The technical reasons for the general unsuitability of using linear regression for the precise counting of deaths are well-known. Nevertheless, the question remains whether, under certain circumstances, the use of linear regression can provide a valid and useful tool in a specific context, for example, to highlight the slopes of seasonal growth/decline in deaths more quickly and clearly. Given this background, this paper presents a comparison between the use of linear regression and a Poisson GLM with the aforementioned death data, leading to the following conclusions. Appropriate statistical hypothesis testing procedures have demonstrated that the conditions of a normal distribution of residuals, their homoscedasticity, and the lack of autocorrelation were essentially guaranteed in this particular Italian case (weekly COVID-19 deaths in Italy, from 2021 to 2025) with very rare exceptions, thus ensuring the acceptable performance of linear regression. Furthermore, the development of a Poisson GLM definitively confirmed a strong agreement between the two models in identifying COVID-19 mortality trends. This was supported by a Kolmogorov–Smirnov test, which found no statistically significant difference between the slopes calculated by the two models. Both the Poisson and the linear model also demonstrated a comparably high accuracy in counting COVID-19 deaths, with MAE values of 62.76 and a comparable 88.60, respectively. Based on an average of approximately 6300 deaths per period, this translated to a percentage error of just 1.15% for the Poisson and only a slightly higher 1.48% for the linear model. Full article

Count data are present in many areas of everyday life. Unfortunately, such data are often characterized by over- and under-dispersion. In 1986, Efron introduced the Double Poisson distribution to account for this problem. The aim of this work is to examine the application of this distribution in regression analyses performed in health-related literature by means of a narrative review. The databases Science Direct, PBSC, Pubmed PsycInfo, PsycArticles, CINAHL and Google Scholar were searched for applications. Two independent reviewers extracted data on Double Poisson Regression Models and their applications in the health and life sciences. From a total of 1644 hits, 84 articles were pre-selected and after full-text screening, 13 articles remained. All these articles were published after 2011 and most of them targeted epidemiological research. Both over- and under-dispersion was present and most of the papers used the generalized additive models for location, scale, and shape (GAMLSS) framework. In summary, this narrative review shows that the first steps in applying Efron’s idea of double exponential families for empirical count data have already been successfully taken in a variety of fields in the health and life sciences. Approaches to ease their application in clinical research should be encouraged. Full article

This paper establishes two novel recurrence relations for Stirling numbers of the second kind—an L recurrence and a vertical recurrence—discovered through a probabilistic analysis of Poisson higher-order origin moments. While the link between these moments and Stirling numbers is known, our derivation via a specific expectation identity provides a clear and efficient pathway to their computation, circumventing the need for infinite series. The primary theoretical contribution is the proof of these previously undocumented combinatorial recurrences, which are of independent mathematical interest. Furthermore, we demonstrate the severe practical inadequacy of high-order sample moments as estimators, highlighting the necessity of our analytical approach to obtaining reliable estimates in applied fields. Full article

In this article, the mechanism of relaxation polarization currents occurring at a constant temperature (isothermal process) in crystals with ionic-molecular chemical bonds (CIMBs) in an alternating electric field was investigated. Methods of the quasi-classical kinetic theory of dielectric relaxation, based on solutions of the nonlinear system of Fokker–Planck and Poisson equations (for the blocking electrode model) and perturbation theory (by expanding into an infinite series in powers of a dimensionless small parameter) were used. Generalized nonlinear mathematical expressions for calculating the complex amplitudes of relaxation modes of the volume-charge distribution of the main charge carriers (ions, protons, water molecules, etc.) were obtained. On this basis, formulas for the current density of relaxation polarization (for transient processes in a dielectric) in the k-th approximation of perturbation theory were constructed. The isothermal polarization currents are investigated in detail in the first four approximations (k = 1, 2, 3, 4) of perturbation theory. These expressions will be applied in the future to compare the results of theory and experiment, in analytical studies of the kinetics of isothermal ion-relaxation (in crystals with hydrogen bonds (HBC), proton-relaxation) polarization and in calculating the parameters of relaxers (molecular characteristics of charge carriers and crystal lattice parameters) in a wide range of field parameters (0.1–1000 MV/m) and temperatures (1–1550 K). Asymptotic (far from transient processes) recurrent formulas are constructed for complex amplitudes of relaxation modes and for the polarization current density in an arbitrary approximation k of perturbation theory with a multiplicity r by the polarizing field (a multiple of the fundamental frequency of the field). The high degree of reliability of the theoretical results obtained is justified by the complete agreement of the equations of the mathematical model for transient and stationary processes in the system with a harmonic external disturbance. This work is of a theoretical nature and is focused on the construction and analysis of nonlinear properties of a physical and mathematical model of isothermal ion-relaxation polarization in CIMB crystals under various parameters of electrical and temperature effects. The theoretical foundations for research (construction of equations and working formulas, algorithms, and computer programs for numerical calculations) of nonlinear kinetic phenomena during thermally stimulated relaxation polarization have been laid. This allows, with a higher degree of resolution of measuring instruments, to reveal the physical mechanisms of dielectric relaxation and conductivity and to calculate the parameters of a wide class of relaxators in dielectrics in a wide experimental temperature range (25–550 K). Full article