Search Results (40)

The uniaxial tensile test is a common and fundamental test in materials science and engineering, in which a specimen is subjected to controlled tension until failure. From this, the stress–strain curve and many property parameters of the material can be calculated, such as tensile strength, ultimate strength, maximum elongation, Young’s modulus, Poisson’s ratio, and yield strength. As fibrous materials, such as paper and paperboard, become more popular, accurately measuring their mechanical properties becomes essential for developing and applying these materials, especially in packaging. However, since they are anisotropic and inherently inhomogeneous due to the arrangement of the fibers, accurately determining their mechanical properties is not straightforward. This study investigated how several key factors influence the results of tensile tests on fiber-based materials: sample size and deformation measurement techniques using three fiber materials. This study also compared three different strain recording methods: digital image correlation (DIC), video extensometer, and conventional extensometer (Traverse). The DIC technique emphasized the effect of the inherent inhomogeneity of the paperboard on the overall mechanical properties obtained from tensile tests. The results indicated that sample size has a negligible effect on the stress–strain curve, and any apparent influence likely stems from slip at the grips during tensile testing. However, sample size does affect paperboard fracture to some extent. The study also provided recommendations for optimal specimen geometry and deformation recording methods to improve the accuracy and repeatability of tensile testing of fiber-based materials. Full article

In cosmological scenarios where the Peccei–Quinn symmetry is broken after inflation, small-scale axion field inhomogeneities can undergo gravitational collapse, leading to the formation of bound structures. The dynamics of these systems are commonly described using cosmological perturbation theory applied to the Einstein–Klein–Gordon equations. In the non-relativistic regime, this description reduces to the Gross–Pitaevskii–Poisson or Schrödinger–Poisson equations, depending on whether axion self-interactions are included. In this work, we extend the axion’s relativistic action by introducing a non-minimal scalar-curvature coupling of the form $\xi R{\varphi }^4$, which effectively induces a gravitationally mediated pairwise interaction. By performing a perturbative expansion and subsequently taking the non-relativistic limit, we derive a modified set of evolution equations governing the early stages of axion structure formation. Full article

This paper presents a comprehensive study of statistical tests for comparing temporal point processes in general, with a particular focus on Poisson processes. We explore three key approaches: (1) an intensity-based test specifically for Poisson processes, (2) general parametric tests using the notion of maximum likelihood estimation, and (3) a general nonparametric test using the Isometric Log-Ratio (ILR) transformation. The first approach adopts a three-step procedure for comparing inhomogeneous Poisson processes by testing total and normalized intensities separately and then combining the corresponding p-values using Fisher’s method. The second method proposes a likelihood-based parametric test to examine the conditional intensity functions in point processes, emphasizing the application to Hawkes processes. Lastly, the third approach introduces a nonparametric test for general point processes, by transforming inter-event times into a Euclidean space via the ILR transformation, followed by conventional depth-based methods on multivariate data. We then conduct thorough studies on simulations as well as real-world data to illustrate these testing procedures and demonstrate their effectiveness. Full article

This study investigates the effect of temperature on the performance of the single-walled carbon nanotube (SWCNT) film/Si photodetector. Specifically, the photocurrent across a SWCNT/Si heterojunction when illuminated with light of 632.8 nm wavelength of different powers was studied in detail in a wide temperature range, from 20 to 300 K. The objective was to determine the parameters of the heterojunction, which is inherently inhomogeneous, and to identify the main ones that determine the optoelectronic figures of merit of a photodetector based on it. The barrier height and its temperature dependence were determined within the framework of the theory of thermionic emission, taking into account the non-uniform distribution of the barrier height over the heterojunction area. The parameters of the heterojunction and SWCNT/Si interface and their temperature dependences were calculated based on the known temperature dependences of the concentration of charge carriers and ionized impurities in Si using the Poisson equation based on Fermi–Dirac statistics. The obtained results indicate the importance of interplay between the effects of reducing the barrier height and the processes of decreasing the separation efficiency of nonequilibrium charge carriers and increasing the rate of their recombination. Full article

Effective operation of any service system requires optimal organization of the sharing of resources between the users (customers). To this end, it is necessary to elaborate on the mechanisms that allow for the mitigation of congestion, i.e., the accumulation of many users requiring service. Due to the randomness of the user’s arrival process, congestions can occur even when an arrival rate is constant, e.g., the arrivals are described by the stationary Poisson process, which is assumed in the majority of existing papers. However, congestions can be more severe if the possibility of fluctuation of the instantaneous arrival rate exists. Such a possibility is an inherent feature of many systems and can be taken into account via the description of arrivals by the Markov arrival process (MAP). This makes the problem of congestion avoidance drastically more challenging. In many real-world systems, there exists the possibility of customer admission control via dynamic pricing. We propose a novel predictive mechanism of dynamic pricing. Decision moments coincide with the transition moments of the underlying process of the MAP. A customer may join or balk the system or postpone joining the system depending on the current cost. We illustrate the application of this mechanism in a multi-server retrial queueing model with dynamic service pricing. The behavior of the system is described by a multidimensional Markov chain with state-inhomogeneous transitions. Its stationary distribution is computed and may be used for solving the various problems of system revenue maximization via the choice of the proper pricing strategy. Full article

This article proposes various new approximate analytical solutions of the boundary value problem for the non-stationary system of Nernst–Planck–Poisson (NPP) equations in the diffusion layer of an ideally selective ion-exchange membrane at overlimiting current densities. As is known, the diffusion layer in the general case consists of a space charge region and a region of local electroneutrality. The proposed analytical solutions of the boundary value problems for the non-stationary system of Nernst–Planck–Poisson equations are based on the derivation of a new singularly perturbed nonlinear partial differential equation for the potential in the space charge region (SCR). This equation can be reduced to a singularly perturbed inhomogeneous Burgers equation, which, by the Hopf–Cole transformation, is reduced to an inhomogeneous singularly perturbed linear equation of parabolic type. Inside the extended SCR, there is a sufficiently accurate analytical approximation to the solution of the original boundary value problem. The electroneutrality region has a curvilinear boundary with the SCR, and with an unknown boundary condition on it. The article proposes a solution to this problem. The new analytical solution methods developed in the article can be used to study non-stationary boundary value problems of salt ion transfer in membrane systems. The new analytical solution methods developed in the article can be used to study non-stationary boundary value problems of salt ion transport in membrane systems. Full article

Simplified methods of static free head stiffness of the semi-rigid foundation under lateral loads were limited to flexible or rigid behavior by the critical length of piles. This would lead to errors when predicting the static or dynamic performance of their upper structures in OWT Systems. This paper presents a comprehensive analysis of the head static stiffness of the semi-rigid pile without considering the critical length. Firstly, case studies using the energy-based variational method encompassing nearly twenty thousand cases were conducted. These cases involved different types of foundations, including steel pipe piles and concrete caissons, in three types of soil: homogeneous soil, linearly inhomogeneous soil, and heterogeneous soil. Through the analysis of these cases, a series of polynomial equations of three kinds of head static stiffness, containing the relative stiffness of the pile and soil, the slenderness ratio, and Poisson’s ratio, were developed to capture the semi-rigid behavior of the foundations. Furthermore, the lateral deflection, the rotation for concrete caissons in the bridge projects, and several natural frequencies of three cases about the OWT system considering the SSI effect were carried out. the error of high-order frequency of the OWT system reached 13% after considering the semi-rigid effect of the foundation. Full article

Ecological niche partitioning is crucial in reducing interspecific competition, fostering species coexistence, and preserving biodiversity. Our research, conducted in a hybrid mixed oak forest in Yushan, Jiangsu, China, focuses on Quercus acutissima, Q. variabilis, Q. fabri, and Q. serrata var. brevipetiolata. Using Point Pattern Analysis, we investigated the spatial relationships and ecological trait autocorrelation, including total carbon (TC), nitrogen (TN), phosphorus (TP), potassium (TK), and breast height diameter (DBH). Our findings show aggregated distribution patterns within the oak populations. The Inhomogeneous Poisson Point model highlights the impact of environmental heterogeneity on Q. variabilis, leading to distinct distribution patterns, while other species showed wider dispersion. This study reveals aggregated interspecific interactions, with a notable dispersal pattern between Q. acutissima and Q. variabilis. We observed significant variability in nutrient elements, indicating distinct nutrient dynamics and uptake processes. The variations in total carbon (TC), nitrogen (TN), phosphorus (TP), and potassium (TK) suggest distinct nutrient dynamics, with TK showing the highest variability. Despite variations in TC, TK, and TP, the species did not form distinct classes, suggesting overlapping nutritional strategies and environmental adaptations. Furthermore, spatial autocorrelation analysis indicates strong positive correlations for DBH, TC, and TP, whereas TK and TN correlations are non-significant. The results suggest habitat filtering as a key driver in intraspecific relationships, with a finer spatial scale of ecological niche division through TC and TP, which is crucial for maintaining coexistence among these oak species. Full article

Traditional insurance’s earthquake contingency costs are insufficient for earthquake funding due to extreme differences from actual losses. The earthquake bond (EB) links insurance to capital market bonds, enabling higher and more sustainable earthquake funding, but challenges persist in pricing EBs. This paper presents zero-coupon and coupon-paying EB pricing models involving the inconstant event intensity and maximum strength of extreme earthquakes under the risk-neutral pricing measure. Focusing on extreme earthquakes simplifies the modeling and data processing time compared to considering infinite earthquake frequency occurring over a continuous time interval. The intensity is accommodated using the inhomogeneous Poisson process, while the maximum strength is modeled using extreme value theory (EVT). Furthermore, we conducted model experiments and variable sensitivity analyses on EB prices using earthquake data from Indonesia’s National Disaster Management Authority from 2008 to 2021. The sensitivity analysis results show that choosing inconstant intensity rather than a constant one implies significant EB price differences, and the maximum strength distribution based on EVT matches the data distribution. The presented model and its experiments can guide EB issuers in setting EB prices. Then, the variable sensitivities to EB prices can be used by investors to choose EB according to their risk tolerance. Full article

The paving layer on the steel box girder bridge deck is widely used when constructing pavements for steel bridges. Owing to the orthotropic feature of steel decks, a transverse clapboard and rib can lead to a concentration of stress. Consequently, fatigue cracks are often identified in asphalt concrete pavement layers due to re-compaction caused by heavy vehicles. This study aims to derive an evaluation method of fatigue life for asphalt pavement based on the inhomogeneous Poisson stochastic process in view of the highly random and uncertain working conditions of layered composite structures. According to the inhomogeneous Poisson stochastic process, along with Miner’s fatigue damage accumulation theory and the linear elastic fracture mechanics theory, the fatigue life formula could be deduced. Meanwhile, fatigue experiments for asphalt concrete are designed to investigate the correlation between the theoretical formula and the actual fatigue damage life of the material. Compared with the test, the accuracy error is within 10%, which is better than other traditional methods. Therefore, the fatigue life prediction model could better reflect the loading order effect and the interaction between loads, providing a new path for the fatigue reliability design of steel bridge deck asphalt pavement. Full article

Cell migration in a biological medium towards a blood vessel is modeled, as a random process, sucessively inside an annulus (two-dimensional domain) and an annular cylinder (three-dimensional domain). The conditional probability function u for the cell moving inside such domains (tissue) fulfills by assumption a diffusion–advection equation that is subject to a Dirichlet boundary condition on the outer boundary and a Robin boundary condition on the inner boundary. The mean first-passage time (MFPT) function determined by u estimates the average time for the travelling cell to reach various interesting targets. The MFPT function fulfills a Poisson equation inside a domain with suitable boundary conditions, which give rise to various mathematical problems. The main novelty of this study is the characterization of such an MFPT function inside an annulus and an annular cylinder, which is subject to a Robin boundary condition on the inner boundary and a Dirichlet boundary condition on the outer one, and these are integral functions whose densities are the solution of an inhomogeneous system of linear integral equations. Full article

The existence of traveling waves in an inhomogeneous medium is a vital problem, the solution of which can help in modeling the wave propagation over long distances. Such waves can be storm waves or tsunami waves in the seas and oceans. The presence of solutions in the form of traveling waves indicates that the wave propagates without reflection and, therefore, can transfer energy over long distances. Traveling waves within the framework of the 1D variable-coefficient wave equation exist only for certain configurations of an inhomogeneous medium, some of which can be found by transforming the original equation to the Euler–Darboux–Poisson equation. The solution of the last equation for certain parameter values is expressed in elementary functions, which are the sum of waves running in opposite directions. The mathematical features of such a transformation are discussed in this paper. Full article

The indentation of a power-law graded elastic half-space by a rigid counter body is considered in the framework of linear elasticity. Poisson’s ratio is assumed to be constant over the half-space. For indenters with an ellipsoidal power-law shape, an exact contact solution is derived, based on the generalizations of Galin’s theorem and Barber’s extremal principle for the inhomogeneous half-space. As a special case, the elliptical Hertzian contact is revisited. Generally, elastic grading with a positive grading exponent reduces the contact eccentricity. Fabrikant’s approximation for the pressure distribution under a flat punch of arbitrary planform is generalized for power-law graded elastic media and compared with rigorous numerical calculations based on the boundary element method (BEM). Very good agreement between the analytical asymptotic solution and the numerical simulation is obtained for the contact stiffness and the contact pressure distribution. A recently published approximate analytic solution for the indentation of a homogeneous half-space by a counter body, whose shape slightly deviates from axial symmetry but is otherwise arbitrary, is generalized for the power-law graded half-space. The approximate procedure for the elliptical Hertzian contact exhibits the same asymptotic behavior as the exact solution. The approximate analytic solution for the indentation by a pyramid with square planform is in very good agreement with a BEM-based numerical solution of the same problem. Full article

In this paper, we consider the 3D problem of laser-induced semiconductor plasma generation under the action of the optical pulse, which is governed by the set of coupled time-dependent non-linear PDEs involving the Poisson equation with Neumann boundary conditions. The main feature of this problem is the non-linear feedback between the Poisson equation with respect to induced electric field potential and the reaction-diffusion-convection-type equation with respect to free electron concentration and accounting for electron mobility (convection’s term). Herein, we focus on the choice of the numerical method for the Poisson equation solution with inhomogeneous Neumann boundary conditions. Despite the ubiquitous application of such a direct method as the Fast Fourier Transform for solving an elliptic problem in simple spatial domains, we demonstrate that applying a direct method for solving the problem under consideration results in a solution distortion. The reason for the Neumann problem’s solvability condition violation is the computational error’s accumulation. In contrast, applying an iterative method allows us to provide finite-difference scheme conservativeness, asymptotic stability, and high computation accuracy. For the iteration technique, we apply both an implicit alternating direction method and a new three-stage iteration process. The presented computer simulation results confirm the advantages of using iterative methods. Full article

A model of a particle flow forming a copy of some image and the distance between the copy and the image are estimated using a special probability metric. The ability of the flow of balls to cover the surface, when grinding the balls, was investigated using formulas of stochastic geometry. Reconstruction of characteristics of an inhomogeneous Poisson flow by inaccurate observations is analysed using the Poisson flow point colouring theorem. The dependence of the Poisson parameter of the distribution of the number of customers in a queuing system with an infinite number of servers and a deterministic service time on the peak load created by an inhomogeneous input Poisson flow is estimated. All these models consist of an inhomogeneous Poisson flow of points and marks glued to each point of the flow and are characterised by their mass, area, volume, observability (or non-observability), and service time. The presence of an asymptotic power–law relationship between model objective functions and parameters of mark crushing is established. These results may be applied in nanotechnology, powder metallurgy, ecology, and consumer services in the implementation of the “Smart City” program. The proposed approach is phenomenological in nature and is justified by the results of real observations and experiments. Full article