Search Results (578)

We propose the zero-inflated Polynomially Adjusted Poisson (zPAP) model. It extends the usual zero-inflated Poisson by multiplying the Poisson kernel with a nonnegative polynomial, enabling the model to handle extra zeros, overdispersion, skewness, and even multimodal counts. We derive the maximum-likelihood framework—including the log-likelihood and score equations under both general and regression settings—and fit zPAP to the zero-inflated, highly dispersed Fish Catch data as well as a synthetic bimodal mixture. In both cases, zPAP not only outperforms the standard zero-inflated Poisson model but also yields reliable inference via parametric bootstrap confidence intervals. Overall, zPAP is a clear and tractable tool for real-world count data with complex features. Full article

This work investigates fractional stochastic Schrödinger evolution equations in a Hilbert space, incorporating complex potential symmetry and Poisson jumps. We establish the existence of mild solutions via stochastic analysis, semigroup theory, and the Mönch fixed-point theorem. Sufficient conditions for exponential stability are derived, ensuring asymptotic decay. We further explore trajectory controllability, identifying conditions for guiding the system along prescribed paths. A numerical example is provided to validate the theoretical results. Full article

A meshless, quasi-convex reproducing kernel particle framework for three-dimensional steady-state thermomechanical coupling problems is presented in this paper. A meshfree, second-order, quasi-convex reproducing kernel scheme is employed to approximate field variables for solving the linear Poisson equation and the elastic thermal stress equation in sequence. The quasi-convex reproducing kernel approximation proposed by Wang et al. to construct almost positive reproducing kernel shape functions with relaxed monomial reproducing conditions is applied to improve the positivity of the thermal matrixes in the final discreated equations. Two numerical examples are given to verify the effectiveness of the developed method. The numerical results show that the solutions obtained by the quasi-convex reproducing kernel particle method agree well with the analytical ones, with a slightly better-improved numerical accuracy than the element-free Galerkin method and the reproducing kernel particle method. The effects of different parameters, i.e., the scaling parameter, the penalty factor, and node distribution on computational accuracy and efficiency, are also investigated. Full article

We introduce a novel family of compactly supported basis functions, termed Legendre Delta-Shaped Functions (LDSFs), constructed using the eigenfunctions of the Legendre differential equation. We begin by proving that LDSFs form a basis for a Haar space. We then demonstrate that interpolation using classical Legendre polynomials is a special case of interpolation with the proposed Legendre Delta-Shaped Basis Functions (LDSBFs). To illustrate the potential of LDSBFs, we apply the corresponding series to approximate a rectangular pulse. The results reveal that Gibbs oscillations decay rapidly, resulting in significantly improved accuracy across smooth regions. This example underscores the effectiveness and novelty of our approach. Furthermore, LDSBFs are employed within the collocation framework to solve Poisson-type equations and systems of nonlinear differential equations arising in energy transfer problems. We also derive new error bounds for interpolation polynomials in a special case, expressed in both the discrete ${(L}_2)$ norm and the Sobolev $\left(H_p\right)$ norm. To validate the proposed method, we compare our results with those obtained using the Legendre pseudospectral method. Numerical experiments confirm that our approach is accurate, efficient, and highly competitive with existing techniques. Full article

This study addresses computational challenges in the immersed boundary method (IBM) with the pressure implicit with split operator (PISO) algorithm for simulating incompressible flows. We introduce a novel time-step splitting method to implement communication overlapping optimization, aiming to reduce costs dominated by the pressure Poisson solver. Using a fast Fourier transform (FFT)-based approach, the Poisson equation is solved efficiently with $O(NlogN)$ complexity. Our method interleaves IBM force calculations with Poisson phases, employing asynchronous communication to overlap computation with global data exchanges. This reduces communication overhead, enhancing scalability. Validation through benchmark simulations, including flow around a cylinder and particle-laden flows, shows improved efficiency and accuracy comparable with traditional methods. Implemented in a custom C++ solver using the FFTW library, tests indicate substantial acceleration, with results showing a 40% speed-up and less than 3% deviation in drag and lift coefficients. This research provides an efficient and promising simulation tool for complex flow. Full article

This article proposes a 3D mathematical model of the influence of electrical heterogeneity of the ion exchange membrane surface on the processes of salt ion transfer in membrane systems with axial symmetry; in particular, we investigate an annular membrane disk in the form of a coupled system of Nernst–Planck–Poisson and Navier–Stokes equations in a cylindrical coordinate system. A hybrid numerical–analytical method for solving the boundary value problem is proposed, and a comparison of the results for the annular disk model obtained by the hybrid method and the independent finite element method is carried out. The areas of applicability of each of these methods are determined. The proposed model of an annular disk takes into account electroconvection, which is understood as the movement of an electrolyte solution under the action of an external electric field on an extended region of space charge formed at the solution–membrane boundary under the action of the same electric field. The main regularities and features of the occurrence and development of electroconvection associated with the electrical heterogeneity of the surface of the membrane disk of the annular membrane disk are determined; namely, it is shown that electroconvective vortices arise at the junction of the conductivity and non-conductivity regions at a certain ratio of the potential jump and angular velocity and flow down in the radial direction to the edge of the annular membrane. At a fixed potential jump greater than the limiting one, the formed electroconvective vortices gradually decrease with an increase in the angular velocity of rotation until they disappear. Conversely, at a fixed value of the angular velocity of rotation, electroconvective vortices arise at a certain potential jump, and with its subsequent increase gradually increase in size. Full article

We explore a modified, including some relativistic effects, Newtonian formalism in cosmology, using a system of constituent equations that includes a modified first Friedmann equation—incorporating its homogeneous counterpart—alongside the classical Poisson equation. Furthermore, we include the dynamical equations arising from stress-energy tensor conservation. Within this framework, we examine stellar equilibrium under spherical symmetry. By specifying the equation of state, we derive the corresponding equilibrium configurations. Finally, we investigate gravitational collapse in this context. Full article

In the classical problem of the motion of a rigid body around a fixed point, which is described by the Euler–Poisson equations, we propose a new method for computing cases of integrability: first, we provide algorithms for computing values of parameters ensuring potential integrability, and then we select cases of global integrability. By this method we have obtained all the known cases of global integrability and six new cases of potential integrability for which the absence of their global integrability is proven. Full article

This article considers the effect of constant and variable Poisson’s ratio on cracking in concrete and rock specimens under uniaxial compression using mechanical systems modeling methods. The article presents an analysis of the data confirming the increase in Poisson’s ratio under specimen loading. A system of equations for modeling the effect of Poisson’s ratio on cracking under uniaxial compression is proposed. The comparison showed that the model with a constant Poisson’s ratio predicts a thickness of the surface layer with cracks that is underestimated by approximately 10%. In practice, this means that the model with a constant Poisson’s ratio underestimates the risk of failure. A technique for analyzing random deviations of Poisson’s ratio from the variable mathematical expectation is proposed. The comparison showed that the model with a variable Poisson’s ratio leads to results that are more cautious, i.e., it does not potentially overestimate the safety factor. The model predicts an increase in uniaxial compression strength when using external reinforcement. An equation is proposed for determining the required wall thickness of a conditional reinforcement shell depending on the axial compressive stress. The study contributes to understanding the potential vulnerability of load-bearing structures and makes a certain contribution to increasing their reliability. Full article

This paper proposes an improved analytical model for a line-start explosion-proof magnet synchronous motor that considers the effect of magnetic bridge saturation. Under the condition of maintaining the air-gap magnetic field unchanged, and taking into account the topological structures of embedded magnets, squirrel cages, and rotor slot openings, a subdomain model partitioning method is systematically investigated. Considering the saturation effect of the magnetic bridge of the rotor, the equivalent magnetic circuit method was utilized to calculate the permeance of the saturated region. It not only facilitates the establishment of subdomain equations and corresponding subdomain boundary conditions, but also ensures the maximum accuracy of the equivalence by maintaining the topology of the rotor. The motor was partitioned into subdomains, and in conjunction with the boundary conditions, the Poisson equation and Laplace equation are solved to obtain the electromagnetic performance of the motor. The accuracy of the analytical model is verified through finite element analysis. The accuracy of the analytical model is verified through finite element analysis (FEA). Compared to the FEA, the improved model maintains high precision while reducing computational time and exhibiting better generality, making it suitable for the initial design and optimization of industrial motors. Full article

The implementation of lean drilling and completion design techniques is a pivotal strategy for the petroleum and natural gas industry to achieve green, low-carbon, and intelligent transformation and innovation. These techniques significantly enhance oil and gas recovery rates. In shale gas development, the shale brittleness index plays a crucial role in evaluating fracturing ability during hydraulic fracturing. Indoor experiments on Gulong shale oil were conducted under a confining pressure of 30 MPa. Based on Rickman’s brittleness evaluation method, this study performed numerical simulations of triaxial compression tests on shale using the finite discrete element method. The fractal dimensions of the fractures formed during shale fragmentation were calculated using the box-counting method. Utilizing the obtained data, a multiple linear regression equation was established with elastic modulus and Poisson’s ratio as the primary variables, and the coefficients were normalized to propose a new brittleness evaluation method. The research findings indicate that the finite discrete element method can effectively simulate the rock fragmentation process, and the established multiple linear regression equation demonstrates high reliability. The weights reassigned for brittleness evaluation based on Rickman’s method are as follows: the coefficient for elastic modulus is 0.43, and the coefficient for Poisson’s ratio is 0.57. Furthermore, the new brittleness evaluation method exhibits a stronger correlation with the brittleness mineral index. The fractal characteristics of crack networks and the relationship between symmetry response and mechanical parameters offer a new theoretical foundation for brittle weight distribution. Additionally, the scale symmetry characteristics inherent in fractal dimensions can serve as a significant indicator for assessing complex crack morphology. Full article

This paper continues a series of papers by the author devoted to unsolved problems in the theory of stability and optimal control for stochastic systems. A delay differential equation with stochastic perturbations of the white noise and Poisson’s jump types is considered. In contrast with the known stability condition, in which it is assumed that stochastic perturbations fade on the infinity quickly enough, a new situation is studied, in which stochastic perturbations can either fade on the infinity slowly or not fade at all. Some unsolved problem in this connection is brought to readers’ attention. Additionally, some unsolved problems of stabilization for one stochastic delay differential equation and one stochastic difference equation are also proposed. Full article

Geometric image transformations are fundamental to image processing, computer vision and graphics, with critical applications to pattern recognition and facial identification. The splitting-integrating method (SIM) is well suited to the inverse transformation $T^{-1}$ of digital images and patterns, but it encounters difficulties in nonlinear solutions for the forward transformation T. We propose improved techniques that entirely bypass nonlinear solutions for T, simplify numerical algorithms and reduce computational costs. Another significant advantage is the greater flexibility for general and complicated transformations T. In this paper, we apply the improved techniques to the harmonic, Poisson and blending models, which transform the original shapes of images and patterns into arbitrary target shapes. These models are, essentially, the Dirichlet boundary value problems of elliptic equations. In this paper, we choose the simple finite difference method (FDM) to seek their approximate transformations. We focus significantly on analyzing errors of image greyness. Under the improved techniques, we derive the greyness errors of images under T. We obtain the optimal convergence rates $O\left(H^2\right)+O(H/N^2)$ for the piecewise bilinear interpolations ($\mu =1$) and smooth images, where $H(\ll 1)$ denotes the mesh resolution of an optical scanner, and N is the division number of a pixel split into $N^2$ sub-pixels. Beyond smooth images, we address practical challenges posed by discontinuous images. We also derive the error bounds $O\left(H^{\beta }\right)+O(H^{\beta }/N^2)$, $\beta \in (0,1)$ as $\mu =1$. For piecewise continuous images with interior and exterior greyness jumps, we have $O\left(\sqrt{H}\right)+O(\sqrt{H}/N^2)$. Compared with the error analysis in our previous study, where the image greyness is often assumed to be smooth enough, this error analysis is significant for geometric image transformations. Hence, the improved algorithms supported by rigorous error analysis of image greyness may enhance their wide applications in pattern recognition, facial identification and artificial intelligence (AI). Full article

In this paper, we study a class of nonlocal Schrödinger–Poisson–Slater equations: $-\Delta u+u+\lambda \left(I_{\alpha }\ast {\left|u\right|}^q\right){\left|u\right|}^{q-2}u={\left|u\right|}^{p-2}u$, where $q,p>1$, $\lambda >0$, and $I_{\alpha }$ is the Riesz potential. We obtain the existence, stability, and symmetry-breaking of solutions for both radial and nonradial cases. In the radial case, we use variational methods to establish the coercivity and weak lower semicontinuity of the energy functional, ensuring the existence of a positive solution when p is below a critical threshold $\overline{p}={\displaystyle \frac{4q+2\alpha }{2+\alpha }}$. In addition, we prove that the energy functional attains a minimum, guaranteeing the existence of a ground-state solution under specific conditions on the parameters. We also apply the Pohozaev identity to identify parameter regimes where only the trivial solution is possible. In the nonradial case, we use the Nehari manifold method to prove the existence of ground-state solutions, analyze symmetry-breaking by studying the behavior of the energy functional and identifying the parameter regimes in the nonradial case, and apply concentration-compactness methods to prove the global well-posedness of the Cauchy problem and demonstrate the orbital stability of the ground state. Our results demonstrate the stability of solutions in both radial and nonradial cases, identifying critical parameter regimes for stability and instability. This work enhances our understanding of the role of nonlocal interactions in symmetry-breaking and stability, while extending existing theories to multiparameter and higher-dimensional settings in the Schrödinger–Poisson–Slater model. Full article

Vanes are critical components of a rotary-vane compressor. If the vanes do not achieve sufficient contact with the inner wall of the cylinder, the compression chambers do not form completely. However, excessive contact between the vane and the cylinder wall can produce wear on both, also decreasing the lifespan of the compressor. We applied the Poisson equation and the Reynolds equation to calculate the gas force and fluid-reaction force acting on the vane. We solved the equations for the motion of the rigid vane in six degrees of freedom to determine the dynamic motion of the vane. We operated the rotary-vane compressor for 800 h under the same simulation conditions and measured the wear patterns of the vane, the bottom thrust bearing, and the cylinder wall. Finally, we validated the proposed method by confirming that the simulated contact force matches well with the measured wear patterns on the vane and the inner wall of the cylinder. The proposed method overcomes the limitations of the previous three-degrees-of-freedom analyses of the vane and will contribute to developing a robust and efficient rotary-vane compressor. Full article