Search Results (116)

This paper addresses the ill-posed problem in calculating subgroup parameters for resonance self-shielding within nuclear reactor physics. The conventional Pade approximation method often yields negative subgroup cross-sections lacking physical meaning due to its treatment of overdetermined nonlinear systems, making the subgroup transport equations unsolvable. To overcome this, an optimized Pade approximation method is proposed: a resonance factor criterion is used to select energy groups requiring calculation; a systematic procedure dynamically traverses background cross-section combinations starting from a minimal subgroup number, incrementally increasing it until solutions meeting accuracy constraints with positive parameters are found; and, given the insufficiency of background points, a high-resolution resonance integral table is constructed, particularly for ranges exhibiting significant cross-section variations. Numerical validation confirms the method eliminates negative parameters, ensures physical validity, and significantly improves accuracy across benchmark cases including typical fuel pins, burnt pellets, and Gd-bearing lattices. This approach effectively resolves the ill-posedness of the traditional method, offering a more robust and precise subgroup resonance treatment for high-fidelity core neutronics. Full article

We establish a theory whose structure is based on a fixed variable and an algebraic inequality and which improves the well-known least squares theory. The mentioned fixed variable plays a basic role in creating such a theory. In this direction, some new concepts, such as p-covariances with respect to a fixed variable, p-correlation coefficients with respect to a fixed variable, and p-uncorrelatedness with respect to a fixed variable, are defined in order to establish least p-variance approximations. We then obtain a specific system, called the p-covariances linear system, and apply the p-uncorrelatedness condition on its elements to find a general representation for p-uncorrelated variables. Afterwards, we apply the concept of p-uncorrelatedness for continuous functions, particularly for polynomial sequences, and we find some new sequences, such as a generic two-parameter hypergeometric polynomial of the ${}_{4}F_3$ type that satisfies a p-uncorrelatedness property. In the sequel, we obtain an upper bound for 1-covariances, an improvement to the approximate solutions of over-determined systems and an improvement to the Bessel inequality and Parseval identity. Finally, we generalize the concept of least p-variance approximations based on several fixed orthogonal variables. Full article

The equivalent conductivities of two aqueous silicate species, ${\left[\mathrm{SiO}{\left(\mathrm{OH}\right)}_3\right]}^{-}$ and ${\left[\mathrm{Si}{\mathrm{O}}_2{\left(\mathrm{OH}\right)}_2\right]}^{2-}$, are fundamental to understanding many physico-chemical phenomena of silicate materials in electrolyte solutions. These phenomena include diffusion, adsorption, and phase transformations. But significant inconsistencies have been presented in published equivalent conductivities of the two silicate aqueous ions. Also, little work has so far been undertaken to discuss how aspects, such as temperature and solution composition, may influence electrolytic conductivity of silicate aqueous solutions. This work presents the equivalent conductivities of the two silicate species, measured with electrochemical impedance spectroscopy (EIS) from 277.85 K to 308.45 K. A conductivity model for mixed electrolytes of high alkaline was first established. This model was then verified with the electrolyte conductivities of $\mathrm{NaOH}\text{-}{\mathrm{H}}_2\mathrm{O}$ solutions and $\mathrm{NaOH}\text{-}\mathrm{N}{\mathrm{a}}_2\mathrm{C}{\mathrm{O}}_3\text{-}{\mathrm{H}}_2\mathrm{O}$ solutions. Next, the equivalent conductivities of ${\left[\mathrm{SiO}{\left(\mathrm{OH}\right)}_3\right]}^{-}$ and ${\left[\mathrm{Si}{\mathrm{O}}_2{\left(\mathrm{OH}\right)}_2\right]}^{2-}$, were calculated by solving the overdetermined equation groups for different temperatures, based on electrolyte conductivities of $\mathrm{NaOH}\text{-}\mathrm{N}{\mathrm{a}}_2\mathrm{Si}{\mathrm{O}}_3\text{-}{\mathrm{H}}_2\mathrm{O}$ solutions. The accuracy of both calculations and measurements are examined in depth from various viewpoints. This work presents essential inputs for quantitatively understanding multiple physico-chemical properties of silicate materials in electrolyte solutions. Full article

In this study, we propose a self-adaptive weighted multi-mineral inversion model (SQP_AW) based on Sequential Quadratic Programming (SQP) and the Adam optimization algorithm for the accurate evaluation of mineral content in carbonate reservoir rocks, addressing the high costs of traditional experimental methods and the strong parameter dependence in geophysical inversion. The model integrates porosity curves (compensated density, compensated neutron, and acoustic time difference), elastic modulus parameters (shear and bulk moduli), and nuclear magnetic porosity data for the construction of a multi-dimensional linear equation system, with calibration coefficients derived from core X-ray diffraction (XRD) data. The Adam algorithm dynamically optimizes the weights, solving the overdetermined equation system. We applied the method to the Asmari Formation in the M oilfield in the Middle East with 40 core samples for calibration, achieving a 0.91 fit with the XRD data. For eight additional uncalibrated samples from Well A, the fit reaches 0.87. With the introduction of the elastic modulus and nuclear magnetic porosity, the average relative error in mineral content decreases from 9.45% to 6.59%, and that in porosity estimation decreases from 8.1% to 7.1%. The approach is also scalable to elemental logging data, yielding inversion precision comparable to that of commercial software. Although the method requires a complete set of logging data and further validation of regional applicability for weight parameters, in future research, transfer learning and missing curve prediction could be incorporated to enhance its practical utility. Full article

This study examines the relationship between K-Pop and education migration to South Korea in the context of the global internet and the COVID-19 pandemic. It focuses on the phenomenon in which local Asian territories have been widely influenced by the Korean Wave, particularly K-Pop, even during the era of global communication and health risks. This research illuminates some intriguing aspects of the distinctive reception patterns of Korean Wave audiences, as well as their unique characteristics, such as innocence, transgression, and the nuanced dynamics of the fandom during that period. Furthermore, this research engages critically with controversial aspects of cultural politics, such as the transmission of the legacy of K-Pop and the centralisation of femininity more actively. This study concludes that K-Pop has recently been relocated to the conjunctures of mediated and overdetermined influences on students’ education migration to South Korea rather than acting as a direct power and reason for it, particularly in the context of the COVID-19 pandemic and the rapid digitalisation of education. Full article

The number of hologram points in near-field acoustical holography (NAH) for a vibro-acoustic system plays a vital role in conditioning the transfer function between the source and measuring points. The requirement for many overdetermined hologram points for extended sources to obtain high accuracy poses a problem for the practical applications of NAH. Furthermore, overdetermination does not generally ensure enhanced accuracy, stability, and convergence, owing to the problem of rank deficiency. To achieve satisfactory reconstruction accuracy with underdetermined hologram data, the best practice for choosing hologram points and regularization methods is determined by comparing cross-linked sets of data-sorting and regularization methods. Three typical data selection and treatment methods are compared: iterative discarding of the most dependent data, monitoring singular value changes during the data reduction process, and zero padding in the patch holography technique. To test the regularization method for inverse conditioning, which is used together with the data selection method, the Tikhonov method, Bayesian regularization, and the data compression method are compared. The inverse equivalent source method is chosen as the holography method, and a numerical test is conducted with a point-excited thin plate. The simulation results show that selecting hologram points using the effective independence method, combined with regularization via compressed sensing, significantly reduces the reconstruction error and enhances the modal assurance criterion value. The experimental results also support the proposed best practice for inverting underdetermined hologram data by integrating the NAH data selection and regularization techniques. Full article

This work presents a robust box-constrained nonlinear least-squares algorithm for accurately fitting the Jones–Wilkins–Lee (JWL) equation of state parameters, which describes the isentropic expansion of detonation products from high-energy materials. In the energetic material literature, there are plenty of methods that address this problem, and in some cases, it is not fully clear which method is employed. We provide a fully detailed numerical framework that explicitly enforces Chapman–Jouguet (CJ) constraints and systematically separates the contributions of different terms in the JWL expression. The algorithm leverages a trust-region Gauss–Newton method combined with singular value decomposition to ensure numerical stability and rapid convergence, even in highly overdetermined systems. The methodology is validated through comprehensive comparisons with leading thermochemical codes such as CHEETAH 2.0, ZMWNI, and EXPLO5. The results demonstrate that the proposed approach yields lower residual fitting errors and improved consistency with CJ thermodynamic conditions compared to standard fitting routines. By providing a reproducible and theoretically based methodology, this study advances the state of the art in JWL parameter determination and improves the reliability of energetic material simulations. Full article

We investigate an inverse problem involving source and damping term with variable-exponent nonlinearities. We establish adequate conditions on the initial data for the decay of solutions as the integral overdetermination approaches zero over time within an acceptable range of variable exponents. This class of inverse problems, where internal terms such as source and damping are to be determined from indirect measurements, has significant relevance in real-world applications—ranging from geophysical prospecting to biomedical engineering and materials science. The accurate identification of these internal mechanisms plays a crucial role in optimizing system performance, improving diagnostic accuracy, and constructing predictive models. Therefore, the results obtained in this study not only contribute to the theoretical understanding of nonlinear dynamic systems but also provide practical insights for reconstructive analysis and control in applied settings. The asymptotic behavior and decay conditions we derive are expected to be of particular interest to researchers dealing with stability, uniqueness, and identifiability in inverse problems governed by nonstandard growth conditions. Full article

Given the growing complexity and variability of application scenarios, coupled with increasing operational demands, unmanned aerial vehicles (UAVs) are prone to faults. To enhance diagnosability and reliability in this context, this study proposes a causal diagnosability optimization strategy based on the Maximum Mean and Covariance Discrepancy (MMCD) metric and the Grey Wolf Optimization (GWO) algorithm. First, a qualitative assessment method for causal diagnosability is introduced, leveraging structural analysis to evaluate the detectability and isolability of faults. Next, residuals are generated using Minimal Structurally Overdetermined (MSO) sets, and a quantitative diagnosability assessment framework is developed based on the MMCD metric. This framework measures the complexity of diagnosability through the analysis of residual deviations under fault conditions. Finally, a diagnosability optimization technique utilizing the GWO algorithm is proposed. This approach minimizes diagnostic system design costs while maximizing its performance. Simulation results for a UAV structural model demonstrate that the proposed strategy achieves a 100% fault detection rate and fault isolation rate while reducing design costs by 70.59%. Full article

In robot navigation and manipulation, accurately determining the camera’s pose relative to the environment is crucial for effective task execution. In this paper, we systematically prove that this problem corresponds to the Perspective-3-Point (P3P) formulation, where exactly three known 3D points and their corresponding 2D image projections are used to estimate the pose of a stereo camera. In image-based visual servoing (IBVS) control, the system becomes overdetermined, as the six degrees of freedom (DoF) of the stereo camera must align with nine observed 2D features in the scene. When more constraints are imposed than available DoFs, global stability cannot be guaranteed, as the camera may become trapped in a local minimum far from the desired configuration during servoing. To address this issue, we propose a novel control strategy for accurately positioning a calibrated stereo camera. Our approach integrates a feedforward controller with a Youla parameterization-based feedback controller, ensuring robust servoing performance. Through simulations, we demonstrate that our method effectively avoids local minima and enables the camera to reach the desired pose accurately and efficiently. Full article

In this paper, we study the data completion problem for the Cauchy–Stokes equation in a cylindrical domain, $\mathsf{\Omega }$. Neumann and Dirichlet boundary conditions are prescribed on part of the overdetermined boundary, ${\mathsf{\Gamma }}_0$, and the goal is to complete the data on the other part of the boundary, ${\mathsf{\Gamma }}_a$. Here, ${\mathsf{\Gamma }}_0$ and ${\mathsf{\Gamma }}_a$ represent the side faces of the cylinder $\mathsf{\Omega }$. This problem is known to be ill-posed and is formulated as an optimal control problem with a regularized cost function. To directly approximate the missing data on ${\mathsf{\Gamma }}_a$, we employ the method of factorization of elliptic boundary value problems. This technique allows the factorization of a boundary value problem into a product of parabolic problems. It is successfully applied to the optimality system in this work, yielding new and significant results. Full article

We study inverse problems of identification of lower-order coefficients in a second-order parabolic equation. The coefficients are sought in the form of a finite series segment with unknown coefficients, depending on time. The linear case is also considered. Overdetermination conditions are the integrals over the boundary of a solution’s domain with weights. We focus on existence and uniqueness theorems and stability estimates for solutions to these inverse problems. An operator equation to which the problem is reduced is studied with the use of the contraction mapping principle. A solution belongs to some Sobolev space and has all generalized derivatives occurring into the equation summable to some power. The method of the proof is constructive, and it can be used for developing new numerical algorithms for solving the problem. Full article

The article proposes several classes of exact solutions to the Oberbeck–Boussinesq equations to describe convective flows of micropolar fluids. The possibility of using families of exact solutions for convective flows of classical incompressible fluids to micropolar incompressible fluids is discussed. It is shown that the three-dimensional Oberbeck–Boussinesq equation for describing steady and unsteady flows of micropolar fluids satisfies the class of Lin–Sidorov–Aristov exact solutions. The Lin–Sidorov–Aristov ansatz is characterized by a velocity field with a linear dependence on two spatial coordinates. These coordinates are called horizontal or longitudinal. The coefficients of the linear forms of the velocity field depend on the third coordinate (vertical or transverse) and time. The pressure field and the temperature field are described using quadratic forms. Generalizations of the Ostroumov–Birikh class are considered a special case of the Lin–Sidorov–Aristov family for describing unidirectional flows and homogeneous shear flows. An overdetermined system of Oberbeck–Boussinesq equations is investigated for describing non-homogeneous shear flows of non-trivial complex topology in 3D metric space. A compatibility condition is obtained in the Lin–Sidorov–Aristov class. Finally, a class of exact solutions with a vector velocity field that is nonlinear in part of the coordinates is presented in our analysis; such partially invariant solutions correspond to theoretical findings regarding symmetric/asymmetric properties of flow fields in solutions topology in a part of the existence appropriate for symmetry for the obtained invariant solutions. Full article

In the early stages of offshore low-permeability oil field development, it is crucial to ascertain the productivity of production wells to select high-production, high-quality reservoirs, which affects the design of the development plan. Therefore, accurate evaluation of well productivity is essential. Drill Stem Testing (DST) is the only way to obtain the true productivity of offshore reservoirs, but conducting DST in offshore oilfields is extremely costly. This article introduces a novel productivity evaluation method for horizontal wells in offshore low-permeability reservoirs based on an improved theoretical model, which relieves the limitations of traditional methods. Firstly, a new horizontal well productivity evaluation theoretical model is derived, with the consideration of the effects of the threshold pressure gradient, stress sensitivity, skin factor, and formation heterogeneity on fluid flow in low-permeability reservoirs. Then, the productivity profiles are classified based on differences in the permeability distribution of horizontal well sections. Thirdly, the productivity evaluation equation is modified by calculating correction coefficients to maximize the model’s accuracy. Based on the overdetermined equation concepts and existing DST productivity data, the derived correction coefficients in this paper are x₁ = 3.3182, x₂ = 0.7720, and x₃ = 1.0327. Finally, the proposed method is successfully applied in an offshore low-permeability reservoir with nine horizontal wells, increasing the productivity evaluation accuracy from 65.80% to 96.82% compared with the traditional Production Index (PI) method. This technology provides a novel approach to evaluating the productivity of horizontal wells in offshore low-permeability reservoirs. Full article

An efficient approximation is developed for the Laplacian operator by merging the advances of finite difference and finite element approximations. This approach is applicable to a general quadrilateral grid. The optimal coefficients for the approximation are computed using a pointwise optimization process. In this process, an overdetermined system is solved in the least-square sense using weighted polynomial approximation. The proposed algorithm is a vectorized procedure, keeping the computational time at a low level. The performance of this method is demonstrated on a model problem involving the numerical solution of a Poisson problem. Its true potential is evident when applied to moving boundary problems, which typically require a dynamic grid for efficient simulation. Within the framework of the proposed algorithm, we can compute the spatial discretization on the new grid quickly. This procedure is tested in the Stefan problem. For this, we give the simulation algorithm in detail utilizing the quadrilateral grid geometry. The performance is again demonstrated in a series of numerical experiments. Full article