Solution Of Problem Research Articles

Levy flight elitism-enhanced salp swarm algorithms for solving the ORPD problem

The optimal reactive power dispatch (ORPD) challenge is crucial for ensuring the efficient and reliable operation of power systems, hinging on the effective coordination of multiple devices.As a result, solving the ORPD problem involves tackling a complex nonlinear optimization challenge that demands advanced computational algorithms to determine the optimal solution. This article introduces an enhanced version of the modified algorithm, called L-E-SSA, which is inspired by the coordinated movement of a swarm led by a single member (salp swarm algorithm SSA), incorporating Levy Flight elitism, to effectively solve the ORPD problem. This study aims to reduce power losses (Ploss) and total voltage deviation (TVD) by optimizing the control variables. Numerical simulations are carried out on IEEE (30-bus) and IEEE (118-bus) power systems. To evaluate the performance and effectiveness of the modified algorithm (L-E-SSA). The results indicate that the L-E-SSA algorithm delivered strong performance and secured a competitive ranking through statistical analysis. Simulations demonstrate that the proposed method has the potential to be a highly effective solution for the ORPD problem.

Adaptive time step selection for spectral deferred correction

AbstractSpectral Deferred Correction (SDC) is an iterative method for the numerical solution of ordinary differential equations. It works by refining the numerical solution for an initial value problem by approximately solving differential equations for the error, and can be interpreted as a preconditioned fixed-point iteration for solving the fully implicit collocation problem. We adopt techniques from embedded Runge-Kutta Methods (RKM) to SDC in order to provide a mechanism for adaptive time step size selection and thus increase computational efficiency of SDC. We propose two SDC-specific estimates of the local error that are generic and do not rely on problem specific quantities. We demonstrate a gain in efficiency over standard SDC with fixed step size and compare efficiency favorably against state-of-the-art adaptive RKM.

Solution of certain problem with nonlocal boundary condition for one-dimensional wave equation

In this paper, we study a problem with nonlocal boundary condition for one-dimensional wave equation. To prove the solvability of the problem we construct biortogonal basis consisting of eigen- and adjoint-functions of not self adjoint operator.

The First Mean Value Theorem of integral in Perplex Plane

Perplex numbers are an extension of the real numbers, consisting of pairs of real numbers that form a commutative ring. This article considers the partial order structure of perplex numbers and discusses the concept of perplex interval. Based on the definition of integration of perplex functions of perplex variable, this article we investigate the first mean value theorem of integral in perplex plane which can significantly enrich the mathematical toolbox by providing essential methods for estimating and approximating perplex number functions. It also simplifies the solution of complex integral problems involving perplex numbers and fosters theoretical extensions by exploring the behavior of perplex number functions under various conditions. This, in turn, promotes the development of perplex calculus, enhancing the overall theoretical and practical framework of perplex number analysis. In physics, particularly in relativity, studying the first mean value theorem for perplex numbers can provide more precise methods for describing and estimating physical quantities, enhancing the application of hyperbolic numbers in these fields.

Jade Identification Using Ultraviolet Spectroscopy Based on the SpectraViT Model Incorporating CNN and Transformer

Jade is a highly valuable and diverse gemstone, and its spectral characteristics can be used to identify its quality and type. We propose a jade ultraviolet (UV) spectrum recognition model based on deep learning, called SpectraViT, aiming to improve the accuracy and efficiency of jade identification. The algorithm combines residual modules to extract local features and transformers to capture global dependencies of jade’s UV spectrum, and finally classifying jade using fully connected layers. Experiments were conducted on a UV spectrum dataset containing four types of jade (natural diamond, cultivated diamond (CVD/HPHT), and moissanite). The results show that the algorithm can effectively identify different types of jade, achieving an accuracy of 99.24%, surpassing traditional algorithms based on Support Vector Machines (SVM) and Partial Least Squares Discriminant Analysis (PLS_DA), as well as other deep learning methods. This paper also provides a reference solution for other spectral analysis problems.

Stable Difference Scheme for the Numerical Solution of the Source Identification Problem for Hyperbolic Equations

Stable Difference Scheme for the Numerical Solution of the Source Identification Problem for Hyperbolic Equations

Analytical investigation of porous medium effects on the flow of two micropolar fluids in a rotating annulus

Fluids with microstructures and microinertia play a vital role in microfluidics and nanfluidics system. One of such significant fluid is micropolar fluid. The characteristic behavior of micropolar fluid flow in conduit/pipe, etc. filled with porous medium helps us understand the flow behavior of biological fluids in porous media, groundwater flow in aquifiers, rotatory machines or viscometer. To understand such real-world problems, it is necessary to get into the mathematical model of such flow models. One such model with wide number of application is presented in this paper. This work investigated the flow of two micropolar fluids between the region formed by two concentric cylinders. Authors have considered inner cylinder to be at rest and outer cylinder rotating at a constant angular velocity. The region between two concentric cylinder is filled with an isotropic porous material. A slip condition at the outer wall and continuity conditions at interface of two fluids has been utilized to obtain an analytical solution for the proposed model. The numerical solution of the obtained solution for present problem is used to graphically analyze the motion of immisicble micropolar fluids rotating in an annulus filled with the porous medium. It is found that an outer cylinder has a notable influence on the flow behavior of immiscible micropolar fluids, contrary to the effect observed within the inner region. An analytical approach of this work not only helps us obtain precise results and analysis of the flow, but it also serves as a useful validation for future approximations within the scope of this work.

Physics-informed neural network solution for thermo-elastic cavity expansion problem

ABSTRACT This paper proposes a physics-informed neural network (PINN) to solve the thermo-elastic coupled cavity expansion problem under plane strain conditions. The solid is modelled as a linear thermo-elastic material, and cavity expansion is driven by a constant temperature and a radial displacement subjected to the inner cavity wall. Governing partial differential equations (PDEs) for the problem is firstly presented, and an analytical solution is available to help benchmark the PINN approach. Then, the PDEs are normalised into dimensionless forms and neural network details for solving the coupled PDEs are demonstrated. Finally, the performance of the PINN approach is shown by comparison with the analytical benchmark solution and it is found that the PINN can predict thermo-elastic cavity expansion behaviour with high accuracy. The PINN approach and the analytical solution can also serve as a benchmark for solving thermo-elastic coupled problems in geotechnical engineering by more advanced PINN.

Failed cases of collaborative innovation: when a castle turns into a tent

ABSTRACT Co-production is put forward as a potential solution for the many wicked problems governments face today. There is a gap in the literature, however, when it comes to failed cases. Little is known about projects that never get launched or implemented. Secondly, there is an emphasis on knowledge about setting-up and implementing projects. Yet, studies that consider the sustainability of collaborative innovation projects are scarce. This article delves into the elements that make projects of collaborative innovation fail and studies this throughout the innovation cycle. It builds on the data of 32 in-depth interviews with experienced practitioners .

A frequency-independent absorption function surrogate for perfectly matched layer in exterior acoustics

In many engineering applications, the solution of acoustic wave problems in the infinite domain is required over a broad frequency range with densely sampled increments. In order to achieve efficient numerical simulations via a spatial discretization, e.g. finite element method, additional artificial absorbing boundaries are necessary to truncate the computational domain into appropriate bounded sizes. One of the most commonly used non-reflecting techniques to attenuate propagating waves is known as the perfectly matched layer. However, the system matrices arising from the finite element treatment of the Helmholtz equation in the absorbing layers are frequency-dependent, implying that they must be formed and inverted at each frequency of interest. Such a procedure is rather troublesome for frequency sweeps. To address this, a surrogate of perfectly matched layers is proposed, which enables the corresponding system matrices to be independent of the frequency. Moreover, it avoids the use of a relatively large computational domain and relatively thick enclosed layers at low frequencies, thus improving the ability of perfectly matched layers across the entire frequency range. After that, an adaptive projection-based model order reduction scheme is further developed to reduce the computational complexity of exterior acoustic systems. A robust error indicator based on the relative error of two constructed reduced order models is accordingly introduced. The performance of the present solution framework is discussed and compared with other implementation strategies, in the context of multi-frequency solution of two-dimensional test models with single or multiple scatterers.

Calibration-Based ALE Model Order Reduction for Hyperbolic Problems with Self-Similar Travelling Discontinuities

We propose a novel Model Order Reduction framework that is able to handle solutions of hyperbolic problems characterized by multiple travelling discontinuities. By means of an optimization based approach, we introduce suitable calibration maps that allow us to transform the original solution manifold into a lower dimensional one. The novelty of the methodology is represented by the fact that the optimization process does not require the knowledge of the discontinuities location. The optimization can be carried out simply by choosing some reference control points, thus avoiding the use of some implicit shock tracking techniques, which would translate into an increased computational effort during the offline phase. In the online phase, we rely on a non-intrusive approach, where the coefficients of the projection of the reduced order solution onto the reduced space are recovered by means of an Artificial Neural Network. To validate the methodology, we present numerical results for the 1D Sod shock tube problem, for the 2D double Mach reflection problem, also in the parametric case, and for the triple point problem.

Efficient computation of magnetic polarizability tensor spectral signatures for object characterisation in metal detection

PurposeMagnetic polarizability tensors (MPTs) provide an economical characterisation of conducting magnetic metallic objects and their spectral signature can aid in the solution of metal detection inverse problems, such as scrap metal sorting, searching for unexploded ordnance in areas of former conflict and security screening at event venues and transport hubs. In this work, the authors aim to discuss methods for efficiently building large dictionaries for classification approaches.Design/methodology/approachPrevious work has established explicit formulae for MPT coefficients, underpinned by a rigorous mathematical theory. To assist with the efficient computation of MPTs at differing parameters and objects of interest, this work applies new observations about the way the MPT coefficients can be computed. Furthermore, the authors discuss discretisation strategies for hp-finite elements on meshes of unstructured tetrahedra combined with prismatic boundary layer elements for resolving thin skin depths and using an adaptive proper orthogonal decomposition (POD) reduced-order modelling methodology to accelerate computations for varying parameters.FindingsThe success of the proposed methodologies is demonstrated using a series of examples. A significant reduction in computational effort is observed across all examples. The authors identify and recommend a simple discretisation strategy and improved accuracy is obtained using adaptive POD.Originality/valueThe authors present novel computations, timings and error certificates of MPT characterisations of realistic objects made of magnetic materials. A novel postprocessing implementation is introduced and an adaptive POD algorithm is demonstrated.

PUBLIC ADMINISTRATION UNDER MILITARY THREATS: UKRAINIAN EXPERIENCE OF ADAPTING TO CRISIS SITUATIONS

The article examines the Ukrainian experience of public administration under conditions of military threat as of 2022-2024. The key challenges faced by Ukraine during the full-scale war are analyzed, including the destruction of critical infrastructure and the need to ensure uninterrupted provision of public services. Special attention is paid to the digitization of public administration, which played a decisive role in maintaining the stability of state institutions. The role of the «Action» platform and other innovative solutions that enabled interaction between citizens and the government in crisis conditions is described. The impact of decentralization on the ability of local authorities to respond to the challenges of war has been studied. The interaction with international partners within the framework of the SIGMA program, which is aimed at providing support in the reform of public administration with a course towards European integration, is characterized. A comparative analysis of the Ukrainian experience with other European countries that faced large-scale crises was carried out, and unique aspects of the Ukrainian model of adaptation were revealed. The article analyzes strategies for the restoration and modernization of the state administration of Ukraine in crisis conditions. Attention is focused on the interaction between the state and corporate sectors to maintain economic activity even in conditions of active hostilities. The role of business relocation to safer regions and the influence of state support on the stabilization of the labor market and the economy are outlined. Programs aimed at restoring infrastructure and vital services in cooperation with international partners are mentioned. The experience of implementing temporary solutions to ensure the basic needs of the population is described. It examines the impact of international aid and financial support through IMF and World Bank programs that helped maintain budget stability and avoid economic collapse. The perspectives of public administration during Ukraine's integration into European structures and further strengthening of public administration are highlighted. Special attention is paid to the prospects for the development of public administration in the post-war period, the solution of socio-economic problems, the restoration of infrastructure and the attraction of investments. Strategic directions for reforming public administration for the future are proposed, taking into account the experience of the war and cooperation with international institutions.

Turn-Taking in Political Interviews and Its Impact on Building Government Credibility

Television political inquiry is conducted through question-and-answer exchanges with host and government officials on prominent livelihood issues, which helps to improve the efficiency of government governance. Interview participants’ identity, communicative intention, power, and contextual factors have a significant impact on the discourse choices of both parties. This research clarifies the mechanism by which communicators mobilize appropriate discourse strategies to promote the solution of social problems. It adopts qualitative research method and conversation analysis to interpret interview participants’ talk-in-interaction and discourse strategies in “Ask Government Affairs of Shandong”. Research finds that adjacency pairs in political interview perform social behaviors such as greetings, requests, suggestions, apologies, acknowledgement. Interview participants’ turn-taking is divided into claiming for the turn, holding the turn, and giving up the turn. Discourse strategies such as insertion, interruption, and repetition are adopted to claim for the turn. Discourse markers and conversation repair are applied in communicators’ turn-holding stage. Communicators adopt explicit nominations, vague job designations, and silence strategies to give up the turn. Clear, accurate, and highly relevant official responses are conducive to projecting a responsible government image and improving government credibility. The phenomenon of avoidance, hesitation, and pause in official response is likely to cause the masses to question government officials’ work capability, which is not conducive to establishing a positive and trustworthy government image. Suggestions for optimizing the process setting of political interview and official responses are provided to enhance the effect of political enquiry.

An Improved Two‐Step Method for Inverse Eigenvalue Problems

ABSTRACTIn this article, we investigate the numerical solutions of the inverse eigenvalue problem (IEP). Motivated by the techniques of Aishima in 2018, we propose here an improved two‐step method for the IEP. Compared with other existing methods, the proposed method has higher convergence order and/or requires less operations. Under the assumption that the relative generalized Jacobian matrices at a solution are nonsingular, the proposed method is proved to be convergent with cubic root‐convergence rate. Numerical examples demonstrate the effectiveness of the improved method.

On Hidden Rank Deficiency in MCR Problems

ABSTRACTPure component decomposition problems in chemometrics can be classified into rank‐regular and rank‐deficient problems. Rank‐deficient problems are characterized by a spectral data matrix that has a lower rank than the number of chemical species. However, it is possible that there exists rank‐regular factorization of the spectral data matrix, but none of these solutions can be interpreted chemically, and only a solution of the MCR problem with rank deficiency is chemically meaningful. Then we say that the underlying problem suffers from a hidden rank deficiency. In this paper, MCR problems with hidden rank deficiency are introduced and analyzed with several examples for problems of rank 2 and rank 3. The area of feasible solutions is determined with the help of additional constraints on the solution.

Methodical and algorithmic aspects of mathematical modeling of a screw aircraft power plant

The article describes the solution of a scientific problem that consists in expanding the functionality of the program “Calculation of the traction-economic and mass-specific characteristics of the power plant and aircraft motion parameters” through the introduction of additional algorithms and mathematical models for calculating the altitude-speed characteristics of screw aircraft power installations. At the same time, an internal calculation of the aircraft propeller thrust is used according to experimental aerodynamic coefficients, which makes it possible to increase the efficiency and reliability of complex theoretical studies of power plants of various types as part of aircraft at the stage of external design. A description is given of the developed algorithms: an algorithm for converting power on the output shaft of a gas turbine engine into thrust of an aircraft power plant; a mathematical model of a propeller that provides calculation of its thrust from experimental aerodynamic coefficients; an algorithm for determining the thrust of the power plant, taking into account the compressibility of the air and the interaction of the propeller and the elements of the airframe of the aircraft. Some features of the mathematical modeling of an aircraft propeller are revealed, in particular, the principle of propeller control by influencing the blade angle and rotational speed depending on the aircraft flight speed and a method for constructing the field of aerodynamic characteristics of an aircraft propeller in a wide range of blade angle and speed coefficient. In conclusion, the results of verification of the modified program are presented with an analysis of the obtained altitude-speed characteristics.

Achromatic solutions of the color constancy problem: the Helmholtz–Kohlrausch effect explained

For given tristimulus values X, Y, Z of the object with reflectance ρ(λ) viewed under an illuminant S(λ) with tristimulus values X0, Y0, Z0, an earlier algorithm constructs the smoothest metameric estimate ρ0(λ) under S(λ) of ρ(λ), independent of the amplitude of S(λ). It satisfies a physical property of ρ(λ), i.e., 0≤ρ0(λ)≤1, on the visual range. The second inequality secures the condition that for no λ the corresponding patch returns more radiation from S(λ) than is incident on it at λ, i.e., ρ0(λ) is a fundamental metameric estimate; ρ0(λ) and ρ(λ) differ by an estimation error causing perceptual variables assigned to ρ0(λ) and ρ(λ) under S(λ) to differ under the universal reference illuminant E(λ)=1 for all λ, tristimulus values X E , Y E , Z E . This color constancy error is suppressed but not nullified by three narrowest nonnegative achromatic response functions A i (λ) defined in this paper, replacing the cone sensitivities and invariant under any nonsingular transformation T of the color matching functions, a demand from theoretical physics. They coincide with three functions numerically constructed by Yule apart from an error corrected here. S(λ) unknown to the visual system as a function of λ is replaced by its nonnegative smoothest metameric estimate S0(λ) with tristimulus values made available in color rendering calculations, by specular reflection, or determined by any educated guess; ρ(λ) under S(λ) is replaced by its corresponding color R0(λ) under S0(λ) like ρ(λ) independent of the amplitude of S0(λ). The visual system attributes to R0(λ)E(λ) one achromatic variable, in the CIE case defined by y(λ)/Y E , replaced by the narrowest middle wave function A2(λ) normalized such that the integral of A2(λ)E(λ) over the visual range equals unity. It defines the achromatic variable ξ2, A(λ), and ξ as described in the paper. The associated definition of present luminance explains the Helmholtz–Kohlrausch effect in the last figure of the paper and rejects CIE 1924 luminance that fails to do so. It can be understood without the mathematical details.

Riemann–Hilbert problem and soliton solutions with their asymptotic analysis for the focusing nonlocal Hirota equation with step-like initial data

The Riemann–Hilbert (RH) problem is developed to study the Cauchy problem of focusing space symmetric nonlocal Hirota (fsNH) equation with step-like initial data. Firstly, we analyze the characteristics of the Jost solutions and spectral functions, including analyticity, symmetry, and asymptotics as k→∞ and k→0. Then, we discuss three cases of zero point distributions of the spectral functions, and derive the expressions of spectral functions by constructing the special analytic functions and establishing the scalar RH problem. Furthermore, the constraint relations among the zeros of the spectral functions are analyzed. Next, the corresponding RH problem equipped with residual and singularity conditions is successfully derived. These singularity conditions are then transformed into a general residue condition, which reduces the problem of solving the RH problem with reflection-less potential to solving a system of algebraic equations. Ultimately, the corresponding soliton solutions of the fsNH equation and their asymptotics are derived from the solution of the RH problem.

Fractional Viscoelastic Analysis of Transversely Isotropic Surrounding Rock Along Shallow Buried Elliptical Tunnel

ABSTRACTThis study introduces the fractional order Merchant model to analytically solve the stress and displacement fields of the transversely isotropic viscoelastic surrounding rock along shallow elliptical tunnels. First, the stress and displacement solutions of fractional order viscoelastic and transversely isotropic half planes under arbitrary loads are obtained using the Laplace transform and the elastic‐viscoelastic correspondence principle. Second, based on the above half plane solution and the solution of the deep buried elliptical tunnel problem, the Schwarz alternating method is introduced to obtain the analytical solution of the shallow buried elliptical tunnel. A MATLAB program is developed, and the accuracy of the theory and program in this study is verified by comparing it with the results of ABAQUS. Finally, the effects of transversely isotropic parameters, tunnel burial depth, and viscoelastic parameters on the stress and displacement of tunnel surrounding rock are analyzed.