Solution Of Problem Research Articles

A Reduced Order Schwarz Method for Nonlinear Multiscale Elliptic Equations Based on Two-Layer Neural Networks

Neural networks are powerful tools for approximating high dimensional data that have been used in many contexts, including solution of partial differential equations (PDEs). We describe a solver for multiscale fully nonlinear elliptic equations that makes use of domain decomposition, an accelerated Schwarz framework, and two-layer neural networks to approximate the boundary-to-boundary map for the subdomains, which is the key step in the Schwarz procedure. Conventionally, the boundary-to-boundary map requires solution of boundary-value elliptic problems on each subdomain. By leveraging the compressibility of multiscale problems, our approach trains the neural network offline to serve as a surrogate for the usual implementation of the boundary-to-boundary map. Our method is applied to a multiscale semilinear elliptic equation and a multiscale $p$-Laplace equation. In both cases we demonstrate significant improvement in efficiency as well as good accuracy and generalization performance.

An improved golden jackal optimization algorithm for combined economic emission dispatch problems

In this research paper, a new improved golden jackal optimization (IGJO) algorithm is applied to address the combined economic emission dispatch (CEED) problem, along with various thermal generator constraints such as valve point loading (VPL) effect, generator limits (GL) in power system. The hunting behavior of the golden jackals is mimicked in the golden jackal optimization (GJO) algorithm. The main aim of the CEED problem is to find the best optimal generation scheduling while minimizing both fuel cost and emission besides meeting the different power system constraints. The original GJO algorithm faces challenges when dealing with high-dimensional optimization problems, as it tends to get trapped in local optima. To address this issue the opposition-based learning (OBL) method was adopted in this GJO algorithm to obtain the global optimal solution and ensure enhanced performance in finding the solution for the CEED problems. To assess the competitiveness of the IGJO algorithm, it is used for various CEED test problems available in the literature, and results are contrasted with other recent heuristic optimization algorithms. Simulation results show that the proposed IGJO performs more effectively than the other compared algorithms in terms of solution quality, and robustness.

A new identification of Lagrange multipliers to study solutions of nonlinear Caputo–Fabrizio fractional problems

This research aims to provide a new identification of Lagrange multipliers using a novel hybrid method based on the Khalouta transform method and the variational iteration method and to study the solutions of nonlinear fractional problems. This method is called Khalouta variational iteration method (KHVIM). The fractional derivative is considered in Caputo–Fabrizio sense. The uniqueness and convergence results are investigated using Banach fixed point theorem. The results are obtained in the form of successive approximations corresponding to the proposed problem. To demonstrate the accuracy and effectiveness of the proposed method, three different nonlinear fractional partial differential equations are provided. Approximate solutions of the fractional equations were obtained. These solutions quickly converged to exact solutions with lower computational cost. Furthermore, the method used in this study is more generalized and allows our results to be more extensive and cover several new and existing fractional problems in the literature.

Solution of Inverse Geometric Problems Using a Non-Iterative MFS

Solution of Inverse Geometric Problems Using a Non-Iterative MFS

How Does a Decision-Making Tool Enhance Spent Mushroom Substrate Valorization into Polysaccharides?

In mushroom farming, one kilogram harvested results in about five kilograms of spent mushroom substrate (SMS), posing an environmental management challenge. As an in-tune work with the concepts of circular economy, cleaner production, and waste minimization, this study has developed a mathematical model than analyzes the valorization potential of SMS through polysaccharide production. The in-depth mathematical model is based on a system dynamics approach, which explains the interactive interplay amongst the production process, related costs, energy consumption, and caused emissions. The model has been developed in a generic way. Meaning that it can be re-adjusted flexibly for a different cleaner production process. A user-friendly interface has been developed. Users can easily maneuver around the variables within the model that offers instantaneous insight into the environmental and economic impacts of SMS valorization. This interface was later integrated into an educational context to serve as an interactive decision-making tool for cleaner production modelling. The main purpose of the developed tool was to favor understanding of causalities between production chains, energy consumption, labor, emissions, and expenses. This tool has been tested on master’s degree students in a cleaner production course. Survey results show that 82% of students report the need to incorporate similar decision-making tools in their learning curriculum. In sum, the application of system dynamics to the valorization of SMS does not only present an attractive solution for this environmental problem but also shows great potential in setting educational backgrounds for an interactive and close-to-life learning process. It is recommended to develop more interactive tools available for students.

Do nothing, do minimum or do something? Why public project appraisals “always” recommend large projects

PurposeIn the project initiation phase, an appraisal is needed to clarify the strategic problem and alternative solutions. Full-scale construction projects and simple solutions (do-minimum alternatives) should be assessed. The do-nothing alternative is the baseline for the appraisal and an option in itself. The paper explores the role of do-nothing and do-minimum alternatives in public project appraisal, which may significantly impact the attractiveness of a construction project.Design/methodology/approachThe paper presents an empirical study from Norway, which requires external quality assurance (QA) of early project appraisals. The data include an extensive document review of 112 projects and interviews with 41 experts involved in the appraisal processes.FindingsOf 112 appraisals, 110 recommended a major construction project, including cases where the benefits and value were low or uncertain. The do-nothing alternative was generally included as a reference but not treated as a viable option. Do-minimum alternatives were often not explored. By contrast, the external QA reports recommended do-nothing or do-minimum in 28 cases. Interestingly, although political decision-makers rarely reject projects, they may put them on hold indefinitely, implying that the actual outcome in many cases is still do-nothing.Originality/valueThe paper addresses a topic that has been understudied in the literature. The findings contribute to the broader literature on project initiation processes, project appraisal and how to reduce the risk of bias and manipulation in appraisals.

A neural network inverse problem solution for a MIMO magnetic levitation actuator

A multiple-input and multiple-output planar actuator is proposed, which utilizes mechanically driven stator magnet arrays to levitate a permanent magnet mover. A state of levitation and actuation is obtained by mechanically altering the orientation of the stator magnets to control the forces and torques on the mover. A challenge for the design and control of the actuator is inverting the relationship between the force and stator magnet rotation angles, as there is no closed-form analytical solution. In this study, a feed-forward neural network is applied to model the forward relation between stator magnet angle input and a force and torque output to reduce the forward computation time for the design process and for error estimation in real-time applications. Additionally, the neural network is considered for inverting the solution for a motion profile sampled at 1000 Hz. The developed forward model is able to calculate the forces and torques on the mover a factor 10 faster than the equivalent charge or Fourier model with an absolute error of 3 mN and 0.1 mNm for the forces and torques, respectively, and a feed-forward neural network is able to accurately learn an inverse solution for small motion profiles.

Two-Phase Fuzzy Real-Time Approach for Fuzzy Demand Electric Vehicle Routing Problem with Soft Time Windows

Environmental concerns have called for several measures to be taken within the logistics and transportation fields. Among these measures is the adoption of electric vehicles instead of diesel-operated vehicles for personal and commercial-delivery use. The optimized routing of electric vehicles for the commercial delivery of products is the focus of this paper. We study the effect of several practical challenges that are faced when routing electric vehicles. Electric vehicle routing faces the additional challenge of the potential need for recharging while en route, leading to more travel time, and hence cost. Therefore, in this work, we address the issue of electric vehicle routing problem, allowing for partial recharging while en route. In addition, the practical mandate of the time windows set by customers is also considered, where electric vehicle routing problems with soft time windows are studied. Real-life experience shows that the delivery of customers’ demands might be uncertain. In addition, real-time traffic conditions are usually uncertain due to congestion. Therefore, in this work, uncertainties in customers’ demands and traffic conditions are modeled and solved using fuzzy methods. The problems of fuzzy real-time, fuzzy demand, and electric vehicle routing problems with soft time windows are addressed. A mixed-integer programming mathematical model to represent the problem is developed. A novel two-phase solution approach is proposed to solve the problem. In phase I, the classical genetic algorithm (GA) is utilized to obtain an optimum/near-optimum solution for the fuzzy demand electric vehicle routing problem with soft time windows (FD-EVRPSTW). In phase II, a novel fuzzy real-time-adaptive optimizer (FRTAO) is developed to overcome the challenges of recharging and real-time traffic conditions facing FD-EVRPSTW. The proposed solution approach is tested on several modified benchmark instances, and the results show the significance of recharging and congestion challenges for routing costs. In addition, the results show the efficiency of the proposed two-phase approach in overcoming the challenges and reducing the total costs.

Weak solutions of a nonlinear degenerate fourth‐order parabolic equation via the topological degree method

In this paper, we study the existence of weak solutions for the nonlinear parabolic problem associated with the following fourth‐order equation, under Navier boundary conditions: where is a bounded domain. Under some appropriate assumptions, we obtain the existence of a weak solution for the above problem by using the topological degree theory for operators of the type , in the framework space .

Environmental Management Plan and Water Reuse Waste in a Metallurgical Company, Peru, 2023

The main objective of the research was to determine how the Environmental Management Plan improves the reuse of wastewater generated by a steel company, Pisco 2023. The approach of the research was with the methodology of applied type and experimental design, proposed the solution of a practical problem through the application of the environmental management plan, and the intervention with the pre and post-test evaluations. The population and sample consisted of 15 records (5 weeks pretest January-March and 5 weeks posttest May-July 2023). From the sample, the 15 paired means (pretest and post-test) were determined. Data collection was conducted using documentary analysis techniques and instruments: checklist and registration sheets. Statistical analysis with SPSS 22 software determined that implementation of the environmental management plan improved the wastewater reuse rate from 6.41 to 15.73. It was determined that the implementation of the environmental management plan significantly improved the reuse of wastewater generated by a steel company, Pisco 2023.

Numerical solution of eigenvalue problems for a compact integral operator with Green’s kernels

Numerical solution of eigenvalue problems for a compact integral operator with Green’s kernels

Convergence and error estimates of a penalization finite volume method for the compressible Navier–Stokes system

Abstract In numerical simulations a smooth domain occupied by a fluid has to be approximated by a computational domain that typically does not coincide with a physical domain. Consequently, in order to study convergence and error estimates of a numerical method domain-related discretization errors, the so-called variational crimes, need to be taken into account. In this paper we apply the penalty approach to control domain-related discretization errors. We embed the physical domain into a large enough cubed domain and study the convergence of a finite volume method for the corresponding domain-penalized problem. We show that numerical solutions of the penalized problem converge to a generalized, the so-called dissipative weak, solution of the original problem. If a strong solution exists, the dissipative weak solution emanating from the same initial data coincides with the strong solution. In this case, we apply a novel tool of the relative energy and derive the error estimates between the numerical solution and the strong solution. Extensive numerical experiments that confirm theoretical results are presented.

Overlapping finite elements for the Navier-Stokes equations

The purpose of this paper is to investigate the performance of a certain family of low-order quadrilateral finite elements in the solution of the stationary Navier-Stokes equations governing incompressible fluid flows. These finite elements are derived from the ‘overlapping finite elements’, first developed for the solution of problems in solid mechanics [5,9,48] and incorporate features of both meshfree and traditional finite element methods. One of their most remarkable properties is the insensitivity to mesh distortions. Also, since the Shepard functions are replaced by a suitable interpolation, the resulting basis functions are entirely polynomial, which allows the numerical integration of the weak forms to be performed with few integration points [6,49]. We also discuss the theoretical reasons for the stability of the solutions, that is, the absence of spurious pressure modes, and show that the proposed discretization scheme passes the relevant inf-sup test.

Gas Sorption Characterization of Porous Materials Employing a Statistical Theory for Bethe Lattices.

In the present work, a recently developed statistical theory for adsorption and desorption processes in mesoporous solids, modeled by random Bethe lattices, has been applied to obtain pore size distributions and interpore connectivity from sorption isotherms in real random porous materials, employing a robust and validated methodology. Using the experimental adsorption-desorption N2 isotherms at 77.4 K on Vycor glass, a porous material with random pore structure, we demonstrate the solution of the inverse problem resulting in extracted pore size distribution and interpore connectivity, notably different from the predictions of earlier theories. The results presented are corroborated by the analysis of 3D digital images of reconstructed Vycor porous glass, showing excellent agreement between the predictions of geometric analysis and the new statistical theory.

A new hiPSC-based viral expression system to study virus host-cell interaction in hiPSC-derived cardiomyocytes

Abstract Coxsackievirus B3 (CVB3) belongs to the Picornaviridae family and is a member of the enterovirus genus. CVB3 is the most frequently detected pathogen in viral myocarditis, which leads to acute heart infections in 20-40% of cases and to dilated cardiomyopathy (DCM) in cases of prolonged viral persistence. Complex arrhythmias and sudden deaths due to CVB infections have also been reported, particularly in newborns and children. Observed arrhythmias include bradycardia, AV block and junctional ectopic tachycardia, suggesting that in addition to the functioning myocardium, the pacemaker cells and cardiac conduction system may also be impaired by CVB3 infection. The symptomatic phenotype is highly variable and depends on unclear host factors. It ranges from inconspicuous inflammation and rapid healing to acute congestive heart failure or viral persistence with progressive chronic disease. Despite the increasing and profound knowledge about viral myocarditis, it is still a challenge to identify further host factors that contribute to acute and chronic myocarditis, as science lacks sensitive and controllable disease models. The presented project shows the generation of a controlled, inducible virus-expressing hiPSC line that provides a solution for the beforementioned problems. The new human induced pluripotent stem cell line (hiPSC) i can be used to carry out virologic experiments in a controlled manner and without risk to the user. For this purpose, the modified and non-infectious genome of the enterovirus Coxsackievirus B3 (CVB3) is stably integrated into the genome of a wild-type hiPSC line. The CVB3 genome to be stably integrated was modified to prevent the formation of functional capsids by a DVP0 mutation. In addition, the 3'UTR and 5'UTR regions of the CVB3 genome were removed, which prevents uncontrolled self-replication of viral RNA. As a result, work with this CVB3DVP0-UTR genome is classified as S1 compliant. The expression of the CVB3DP0-UTR virus genome can be controlled by adding doxycycline to the cell culture medium by a TeT-On System. The transfected cells are then cultivated as clones and tested for virus expression. The dose-dependent CVB3DVP0 expression is verified using qPCR and FACS after 1 day of doxycycline application in the cell culture medium. Clones isolated and positively tested for CVB3 expression are used to carry out initial experiments on the interaction of the expressed viral proteins with the cell. Particular focus is placed on the induction of cell death, remodelling of the cytoskeleton and increase of reactive oxygen species (ROS) in mitochondria after CVB3DVP0-UTR induction in order to validate the cell system for application. Differentiation of the CVB3-expressing hiPSC-line into cardiomyocytes with subsequent virus induction results in the elevation of mitochondrial ROS, degradation of the cytoskeleton and arrhythmic behaviour of the cells.

Round-trip hub location problem

In this paper, we introduce a novel network design for the Hub Location Problem, inspired by the round-trip structure commonly used by transport service providers. Our design integrates spoke nodes assigned to a central hub node, creating round-trips where the hub node serves as the starting point, visits all assigned spoke nodes, and returns to the hub. To enhance transportation services and provide additional redundancy, we introduce a new type of nodes called runaway nodes to the network. The motivation for this research arises from two real-life cases encountered during consultancy projects, underscoring the necessity for an optimized network design in transportation services. To address the proposed problem, we introduce a mixed-integer linear programming (MIP) mathematical model. However, due to the problem's complexity, the feasibility of the MIP model is limited to small-scale instances. To tackle medium and large-scale instances, we introduce two hyper-heuristic approaches based on reinforcement learning. These hyper-heuristic approaches harness the power of reinforcement learning to guide the selection of low-level heuristics and improve solution quality. We conduct extensive computational experiments to evaluate the efficiency and effectiveness of the proposed approaches. The results of our experiments affirm the efficiency of the proposed hyper-heuristic approaches, showcasing their ability to discover high-quality solutions for the Hub Location Problem.

Modulation of Intermolecular Interactions in Organic Emitters for Highly Efficient Organic Light-Emitting Diodes.

The adverse aggregated-caused quenching (ACQ) problem of most electroluminescent materials existing in highly doped thin films is one of the key factors impeding the commercialization ofhigh-efficiency organic light-emitting diodes (OLEDs) panel. Whereas, by delicately constructing and modulating moderate intermolecular interactions, some aggregates have been demonstrated to present distinct luminescent properties such as tunable emission spectra, improved photoluminescence quantum yields, different emission mechanism and enhanced horizontal transition dipole ratio (Θ) of emitting layer, providing feasible solution for ACQ problem. The luminescence from newly generated emissive state in aggregates is different from the traditional "isolated" molecules in organic electronics and will possess novel properties and applications. Herein, we summarize the different types of intermolecular interactions within emitter aggregates exhibiting distinct luminescent mechanisms, as well as their effects on photoluminescent and electroluminescent properties, offering reliable reference for the advancementof highly efficient OLEDs utilizing aggregated emitters.

Cattaneo–Christov heat and mass flux model and thermal enhancement in three‐dimensional MHD Jeffrey hybrid nanofluid flow over a bi‐directional stretching sheet with convective boundary conditions

AbstractInspired by the progressive relaxation characteristics of the Jeffrey model and its applied advantages in the rheological modeling of various dynamic fluids, the current study is focused to investigate the heat and mass transfer of magnetohydrodynamic (MHD) Jeffrey hybrid nanofluid flow over bi‐directional stretching sheet with convective boundary conditions. Additionally, the Cattaneo–Christov model of heat and mass flux is employed to take into consideration the time relaxation effects. The energy and concentration equation are taken into account to explore the effects of thermophoresis and Brownian motion. Homotopy analysis method (HAM) is employed for the solution of the current problem. Solution methodology is verified by comparing present results with those already published in open literature. The physical aspects of obtained graphical and numerical results are explained in detail to justify acquired trends. From the investigation, it is inferred that the magnetic and viscoelastic factors have a reducing influence on the flow profile along primary and secondary directions, while the stretching parameter has an increasing behavior on the flow profile in the secondary direction. Furthermore, the Brownian motion, magnetic parameter, and thermophoretic parameter have an escalating behavior on thermal distribution; however, the Brownian motion has a declining consequence on the concentration profile. The larger Biot number heightens the thermal and concentration distributions.

A 3UPS/S Spherical Parallel Manipulator Designed for Robot-Assisted Hand Rehabilitation after Stroke

Hand dysfunction is a common symptom in stroke patients. This paper presents a robotic device which assists the rehabilitation process in order to reduce the need of physical therapy, i.e., a 3UPS/S parallel robotic device is employed for repetitive robot-assisted rehabilitation. Euler angle representation was used to solve the robot’s inverse kinematics. The robot’s joint space and rotational workspace were determined for two scenarios. In the first scenario, the workspace was obtained considering the actuator’s stroke limitations, while in the second scenario, the workspace was determined by adding a second condition, i.e., the range of motion of the spherical joints. Singularity analysis was performed using the geometric algebra approach. The robot was manufactured using additive manufacturing technology. The solution of the inverse kinematic problem was employed to control the robot. The robot can perform a full range of motion during wrist ulnar deviation and radial deviation motions, with the exception of limited wrist flexion and extension motions. The robot has singular configurations within its workspace. Although the spherical joints have roles in reducing the workspace, the primary causes are actuator selection, radii of the base and moving platforms, and the length of the central leg. These factors can be considered to improve the workspace. Singularity can be avoided by carefully selecting the rotation of the moving platform about the Z-axis and avoiding same leg lengths.

Higher-Order Radial Hadamard Directional Derivatives and Applications to Set-Valued Equilibrium Problems

In this paper, we first introduce the higher-order lower and upper radial Hadamard directional derivatives for set-valued maps, which can capture the global information of concerning maps, and discuss the relationships with other existed higher-order derivatives. Second, based on the introduced derivatives, we establish optimality conditions for Henig efficient solutions of a set-valued equilibrium problem with constraints. Particularly, the optimality conditions hold in the case where the derivatives of objective and constraint functions are separated. Finally, we give some duality theorems for a mixed type of primal-dual set-valued equilibrium problem. The main results of this paper are illustrated by several concrete examples.