Accurate Solutions Research Articles

Lagrangian relaxation-based approaches for cooperative location and assignment of emergency responders

Efficient fire response and the coordination of various fire vehicles are paramount for delivering optimal services and conducting effective rescue operations. This study explores the challenges of cooperative station location and vehicle assignment, focusing on the synergistic dispatch of fire vehicles from multiple stations. It highlights that the response time of the last arriving vehicle, crucial for forming a complete and effective response unit, is a critical determinant in the overall success of fire rescue operations. The primary objective of the model is to minimize the total system cost, encompassing both the capital investment in fire stations and the potential losses from fire incidents. By employing a Lagrangian relaxation technique, the model effectively simplifies the optimization challenge into more manageable sub-problems, thereby enhancing solution accuracy. The robustness and flexibility of the model were tested through simulations in a hypothetical network and a real-world scenario, using data from urban fire services. The results demonstrate the model’s scalability and adaptability to different network configurations and operational constraints, showcasing its potential to substantially enhance emergency response efficiency and decision-making in urban fire management. This research makes a significant contribution to emergency response management by providing a validated framework that improves the coordination and effectiveness of fire rescue operations, thereby reducing fire damage and enhancing public safety.

Towards to Theory of the X-ray Diffraction Tomography of Crystals with Nano-Sized Defects

X-ray diffraction tomography is an innovative method that is widely used to obtain 2D-phase-contrast diffraction images and their subsequent 3D-reconstruction of structural defects in crystals. The most frequent objects of research are linear and helical dislocations in a crystal, for which plane wave diffraction images are the most informative, since they do not contain additional interference artifacts unrelated to the images of the defects themselves. In this work the results of modeling and analysis of 2D plane wave diffraction images of a nano-dimensional Coulomb-type defect in a Si(111) thin crystal are presented based on the construction of numerical solutions of the dynamic Takagi-Taupin equations. An adapted physical expression for the elastic displacement field of the point defect, which excludes singularity at the defect location in the crystal, is used. A criterion for evaluating the accuracy of numerical solutions of the Takagi-Taupin equations is proposed and used in calculations. It is shown that in the case of the Coulomb-type defect elastic displacement field, out of the two difference algorithms for solving the Takagi-Taupin equations used in their numerical solution, only the algorithm for solving the Takagi-Taupin equations where the displacement field function enters in exponential form is acceptable in terms of the required accuracy-duration of the calculations.

Characteristic features of strong correlation: lessons from a 3-fermionone-dimensional harmonic trap

Abstract Many quantum phenomena responsible for key applications in material science and quantum
chemistry arise in the strongly correlated regime. This is at the same time, a costly regime for
computer simulations. In the limit of strong correlation analytic solutions exist, but as we move
away from this limit numerical simulation are needed, and accurate quantum solutions do not scale
well with the number of interacting particles. In this work we propose to use few-particle harmonic
traps in combination with twisted light as a quantum emulator to investigate the transition into a
strongly-correlated regime. Using both analytic derivations and numerical simulations we generalize
previous findings on 2 Coulomb interacting fermions trapped in a one-dimensional harmonic trap
to the case of 3 fermions. The 4 signatures of strong correlation we have identified in the one-
dimensional harmonic trap are: i) the ground state density is highly localized around N equilibrium
positions, where N is the number of particles, ii) the symmetric and antisymmetric ground state
wavefunctions become degenerate, iii) the von Neumann entropy grows, iv) the energy spectrum is
fully characterized by N normal modes or less. Our findings describe the low-energy behavior of
electrons in quantum wires and ions in Paul traps. Similar features have also been reported for cold
atoms in optical lattices.

Insights into metachronal propulsion's influence on Ellis fluid flow across tri‐layers amid dynamic thermal transport: Theoretical study

AbstractCilia‐based therapies are emerging for treating ciliopathies, such as inhalable drugs to propel mucus out of the lungs of patients with cystic fibrosis. This has motivated scientists and researchers to investigate cilia motion mechanics and viscoelastic fluid properties for biomedical engineering applications and disease treatments. In line with the diverse biological implications, this study focuses on the mass and heat transfer flow of tri‐layered non‐Newtonian fluids propelled by ciliary beating in a cylindrical tube. The fluid remains incompressible, with distinct layers that do not mix. The study considers the impact of mass and heat transfer in three distinct regimes, ensuring continuity at the interfaces. Mathematical modeling incorporating the lubrication approximation, small Reynolds number, and long wavelength approximation is employed for simplification. The resulting differential equations, along with boundary conditions, yield accurate solutions for temperature, velocity, and concentration fields in the three fluid layers and are discussed graphically. Key findings demonstrate that velocity and temperature fields are most pronounced in the inner fluid layer (PCL), while the concentration profile is most prominent in the outer layers (ACL), with moderate behavior in the central region. The implications of this research extend to diverse fields, including mucus clearance from the respiratory tract, microfluidics, esophageal transport, biofluid mechanics, and other areas of physiology. The insights gained from this study have promising applications in developing new treatments and biomedical engineering solutions.

An efficient static solver for the lattice discrete particle model

AbstractThe lattice discrete particle model (LDPM) has been proven to be one of the most appealing computational tools to simulate fracture in quasi‐brittle materials. Despite tremendous advancements in the definition and implementation of the method, solution strategies are still limited to dynamic algorithms, resulting in prohibitive computational costs and challenges related to solution accuracy for quasi‐static conditions. This study presents a novel static solver for LDPM, introducing fundamental innovation: (1) LDPM constitutive laws are modified to provide continuous response through all possible strain/stress states; (2) an adaptive arc‐length method is proposed in combination with a criterion to select the sign of the iterative load factor; (3) an adaptive limit‐unloading–reloading path switch algorithm is proposed to restrict oscillations in the global stiffness matrix. Extensive validation of the proposed approach is presented. Numerical results demonstrate that the static solver exhibits satisfactory convergence rates, significantly outperforming available dynamic solutions in computational efficiency.

Harmonic Mean Optimizer (HMO) for global problems solving

This study introduces the Harmonic Mean Optimizer (HMO), a novel meta-heuristic algorithm designed to address complex global optimization problems. The primary objective of this research is to develop an optimization technique that effectively balances exploration and exploitation without requiring extensive parameter tuning, thereby simplifying the optimization process and enhancing its robustness across various problem domains. The HMO employs a unique dual-fitness index that leverages the harmonic mean to assess both the quality and diversity of candidate solutions dynamically. This approach ensures a balanced search process that avoids premature convergence and improves the ability to find global optima. The methodology involves extensive benchmarking of the HMO against a comprehensive set of test functions, including 23 traditional functions from the Congress on Evolutionary Computation (CEC) 2017 test suite. The performance of the HMO is compared with that of established meta-heuristic algorithms, such as Genetic Algorithms (GA) and Particle Swarm Optimization (PSO), to validate its efficacy in terms of convergence speed and solution accuracy. Additionally, the HMO is applied to several real-world engineering problems to demonstrate its practical utility. The results show that the HMO consistently outperforms the benchmark algorithms, achieving faster convergence and higher accuracy in finding optimal solutions across a diverse range of test problems. In practical applications, the HMO effectively optimized complex engineering tasks, achieving significant improvements in both solution quality and computational efficiency. These findings highlight the potential of the HMO as a versatile and powerful tool for global optimization tasks. the HMO offers a significant advancement in optimization methodologies by providing a robust, parameter-free approach that effectively balances exploration and exploitation. This study underscores the HMO’s applicability to a wide range of optimization challenges and sets the foundation for future research and development in enhancing and applying this innovative algorithm to more complex and diverse problem domains.

Loop-mediated isothermal amplification (LAMP) assay for early on-site detection of Group B Streptococcus infection in neonatal sepsis blood sample.

Neonatal sepsis, often attributed to Group B Streptococcus (GBS) infection, poses a critical health risk to infants, demanding rapid and accurate diagnostic approaches. Existing diagnostic approaches are dependent on traditional culture methods, a process that requires substantial time and has the potential to delay crucial therapeutic assessments. This study introduces an innovative Loop-Mediated Isothermal Amplification (LAMP) assay for the early on-site detection of GBS infection from neonatal sepsis blood samples. To develop a LAMP assay, the primers are designed for the selective targeting of a highly conserved segment within the cfb gene encoding the CAMP factor in Streptococcus agalactiae ensuring high specificity. Rigorous optimization of reaction conditions, including temperature and incubation time, enhances the efficiency of the LAMP assay, enabling rapid and reliable GBS detection within a short timeframe. The diagnostic efficacy of the LAMP assay was evaluated using spiked blood samples by eliminating the DNA extraction step. The simplified colorimetric LAMP assay has the capability to detect S. agalactiae in a neonatal blood sample containing 2 CFU/mL during sepsis. Additionally, the LAMP assay effectively detected S. agalactiae in both the standard and spiked blood samples, with no detectable interference with blood. This optimised LAMP assay emerges as a promising tool for early GBS detection, offering a rapid and accurate on-site solution that has the potential to inform timely interventions and improve outcomes in neonatal sepsis cases.

Generalization of Bernoulli polynomials to find optimal solution of fractional hematopoietic stem cells model

The study introduces a fractional mathematical model in the Caputo sense for hematopoietic stem cell-based therapy, utilizing generalized Bernoulli polynomials (GBPs) and operational matrices to solve a system of nonlinear equations. The significance of the study lies in the potential therapeutic applications of hematopoietic stem cells (HSCs), particularly in the context of HIV infection treatment, and the innovative use of GBPs and Lagrange multipliers in solving the fractional hematopoietic stem cells model (FHSCM). The aim of the study is to introduce an optimization algorithm for approximating the solution of the FHSCM using GBPs and Lagrange multipliers and to provide a comprehensive exploration of the mathematical techniques employed in this context. The research methodology involves formulating operational matrices for fractional derivatives of GBPs, conducting a convergence analysis of the proposed method, and demonstrating the accuracy of the method through numerical simulations. The major conclusion is the successful introduction of GBPs in the context of the FHSCM, featuring innovative control parameters and a novel optimization technique. The study also highlights the significance of the proposed method in providing accurate solutions for the FHSCM, thus contributing to the field of mathematical modeling in biological and medical research.

Fourier-Based Function Generation of Four-Bar Linkages with an Improved Sampling Points Adjustment and Sylvester's Dialytic Elimination Method

Abstract Four-bar linkages are critical fundamental elements of many mechanical systems, and their design synthesis is often mathematically complicated with iterative numerical solutions. Analytical methods based on Fourier coefficients can circumvent these difficulties but have difficulties with sampling points adjustment and solutions of the design equations in previous studies. In this paper, an improved Fourier-based analytical synthesis method is presented, which transforms the function generation synthesis of planar four-bar linkages into a problem of solving design equations. Calculation of the Fourier coefficients is discussed, including the discretization of the prescribed function and an improved sampling points adjustment method. It is shown that the Fourier coefficients can be computed efficiently and accurately by discretizing the prescribed function with a small number of sampling points. The proposed sampling adjustment method overcomes the difficulty of easily resulting in non-Grashof solutions by considering the complete period of the prescribed function. An improved Sylvester's dialytic elimination method is presented to solve design equations. The method reduces the computation time and avoids cumbersome procedures without generating additional invalid solutions. Several examples are presented to demonstrate the advantages of the proposed synthesis method, which is easy-understanding and efficient and yields more accurate solutions than available synthesis methods.

Recent Advancements in Geothermal Energy Piles Performance and Design

Geothermal energy piles or ground heat exchange (GHE) systems embrace a sustainable source of energy that utilizes the geothermal energy naturally found inside the ground in order to heat and/or cool buildings. GHE is a highly innovative system that consists of energy loops within foundation elements (shallow foundations or piles) through which a heat carrier fluid circulates, enabling heat extraction or storage in the ground. Despite the innovation and potential of GHE systems, there are significant challenges in harmonizing their thermal and mechanical designs due to the complex interactions involved. This review critically examines state-of-the-art design methodologies developed to address these complexities, providing insights into the most recent advancements in GHE performance and design. Key findings include innovative techniques such as advanced numerical modeling to predict thermomechanical behavior, the use of different pipe configurations to optimize heat transfer, and strategies to minimize thermal stress on the foundation. Additionally, this review identifies research gaps, including the need for more comprehensive full-scale experimental validations, the impact of soil properties on system performance, and the long-term effects of thermal cycling on pile integrity. These insights aim to contribute to a better understanding of the thermomechanical behavior of energy piles, ultimately facilitating more accurate and effective design solutions.

Multi-objective hull form optimization utilizing sequential sampling optimization method

With advancements in computer technology, Computational fluid dynamics (CFD) theory provides a numerical tool for evaluating the comprehensive hydrodynamic performance of ships. On this basis, the Simulation-based design (SBD) technology based on the static sampling method (SSM) which is termed as SBD-SSM in this paper is recognized as a hull form optimization method with significant advantages. However, in the SBD-SSM method, the excessive pursuit of the global accuracy of the surrogate model leads to the need for more CFD evaluations. Consequently, this demands the substantiality of computing resources and diminishes optimization efficiency. We apply a novel hull form optimization method based on the Sequential Sampling-based Optimization (SBO) method to address this challenge. Furthermore, to strike an appropriate balance between prediction value and uncertainty while finding optimal solutions, we employ the adaptive sampling method known as Pseudo Expected Improvement Matrix (PEIM). By integrating SBO with PEIM, we introduce the SBO-PEIM optimization method, initially applied through mathematical optimization functions to verify its feasibility in optimization. Subsequently, we apply this method to optimize the total resistance and wake performance of the KCS ship. Our findings demonstrate that the SBO-PEIM method achieves higher prediction accuracy in near-optimal solutions than the SBD-SSM method, enhancing optimization efficiency by at least 17.5%. It validates the efficacy of the SBO-PEIM approach in addressing real-world engineering optimization challenges.

Computational Simulation of Monopile Scour under Tidal Flow Considering Suspended Energy Dissipation

Local scour around bridge foundations significantly impacts the stability and safety of marine structures. The development of scour holes adjacent to the pile foundations of sea-crossing bridges, influenced by tidal currents, involves multidimensional physical fields, multiscale coupling, and complex variations in marine loads. However, experimental models alone are inadequate for investigating the underlying mechanisms. Numerical simulation, a critical tool for studying local scour processes, faces the challenge of accurately modeling sediment transport, particularly under tidal flow conditions near pile foundations. To solve this challenge, this research considers the effect of reciprocating flow on sediment shear as well as its characteristic dissipation based on the immersed boundary method, introduces a reciprocating flow dissipation mechanism, and adds a momentum exchange term between the fluid and the sediment to derive a new controlling equation; a new tidal flow localized scour solver is ultimately constructed, termed TidalflowFOAM. The solver effectively simulates complex flow conditions under tidal currents, extending the modeling capabilities to more realistic three-dimensional bridge scour scenarios under combined wave and current conditions. Validation through cases reported in the literature and a series of controlled experiments, encompassing varying depths, flow velocities, and pile diameters, demonstrates the solver’s proficiency in capturing post-vortex data and accurately reflecting the influence of key factors on scour depth. However, the fidelity of the simulated scour hole morphology under tidal flow conditions behind the piles requires enhancement. The proposed numerical model for tidal flow conditions has high solution accuracy and can guide practical engineering applications.

A local meshless method for the numerical solution of multi-term time-fractional generalized Oldroyd-B fluid model

This work presents an accurate and efficient method, for solving a two dimensional time-fractional Oldroyd-B fluid model. The proposed method couples the Laplace transform (LT) with a radial basis functions based local meshless method (LRBFM). The suggested numerical scheme first uses the LT which transform the given equation to an elliptic equation in LT space, and then it utilizes the LRBFM to solve transformed equation in LT space, and then the solution is converted back into the time domain via the improved Talbot's scheme. The local meshless methods are widely recognized for scattered data interpolation and for solving PDEs in complex shaped domains. The adaptability, simplicity, and ease of use are features that have led to the popularity of local meshless methods. The local meshless methods are easy and straightforward, they only requires to solve linear system of equations. The main objective of using the LT is to avoid the computation of costly convolution integral in time-fractional derivative and the effect of time stepping on accuracy and stability of numerical solution. The stability and the convergence of the proposed numerical scheme are discussed. Further, the Ulam-Hyers (UH) stability of the proposed model is discussed. The accuracy and efficiency of the suggested numerical approach have been demonstrated using numerical experiments on five different domains with regular nodes distribution.

Collaborative credentials for the Internet of Things

The Self-Sovereign Identity (SSI) paradigm has emerged as a decentralized Identity Management model with interesting capabilities for the Internet of Things (IoT). However, current standard SSI protocols and procedures only consider that individuals store their own identity, failing to provide an accurate solution for the identity management of groups where participants might use credentials from different identities and collaborate to meet a set of verifier´s requirements. The present work introduces the concept of Collaborative Credentials (CCs) to formalize identity management procedures that model the collaboration within a group of participants. CCs allow to leverage use cases requiring collaboration that cannot be solved with standard SSI verifiable credentials, increase the privacy of group participants and enable the development of a software framework that any verifier/holder could use to generate a generic application. In the paper, a generic model for CCs is presented, together with an implementation example that is subsequently evaluated in an experimental testbed.

Performance analysis of linearization schemes for modelling multi-phase flow in porous media

Reservoir simulation is crucial for understanding the flow response in underground reservoirs, and it significantly helps reduce uncertainties in geological characterization and optimize methodologies for field development strategies. However, providing efficient and accurate solutions for the strong heterogeneity remains challenging, as most of the discretization methods cannot handle this complexity. In this work, we perform a comprehensive assessment of various numerical linearization techniques employed in reservoir simulation, particularly focusing on the performance of the nonlinear solver for problem dealing with fluid flow in porous media. The primary linearization methods examined are finite difference central (FDC), finite forward difference (FDF), and operator-based linearization (OBL). These methods are rigorously analyzed and compared in terms of their accuracy, computational efficiency, and adaptability to changing reservoir conditions. The results demonstrate that each method has distinct strengths and limitations. The FDC method is more accurate particularly in complex simulations where strong heterogeneity are introduced but is generally slower in convergence. The OBL on the other hand, is more efficient and converges quickly, which makes it suitable for scenarios with limited computational resources and simple physics, while the FDF method provides a balanced combination of precision and computational speed, contingent upon careful step size management of the derivative estimations. This paper aims to guide the selection of appropriate linearization techniques for enhancing nonlinear solvers’ accuracy and efficiency in reservoir simulation .

Maximum principle preserving time implicit DGSEM for linear scalar hyperbolic conservation laws

The properties of the high-order discontinuous Galerkin spectral element method (DGSEM) with implicit backward Euler time stepping are investigated for the approximation of hyperbolic linear scalar conservation equation in multiple space dimensions. We first prove that the DGSEM scheme in one space dimension preserves a maximum principle for the cell-averaged solution when the time step is large enough. This property however no longer holds in multiple space dimensions and we propose to use the flux-corrected transport (FCT) limiting [5] based on a low-order approximation using graph viscosity to impose a maximum principle on the cell-averaged solution. These results allow us to use a linear scaling limiter [58] in order to impose a maximum principle at nodal values within elements, while limiting the cell average with the FCT limiter improves the accuracy of the limited solution. Then, we investigate the inversion of the linear systems resulting from the time implicit discretization at each time step. We prove that the diagonal blocks are invertible and provide efficient algorithms for their inversion. Numerical experiments in one and two space dimensions are presented to illustrate the conclusions of the present analyses.

Boundary integrated neural networks for 2D elastostatic and piezoelectric problems

In this paper, we make the first attempt to adopt the boundary integrated neural networks (BINNs) for the numerical solution of two-dimensional (2D) elastostatic and piezoelectric problems. The proposed BINNs combine the artificial neural networks with the exact boundary integral equations (BIEs) to effectively solve the boundary value problems based on the corresponding partial differential equations (PDEs). The BIEs are utilized to localize all the unknown physical quantities on the boundary, which are approximated by using artificial neural networks and resolved via a training process. In contrast to many traditional neural network methods based on a domain discretization, the present BINNs offer several distinct advantages. Firstly, by embedding the analytical BIEs into the learning procedure, the present BINNs only need to discretize the boundary of the problem domain, which reduces the number of the unknowns and can lead to a faster and more stable learning process. Secondly, the differential operators in the original PDEs are substituted by integral operators, which can effectively eliminate the need for additional differentiations of the neural networks (high-order derivatives of the neural networks may lead to instabilities in the learning process). Thirdly, the loss function of the present BINNs only contains the residuals of the BIEs, as all the boundary conditions have been inherently incorporated within the formulation. Therefore, there is no necessity for employing any weighting functions, which are commonly used in most traditional methods to balance the gradients among the different objective functions. Extensive numerical experiments show that the present BINNs are much easier to train and can usually provide more accurate solutions as compared to many traditional neural network methods.

Adaptive Cubature Kalman Filter for Inertial/Geomagnetic Integrated Navigation System Based on Long Short-Term Memory Network

Inertial navigation systems experience error accumulation over time, leading to the use of integrated navigation as a classical solution to mitigate inertial drift. This provides a novel approach to navigation and positioning by using the combined advantages of inertial and geomagnetic navigation systems. However, inertial/geomagnetic navigation is affected by significant magnetic interference in practical scenarios, resulting in reduced navigation accuracy. This research introduces a new neural network-assisted integrated inertial–geomagnetic navigation method (IM-NN), and utilizes the adaptive cubature Kalman filter to integrate attitude information from geomagnetism and inertial sensors. A model was created utilizing a Long Short-Term Memory Network (LSTM) to represent the relationship between specific force, angular velocity, and integrated navigation attitude information. The dynamics were estimated based on current and previous Inertial Measurement Unit (IMU) data using IM-NN. This study demonstrated that the method effectively corrected inertial accumulation errors and mitigated geomagnetic disruption, resulting in a more accurate and dependable navigation solution in environments with geomagnetic rejection compared to conventional single inertial navigation methods.

Adaptive Cubature Kalman Filter for Inertial/Geomagnetic Integrated Navigation System Based on Long Short-Term Memory Network

Inertial navigation systems experience error accumulation over time, leading to the use of integrated navigation as a classical solution to mitigate inertial drift. This provides a novel approach to navigation and positioning by using the combined advantages of inertial and geomagnetic navigation systems. However, inertial/geomagnetic navigation is affected by significant magnetic interference in practical scenarios, resulting in reduced navigation accuracy. This research introduces a new neural network-assisted integrated inertial–geomagnetic navigation method (IM-NN), and utilizes the adaptive cubature Kalman filter to integrate attitude information from geomagnetism and inertial sensors. A model was created utilizing a Long Short-Term Memory Network (LSTM) to represent the relationship between specific force, angular velocity, and integrated navigation attitude information. The dynamics were estimated based on current and previous Inertial Measurement Unit (IMU) data using IM-NN. This study demonstrated that the method effectively corrected inertial accumulation errors and mitigated geomagnetic disruption, resulting in a more accurate and dependable navigation solution in environments with geomagnetic rejection compared to conventional single inertial navigation methods.

Quantifying local and global mass balance errors in physics-informed neural networks

Physics-informed neural networks (PINN) have recently become attractive for solving partial differential equations (PDEs) that describe physics laws. By including PDE-based loss functions, physics laws such as mass balance are enforced softly in PINN. This paper investigates how mass balance constraints are satisfied when PINN is used to solve the resulting PDEs. We investigate PINN’s ability to solve the 1D saturated groundwater flow equations (diffusion equations) for homogeneous and heterogeneous media and evaluate the local and global mass balance errors. We compare the obtained PINN’s solution and associated mass balance errors against a two-point finite volume numerical method and the corresponding analytical solution. We also evaluate the accuracy of PINN in solving the 1D saturated groundwater flow equation with and without incorporating hydraulic heads as training data. We demonstrate that PINN’s local and global mass balance errors are significant compared to the finite volume approach. Tuning the PINN’s hyperparameters, such as the number of collocation points, training data, hidden layers, nodes, epochs, and learning rate, did not improve the solution accuracy or the mass balance errors compared to the finite volume solution. Mass balance errors could considerably challenge the utility of PINN in applications where ensuring compliance with physical and mathematical properties is crucial.