Point Method Research Articles

Improved order in Hilfer fractional differential systems: Solvability and optimal control problem for hemivariational inequalities

The main objective of this study is to analyze the optimal control results and solvability concerning Hilfer fractional differential hemivariational inequalities within the range of (1<ϱ<2). Initially, we explore the solvability of a mild solutions for the Hilfer fractional hemivariational inequality. Subsequently, we investigate the optimal control strategies for the given problems by employing cost functionals, cosine operators, mild solutions, the fixed point method for multivalued functions, and a generalized Clarke subdifferential approach. To illustrate our findings, we provide a practical example and a filter diagram.

Optical interferometry implementation considerations for sinusoidal low frequency accelerometer measurements and calibrations

Vibration metrology utilizing sine excitation stimulus, based either on fringe counting or minimum point methods, employs Michelson interferometers for the calibration of accelerometers. The former method combines the optical reference and measurements arms from a static mirror and reflected by the accelerometer respectively which are then directed to a suitable photodiode for processing. The stroking motion due to the oscillation of the accelerometer will contribute to the misalignment of the two optical paths and there are three methods to compensate for this. The first requires the mounting of a mirror on the accelerometer itself and the effect of the added mass from the mirror can be accounted for and corrected. The second requires the mounting of three mirrors on the mounting surface of the accelerometer but this requires the alignment of the Michelson interferometer for each mirror. The third is to use two retro reflectors so that the returning measurement beams are always along the same path with the reference; however, this requires the alignment of the interferometer for each retro-reflector. This paper will discuss such considerations on the optical systems, their components and associated instrumentation and discuss the design of an alternative approach that can overcome certain limitations.

A robust force identification method based on L1+2-norm approximation theory

Obtaining the real force of the structure is the basic condition for efficient vibration reduction design. However, the uneasiness and instability of the inverse problem make the force identification still challenging. On the basis of L2-norm regularization, we propose a new method for force identification based on L1+2-norm approximation theory. By introducing the L1-norm penalty operator, a joint norm approximation optimization model is constructed to limit the non-zero force and punish the force value which approaching to zero, so that it can adapt to the identification of various types of forces. Then the optimal force solution is obtained by using the Primal-dual interior point method. Finally, the effectiveness and accuracy of the proposed method are verified by numerical simulation and experiment of asymmetric plate and double-layer plate structures. Different from previous studies, the L1+2-norm method in this work has high robustness, considers the characteristics of sparse regularization and L2-norm regularization, and can adapt to the identification of continuous forces and sparse forces at the same time, which has potential engineering application value.

On the convergence of the fixed point method for solving neutron transport alpha eigenvalue problems

It was shown that the Fixed Point Method (also known as the Rayleigh Quotient Method) is several times faster than the Critical Search Method for solving neutron transport alpha eigenvalue problems. It was also shown that the Fixed Point Method is able to determine the alpha eigenvalues of sub-critical systems that are beyond the reach of the Critical Search Method. Despite these significant advances, the Fixed Point Method remains an unproven algorithm. This report provides a proof.

Solving Max-cut Problem with a mixed penalization method for Semidefinite Programming

This paper is an attempt to exploit the opportunity of Semi Definite Programming (SDP), which is an area of convex and conic optimization. Indeed, Numerous NP-hard problems can be solveby using this approach. Hence, we intend to investigate the strength of SDP to model and provide tight relaxations of combinatorial and quadratic problems in order to present a new polynomial time algorithm for solving this robust model. This algorithm was firstly use to solve the nonlinear programs, the reason for which we search to extend it to the SDP programs. Actually, this algorithm designs the combination of two penalization methods. The first one is a primal-dual interior point (PDIM) method while the second one is a primal-dual exterior point (PDEM) method. Unlike the first method, which converges globally, the second one, also called the primal dual nonlinear rescaling method, has local super linear/quadratic convergence. Therefore, it seems appropriate to use a mixed algorithm based on the interior-exterior point method (IEPM). In fact, this resolution starts from the interior method, and at a certain level of execution, it proceeds to exterior method. Hence, a convergence evaluation function is use to know the level of permutation. Through evaluation, it has been approve that our approach is use to solve some instances of max-cut problem. This problem is a central graph theory model that occurs in many real problems and it is one of many NP-hard problems, which has attracted many researchers over the years. Then, we have used a semi definite programming solver SDPA (Semi Definite Programming Algorithm) that is modify to include the exterior point method subroutine. From the computational performance, we conclude that as the problem size increases, interior-exterior point algorithm gets relatively faster. The numerical results obtained are promising.

An MP-Newton method for computing nonlinear eigenpairs and its application for solving a semilinear Schrödinger equation

ln Yao and Zhou (2008), a minimax method for computing nonlinear eigenpairs by calculating critical points of the Lagrange multiplier function is presented. But, the method is slow and can find limited amount of eigenpairs. In this paper, a new general characterization, orthogonal-max characterization, for critical points of the Lagrange multiplier function is suggested. An MP-Newton method for finding orthogonal-max type critical points is designed through analyzing how the minimax method works. The new method becomes fast and able to calculate more nonlinear eigenpairs. Numerical experiment confirms these two progresses. Also, the MP-Newton method inherits the advantages of the minimax method. A convergence result for the method is established. Finally, an application for solving a semilinear Schrödinger equation is discussed.

Density clustering method based on k-nearest neighbor propagation

Abstract Density clustering, an effective data analysis tool, performs well on arbitrary shapes and non-convex datasets. However, it still has some limitations in identifying the cluster structures of datasets with irregular shapes and uneven density distribution. Aiming at the above problem, this paper proposes a density clustering method based on k-nearest neighbor propagation. Firstly, based on the theory of k-nearest neighbor, the nearest hub points are defined to replace the sample points within their k-nearest neighbors, and the cluster boundary is ascertained relying on the propagation of the nearest hub points with density gradient trend so as to divide the nearest hub points into multiple groups; secondly, a group merging method of the nearest hub points based on the set similarity is given to obtain the set of nearest hub points; and finally, the remaining sample points are assigned to the set of their nearest hub points to obtain the final clusters. The correctness and effectiveness of the algorithm are verified by experiments on synthetic and UCI datasets, and the results show that the algorithm can better cope with the clustering needs of multiple complex data distributions compared with other comparative algorithms.

An investigation into the implications of partial substitution of selenium with lead on the thermal properties for S60Se40-XPbX Chalcogenide Compound

Abstract This study includes the manufacture of four ternary alloys represented S60Se40-XPbX with weight ratios x = 0, 10, 20, and 30 by the melting point method. The components of each alloy were mixed separately, then placed in quartz ampoules and vacuumed out with a vacuum of roger that 10−4 Torr. The ampule was heated in two stages to avoid sudden dissipation and precipitation of selenium on the inner mass of the quartz tube. The ampoule was gradually heated and kept at 450°C for approximately 4 hours followed by 950°C for 10 hours.at a rate of 10 degrees Celsius, the temperature of the electric furnace was increased, and then the ampoule was subjected to rapid cooling with cold water to reach a state of solidity glass-like. The research aims to investigate the effect of adding lead to selenium on the properties of thermal conductivity and heat flux density. It has been noted that the partial replacement of selenium with lead affected these properties significantly.

Collision-Free Tracking for a Mobile Robot Based on Purely Geometric Planning

A purely geometric planning method for a mobile robot in unknown environments is proposed to ensure robot collision avoidance against obstacles within the safety time interval while moving to the goal. The robot initially detects a point cloud of obstacles using a 2D LiDAR. Euclidean clustering is employed to classify the point cloud into point classes. The obstacle is then identified as a directed closed-loop rectangle for each point class. A relative orientation kd-tree is designed to store the vertices of the obstacles and to determine the obstacles to be considered in the obstacle avoidance algorithm. A velocity divider is introduced to obtain a linear convex area of possible obstacle avoidance velocities. Thus, linear planning is employed to calculate the optimal obstacle avoidance velocity for control. A virtual reference point method is proposed to solve the problem of an unreachable goal in a singular configuration. Experimental results show that the directed closed-loop rectangle and the relative orientation kd-tree facilitate the quick updating of required obstacle points with low-cost sensor equipment. The deterministic path for a given scenario can be obtained, demonstrating the reliability of geometric planning for both the obstacle avoidance velocity region and the optimal obstacle avoidance velocity. The proposed algorithm is finally validated for multiple obstacles and dynamic environments with moving obstacles.

Elliptical Halbach magnet and gradient modules for low-field portable magnetic resonance imaging.

This study aims to develop methods to design the complete magnetic system for a truly portable MRI scanner for neurological and musculoskeletal (MSK) applications, optimized for field homogeneity, field of view (FoV), and gradient performance compared to existing low-weight configurations. We explore optimal elliptic-bore Halbach configurations based on discrete arrays of permanent magnets. In this way, we seek to improve the field homogeneity and remove constraints to the extent of the gradient coils typical of Halbach magnets. Specifically, we have optimized a tightly packed distribution of magnetic Nd2Fe14B cubes with differential evolution algorithms and a second array of shimming magnets with interior point and differential evolution methods. We have also designed and constructed an elliptical set of gradient coils that extend over the whole magnet length, maximizing the distance between the lobe centers. These are optimized with a target field method minimizing a cost function that considers also heat dissipation. We have employed the new toolbox to build the main magnet and gradient modules for a portable MRI scanner designed for point-of-care and residential use. The elliptical Halbach bore has semi-axes of 10 and 14& cm, and the magnet generates a field of 87& mT homogeneous down to 5700& ppm (parts per million) in a 20-cm diameter FoV; it weighs 216& kg and has a width of 65& cm and a height of 72& cm. Gradient efficiencies go up to around 0.8& mT/m/A, for a maximum of 12& mT/m within 0.5& ms with 15& A and 15& V amplifier. The distance between lobes is 28& cm, significantly increased with respect to other Halbach-based scanners. Heat dissipation is around 25& W at maximum power, and gradient deviations from linearity are below 20% in a 20-cm sphere. Elliptic-bore Halbach magnets enhance the ergonomicity and field distribution of low-cost portable MRI scanners, while allowing for full-length gradient support to increase the FoV. This geometry can be potentially adapted for a prospective low-cost whole-body technology.

Developing Flowcharts for Hazard Analysis in Seafood Retail: Critical Control Point Verification

Background: Implementing Hazard Analysis and Critical Control Point (HACCP) management across the supply chain is promoted globally to ensure the safety of marine food products due to their rapid quality deterioration. However, many seafood retail stores deviate from adopting these practices. Therefore, in this study, we aimed to create a flowchart based on HACCP and validate it in retail stores. Methods: Chub mackerel (Scomber japonicus), scallops (Patinopecten yessoensis), and whiteleg shrimp (Litopenaeus vannamei) specimens were purchased from a supermarket from August to December 2020. The handling information of these products from receipt to sales was obtained to prepare an HACCP plan for retail stores. Groups adhering to and deviating from flowchart conditions were categorized as Critical Control Point (CCP)-compliant and CCP-deviant, respectively. Four samples of each product for each condition were analyzed. Bacterial viability was evaluated using the flat agar culture method. Escherichia coli and Vibrio parahaemolyticus were detected using the Brilliant Green-Lactose-Bile and material point methods, respectively. Product freshness was assessed by determining K-values using High-Performance Liquid Chromatography. Results were compared using Student’s t-test. Results: At elevated storage temperatures, bacterial growth rates were higher in chub mackerel and whiteleg shrimp than those in scallops. E. coli was not detected in any sample, whereas V. parahaemolyticus was detected in scallops and whiteleg shrimp but not in chub mackerel. CCP-deviant refrigerated scallops had increased V. parahaemolyticus counts; however, it did not differ between the frozen scallop and whiteleg shrimp. K-values increased more rapidly in CCP-deviant chub mackerel, whiteleg shrimp, and refrigerated scallops, but not in frozen scallops. Inadequate temperature control during display and sale markedly deteriorated the quality of marine products. Conclusion: Setting CCPs for marine food product display and sale while controlling temperature can preserve product quality. The flowchart created in this study can be broadly used for marine retail stores.

Hyers–Ulam stability of Nipah virus model using Atangana–Baleanu–Caputo fractional derivative with fixed point method

In this study, we present a novel investigation into the dynamics of the Nipah virus through the lens of fractional differential equations (FDEs), employing the Atangana–Baleanu–Caputo fractional derivative (ABCFD) and the fixed-point approach (FPA). The core contribution of this work lies in establishing the existence and uniqueness of solutions to the proposed FDEs, a critical step for validating the model. Furthermore, we explore the Hyers–Ulam (HU) stability of these generalized FDEs, providing a rigorous mathematical foundation for the stability analysis within the context of viral dynamics. By leveraging the ABCFD, our work extends the classical stability criteria, offering new insights into the role of memory effects in disease modeling. Additionally, we present approximate solutions across various compartments and fractional orders, highlighting the sensitivity of the system to key parameters. Numerical simulations, conducted using the Cullis method, illustrate the impact of fractional orders and validate the theoretical findings, positioning this work as a significant advancement in the application of fractional calculus to epidemiological models.

An improved SLAM algorithm for substation inspection robot based on the fusion of IMU and visual information

In the past, manual inspection was often used for equipment inspection in indoor environments such as substation rooms and chemical plant rooms. This way often accompanies high labor intensity, low inspection efficiency, and low safety, which is difficult to meet the increasingly stringent requirements of indoor equipment operation and maintenance management. For dealing with these issues, a VIORB-SLAM2 algorithm based on the integration of IMU and visual information, was proposed by this paper. Firstly, the IMU data and image data were integrated to restore scale information of cameras, and then an error function was established to enhance the algorithm’s robustness. Secondly, in order to improve the accuracy of the algorithm, the random sampling consensus method was used to eliminate the wrong matching points in feature point matching, and the normalized cross-correlation matching was employed to constrain key frame matching conditions. Finally, through the iterative closest point method to stitch the point clouds, a dense map for navigation was constructed. The experimental results show that the algorithm designed by this paper has solved the shortcomings of applying the ORB-SLAM2 algorithm to indoor inspection robots while achieving high positioning accuracy, which can be combined with other algorithms in the field of artificial intelligence for object detection and semantic map construction in the future.

Remote sensing identification and hazard assessment methods for spoil sites

Spoil sites, as loose accumulations, are prone to instability after disturbances and are a serious threat to the safety of downstream communities. This research aims to rapidly and accurately assess the potential hazards of the numerous spoil sides. An integrated approach that combines spatial, aerial, and ground techniques was developed to rapidly identify and interpret the key factors influencing the stability of spoil sites. Subsequently, based on the results of numerical simulation of multiple combinations of unfavorable working conditions by the material point method, a hazard assessment methodology for spoil sites is proposed, which combines the limit equilibrium method with the improved hierarchical analysis. The proposed method is applied and validated on spoil sites along an expressway. The achieved results reveal that remote sensing combined with unmanned aerial vehicle (UAV) verification technology is capable of quickly and accurately identifying the critical elements of spoil sites. The hazard assessment of the spoil site is represented by the hazard coefficient (P), where 0 < P < 1 indicates safety, 1 ≤ P < 5 signifies instability, and P ≥ 5 represents extreme instability. The effectiveness of the proposed assessment approach is then verified through the on-site validation, which provides a vital reference for rapid identification and batch assessment of spoil sites.

Complexity analysis of primal-dual interior-point methods for semidefinite optimization based on a new type of kernel functions

Kernel functions are essential for designing and analyzing interior-point methods (IPMs). They are used to determine search directions and reduce the computational complexity of the interior point method. Currently, IPM based on kernel functions is one of the most effective methods for solving LO [1,20], second-order cone optimization (SOCO) [2], and symmetric optimization (SO) and is a very active research area in mathematicalprogramming. This paper presents a large-update primal-dual IPM for SDO based on a new bi-parameterized hyperbolic kernel function. Then we proved that the proposed large-update IPM has the same complexity bound as the best-known IPMs for solving these problems. Taking advantage of the favorable characteristics of the kernel function, we can deduce that the iteration bound for the large update method is $\mathcal{O}\left( \sqrt{n}\log n\log\dfrac{n}{\varepsilon }\right) $ when a takes a special value utilizing the favorable properties of the kernel function. These theoretical results play an essential role in the design and analysis of IPMs for CQSCO [7] and the Cartesian$\ P_{\ast }\left( \kappa \right) $-SCLCP [8]. The proximity function has never been used. In order to validate the efficacy of our algorithm and verify the effectiveness of our algorithm, examples aregiven to illustrate the applicability of our main results, and we compare our numerical results with some alternatives presented in the literature.

Mixed material point method formulation, stabilization, and validation for a unified analysis of free-surface and seepage flow

This paper presents a novel stabilized mixed material point method (MPM) designed for the unified modeling of free-surface and seepage flow. The unified formulation integrates the Navier-Stokes equation with the Darcy-Brinkman-Forchheimer equation, effectively capturing flows in both non-porous and porous domains. In contrast to the conventional Eulerian computational fluid dynamics (CFD) solver, which solves the velocity and pressure fields as unknown variables, the proposed method employs a monolithic displacement-pressure formulation adopted from the mixed-form updated-Lagrangian finite element method (FEM). To satisfy the discrete inf-sup stability condition, a stabilization strategy based on the variational multiscale method (VMS) is derived and integrated into the proposed formulation. Another distinctive feature is the implementation of blurred interfaces, which facilitate a seamless and stable transition of flows between free and porous domains, as well as across two distinct porous media. The efficacy of the proposed formulation is verified and validated through several benchmark cases in 1D, 2D, and 3D scenarios. Conducted numerical examples demonstrate enhanced accuracy and stability compared to analytical, experimental, and other numerical solutions.

Approximate proximal methods for variational inequalities on Hadamard manifolds

ABSTRACT In this paper, we present an approximate proximal point method for addressing the variational inequality problem on Hadamard manifolds, and we analyse its convergence properties. The proposed algorithm exhibits inexactness in two aspects. Firstly, each proximal subproblem is approximated by utilizing the enlargement of the vector field under consideration, and subsequently, the next iteration is obtained by solving this subproblem while allowing for a suitable error tolerance. As an illustrative application, we develop an approximate proximal point method for nonlinear optimization problems on Hadamard manifolds.

A regularized microplane damage material model in the implicit material point method

A regularized microplane damage material model in the implicit material point method

Time‐periodic solutions to heated ferrofluid flow models

AbstractIn this work, we prove the existence of time‐periodic solutions to a model describing a ferrofluid flow heated from below. Navier–Stokes equations satisfied by the fluid velocity are coupled to the temperature equation and the magnetostatic equation satisfied by the magnetic potential. The magnetization is assumed to be parallel to the magnetic field and is given by a nonlinear magnetization law generalizing the Langevin law. The proof is based on a semi‐Galerkin approximation and regularization methods together with the fixed point method.

Numerical analysis of nonlinear Klein–Gordon equations by a meshless superconvergent finite point method

In this paper, we introduce a meshless method for numerical simulation of nonlinear Klein–Gordon equations. The method begins with a temporal discretization to address time derivatives. The stability and error of the temporal discretization scheme are theoretically analyzed. Subsequently, meshless algebraic systems of Klein–Gordon solitons are established by using the superconvergent finite point method (SFPM) for spatial discretization. The moving least squares approximation and its smoothed derivatives are adopted in the SFPM to ensure the high accuracy and remarkable superconvergence. Accuracy and convergence of the meshless numerical simulation for nonlinear Klein–Gordon equations are analyzed in theory. Numerical results validate the superconvergence and effectiveness of the method and confirm the theoretical analysis.