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Topology optimization of structures under self-weight loading is a challenging problem which has received increasing attention in the past years. The use of standard formulations based on compliance minimization under volume constraint suffers from numerous difficulties for self-weight dominant scenarios, such as non-monotonic behaviour of the compliance, possible unconstrained character of the optimum and parasitic effects for low densities in density-based approaches. This paper aims to propose an alternative approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading.

In order to overcome the above first two issues, a regularized formulation of the classical compliance minimization problem under volume constraint is adopted, which enjoys two important features: (a) it allows for imposing any feasible volume constraint and (b) the standard (original) formulation is recovered once the regularizing parameter vanishes. The resulting topology optimization problem is solved with the help of the topological derivative method, which naturally overcomes the above last issue since no intermediate densities (grey-scale) approach is necessary.

A novel and simple approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading is proposed. A set of benchmark examples is presented, showing not only the effectiveness of the proposed approach but also highlighting the role of the self-weight loading in the final design, which are: (1) a bridge structure is subject to pure self-weight loading; (2) a truss-like structure is submitted to an external horizontal force (free of self-weight loading) and also to the combination of self-weight and the external horizontal loading; and (3) a tower structure is under dominant self-weight loading.

An alternative regularized formulation of the compliance minimization problem that naturally overcomes the difficulties of dealing with self-weight dominant scenarios; a rigorous derivation of the associated topological derivative; computational aspects of a simple FreeFEM implementation; and three-dimensional numerical benchmarks of bridge, truss-like and tower structures.

The primary objective of this study is to tackle the enduring challenge of preserving feature integrity during the manipulation of geometric data in computer graphics. Our work aims to introduce and validate a variational sparse diffusion model that enhances the capability to maintain the definition of sharp features within meshes throughout complex processing tasks such as segmentation and repair.

We developed a variational sparse diffusion model that integrates a high-order L₁ regularization framework with Dirichlet boundary constraints, specifically designed to preserve edge definition. This model employs an innovative vertex updating strategy that optimizes the quality of mesh repairs. We leverage the augmented Lagrangian method to address the computational challenges inherent in this approach, enabling effective management of the trade-off between diffusion strength and feature preservation. Our methodology involves a detailed analysis of segmentation and repair processes, focusing on maintaining the acuity of features on triangulated surfaces.

Our findings indicate that the proposed variational sparse diffusion model significantly outperforms traditional smooth diffusion methods in preserving sharp features during mesh processing. The model ensures the delineation of clear boundaries in mesh segmentation and achieves high-fidelity restoration of deteriorated meshes in repair tasks. The innovative vertex updating strategy within the model contributes to enhanced mesh quality post-repair. Empirical evaluations demonstrate that our approach maintains the integrity of original, sharp features more effectively, especially in complex geometries with intricate detail.

The originality of this research lies in the novel application of a high-order L₁ regularization framework to the field of mesh processing, a method not conventionally applied in this context. The value of our work is in providing a robust solution to the problem of feature degradation during the mesh manipulation process. Our model’s unique vertex updating strategy and the use of the augmented Lagrangian method for optimization are distinctive contributions that enhance the state-of-the-art in geometry processing. The empirical success of our model in preserving features during mesh segmentation and repair presents an advancement in computer graphics, offering practical benefits to both academic research and industry applications.

In a dual-robot system, the relative position error is a superposition of errors from each mono-robot, resulting in deteriorated coordination accuracy. This study aims to enhance relative accuracy of the dual-robot system through direct compensation of relative errors. To achieve this, a novel calibration-driven transfer learning method is proposed for relative error prediction in dual-robot systems.

A novel local product of exponential (POE) model with minimal parameters is proposed for error modeling. And a two-step method is presented to identify both geometric and nongeometric parameters for the mono-robots. Using the identified parameters, two calibrated models are established and combined as one dual-robot model, generating error data between the nominal and calibrated models’ outputs. Subsequently, the calibration-driven transfer, involving pretraining a neural network with sufficient generated error data and fine-tuning with a small measured data set, is introduced, enabling knowledge transfer and thereby obtaining a high-precision relative error predictor.

Experimental validation is conducted, and the results demonstrate that the proposed method has reduced the maximum and average relative errors by 45.1% and 30.6% compared with the calibrated model, yielding the values of 0.594 mm and 0.255 mm, respectively.

First, the proposed calibration-driven transfer method innovatively adopts the calibrated model as a data generator to address the issue of real data scarcity. It achieves high-accuracy relative error prediction with only a small measured data set, significantly enhancing error compensation efficiency. Second, the proposed local POE model achieves model minimality without the need for complex redundant parameter partitioning operations, ensuring stability and robustness in parameter identification.

The susceptible-infectious-susceptible (SIS) infectious disease models without spatial heterogeneity have limited applications, and the numerical simulation without considering models’ global existence and uniqueness of classical solutions might converge to an impractical solution. This paper aims to develop a robust and reliable numerical approach to the SIS epidemic model with spatial heterogeneity, which characterizes the horizontal and vertical transmission of the disease.

This study used stability analysis methods from nonlinear dynamics to evaluate the stability of SIS epidemic models. Additionally, the authors applied numerical solution methods from diffusion equations and heat conduction equations in fluid mechanics to infectious disease transmission models with spatial heterogeneity, which can guarantee a robustly stable and highly reliable numerical process. The findings revealed that this interdisciplinary approach not only provides a more comprehensive understanding of the propagation patterns of infectious diseases across various spatial environments but also offers new application directions in the fields of fluid mechanics and heat flow. The results of this study are highly significant for developing effective control strategies against infectious diseases while offering new ideas and methods for related fields of research.

Through theoretical analysis and numerical simulation, the distribution of infected persons in heterogeneous environments is closely related to the location parameters. The finding is suitable for clinical use.

The theoretical analysis of the stability theorem and the threshold dynamics guarantee robust stability and fast convergence of the numerical solution. It opens up a new window for a robust and reliable numerical study.

In the present work, we focus on developing an in-house parallel meshless local Petrov-Galerkin (MLPG) code for the analysis of heat conduction in two-dimensional and three-dimensional regular as well as complex geometries.

The parallel MLPG code has been implemented using open multi-processing (OpenMP) application programming interface (API) on the shared memory multicore CPU architecture. Numerical simulations have been performed to find the critical regions of the serial code, and an OpenMP-based parallel MLPG code is developed, considering the critical regions of the sequential code.

Based on performance parameters such as speed-up and parallel efficiency, the credibility of the parallelization procedure has been established. Maximum speed-up and parallel efficiency are 10.94 and 0.92 for regular three-dimensional geometry (343,000 nodes). Results demonstrate the suitability of parallelization for larger nodes as parallel efficiency and speed-up are more for the larger nodes.

Few attempts have been made in parallel implementation of the MLPG method for solving large-scale industrial problems. Although the literature suggests that message-passing interface (MPI) based parallel MLPG codes have been developed, the OpenMP model has rarely been touched. This work is an attempt at the development of OpenMP-based parallel MLPG code for the very first time.

This paper aims to study almost Ricci–Yamabe soliton in the context of certain contact metric manifolds.

The paper is designed as follows: In Section 3, a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator admitting almost Ricci–Yamabe soliton is considered. In Section 4, a complete K-contact manifold admits gradient Ricci–Yamabe soliton is studied. Then in Section 5, gradient almost Ricci–Yamabe soliton in non-Sasakian (k, μ)-contact metric manifold is assumed. Moreover, the obtained result is verified by constructing an example.

We prove that if the metric g admits an almost (α, β)-Ricci–Yamabe soliton with α ≠ 0 and potential vector field collinear with the Reeb vector field ξ on a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator, then the manifold is compact Einstein Sasakian and the potential vector field is a constant multiple of the Reeb vector field ξ. For the case of complete K-contact, we found that it is isometric to unit sphere S²ⁿ⁺¹ and in the case of (k, μ)-contact metric manifold, it is flat in three-dimension and locally isometric to Eⁿ⁺¹ × Sⁿ(4) in higher dimension.

All results are novel and generalizations of previously obtained results.

The purpose of this study is to determine the impact of two-phase power law nanofluid on a curved arterial blood flow under the presence of ovelapped stenosis. Over the past couple of decades, the percentage of deaths associated with blood vessel diseases has risen sharply to nearly one third of all fatalities. For vascular disease to be stopped in its tracks, it is essential to understand the vascular geometry and blood flow within the artery. In recent scenarios, because of higher thermal properties and the ability to move across stenosis and tumor cells, nanoparticles are becoming a more common and effective approach in treating cardiovascular diseases and cancer cells.

The present mathematical study investigates the blood flow behavior in the overlapped stenosed curved artery with cylinder shape catheter. The induced magnetic field and entropy generation for blood flow in the presence of a heat source, magnetic field and nanoparticle (Fe₃O₄) have been analyzed numerically. Blood is considered in artery as two-phases: core and plasma region. Power-law fluid has been considered for core region fluid, whereas Newtonian fluid is considered in the plasma region. Strongly implicit Stone’s method has been considered to solve the system of nonlinear partial differential equations (PDE’s) with 10–6 tolerance error.

The influence of various parameters has been discussed graphically. This study concludes that arterial curvature increases the probability of atherosclerosis deposition, while using an external heating source flow temperature and entropy production. In addition, if the thermal treatment procedure is carried out inside a magnetic field, it will aid in controlling blood flow velocity.

The findings of this computational analysis hold great significance for clinical researchers and biologists, as they offer the ability to anticipate the occurrence of endothelial cell injury and plaque accumulation in curved arteries with specific wall shear stress patterns. Consequently, these insights may contribute to the potential alleviation of the severity of these illnesses. Furthermore, the application of nanoparticles and external heat sources in the discipline of blood circulation has potential in the medically healing of illness conditions such as stenosis, cancer cells and muscular discomfort through the usage of beneficial effects.