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Braided stents are self-expandable devices widely used in many different clinical applications. In-silico methods could be a useful tool to improve the design stage and preoperative planning; however, numerical modeling of braided structures is not trivial. The geometries are often challenging, and a parametric representation is not always easily achieved. Moreover, in the literature, different options have been proposed to handle the contact among the wires, but an extensive comparison of these modeling techniques is missing.In this work, both the geometry and contact issues are discussed. Firstly, an effective strategy based on parametric equations to draw complex braided geometries is illustrated and exploited to build three beam meshes resembling commercial devices. Secondly, three finite element simulations (bending, crimping and confined release) were carried out to compare simplified contact techniques involving connector elements with the more realistic but computationally expensive option based on the general contact algorithm, which has already been validated in the literature through comparisons with experimental results. Both local (stress distribution) and global quantities (forces/displacements) were analyzed.The results obtained using the connectors are significantly affected by wire interpenetrations and over-constraint.The percentage errors reached considerably high values, exceeding 100% in the confined release test and 50% in the remaining cases study. Moreover, the errors do not show uniform trends but vary according to the stent geometry, boundary conditions, connector type and investigated entity, suggesting that it is not possible to replace the use of the general contact algorithm with simplified approaches.

This paper introduces a dedicated algorithm for the automatic generation of water distribution network (WDN) layouts in EPANET, utilizing exclusively the street layout information contained in CAD files. The methodology involves reading and converting all elements constituting street boundaries into lines, which are then mathematically processed through parametric equations of lines. Subsequently, the central street lines are extracted and extended to generate intersection points. These points are then employed to define the network nodes, and, upon verifying connectivity among them, the pipes are automatically generated. The model's efficacy was evaluated on two distinct street layouts, and for both, the algorithm exhibited satisfactory results, automatically generating 100% of the network layout in EPANET input file. The model demonstrated swift performance for the considered layouts, with an average execution time of only 0.30 s. Furthermore, a comparison was conducted with the results obtained by the model proposed by Costa and Rodrigues (Water Resour Manage 35:1299–1319, 2021), with the performance of the model proposed in this work proving superior in both layout quality and computational time.

Today, Physics-informed machine learning (PIML) methods are one of the effective tools with high flexibility for solving inverse problems and operational equations. Among these methods, physics-informed learning model built upon Gaussian processes (PIGP) has a special place due to provide the posterior probabilistic distribution of their predictions in the context of Bayesian inference. In this method, the training phase to determine the optimal hyper parameters is equivalent to the optimization of a non-convex function called the likelihood function. Due to access the explicit form of the gradient, it is recommended to use conjugate gradient (CG) optimization algorithms. In addition, due to the necessity of computation of the determinant and inverse of the covariance matrix in each evaluation of the likelihood function, it is recommended to use CG methods in such a way that it can be completed in the minimum number of evaluations. In previous studies, only special form of CG method has been considered, which naturally will not have high efficiency. In this paper, the efficiency of the CG methods for optimization of the likelihood function in PIGP has been studied. The results of the numerical simulations show that the initial step length and search direction in CG methods have a significant effect on the number of evaluations of the likelihood function and consequently on the efficiency of the PIGP. Also, according to the specific characteristics of the objective function in this problem, in the traditional CG methods, normalizing the initial step length to avoid getting stuck in bad conditioned points and improving the search direction by using angle condition to guarantee global convergence have been proposed. The results of numerical simulations obtained from the investigation of seven different improved CG methods with different angles in angle condition (four angles) and different initial step lengths (three step lengths), show the significant effect of the proposed modifications in reducing the number of iterations and the number of evaluations in different types of CG methods. This increases the efficiency of the PIGP method significantly, especially when the traditional CG algorithms fail in the optimization process, the improved algorithms perform well. Finally, in order to make it possible to implement the studies carried out in this paper for other parametric equations, the compiled package including the methods used in this paper is attached.

Areal sweep efficiency is a critical indicator in reservoir development. Accurate calculation of the waterflood areal sweep efficiency of a well pattern provides a theoretical basis for optimizing injection-production strategies and enhancing effective field development. However, in calculating the areal sweep efficiency of irregular well patterns, the inclusion of streamlines with excessively low corresponding flow rates can lead to an overestimation of the swept area. To address this issue, the concepts of critical flow velocity and critical streamlines were introduced, leading to the derivation of the parametric equation for critical streamlines. By considering the boundary-curve equations of the swept region for each well pair, an analytical solution for the areal sweep efficiency was obtained, thereby proposing a calculation method for the areal sweep efficiency of irregular well patterns. Compared with theoretical results for regular well patterns, the relative error of the calculated areal sweep efficiency is less than 5%, with the critical flow velocity corresponding to a pressure gradient magnitude of 0.05 times the average pressure gradient along the main streamline of the well pair. When applied to an actual irregular well pattern, the method yields an areal sweep efficiency of 0.119 km2, corresponding to a sweep coefficient of 27.2%.

The method of forest biomass estimation based on a relationship between the volume and biomass has been applied conventionally for estimating stand above- and below-ground biomass (SABB, t ha−1) from mean growing stock volume (m3 ha−1). However, few studies have reported on the diagnosis of the volume-SABB equations fitted using field data. This paper addresses how to (i) check parameters of the volume-SABB equations, and (ii) reduce the bias while building these equations. In our analysis, all equations were applied based on the measurements of plots (biomass or volume per hectare) rather than individual trees. The volume-SABB equation is re-expressed by two Parametric Equations (PEs) for separating regressions. Stem biomass is an intermediate variable (parametric variable) in the PEs, of which one is established by regressing the relationship between stem biomass and volume, and the other is created by regressing the allometric relationship of stem biomass and SABB. A graphical analysis of the PEs proposes a concept of “restricted zone,” which helps to diagnose parameters of the volume-SABB equations in regression analyses of field data. The sampling simulations were performed using pseudo data (artificially generated in order to test a model) for the model test. Both analyses of the regression and simulation demonstrate that the wood density impacts the parameters more than the allometric relationship does. This paper presents an applicable method for testing the field data using reasonable wood densities, restricting the error in field data processing based on limited field plots, and achieving a better understanding of the uncertainty in building those equations.

The effective notch stress approach for evaluating the fatigue strength of rib—deck welds requires notch stress concentration factors obtained from complex finite element analysis. To improve the efficiency of the approach, the notch stress concentration factors for three typical fatigue-cracking modes (i.e., root—toe, root—deck, and toe—deck cracking modes) were thoroughly investigated in this study. First, we developed a model for investigating the effective notch stress in rib—deck welds. Then, we performed a parametric analysis to investigate the effects of multiple geometric parameters of a rib—deck weld on the notch stress concentration factors. On this basis, the multiple linear stepwise regression analysis was performed to obtain the optimal regression functions for predicting the notch stress concentration factors. Finally, we employed the proposed formulas in a case study. The notch stress concentration factors estimated from the developed formulas show agree well with the finite element analysis results. The results of the case study demonstrate the feasibility and reliability of the proposed formulas. It also shows that the fatigue design curve of FAT225 seems to be conservative for evaluating the fatigue strength of rib—deck welds.

We analyze the convergence of compressive sensing based sampling techniques for the efficient evaluation of functionals of solutions for a class of high-dimensional, affine-parametric, linear operator equations which depend on possibly infinitely many parameters. The proposed algorithms are based on so-called “non-intrusive” sampling of the high-dimensional parameter space, reminiscent of Monte Carlo sampling. In contrast to Monte Carlo, however, a functional of the parametric solution is then computed via compressive sensing methods from samples of functionals of the solution. A key ingredient in our analysis of independent interest consists of a generalization of recent results on the approximate sparsity of generalized polynomial chaos representations (gpc) of the parametric solution families in terms of the gpc series with respect to tensorized Chebyshev polynomials. In particular, we establish sufficient conditions on the parametric inputs to the parametric operator equation such that the Chebyshev coefficients of gpc expansion are contained in certain weighted ℓp\\ell _p-spaces for 0>p≤10>p\\leq 1. Based on this we show that reconstructions of the parametric solutions computed from the sampled problems converge, with high probability, at the L2L_2, resp. L∞L_\\infty, convergence rates afforded by best ss-term approximations of the parametric solution up to logarithmic factors.

The knowledge of pollutants dispersion in water bodies is a matter of concern in water quality control, especially when a new industrial development is installed e.g. near riverbanks. To predict pollutants dispersion in rivers, analytical, experimental and in-situ measurement can be performed. However, analytical estimation usually results in low accuracy, while experimental or in situ measurement are quite expensive in time and equipment. Hence, Computational Fluid Dynamics (CFD) approach is other alternative that can be used to obtain simple and accurate results for mass transport in rivers. In other words, it is a good alternative to analyse pollutants dispersion. As it is known, longitudinal diffusion coefficient (E) has strong influence on pollutants spreading into the water body. Therefore, the purpose of this paper is to analyse the effects of E on the mass transport of a conservative pollutant in rivers and channels via CFD. Contaminant dispersion is carried out by a scalar advection-diffusion transport equation that represents the conservation of mass. The velocity and pressure fields are calculated, considering an incompressible fluid, through the Navier-Stokes and the continuity equations. Numerical and analytical results, for one-dimensional (1D) flow, are compared in order to obtain the concentration field, over time and space, using different parametric equations. The concentration field showed significant differences of concentration peak and arrival time of the plume depending on the equation used to predict E. Numerical results, for two-dimensional (2D) flow, are compared with the experimental data from Modenesi et al. (2004). Such analyses are necessary to establish an appropriate correlation between simulated and real channel. The use of different parametric equations for the E in a 2D channel reveals significant differences of concentration peak and arrival time of the plume. As expected, the numerical results of the transport of pollutants show the dependence on the parameterization of the longitudinal dispersion coefficient. The one that best represents the distribution of pollutants is that proposed by Kashfipour & Falconer.

In this article, the design of a nonrelative sliding gear mechanism for parallel axes transmission is presented. First, the general meshing line functions were actively designed for the nonrelative sliding transmission between parallel axes. The parametric equations of contact curves on the driving and driven gears were deduced by the coordinate transformations of function-oriented design of meshing line functions. The meshing between two contact curves on driving and driven gears follows the principle of space curve meshing. Based on two types of motion equations of meshing points, the parametric equations of driving and driven tooth surfaces were deduced according to the helical motion along the calculated contact curves. According to the calculation equations, two pairs of numerical examples were designed and material prototype samples were fabricated to experimentally validate the kinematic performances. After the two types of meshing line motion functions for nonrelative sliding meshing for parallel axes transmission were analyzed, a tooth contact comparative analysis was carried out between the nonrelative sliding gears with uniform motion of meshing points and involute gears, exhibiting better performances. This article introduces a new design method of nonrelative sliding gear mechanism for parallel axes transmission based on function-oriented design of meshing line functions.

Various curvatures can be drawn between two different points. However, what curve will yield the fastest descent for an object to travel from the higher point to the lower point under the force of gravity alone? This essay utilizes theoretical methods such as calculus, optimization, and parametric equations and experimental approaches to show that a curve - shaped like a cycloid - will yield the fastest descent. This conclusion has practical applications for the design of roller coaster trajectories along with other entertainment facilities.